diff --git a/.gitignore b/.gitignore index 8492824..f7c1118 100644 --- a/.gitignore +++ b/.gitignore @@ -10,5 +10,7 @@ public/toolchains/*.forge-chunk-* coverage/ .forge-library-build-*/ **/target/ +__pycache__/ +*.pyc *.tsbuildinfo .DS_Store diff --git a/IDEA.md b/IDEA.md new file mode 100644 index 0000000..8d1efc6 --- /dev/null +++ b/IDEA.md @@ -0,0 +1,138 @@ +## Inspiration + +Online judging has a resource problem. + +Every compilation, sample run, custom test case, and resubmission consumes server CPU and memory. This becomes especially expensive in education, where learners are expected to experiment frequently—and are also more likely to accidentally submit infinite loops, excessive allocations, or algorithms that exceed their intended complexity. + +A traditional online judge must provision enough infrastructure for all of that work. As more learners arrive, compilation and execution become a centralized scalability bottleneck. + +The obvious solution is to move some of the work to the user’s own device. Modern browsers are capable execution environments. If learners can compile and test locally, a platform can serve many more users without scaling server capacity at the same rate. + +But that creates a second problem. + +A fast desktop, an older laptop, a busy server, and a throttled browser do not execute a program in the same amount of wall-clock time. Even on the same machine, the same program may appear faster or slower depending on background activity and changing system conditions. + +If judging depends on elapsed time, distributing execution across heterogeneous devices makes results inconsistent. + +That became the central question behind WASM-OJ: + +> **How can we distribute compilation and execution without distributing the meaning of the result?** + +## Our Answer + +WASM-OJ is a distributed, multi-language online judge that can compile and execute submissions in the browser or on the server while preserving consistent execution and judging semantics. + +It uses WebAssembly and WASI as a portable execution foundation and measures computational work through a deterministic, host-independent resource model. Host speed may change how long a learner waits, but it does not change how much work the judge records. + +The learner’s device can perform compilation and test execution, while the platform retains a reproducible basis for resource limits and verdicts. + +Our guiding principle is: + +> **Scale the judge, not the server.** + +## What We Built + +WASM-OJ turns the browser into a self-contained programming and judging environment. It supports both compiled and interpreted languages through a shared portable execution model. + +Learners can: + +- Write and build programs in the browser +- Run sample and custom tests locally +- Receive structured compilation, execution, and resource-limit feedback +- Preserve their work and iterate without creating a server job for every attempt + +The same conceptual boundaries support server-side execution. A platform can choose where each workload runs while preserving one judging model. + +## Why WebAssembly and WASI + +WebAssembly provides a portable execution model and a sandboxed boundary. WASI gives programs a consistent interface to their surrounding environment. Together, they allow the same program artifact to run across operating systems and hardware architectures. + +Portability alone does not guarantee reproducible behavior. Programs can observe time, randomness, files, process settings, and other environmental state. WASM-OJ brings these sources of variation under an explicit execution policy. + +Given the same program, input, and configuration, browser and server executions can therefore be evaluated under the same rules for observable behavior, resource use, and judging. + +## Measuring Work Instead of Waiting for Time + +Wall-clock duration remains useful for understanding the learner’s experience. The portable resource signal, however, is a deterministic measure of executed work. + +This separates the meaning of a result from the speed and current load of the host device. A slower machine may finish later, but it receives the same deterministic cost for the same execution. Runaway programs stop when they exhaust a defined work budget instead of consuming resources until an unreliable time threshold is reached. + +Different language environments also carry different amounts of fixed startup work. WASM-OJ normalizes that overhead so the reported measurement better reflects the work associated with the submitted program and its input. This creates a common basis for reasoning about compiled and interpreted languages without requiring identical implementations. + +The resulting measurement is an empirical signal, not an automatic inference of asymptotic complexity. Learners can run increasing input sizes and observe how measured work grows without the comparison being dominated by server load or device speed. + +## A Complete Learning Experience + +The execution model is presented through a complete browser-based learning experience. Learners can write programs, inspect build feedback, run sample and judge cases, preserve their progress, and understand why an execution reached a resource limit. + +Because ordinary edit–test cycles happen locally, experimentation remains fast and places little incremental demand on centralized infrastructure. + +## Architecture + +The system separates three responsibilities: + +1. Compilation turns a source project into a portable program artifact. +2. Execution runs that artifact under an explicit and reproducible resource policy. +3. Judging evaluates test cases and produces structured verdicts. + +Browser and server environments implement these responsibilities through the same contracts. This gives deployments the freedom to distribute ordinary compilation and testing to browsers while reserving server execution for official validation, unsupported environments, or centrally controlled workloads. + +## The Hardest Challenges + +### Bringing real language environments to the browser + +Learners should encounter the languages they expect, including their normal compilation and runtime behavior. Delivering that experience inside a browser requires language environments that remain portable, complete, and practical on a user’s device. + +### Keeping local compilation safe and responsive + +Compilation can be intensive, and submitted programs can fail in unpredictable ways. Local execution must remain isolated, bounded, and responsive throughout repeated edit–test cycles. + +### Making computational work comparable + +Compiled and interpreted languages reach user code through very different execution paths. A useful cross-language resource model must account for fixed environmental overhead while preserving the work caused by the program and its input. The measurement policy must also remain explicit and reproducible as language support evolves. + +## How We Used Codex and GPT-5.6 + +Codex served as an engineering collaborator throughout the project. It helped us study earlier prototypes, clarify the invariants the new system needed to preserve, design shared boundaries, implement and debug the system, and build experiments and regression tests. + +The central product decisions remained explicit: distribute ordinary workloads to learner devices, treat server execution as another host under the same semantics, and measure portable computational work independently of elapsed time. Behavioral and performance claims were accepted only when supported by executable evidence. + +## What Was New During Build Week + +WASM-OJ succeeds earlier experiments, but the integrated system was substantially rebuilt during Build Week. The new work established: + +- Practical multi-language compilation and execution in the browser +- Shared browser and server judging semantics +- Deterministic execution and resource measurement across language environments +- Conformance and performance evidence for the integrated system +- A complete learner-facing online judge experience + +## Impact + +For learners, WASM-OJ enables fast local experimentation and provides a stable way to observe how program cost grows across inputs. + +For educators, it reduces the infrastructure required to serve a classroom while preserving consistent judge semantics across student devices. + +For online-judge platforms, it turns every capable browser into a compilation and execution worker. Server resources can focus on official submissions, unsupported environments, and workloads that require centralized control. + +For researchers and language-tooling developers, it provides an auditable environment for comparing compilation, execution, and resource measurement across languages and hosts. + +## What We Learned + +Distributed execution and reproducible execution must be designed together. + +Moving computation to users addresses the infrastructure bottleneck but introduces hardware diversity. WebAssembly and WASI provide a portable environment; deterministic resource measurement provides a portable definition of computational work. + +Together, they make it possible to distribute the cost of judging without changing the meaning of the result. + +## What’s Next + +The core computation and runtime layer is now in place. Our next phase is the open ecosystem around it: storage, persistence, portability, and sharing. + +First, we plan to define a standard, Git-based repository format for problem collections. A compatible browser judge should be able to load a chosen repository and turn it directly into a practice environment. Educators and problem authors could publish, version, fork, and recombine problem sets without coupling them to a single platform. + +Second, we plan to define a Git-based repository format for learner-owned records. Because compilation, execution, and judging can happen in the browser, each submission can be preserved with its source code and evaluation record. GitHub or another compatible repository host can provide synchronization and version history, allowing a learner’s work and progress to remain durable, portable, and traceable across sessions and tools. + +Together, these two repository standards connect shared learning material with personal learning history. One describes what can be learned; the other records the path each learner takes through it. + +Our long-term goal is an open learning ecosystem in which anyone can publish a problem collection, any compatible browser-based judge can turn it into a local practice environment, and every learner can carry a durable history of their work across platforms. diff --git a/README.md b/README.md index ada34d9..4d13610 100644 --- a/README.md +++ b/README.md @@ -4,7 +4,7 @@ [![npm](https://img.shields.io/npm/v/%40wasm-oj%2Fforge)](https://www.npmjs.com/package/@wasm-oj/forge) [![license](https://img.shields.io/badge/license-MIT-blue.svg)](LICENSE) -WASM OJ Forge is a local-first compiler, deterministic runner, and online-judge library. It is the experimental successor to WASM-OJ's `compilet` and `wark`. In the browser deployment, source compilation, linking, execution, diagnostics, and all 20 original problems stay on the device. Compiler and language-runtime packages execute under the Wasmer JavaScript SDK; submitted programs execute under a portable Rust/Wasmer runtime core compiled for both WebAssembly and native server hosts. +WASM OJ Forge is a local-first compiler, deterministic runner, and online-judge library. It is the experimental successor to WASM-OJ's `compilet` and `wark`. In the browser deployment, source compilation, linking, execution, diagnostics, and all 45 original problems stay on the device. Compiler and language-runtime packages execute under the Wasmer JavaScript SDK; submitted programs execute under a portable Rust/Wasmer runtime core compiled for both WebAssembly and native server hosts. All production compatibility is governed by one `wasm-oj-forge-v1` contract. It jointly versions compilation, execution, determinism, metering, artifacts, @@ -13,7 +13,7 @@ compiler/determinism/resource/judge counters. See [versioning policy](docs/versi ## Judge experience -- Browse and filter 20 progressively harder Traditional Chinese problems. +- Browse 45 systems-algorithm problems in a topic-grouped, prerequisite-aware learning path; search by number, title, track, or tag in Traditional Chinese or English. - Work in C, C++, Rust, Go, Python, JavaScript, or TypeScript with Monaco and multi-file projects. - Build once, run the sample, then execute each judge case locally through Wasmer. - Compare normalized stdout, surface compile/runtime/time-limit/wrong-answer verdicts, and retain solved progress in browser storage. @@ -21,30 +21,24 @@ compiler/determinism/resource/judge counters. See [versioning policy](docs/versi Because the judge is completely local, its test data can be inspected by a determined user. This is an explicit privacy and learning tradeoff: the product is for practice and self-verification, not cheat-resistant competition. -## The 20-problem track - -| # | Problem | Topic | Difficulty | -| --- | --- | --- | --- | -| 01 | 兩數的本機握手 | Basic I/O | Easy | -| 02 | 三站溫差 | Conditions | Easy | -| 03 | 秒數時鐘 | Arithmetic | Easy | -| 04 | 閏年守門員 | Conditions | Easy | -| 05 | 一到 N 的捷徑 | Mathematics | Easy | -| 06 | 階乘尾端的零 | Number theory | Easy | -| 07 | 歐幾里得的節拍 | GCD | Easy | -| 08 | 最早的共同週期 | LCM | Easy | -| 09 | 質數守門員 | Primality | Medium | -| 10 | 數字鏡像 | Digit processing | Medium | -| 11 | 數位能量 | Digit processing | Medium | -| 12 | Collatz 計步器 | Simulation | Medium | -| 13 | 十億階 Fibonacci | Fast doubling | Hard | -| 14 | 模數引擎 | Binary exponentiation | Medium | -| 15 | 串流最高點 | Streaming | Medium | -| 16 | 能量帳本 | Prefix sums | Medium | -| 17 | 最長上升航段 | Linear scan | Medium | -| 18 | 一次交易 | Greedy | Medium | -| 19 | 多數訊號 | Boyer–Moore | Hard | -| 20 | 最大連續能量 | Dynamic programming | Hard | +## The 45-problem systems track + +The canonical collection is published independently at +[`wasm-oj/problems`](https://github.com/wasm-oj/problems). Its small browser index +lists localized titles and integrity-addressed per-problem bundles. Forge loads +that index by default, downloads a full bundle only when the learner opens a +problem, verifies its exact byte length and SHA-256 digest, then caches it by +content hash. The GitHub owner, repository, ref, and index path are user +configurable. The local generated TypeScript catalog remains a deterministic +development/test fixture; it is not the browser's runtime data source. +See the [problem catalog contract](docs/problem-catalog.md) for discovery, +localization, generation, and cumulative scoring behavior. + +The learner-facing order starts with five foundations problems, then progresses through metering +and resource limits, filesystems and packaging, build scheduling and caching, graph algorithms, +and knapsack variants. Stable source manifest IDs remain unchanged so calibration evidence and +GitHub API paths do not drift when the pedagogical sequence changes. No original 20-problem +fixture or compatibility catalog remains. ## Language support @@ -176,7 +170,7 @@ manage scheduling and lifecycle. Public asynchronous infrastructure failures are `ForgeError` records; compiler diagnostics, guest termination, and judge verdicts remain result data. A production browser host must provide `Cross-Origin-Opener-Policy: same-origin`, -`Cross-Origin-Embedder-Policy: credentialless`, and +`Cross-Origin-Embedder-Policy: require-corp`, and `Cross-Origin-Resource-Policy: same-origin`. Forge uses same-origin `blob:` bootstraps for its module Workers, so a Content Security Policy must include `worker-src 'self' blob:`. The packed compiler, runner, Python-stage, diff --git a/app/globals.css b/app/globals.css index 0bcacf3..0e1d96e 100644 --- a/app/globals.css +++ b/app/globals.css @@ -206,7 +206,17 @@ button:disabled { cursor: not-allowed; opacity: .48; } .difficulty-filter button:hover { background: #1c1b17; color: var(--text-soft); } .difficulty-filter button.active { background: #26251f; color: var(--text); box-shadow: inset 0 0 0 1px #343229; } +.catalog-search { height: 34px; display: flex; align-items: center; gap: 6px; margin: 7px 8px 2px; padding: 0 8px; border: 1px solid #302e27; border-radius: 6px; background: #10100d; color: #6f7863; } +.catalog-search:focus-within { border-color: #596c42; box-shadow: 0 0 0 1px #354129; color: #a8be8a; } +.catalog-search input { min-width: 0; flex: 1; border: 0; outline: 0; background: transparent; color: #d3cec4; font-size: 9px; } +.catalog-search input::placeholder { color: #68635b; } +.catalog-search input::-webkit-search-cancel-button { display: none; } +.catalog-search button { width: 20px; height: 20px; display: grid; place-items: center; padding: 0; border: 0; border-radius: 4px; background: transparent; color: #777269; } +.catalog-search button:hover { background: #25231e; color: #c8c2b8; } + .problem-list { min-height: 0; flex: 1; overflow-y: auto; padding: 5px; } +.problem-track + .problem-track { margin-top: 5px; } +.problem-track h2 { margin: 0; padding: 7px 8px 4px; color: #737c67; font-size: 8px; font-weight: 760; letter-spacing: .08em; text-transform: uppercase; } .problem-row { width: 100%; min-height: 46px; @@ -243,7 +253,13 @@ button:disabled { cursor: not-allowed; opacity: .48; } .difficulty-dot.easy { background: #72b77a; } .difficulty-dot.medium { background: #dcae59; } .difficulty-dot.hard { background: #ef7568; } -.judge-privacy { margin-top: 3px; } +.catalog-empty { min-height: 120px; display: flex; flex-direction: column; align-items: center; justify-content: center; gap: 7px; color: #716c63; font-size: 9px; text-align: center; } +.collection-source-card { display: flex; align-items: flex-start; gap: 8px; margin: 0 8px 8px; padding: 8px 10px; border: 1px solid #2e2b25; border-radius: 7px; background: #14130f; color: #7e8e69; } +.collection-source-card svg { flex: 0 0 auto; margin-top: 1px; } +.collection-source-card div { min-width: 0; display: flex; flex-direction: column; gap: 2px; } +.collection-source-card strong, .collection-source-card span { overflow: hidden; text-overflow: ellipsis; white-space: nowrap; } +.collection-source-card strong { color: #aaa99f; font-size: 9px; } +.collection-source-card span { color: #6f6b62; font-family: var(--font-mono), monospace; font-size: 8px; } .problem-statement { min-height: 0; @@ -261,6 +277,29 @@ button:disabled { cursor: not-allowed; opacity: .48; } .problem-metrics { display: flex; flex-wrap: wrap; gap: 6px; margin: 17px 0 27px; } .problem-metrics span { height: 25px; display: flex; align-items: center; gap: 5px; padding: 0 7px; border: 1px solid #302e27; border-radius: 5px; background: #1b1a16; color: #8f897f; font-family: var(--font-mono), monospace; font-size: 8px; } .problem-metrics svg { color: #91aa6c; } +.problem-policy-grid { display: grid; grid-template-columns: repeat(3, minmax(0, 1fr)); gap: 6px; margin: -12px 0 22px; } +.problem-policy-grid > div { min-width: 0; display: grid; grid-template-columns: minmax(0, 1fr) auto; gap: 3px 7px; padding: 8px; border: 1px solid #302e27; border-radius: 6px; background: #191814; } +.problem-policy-grid span { overflow: hidden; color: #aaa49a; font-size: 8px; font-weight: 720; text-overflow: ellipsis; white-space: nowrap; } +.problem-policy-grid strong { color: #b8ce99; font-family: var(--font-mono), monospace; font-size: 8px; } +.problem-policy-grid small { grid-column: 1 / -1; overflow: hidden; color: #6f6a62; font-family: var(--font-mono), monospace; font-size: 7px; text-overflow: ellipsis; white-space: nowrap; } +.problem-document-tabs { display: flex; gap: 5px; margin: 0 0 22px; padding-bottom: 9px; border-bottom: 1px solid #2b2923; } +.problem-document-tabs button { height: 27px; padding: 0 10px; border: 1px solid #302e27; border-radius: 5px; background: #1b1a16; color: #817b72; font-size: 9px; font-weight: 700; } +.problem-document-tabs button:hover { border-color: #48533a; color: #b9c9a4; } +.problem-document-tabs button.active { border-color: #60754a; background: #202719; color: #c9e3a7; } +.problem-document-tabs .ask-chatgpt-button { height: 27px; display: inline-flex; align-items: center; gap: 6px; margin-left: auto; padding: 0 10px; border: 1px solid #596c42; border-radius: 5px; background: #202719; color: #c9e3a7; font-size: 9px; font-weight: 720; text-decoration: none; white-space: nowrap; } +.problem-document-tabs .ask-chatgpt-button:hover { border-color: #819c5c; background: #29331f; color: #e0f4c4; } +.problem-document-tabs .ask-chatgpt-button:focus-visible { outline: 1px solid var(--accent); outline-offset: 2px; } + +.problem-markdown h2 { margin: 25px 0 9px; color: #d8d4ca; font-size: 12px; font-weight: 760; letter-spacing: .012em; } +.problem-markdown h3 { margin: 18px 0 8px; color: #bbb6ac; font-size: 10px; font-weight: 720; } +.problem-markdown p, .problem-markdown li { color: #9c968c; font-size: 11px; line-height: 1.75; } +.problem-markdown p { margin: 0 0 10px; } +.problem-markdown ul, .problem-markdown ol { margin: 0 0 12px; padding-left: 20px; } +.problem-markdown li { margin: 3px 0; padding-left: 2px; } +.problem-markdown code { border-radius: 3px; background: #11100e; color: #c9d9b5; padding: 1px 4px; font-family: var(--font-mono), monospace; font-size: .9em; } +.problem-markdown pre { margin: 9px 0 14px; overflow-x: auto; border: 1px solid #302e27; border-radius: 6px; background: #11100e; padding: 10px; } +.problem-markdown pre code { display: block; min-width: max-content; background: transparent; color: #d6d1c7; padding: 0; font-size: 9px; line-height: 1.55; } +.problem-markdown strong { color: #c9c4b9; } .statement-section { margin-top: 23px; } .statement-section h2 { margin: 0 0 9px; color: #d8d4ca; font-size: 11px; font-weight: 720; letter-spacing: .015em; } .statement-section p, .statement-section li { color: #9c968c; font-size: 11px; line-height: 1.75; } @@ -277,7 +316,14 @@ button:disabled { cursor: not-allowed; opacity: .48; } .local-judge-note p { margin: 0; color: #7f8874; font-size: 9px; line-height: 1.55; } .local-judge-note strong { display: block; margin-bottom: 2px; color: #b9ca9f; } -.judge-editor-stack { grid-template-rows: 36px minmax(210px, 1fr) 250px; } +.editor-stack.judge-editor-stack { grid-template-rows: 36px minmax(210px, 1fr) 7px var(--judge-bottom-panel-height, 360px); } +.judge-editor-stack.resizing-bottom-panel { cursor: row-resize; user-select: none; } +.bottom-panel-resizer { position: relative; z-index: 2; display: grid; place-items: center; min-height: 7px; outline: 0; background: #11100e; cursor: row-resize; touch-action: none; } +.bottom-panel-resizer::before { content: ""; position: absolute; inset: 3px 0 auto; height: 1px; background: var(--line-strong); transition: background-color 120ms ease; } +.bottom-panel-resizer span { position: relative; width: 38px; height: 3px; border-radius: 2px; background: #38362f; transition: background-color 120ms ease, transform 120ms ease; } +.bottom-panel-resizer:hover::before, .bottom-panel-resizer:focus-visible::before, .resizing-bottom-panel .bottom-panel-resizer::before { background: #617746; } +.bottom-panel-resizer:hover span, .bottom-panel-resizer:focus-visible span, .resizing-bottom-panel .bottom-panel-resizer span { background: var(--accent); transform: scaleX(1.15); } +.bottom-panel-resizer:focus-visible { box-shadow: 0 0 0 1px #7f9a59 inset; } .file-tabs { min-width: 0; overflow: hidden; } .file-tab { height: 35px; min-width: 110px; max-width: 180px; display: flex; align-items: center; border-right: 1px solid var(--line); background: #141310; } .file-tab.active { border-top: 1px solid var(--accent); background: #191814; } @@ -293,35 +339,73 @@ button:disabled { cursor: not-allowed; opacity: .48; } .verdict-mini { display: inline-grid; place-items: center; min-width: 27px; height: 15px; margin-left: 5px; padding: 0 4px; border-radius: 8px; background: #2b2a24; color: #938d82; font-family: var(--font-mono), monospace; font-size: 8px; } .verdict-mini.accepted { background: #24331c; color: var(--accent); } -.verdict-mini.wrong-answer, .verdict-mini.runtime-error, .verdict-mini.time-limit, .verdict-mini.compile-error { background: #38201c; color: #ff9488; } +.verdict-mini.wrong-answer, .verdict-mini.runtime-error, .verdict-mini.time-limit, .verdict-mini.judge-error, .verdict-mini.compile-error { background: #38201c; color: #ff9488; } .judge-empty strong { color: #8a857c; font-size: 10px; } .judge-empty span { font-size: 8px; } .judge-results { min-height: 100%; padding: 9px; } .verdict-banner { min-height: 48px; display: flex; align-items: center; gap: 9px; padding: 8px 11px; border: 1px solid #35322b; border-radius: 7px; background: #191814; } .verdict-banner.accepted { border-color: #536a3e; background: #1b2516; } -.verdict-banner.wrong-answer, .verdict-banner.runtime-error, .verdict-banner.time-limit, .verdict-banner.compile-error { border-color: #70423a; background: #281916; } +.verdict-banner.wrong-answer, .verdict-banner.runtime-error, .verdict-banner.time-limit, .verdict-banner.judge-error, .verdict-banner.compile-error { border-color: #70423a; background: #281916; } .verdict-banner.cancelled { border-color: #4a4740; background: #1e1d19; } .verdict-icon { width: 29px; height: 29px; flex: 0 0 auto; display: grid; place-items: center; border-radius: 6px; background: #24221d; color: #aaa399; } .verdict-banner.accepted .verdict-icon { background: #293b1f; color: var(--accent); } -.verdict-banner.wrong-answer .verdict-icon, .verdict-banner.runtime-error .verdict-icon, .verdict-banner.time-limit .verdict-icon, .verdict-banner.compile-error .verdict-icon { background: #3a211d; color: #ff8b7e; } +.verdict-banner.wrong-answer .verdict-icon, .verdict-banner.runtime-error .verdict-icon, .verdict-banner.time-limit .verdict-icon, .verdict-banner.judge-error .verdict-icon, .verdict-banner.compile-error .verdict-icon { background: #3a211d; color: #ff8b7e; } .verdict-banner > div { display: flex; flex-direction: column; gap: 3px; } .verdict-banner strong { color: var(--text); font-size: 11px; } .verdict-banner > div span { color: var(--muted); font-family: var(--font-mono), monospace; font-size: 8px; } .judge-link { margin: 7px 0 0; border: 0; background: transparent; color: #e5978d; font-size: 9px; } .case-list { display: grid; grid-template-columns: repeat(auto-fill, minmax(175px, 1fr)); gap: 5px; margin-top: 8px; } -.case-row { min-height: 33px; display: grid; grid-template-columns: 18px 54px minmax(0, 1fr) auto; align-items: center; gap: 5px; padding: 6px 7px; border: 1px solid #2c2a24; border-radius: 5px; background: #161512; color: #8d877e; font-size: 8px; } -.case-row.accepted { border-color: #33422a; } -.case-row.wrong-answer, .case-row.runtime-error, .case-row.time-limit { grid-column: 1 / -1; border-color: #5a342f; } +.case-card { min-width: 0; overflow: hidden; border: 1px solid #2c2a24; border-radius: 5px; background: #161512; } +.case-card.accepted { border-color: #33422a; } +.case-card.wrong-answer, .case-card.runtime-error, .case-card.time-limit, .case-card.judge-error { grid-column: 1 / -1; border-color: #5a342f; } +.case-card.selected { border-color: #758f51; box-shadow: 0 0 0 1px #52663a inset; } +.case-row { width: 100%; min-height: 37px; display: grid; grid-template-columns: 18px 54px minmax(0, 1fr) auto; align-items: center; gap: 5px; padding: 6px 7px; border: 0; background: transparent; color: #8d877e; font-size: 8px; text-align: left; } +.case-row:hover { background: #1d1c17; } .case-status { display: grid; place-items: center; color: #767168; } -.case-row.accepted .case-status { color: #91bd66; } -.case-row:not(.accepted) .case-status { color: #ee7c70; } +.case-card.accepted .case-status { color: #91bd66; } +.case-card:not(.accepted) .case-status { color: #ee7c70; } .case-row strong { color: #bdb7ad; font-family: var(--font-mono), monospace; font-size: 8px; } .case-row time { color: #68635b; font-family: var(--font-mono), monospace; font-size: 7px; } -.case-diff { grid-column: 1 / -1; display: grid; grid-template-columns: 1fr 1fr; gap: 5px; width: 100%; margin-top: 3px; } +.case-metrics-summary { grid-column: 2 / -1; color: #777f69; font-family: var(--font-mono), monospace; font-size: 7px; } +.case-diff { display: grid; grid-template-columns: 1fr 1fr; gap: 5px; width: 100%; padding: 0 7px 7px; } .case-diff > div { min-width: 0; overflow: hidden; border: 1px solid #302a26; border-radius: 4px; background: #11100e; } .case-diff pre { max-height: 70px; overflow: auto; color: #c9c3ba; } +.case-score-details { margin-top: 8px; padding: 9px 10px 10px; border: 1px solid #34382b; border-radius: 7px; background: #151611; } +.case-score-details > header { display: flex; align-items: center; justify-content: space-between; gap: 12px; } +.case-score-details > header > div { display: flex; align-items: baseline; gap: 7px; } +.case-score-details > header strong { color: var(--text); font-family: var(--font-mono), monospace; font-size: 9px; } +.case-score-details > header span { color: #777268; font-size: 8px; } +.case-score-details > header > b { color: var(--accent); font-family: var(--font-mono), monospace; font-size: 10px; } +.next-threshold-message { margin: 6px 0 8px; padding: 6px 8px; border-left: 2px solid #8baa5e; background: #1b2016; color: #b9c8a4; font-size: 8px; line-height: 1.4; } +.case-metric-cards { display: grid; grid-template-columns: repeat(3, minmax(0, 1fr)); gap: 5px; } +.case-metric-cards > div { min-width: 0; display: flex; flex-direction: column; gap: 2px; padding: 6px 7px; border: 1px solid #2c2c25; border-radius: 5px; background: #11110e; } +.case-metric-cards span { color: #777269; font-size: 7px; text-transform: uppercase; letter-spacing: .04em; } +.case-metric-cards strong { color: #d5d0c7; font-family: var(--font-mono), monospace; font-size: 10px; } +.case-metric-cards small { overflow: hidden; color: #656159; font-family: var(--font-mono), monospace; font-size: 7px; text-overflow: ellipsis; white-space: nowrap; } +.case-score-axes { display: grid; grid-template-columns: 1fr 1fr; gap: 9px; margin-top: 8px; } +.score-axis { min-width: 0; padding: 7px 8px; border: 1px solid #2b2b24; border-radius: 5px; background: #11110e; } +.score-axis-heading { display: flex; align-items: center; justify-content: space-between; gap: 8px; } +.score-axis-heading strong { color: #aaa59b; font-size: 8px; } +.score-axis-heading span { color: #777168; font-family: var(--font-mono), monospace; font-size: 7px; } +.score-axis-track { position: relative; height: 5px; margin: 19px 5px 17px; border-radius: 3px; background: linear-gradient(90deg, #4f7134 0%, #7c7a39 65%, #784339 100%); box-shadow: 0 0 0 1px #26251f; } +.score-axis-threshold, .score-axis-actual { position: absolute; left: var(--axis-position); top: 50%; width: 0; height: 0; } +.score-axis-threshold i { position: absolute; left: -1px; top: -8px; width: 2px; height: 16px; background: #c5c0b6; opacity: .72; } +.score-axis-threshold b { position: absolute; left: 0; bottom: 8px; transform: translateX(-50%); color: #8f8a80; font-family: var(--font-mono), monospace; font-size: 6px; white-space: nowrap; } +.score-axis-actual i { position: absolute; left: -4px; top: -4px; width: 8px; height: 8px; transform: rotate(45deg); border: 1px solid #11110e; background: #d8ff91; box-shadow: 0 0 0 1px #94b85e; } +.score-axis-actual b { position: absolute; left: 0; top: 8px; transform: translateX(-50%); color: #b6d580; font-family: var(--font-mono), monospace; font-size: 6px; white-space: nowrap; } +.score-axis-limits { display: flex; flex-wrap: wrap; gap: 3px 9px; color: #68645b; font-family: var(--font-mono), monospace; font-size: 6px; } +.score-axis-limits span { display: inline-flex; align-items: center; gap: 4px; } +.score-axis-limits i { width: 4px; height: 4px; border-radius: 50%; background: #98938a; } +.case-policy-results { display: grid; grid-template-columns: repeat(3, minmax(0, 1fr)); gap: 5px; margin-top: 8px; } +.case-policy-results > div { min-width: 0; display: flex; flex-direction: column; gap: 2px; padding: 6px 7px; border: 1px solid #34312a; border-radius: 5px; background: #171612; } +.case-policy-results > div.earned { border-color: #40552f; background: #182015; } +.case-policy-results > div.missed { border-color: #58372f; background: #201613; } +.case-policy-results strong { overflow: hidden; color: #c7c1b7; font-family: var(--font-mono), monospace; font-size: 7px; text-overflow: ellipsis; white-space: nowrap; } +.case-policy-results .earned strong { color: #acd77a; } +.case-policy-results .missed strong { color: #e39789; } +.case-policy-results span { color: #777168; font-size: 7px; } .drawer-judge-note { margin: 0 0 16px; } .profile-notice code { color: #f0d69c; font-family: var(--font-mono), monospace; } @@ -341,23 +425,18 @@ button:disabled { cursor: not-allowed; opacity: .48; } .tone-js { color: #eee26c !important; } .tone-ts { color: #6bb7ff !important; } -.privacy-card { display: flex; gap: 9px; margin: 8px; padding: 10px; border: 1px solid #2d3424; border-radius: 7px; background: #171a13; color: #95ad70; } -.privacy-card svg { flex: 0 0 auto; margin-top: 1px; } -.privacy-card div { min-width: 0; display: flex; flex-direction: column; gap: 3px; } -.privacy-card strong { color: #c6dba6; font-size: 10px; } -.privacy-card span { color: #747d67; font-size: 9px; line-height: 1.4; } - .editor-stack { min-width: 0; min-height: 0; display: grid; grid-template-rows: 35px minmax(180px, 1fr) 218px; } .editor-tabs { display: flex; background: #11100e; border-bottom: 1px solid var(--line); } .editor-actions { flex: 1; display: flex; align-items: center; justify-content: flex-end; padding-right: 7px; } .editor-surface { position: relative; min-height: 0; background: #151411; } -.bottom-panel { min-height: 0; display: grid; grid-template-rows: 35px minmax(0, 1fr); background: #12110f; border-top: 1px solid var(--line-strong); } +.bottom-panel { min-height: 0; display: grid; grid-template-rows: 35px minmax(0, 1fr); background: #12110f; } .bottom-tabs { display: flex; align-items: stretch; padding: 0 8px; border-bottom: 1px solid #23211d; } .bottom-tabs > button:not(.bare-button) { position: relative; height: 35px; padding: 0 10px; border: 0; background: transparent; color: var(--muted); font-size: 10px; font-weight: 650; } .bottom-tabs > button:not(.bare-button).active { color: var(--text); } .bottom-tabs > button:not(.bare-button).active::after { content: ""; position: absolute; height: 1px; left: 9px; right: 9px; bottom: 0; background: var(--accent); } .count-badge { display: inline-grid; place-items: center; min-width: 16px; height: 16px; margin-left: 5px; border-radius: 8px; background: #34201d; color: #ff978d; font-size: 9px; } +.test-count-badge { display: inline-grid; place-items: center; min-width: 27px; height: 16px; margin-left: 5px; padding: 0 5px; border-radius: 8px; background: #26301f; color: #a9c77e; font-family: var(--font-mono), monospace; font-size: 8px; } .panel-status { margin-left: auto; display: flex; align-items: center; gap: 6px; color: var(--muted); font-family: var(--font-mono), monospace; font-size: 9px; } .panel-status svg { color: var(--accent); } .panel-download { align-self: center; margin-left: 8px; } @@ -380,17 +459,231 @@ button:disabled { cursor: not-allowed; opacity: .48; } .terminal-output pre.system { color: #7e8e69; } .prompt { color: var(--accent); } +.self-test-workbench { height: 100%; min-height: 0; display: grid; grid-template-columns: minmax(285px, .9fr) minmax(280px, 1.1fr); background: #12110f; } +.self-test-cases { min-width: 0; min-height: 0; display: grid; grid-template-rows: auto minmax(0, 1fr); border-right: 1px solid var(--line); } +.self-test-toolbar { min-height: 48px; display: flex; align-items: center; justify-content: space-between; gap: 10px; padding: 7px 9px; border-bottom: 1px solid #292720; background: #161512; } +.self-test-toolbar > div:first-child { min-width: 0; display: flex; flex-direction: column; gap: 2px; } +.self-test-toolbar strong { color: #d0cbc1; font-size: 9px; } +.self-test-toolbar span { overflow: hidden; color: #706b62; font-size: 7px; text-overflow: ellipsis; white-space: nowrap; } +.self-test-toolbar > div:last-child { display: flex; align-items: center; gap: 5px; } +.self-test-toolbar button { min-height: 27px; display: inline-flex; align-items: center; gap: 4px; padding: 0 7px; border: 1px solid #36332c; border-radius: 4px; background: #1d1b17; color: #99938a; font-size: 8px; white-space: nowrap; } +.self-test-toolbar button:hover:not(:disabled) { border-color: #52633d; color: #c5d7ab; } +.self-test-toolbar button.self-test-run-all { border-color: #5d7540; background: #25331a; color: var(--accent); } +.self-test-toolbar button:disabled, .self-test-card button:disabled, .self-test-card input:disabled, .self-test-card textarea:disabled { cursor: not-allowed; opacity: .48; } +.self-test-list { min-height: 0; overflow: auto; padding: 7px; } +.self-test-card { margin-bottom: 6px; overflow: hidden; border: 1px solid #302e27; border-radius: 6px; background: #161512; } +.self-test-card.selected { border-color: #637b46; box-shadow: 0 0 0 1px #40532f inset; } +.self-test-card > header { height: 31px; display: grid; grid-template-columns: auto minmax(80px, 1fr) 27px 27px; align-items: center; gap: 3px; padding: 3px 4px; border-bottom: 1px solid #292720; } +.self-test-card > header > button { height: 25px; display: grid; place-items: center; border: 0; border-radius: 4px; background: transparent; color: #777168; } +.self-test-card > header > button:hover:not(:disabled) { background: #25231e; color: var(--text); } +.self-test-card .self-test-selector { min-width: 43px; display: flex; align-items: center; justify-content: flex-start; gap: 5px; padding: 0 5px; font-family: var(--font-mono), monospace; font-size: 7px; } +.self-test-card .self-test-selector svg { color: #899d6e; } +.self-test-card > header > input { min-width: 0; height: 24px; border: 1px solid transparent; border-radius: 4px; outline: 0; background: transparent; color: #bbb5ab; padding: 0 5px; font-size: 8px; font-weight: 680; } +.self-test-card > header > input:focus { border-color: #4c5d39; background: #11110e; } +.self-test-card label { display: block; padding: 5px 6px 6px; } +.self-test-card label > span { display: block; margin: 0 0 4px 2px; color: #69785b; font-family: var(--font-mono), monospace; font-size: 6px; font-weight: 760; letter-spacing: .12em; } +.self-test-card textarea { width: 100%; min-height: 61px; resize: vertical; border: 1px solid #2b2923; border-radius: 4px; outline: 0; background: #11100e; color: #d4cfc5; padding: 6px 7px; font-family: var(--font-mono), monospace; font-size: 9px; line-height: 1.5; } +.self-test-card textarea:focus { border-color: #617746; box-shadow: 0 0 0 2px #c9f27b0d; } +.self-test-result { min-width: 0; min-height: 0; display: grid; grid-template-rows: 48px minmax(0, 1fr); } +.self-test-result > header { display: flex; align-items: center; justify-content: space-between; gap: 10px; padding: 7px 10px; border-bottom: 1px solid #292720; background: #151411; } +.self-test-result > header > div { min-width: 0; display: flex; flex-direction: column; gap: 2px; } +.self-test-result > header > div span { color: #69785b; font-family: var(--font-mono), monospace; font-size: 6px; font-weight: 760; letter-spacing: .13em; } +.self-test-result > header strong { overflow: hidden; color: #d1ccc2; font-size: 10px; text-overflow: ellipsis; white-space: nowrap; } +.self-test-result > header > span { flex: 0 0 auto; padding: 4px 6px; border-radius: 4px; font-family: var(--font-mono), monospace; font-size: 7px; } +.self-test-result > header > span.success { background: #22301b; color: #acd27d; } +.self-test-result > header > span.failure { background: #38201c; color: #ed8e83; } +.self-test-result-body { min-height: 0; overflow: auto; padding: 8px; } +.self-test-metrics { display: grid; grid-template-columns: repeat(4, minmax(0, 1fr)); gap: 5px; margin-bottom: 7px; } +.self-test-metrics > div { min-width: 0; display: flex; flex-direction: column; gap: 3px; padding: 6px 7px; border: 1px solid #2c2a24; border-radius: 5px; background: #171612; } +.self-test-metrics span { color: #706b62; font-size: 6px; text-transform: uppercase; letter-spacing: .04em; } +.self-test-metrics strong { overflow: hidden; color: #c8c2b8; font-family: var(--font-mono), monospace; font-size: 8px; text-overflow: ellipsis; white-space: nowrap; } +.self-test-stream { margin-top: 6px; overflow: hidden; border: 1px solid #2b2923; border-radius: 5px; background: #0f0f0d; } +.self-test-stream > span { display: block; padding: 5px 7px; border-bottom: 1px solid #25231e; color: #69785b; font-family: var(--font-mono), monospace; font-size: 6px; font-weight: 760; letter-spacing: .12em; } +.self-test-stream pre { min-height: 42px; max-height: 180px; margin: 0; overflow: auto; padding: 7px 8px; white-space: pre-wrap; overflow-wrap: anywhere; color: #d7d2c8; font-family: var(--font-mono), monospace; font-size: 9px; line-height: 1.5; } +.self-test-stream.stderr { border-color: #4a2e29; } +.self-test-stream.stderr > span, .self-test-stream.stderr pre { color: #e58e85; } + .statusbar { min-width: 0; display: flex; align-items: center; gap: 17px; padding: 0 10px; background: #191812; border-top: 1px solid #2b2a21; color: #7f7a70; font-family: var(--font-mono), monospace; font-size: 9px; } .statusbar > div { display: flex; align-items: center; gap: 5px; white-space: nowrap; } .statusbar > div:first-child { color: #9db979; } .status-spacer { flex: 1; } +.onboarding-backdrop { + position: fixed; + inset: 0; + z-index: 200; + display: grid; + place-items: center; + padding: 24px; + background: #080806d9; + backdrop-filter: blur(8px); +} +.onboarding-dialog { + width: min(1040px, calc(100vw - 48px)); + height: min(760px, calc(100vh - 48px)); + min-height: 600px; + display: grid; + grid-template-rows: 58px minmax(0, 1fr) 62px; + overflow: hidden; + border: 1px solid #49453b; + border-radius: 13px; + outline: none; + background: #151411; + box-shadow: 0 30px 100px #000c, 0 0 0 1px #ffffff08 inset; +} +.onboarding-header { + display: grid; + grid-template-columns: 1fr auto 1fr; + align-items: center; + gap: 18px; + padding: 0 15px; + border-bottom: 1px solid #302e27; + background: #12110e; +} +.onboarding-header > div:first-child { display: flex; align-items: center; gap: 10px; } +.onboarding-header > div:first-child > div { display: flex; flex-direction: column; gap: 2px; } +.onboarding-header > div:first-child strong { font-size: 11px; letter-spacing: .01em; } +.onboarding-header > div:first-child span:not(.brand-mark) { color: #78736a; font-size: 8px; } +.onboarding-header > button { justify-self: end; } +.onboarding-progress { display: flex; align-items: center; gap: 5px; } +.onboarding-progress span { width: 24px; height: 3px; border-radius: 2px; background: #333028; transition: background .2s ease; } +.onboarding-progress span.active { background: #97b965; } + +.onboarding-layout { min-height: 0; display: grid; grid-template-columns: 216px minmax(0, 1fr); } +.onboarding-nav { min-height: 0; display: flex; flex-direction: column; gap: 5px; padding: 22px 11px 14px; border-right: 1px solid #302e27; background: #11100e; } +.onboarding-nav > span { margin: 0 9px 8px; color: #69765a; font-family: var(--font-mono), monospace; font-size: 7px; font-weight: 760; letter-spacing: .14em; } +.onboarding-nav > button { + min-height: 55px; + display: flex; + align-items: center; + gap: 10px; + padding: 8px 9px; + border: 1px solid transparent; + border-radius: 7px; + background: transparent; + color: #747067; + text-align: left; +} +.onboarding-nav > button:hover { border-color: #333129; background: #191814; color: #aaa59b; } +.onboarding-nav > button.active { border-color: #495a36; background: #1b2116; color: #c9f27b; box-shadow: 0 0 0 1px #c9f27b08 inset; } +.onboarding-nav > button > i { width: 29px; height: 29px; display: grid; place-items: center; flex: 0 0 auto; border: 1px solid #343129; border-radius: 6px; background: #171612; font-style: normal; } +.onboarding-nav > button.active > i { border-color: #53673d; background: #232d1a; } +.onboarding-nav > button > span { min-width: 0; display: flex; flex-direction: column; gap: 3px; } +.onboarding-nav > button small { color: #68645c; font-family: var(--font-mono), monospace; font-size: 6px; font-weight: 750; letter-spacing: .08em; text-transform: uppercase; } +.onboarding-nav > button.active small { color: #819b60; } +.onboarding-nav > button strong { overflow: hidden; font-size: 9px; text-overflow: ellipsis; white-space: nowrap; } +.onboarding-nav-note { display: flex; align-items: flex-start; gap: 7px; margin: auto 8px 0; padding-top: 14px; border-top: 1px solid #292720; color: #647256; font-size: 7px; line-height: 1.45; } +.onboarding-nav-note svg { flex: 0 0 auto; } + +.onboarding-content { min-height: 0; overflow-y: auto; padding: 29px 34px 34px; scroll-behavior: smooth; } +.onboarding-step-body { width: min(100%, 750px); margin: 0 auto; } +.onboarding-step-body h2 { margin: 5px 0 10px; outline: none; color: #eeebe4; font-size: clamp(22px, 2.2vw, 29px); line-height: 1.15; letter-spacing: -.045em; } +.onboarding-eyebrow { margin: 0; color: #8ea96c; font-family: var(--font-mono), monospace; font-size: 8px; font-weight: 780; letter-spacing: .14em; text-transform: uppercase; } +.onboarding-lead { max-width: 720px; margin: 0 0 22px; color: #9a958c; font-size: 11px; line-height: 1.7; } +.onboarding-hero-mark { width: 49px; height: 49px; display: grid; place-items: center; margin-bottom: 17px; border: 1px solid #586a41; border-radius: 11px; background: #202819; color: var(--accent); box-shadow: 0 8px 26px #0005; } +.onboarding-welcome { min-height: 100%; display: flex; flex-direction: column; justify-content: center; } +.onboarding-welcome .onboarding-lead { max-width: 700px; } + +.onboarding-audience-grid { display: grid; grid-template-columns: 1fr 1fr; gap: 10px; margin: 22px 0 18px; } +.onboarding-audience-grid article { display: flex; align-items: flex-start; gap: 11px; padding: 14px; border: 1px solid #343129; border-radius: 8px; background: #1a1915; } +.onboarding-audience-grid article > svg { flex: 0 0 auto; color: #a6c47e; } +.onboarding-audience-grid strong { color: #d3cfc6; font-size: 10px; } +.onboarding-audience-grid p { margin: 5px 0 0; color: #858077; font-size: 9px; line-height: 1.55; } +.onboarding-flow { display: grid; grid-template-columns: repeat(4, 1fr); overflow: hidden; border: 1px solid #3a422f; border-radius: 8px; background: #171b14; } +.onboarding-flow > div { position: relative; min-height: 55px; display: flex; align-items: center; gap: 8px; padding: 11px 12px; } +.onboarding-flow > div + div { border-left: 1px solid #30382a; } +.onboarding-flow span { width: 20px; height: 20px; display: grid; place-items: center; flex: 0 0 auto; border: 1px solid #566841; border-radius: 50%; color: #acd07d; font-family: var(--font-mono), monospace; font-size: 7px; } +.onboarding-flow strong { color: #b9c9a3; font-size: 9px; } +.onboarding-flow i { position: absolute; right: -5px; z-index: 1; color: #69785a; font-size: 11px; font-style: normal; } + +.onboarding-pipeline { display: grid; grid-template-columns: 1fr auto 1.25fr auto 1fr auto 1.25fr; align-items: stretch; gap: 7px; margin: 21px 0; } +.onboarding-pipeline > div { min-height: 68px; display: flex; flex-direction: column; align-items: center; justify-content: center; gap: 7px; padding: 9px; border: 1px solid #39362e; border-radius: 8px; background: #191814; color: #9fba78; text-align: center; } +.onboarding-pipeline > div span { color: #bdb8ae; font-size: 8px; font-weight: 680; } +.onboarding-pipeline > i { align-self: center; color: #687759; font-size: 12px; font-style: normal; } +.onboarding-feature-grid { display: grid; grid-template-columns: repeat(3, 1fr); gap: 9px; } +.onboarding-feature-grid article { min-height: 129px; display: flex; flex-direction: column; align-items: flex-start; padding: 13px; border: 1px solid #302e28; border-radius: 8px; background: #181713; } +.onboarding-feature-grid svg { margin-bottom: 9px; color: #99b772; } +.onboarding-feature-grid strong { color: #cac5bb; font-size: 9px; } +.onboarding-feature-grid p { margin: 5px 0 0; color: #817c73; font-size: 8px; line-height: 1.55; } +.onboarding-boundary-note, .onboarding-score-note { display: flex; align-items: flex-start; gap: 11px; margin-top: 13px; padding: 13px 14px; border: 1px solid #5b452b; border-radius: 8px; background: #241e15; color: #e4b969; } +.onboarding-boundary-note > svg, .onboarding-score-note > svg { flex: 0 0 auto; } +.onboarding-boundary-note strong, .onboarding-score-note strong { color: #e4c787; font-size: 9px; } +.onboarding-boundary-note p, .onboarding-score-note p { margin: 4px 0 0; color: #b3a386; font-size: 8px; line-height: 1.55; } + +.onboarding-workflow-list { display: grid; grid-template-columns: 1fr 1fr; gap: 9px; } +.onboarding-workflow-list article { display: flex; align-items: flex-start; gap: 12px; min-height: 104px; padding: 13px; border: 1px solid #343129; border-radius: 8px; background: #191814; } +.onboarding-workflow-list article > span { width: 32px; height: 32px; display: grid; place-items: center; flex: 0 0 auto; border: 1px solid #495a37; border-radius: 7px; background: #202719; color: #a8c47e; } +.onboarding-workflow-list strong { color: #cbc6bc; font-size: 10px; } +.onboarding-workflow-list p { margin: 5px 0 0; color: #837e75; font-size: 8px; line-height: 1.55; } +.onboarding-tip { display: flex; align-items: center; gap: 9px; margin-top: 11px; padding: 11px 13px; border: 1px solid #3e4c31; border-radius: 7px; background: #192016; color: #9ebc78; font-size: 8px; line-height: 1.5; } +.onboarding-tip svg { flex: 0 0 auto; } + +.onboarding-verdict-grid { display: grid; grid-template-columns: 1fr 1fr; gap: 7px; } +.onboarding-verdict-grid article { min-height: 66px; display: grid; grid-template-columns: 40px minmax(0, 1fr); align-items: start; gap: 10px; padding: 10px; border: 1px solid #343129; border-radius: 7px; background: #191814; } +.onboarding-verdict-grid article > span { min-height: 25px; display: grid; place-items: center; border-radius: 5px; background: #292720; color: #aca79d; font-family: var(--font-mono), monospace; font-size: 8px; font-weight: 780; } +.onboarding-verdict-grid article strong { color: #c8c3b9; font-size: 9px; } +.onboarding-verdict-grid article p { margin: 3px 0 0; color: #7f7a71; font-size: 7px; line-height: 1.5; } +.onboarding-verdict-grid article.accepted { border-color: #405332; } +.onboarding-verdict-grid article.accepted > span { background: #26341e; color: #a9d47d; } +.onboarding-verdict-grid article.wrong-answer, .onboarding-verdict-grid article.runtime-error, .onboarding-verdict-grid article.compile-error { border-color: #55342f; } +.onboarding-verdict-grid article.wrong-answer > span, .onboarding-verdict-grid article.runtime-error > span, .onboarding-verdict-grid article.compile-error > span { background: #38201c; color: #ee9186; } +.onboarding-verdict-grid article.time-limit { border-color: #5c472c; } +.onboarding-verdict-grid article.time-limit > span { background: #342817; color: #e9bd68; } +.onboarding-verdict-grid article.judge-error > span { background: #2d2538; color: #c5a4eb; } +.onboarding-score-note { border-color: #485c35; background: #1c2417; color: #a9cc7d; } +.onboarding-score-note strong { color: #b9d497; } +.onboarding-score-note p { color: #92a77b; } + +.onboarding-comparison { overflow-x: auto; border: 1px solid #36332c; border-radius: 8px; background: #171612; } +.onboarding-comparison > div { min-width: 650px; display: grid; grid-template-columns: 135px 1fr 1fr; } +.onboarding-comparison > div + div { border-top: 1px solid #2d2a24; } +.onboarding-comparison > div > * { display: flex; align-items: center; padding: 9px 11px; color: #8b867d; font-size: 8px; line-height: 1.45; } +.onboarding-comparison > div > * + * { border-left: 1px solid #2d2a24; } +.onboarding-comparison > div > strong { color: #b7b1a7; font-size: 8px; } +.onboarding-comparison > div > span:last-child { background: #192016; color: #9eb584; } +.onboarding-comparison-head { background: #1d1b17; } +.onboarding-comparison-head > span { gap: 6px; color: #b1aca2 !important; font-size: 8px !important; font-weight: 720; } +.onboarding-comparison-head > span:last-child { color: #b8d590 !important; } +.onboarding-ready-card { display: flex; align-items: flex-start; gap: 12px; margin-top: 13px; padding: 14px; border: 1px solid #4c6038; border-radius: 8px; background: #1d2618; color: #add07e; } +.onboarding-ready-card svg { flex: 0 0 auto; } +.onboarding-ready-card strong { color: #c4dfa1; font-size: 10px; } +.onboarding-ready-card p { margin: 4px 0 0; color: #92a77b; font-size: 8px; line-height: 1.55; } + +.onboarding-footer { display: grid; grid-template-columns: 1fr auto 1fr; align-items: center; gap: 15px; padding: 0 15px; border-top: 1px solid #302e27; background: #12110e; } +.onboarding-footer > span { color: #746f66; font-family: var(--font-mono), monospace; font-size: 8px; } +.onboarding-footer > div { justify-self: end; display: flex; gap: 7px; } +.onboarding-footer button { min-height: 32px; display: inline-flex; align-items: center; justify-content: center; gap: 5px; border-radius: 6px; padding: 0 11px; font-size: 9px; font-weight: 680; } +.onboarding-skip { justify-self: start; border: 0; background: transparent; color: #777168; } +.onboarding-skip:hover { color: #bbb5ab; } +.onboarding-back { border: 1px solid #3a362f; background: #1b1916; color: #aaa49b; } +.onboarding-next { border: 1px solid #7c9953; background: #c9f27b; color: #17200c; } +.onboarding-next:hover { background: #d5fa8d; } + .drawer-backdrop { position: fixed; inset: 0; z-index: 100; display: flex; justify-content: flex-end; background: #080806aa; } -.settings-drawer { width: min(470px, 92vw); height: 100%; overflow-y: auto; padding: 22px; border-left: 1px solid var(--line-strong); background: #171613; box-shadow: -22px 0 70px #0008; } +.settings-drawer { width: min(520px, 94vw); height: 100%; overflow-y: auto; padding: 22px; border-left: 1px solid var(--line-strong); background: #151411; box-shadow: -22px 0 70px #0008; } .drawer-heading { display: flex; justify-content: space-between; align-items: flex-start; margin-bottom: 20px; } .drawer-heading span { color: var(--muted); font-size: 9px; font-weight: 750; letter-spacing: .14em; } .drawer-heading h2 { margin: 5px 0 0; font-size: 20px; letter-spacing: -.035em; } -.toolchain-card { display: flex; gap: 12px; padding: 12px; margin-bottom: 18px; border: 1px solid #333028; background: #1c1a16; border-radius: 8px; } +.drawer-heading p { margin: 6px 0 0; color: #777168; font-size: 9px; } +.problem-source-section { margin: 0 0 18px; padding: 13px; border: 1px solid #3a412e; border-radius: 8px; background: #181b14; } +.problem-source-heading { display: flex; align-items: flex-start; justify-content: space-between; gap: 12px; } +.problem-source-heading > div { display: flex; flex-direction: column; gap: 4px; } +.problem-source-heading span { color: #7e8e69; font-size: 8px; font-weight: 750; letter-spacing: .12em; } +.problem-source-heading strong { font-size: 12px; } +.problem-source-heading code { color: #8f9b7d; font-size: 8px; } +.problem-source-section > p { margin: 8px 0 12px; color: #858076; font-size: 9px; line-height: 1.5; } +.problem-source-form .form-field { margin-bottom: 9px; } +.problem-source-actions { display: flex; justify-content: flex-end; gap: 7px; } +.problem-source-actions button, .problem-source-retry { min-height: 30px; padding: 0 9px; border: 1px solid var(--line-strong); border-radius: 5px; background: var(--surface-2); color: var(--text-soft); font-size: 9px; } +.problem-source-actions .problem-source-apply { border-color: #607642; background: #26331b; color: var(--accent); } +.problem-source-error { margin: 0 0 9px; color: var(--danger); font-size: 9px; line-height: 1.45; } +.settings-section { position: relative; margin: 0 0 12px; padding: 13px; border: 1px solid #302e27; border-radius: 8px; background: #191814; } +.settings-section::before { content: ""; position: absolute; left: 13px; top: -1px; width: 34px; height: 1px; background: #677e45; } +.settings-section-heading { display: flex; flex-direction: column; gap: 3px; margin-bottom: 13px; } +.settings-section-heading > span { color: #71805e; font-family: var(--font-mono), monospace; font-size: 7px; font-weight: 760; letter-spacing: .13em; } +.settings-section-heading > strong { color: #d5d0c6; font-size: 12px; } +.settings-section-heading > p { margin: 0; color: #777168; font-size: 8px; line-height: 1.45; } +.toolchain-card { display: flex; gap: 12px; padding: 12px; margin-bottom: 14px; border: 1px solid #333028; background: #1c1a16; border-radius: 8px; } .toolchain-mark { flex: 0 0 auto; width: 34px; height: 34px; display: grid; place-items: center; border: 1px solid currentColor; border-radius: 7px; background: #151410; } .toolchain-card strong { font-size: 12px; } .toolchain-card p { margin: 4px 0 0; color: var(--muted); font-size: 10px; line-height: 1.5; } @@ -410,6 +703,8 @@ button:disabled { cursor: not-allowed; opacity: .48; } .cache-section button { height: 30px; display: flex; align-items: center; gap: 6px; padding: 0 9px; border: 1px solid var(--line-strong); border-radius: 5px; background: var(--surface-2); color: var(--text-soft); font-size: 9px; } .drawer-footer { display: flex; gap: 8px; margin-top: 17px; color: #82966a; font-size: 9px; line-height: 1.5; } .drawer-footer svg { flex: 0 0 auto; } +.settings-section > :last-child { margin-bottom: 0; } +.settings-storage-section .cache-section { margin-top: 0; } @media (max-width: 900px) { .brand { min-width: auto; } @@ -418,8 +713,53 @@ button:disabled { cursor: not-allowed; opacity: .48; } .statusbar > div:nth-child(2), .statusbar > div:nth-child(3) { display: none; } } +@media (max-width: 760px) { + .onboarding-backdrop { padding: 0; } + .onboarding-dialog { width: 100vw; height: 100dvh; min-height: 0; border: 0; border-radius: 0; } + .onboarding-layout { grid-template-columns: 1fr; grid-template-rows: 72px minmax(0, 1fr); } + .onboarding-nav { flex-direction: row; overflow-x: auto; gap: 6px; padding: 9px; border-right: 0; border-bottom: 1px solid #302e27; } + .onboarding-nav > span, .onboarding-nav-note { display: none; } + .onboarding-nav > button { min-width: 128px; min-height: 52px; padding: 6px 8px; } + .onboarding-content { padding: 23px 22px 28px; } + .onboarding-step-body h2 { font-size: 23px; } +} + @media (max-width: 650px) { body { overflow: auto; } .studio-shell { min-width: 1080px; } .topbar { position: sticky; top: 0; z-index: 10; } } + +@media (max-width: 520px) { + .onboarding-header { grid-template-columns: 1fr auto; } + .onboarding-progress { display: none; } + .onboarding-content { padding: 20px 16px 26px; } + .onboarding-audience-grid, .onboarding-feature-grid, .onboarding-workflow-list, .onboarding-verdict-grid { grid-template-columns: 1fr; } + .onboarding-flow { grid-template-columns: 1fr 1fr; } + .onboarding-flow > div:nth-child(3) { border-left: 0; border-top: 1px solid #30382a; } + .onboarding-flow > div:nth-child(4) { border-top: 1px solid #30382a; } + .onboarding-flow i { display: none; } + .onboarding-pipeline { grid-template-columns: 1fr; } + .onboarding-pipeline > i { transform: rotate(90deg); } + .onboarding-feature-grid article { min-height: 0; } + .onboarding-footer { grid-template-columns: auto 1fr; } + .onboarding-footer > span, .onboarding-skip { display: none; } + .onboarding-footer > div { grid-column: 2; } +} +/* Browser-only problem data is loaded from a verified, configurable collection. */ +.problem-catalog-status { + align-items: center; + background: var(--bg); + color: var(--muted); + display: flex; + gap: 10px; + inset: 0; + justify-content: center; + min-height: 100vh; +} +.problem-source-recovery { flex-direction: column; padding: 28px; text-align: center; } +.problem-source-locale { position: absolute; top: 18px; right: 18px; display: flex; align-items: center; gap: 8px; color: var(--muted); font-size: 9px; } +.problem-source-locale select { min-height: 30px; border: 1px solid var(--line-strong); border-radius: 5px; background: var(--surface-2); color: var(--text-soft); padding: 0 8px; font-size: 9px; } +.problem-source-recovery > strong { color: var(--text); } +.problem-source-recovery > span { max-width: 680px; font-size: 11px; line-height: 1.5; } +.problem-source-recovery .problem-source-form { width: min(680px, 92vw); margin-top: 12px; padding: 14px; border: 1px solid var(--line); border-radius: 8px; background: var(--surface-1); text-align: left; } diff --git a/app/layout.tsx b/app/layout.tsx index 2a07408..9d3257b 100644 --- a/app/layout.tsx +++ b/app/layout.tsx @@ -14,7 +14,7 @@ export async function generateMetadata(): Promise { forwardedProtocol: requestHeaders.get("x-forwarded-proto"), host: requestHeaders.get("host"), }); - const description = "A private, fully in-browser online judge with 20 original challenges and six Wasmer-powered languages."; + const description = "A private, fully in-browser online judge with 45 original challenges and seven Wasmer-powered languages."; return { metadataBase, title: "WASM OJ Forge", @@ -22,14 +22,14 @@ export async function generateMetadata(): Promise { icons: { icon: "/favicon.svg" }, openGraph: { title: "WASM OJ Forge", - description: "20 challenges. Six languages. Zero code uploads.", + description: "45 challenges. Seven languages. Zero code uploads.", type: "website", images: [{ url: new URL("/og.png", metadataBase).toString(), width: 1200, height: 630, alt: "WASM OJ Forge — deterministic browser-local compilation and judging" }], }, twitter: { card: "summary_large_image", title: "WASM OJ Forge", - description: "20 challenges. Six languages. Zero code uploads.", + description: "45 challenges. Seven languages. Zero code uploads.", images: [new URL("/og.png", metadataBase).toString()], }, }; @@ -37,7 +37,7 @@ export async function generateMetadata(): Promise { export default function RootLayout({ children }: Readonly<{ children: React.ReactNode }>) { return ( - + {children} ); diff --git a/app/page.tsx b/app/page.tsx index 3bab4fd..d49b28c 100644 --- a/app/page.tsx +++ b/app/page.tsx @@ -1,7 +1,12 @@ "use client"; -import { JudgeStudio } from "@/src/components/judge-studio"; +import dynamic from "next/dynamic"; + +const JudgeStudioLoader = dynamic( + () => import("@/src/components/judge-studio").then((module) => module.JudgeStudioLoader), + { ssr: false }, +); export default function Home() { - return ; + return ; } diff --git a/calibration/forge-v1/README.md b/calibration/forge-v1/README.md new file mode 100644 index 0000000..16b2290 --- /dev/null +++ b/calibration/forge-v1/README.md @@ -0,0 +1,89 @@ +# Forge v1 instruction-cost calibration + +This directory is the audit trail for every `instructionBudget` in the catalog. + +The catalog binding was refreshed when the repository moved from the +single-title catalog to localized `wasm-oj-catalog-v2` / `wasm-oj-problem-v3`. +That migration changed only titles and statement/editorial paths. Every measured +solution SHA-256, test input/output SHA-256, Forge content identity, and recorded +cost remains unchanged; the derivation tool rechecks all of those byte-level +measurement inputs before accepting the refreshed catalog hash. + +- `reference-costs.json` contains 315 records (45 problems × 7 languages) and + 1,281 case executions. Every record binds the source, input, expected output, + artifact profile, compiler, runner, generated Forge library, toolchains, Node + runtime, and the two external JavaScript dependency trees by SHA-256. +- `derived-policies.json` is a deterministic projection of that evidence. It + records every language's worst stored-case cost, every tier contributor, and + the three resulting budgets. Aggregate numerators are decimal strings so the + four-language sum remains exact even when it exceeds JavaScript's safe integer + range; division, headroom, and rounding use integer arithmetic throughout. + +The isolated measurement checkout reports `?? node_modules` because its +dependency directory was a local symlink into the pinned Forge installation. +This path was not an engine input by name: the exact `@wasmer/sdk` and `fflate` +trees reached through the symlink are content-bound in `forge.dependencyTreeSha256`. +The Forge source commit, compiler/runner binaries, generated library, and +toolchains are independently bound as well. + +## Reproduce or refresh + +Build Forge, then run the calibration against an absolute Forge checkout path: + +```bash +node tools/calibrate_costs.mjs --forge /absolute/path/to/forge +node tools/derive_cost_policies.mjs --write +``` + +The measurement command refuses to overwrite existing evidence. Use `--resume` +only with the same catalog and exact runtime identity. For an append-only catalog +extension, add `--extend`: the tool first verifies the exact compiler, runner, +library, toolchain, and dependency digests, then rehashes every previously +measured solution and test pair before preserving any old records. `--problem` +and `--language` can narrow an interrupted run; a production derivation still +requires all 315 records. + +After changing a reference implementation, replace its stale records explicitly: + +```bash +node tools/calibrate_costs.mjs --forge /absolute/path/to/forge \ + --problem 11 --resume --replace +``` + +`--replace` requires at least one problem selection and removes only the selected +problem/language records before remeasuring them. + +Normal validation is read-only and fails closed if a solution, stored case, +evidence file, derivation, or manifest budget is stale: + +```bash +node tools/derive_cost_policies.mjs +``` + +For problem `p`, language `l`, and stored case `c`, the method is: + +```text +languageWorst[p,l] = max(cost[p,l,c]) +compiled[p] = [languageWorst[p,C], languageWorst[p,C++], + languageWorst[p,Rust], languageWorst[p,Go]] +rawOptimal[p] = ceil(sum(compiled[p]) × 105 / (4 × 100)) +rawEfficient[p] = ceil(max(compiled[p]) × 105 / 100) +rawBaseline[p] = ceil(max(languageWorst[p,*]) × 105 / 100) +quantum(x) = 5 × 10^(decimalDigits(x) - 2) when decimalDigits(x) >= 3 +quantum(x) = 1 otherwise +budget(x) = ceil(x / quantum(x)) × quantum(x) +optimal[p] = budget(rawOptimal[p]) +efficient[p] = budget(rawEfficient[p]) +baseline[p] = budget(rawBaseline[p]) +``` + +All costs are Forge `wasm-oj-forge-v1` baseline-normalized net weighted costs. +The strict tier averages the four compiled reference languages instead of using +a single fastest-language witness. The efficient tier admits the slowest of +those four compiled references, while baseline admits the slowest of all seven +references. The fixed 5% headroom is followed only by safe upward decimal +rounding: from three digits onward, a budget is rounded up to a multiple of +`5 × 10^(digits - 2)`. +For example, `28,995` becomes `30,000` and `10,170,535` becomes `15,000,000`. +The rounding never lowers the unrounded bound. Wall time is not part of the +derivation. diff --git a/calibration/forge-v1/derived-policies.json b/calibration/forge-v1/derived-policies.json new file mode 100644 index 0000000..2d499ca --- /dev/null +++ b/calibration/forge-v1/derived-policies.json @@ -0,0 +1,7424 @@ +{ + "schema": "wasm-oj-derived-cost-policies-v2", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "sourceEvidence": "calibration/forge-v1/reference-costs.json", + "sourceEvidenceSha256": "02b9facb1f712c95d0b136456d82b184c779312c01b5e39905b1142406ae6514", + "basis": "compiled-language-average-optimal-with-compiled-and-all-language-maximum-tiers", + "headroom": { + "numerator": 105, + "denominator": 100 + }, + "rounding": { + "mode": "ceiling", + "quantumFormula": "5 * 10^(decimalDigits(unroundedInstructionBudget) - 2)", + "appliesFromDecimalDigits": 3 + }, + "policyBasis": { + "baseline": { + "aggregation": "maximum", + "languages": [ + "c", + "cpp", + "rust", + "go", + "python", + "javascript", + 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"maximumMemoryBytes": 8519680 + } + ], + "minimumLanguage": "rust", + "minimumWorstCaseCost": 1187965236 + } + ] +} diff --git a/catalog.json b/catalog.json new file mode 100644 index 0000000..8d4c834 --- /dev/null +++ b/catalog.json @@ -0,0 +1,238 @@ +{ + "schema": "wasm-oj-catalog-v2", + "problemSchema": "wasm-oj-problem-v3", + "localization": { + "defaultLocale": "zh-TW", + "supportedLocales": [ + "zh-TW", + "en" + ] + }, + "problems": [ + { + "id": 1, + "slug": "weighted-opcode-scale", + "manifest": "problems/001-weighted-opcode-scale/problem.json" + }, + { + "id": 2, + "slug": "baseline-calibration", + "manifest": "problems/002-baseline-calibration/problem.json" + }, + { + "id": 3, + "slug": "memory-gate", + "manifest": "problems/003-memory-gate/problem.json" + }, + { + "id": 4, + "slug": "shared-output-pool", + "manifest": "problems/004-shared-output-pool/problem.json" + }, + { + "id": 5, + "slug": "transactional-vfs-quota", + "manifest": 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index 2d1e87e..64721bb 100644 --- a/docs/architecture.md +++ b/docs/architecture.md @@ -37,9 +37,9 @@ The UI sends immutable requests to dedicated compiler and runner module Workers. ## Local judging -The catalog is a static, typed set of 20 original problems. Every problem defines its statement, input/output contract, constraints, examples, deterministic weighted-cost budget, and at least four judge cases. Fixture tests run independent reference solvers against every expected output. +The canonical, API-addressable set of original problems lives in the public `wasm-oj/problems` repository. Its browser projection is split into a small localized index and integrity-addressed per-problem bundles. Forge validates user-configurable GitHub source fields, loads only the index plus the active problem, streams every bundle under an explicit size ceiling, verifies SHA-256 before parsing, and caches verified bytes by digest. Project drafts and solved progress combine the collection source with the active problem digest, so unchanged problems retain state while modified problems are isolated. The local generated catalog is a development/test fixture, not a runtime fallback. Every case runs once under the broadest cost/memory limits, then the same correctness result and Forge metrics are evaluated against cumulative partial-credit policies. -A submission compiles once. For each case, `JudgeEngine` resolves `JudgeCaseSpec.input` and creates an independent `RunConfig`; it does not mutate the compiled project or its build configuration. Output comparison normalizes CRLF and trailing whitespace while preserving leading whitespace. The first wrong answer, non-zero exit, timeout, or runtime failure ends the submission. Accepted problem IDs persist in localStorage; per-problem, per-language drafts persist in IndexedDB. +A submission compiles once. For each case, `JudgeEngine` resolves `JudgeCaseSpec.input` and creates an independent `RunConfig`; it does not mutate the compiled project or its build configuration. Output comparison normalizes CRLF and trailing whitespace while preserving leading whitespace. The first wrong answer, non-zero exit, timeout, or runtime failure ends the submission. The self-test workbench keeps a bounded, collection-and-problem-digest-scoped list of user inputs in localStorage, reuses one current artifact for single-case or sequential multi-case runs, and reports each run's streams and resource metrics separately. Compiler and runtime transcripts share one ordered Output surface instead of presenting duplicate tabs. Accepted source/problem-digest tokens persist in localStorage; per-source, per-problem-digest, per-language drafts persist in IndexedDB. The wall limit is an emergency host safety boundary, not a judging score. Browser and server hosts first apply a separate fixed 120-second preparation deadline. Only after runtime resolution succeeds does the browser start the guest timer; expiry replaces the runner Worker. `ServerForgeRunner` likewise starts the guest timer only for the native child and sends `SIGKILL` on expiry. Guest execution cannot continue after either deadline. Optimizer-derived weighted metering is the deterministic CPU limit, while `logicalTimeLimitMs` is the deterministic elapsed-time limit used for cross-host judging. @@ -157,13 +157,13 @@ IndexedDB has two object stores: - `projects`: autosaved project snapshots keyed by project ID. - `artifacts`: content-addressed build products keyed by SHA-256 of canonical files and build configuration. -The artifact store retains the 20 newest builds. `ForgeStorageCoordinator` joins artifact, dependency, incremental graph, runtime-files, and toolchain storage under one cross-tab Web Locks policy. It records logical size and access time at write/read boundaries, reserves configurable browser-quota headroom, and evicts by retention class followed by LRU. The package exports a service-worker asset plus `registerToolchainCache()`. Within the registration's caller-selected same-origin scope, the worker caches only GET requests carrying exactly one valid expected-SHA-256 query value; it records verified byte length and cache time for the coordinator and is not coupled to a hard-coded `/toolchains/` directory. Cache hits and network responses are rehashed, stale same-path identities are pruned only after a verified replacement is stored, and quota/write failures do not invalidate already verified response bytes. A caller-selected cross-origin `assetBaseUrl` is outside that service-worker cache and follows the static host's caching policy. No compiler or runner resolves a registry package at execution time. The CPython runtime filesystem is stored as a deterministic `FORGEFS1` archive whose exact SHA-256 is recorded in the toolchain manifest and content identity. Browser and server runners include that digest in the cache identity and verify every cache hit and fresh export before structural decoding. A corrupt or oversized cached archive is removed and reported, then handled as a normal cache miss; the replacement must match the pinned digest before it is decoded. A corrupt fresh export fails closed. On the server the same verified archive is stored in the configured cache directory with a 64 MiB read boundary. Browser persistent-storage permission is requested through the coordinator at startup. Solved-problem IDs use a validated localStorage record separate from build artifacts. +The artifact store retains the 20 newest builds. `ForgeStorageCoordinator` joins artifact, dependency, incremental graph, runtime-files, and toolchain storage under one cross-tab Web Locks policy. It records logical size and access time at write/read boundaries, reserves configurable browser-quota headroom, and evicts by retention class followed by LRU. The package exports a service-worker asset plus `registerToolchainCache()`. Within the registration's caller-selected same-origin scope, the worker caches only GET requests carrying exactly one valid expected-SHA-256 query value; it records verified byte length and cache time for the coordinator and is not coupled to a hard-coded `/toolchains/` directory. Cache hits and network responses are rehashed, stale same-path identities are pruned only after a verified replacement is stored, and quota/write failures do not invalidate already verified response bytes. Problem bundles use a separate Cache API namespace keyed by their published digest and are re-hashed on every read. A caller-selected cross-origin `assetBaseUrl` is outside the service-worker cache and follows the static host's caching policy. No compiler or runner resolves a registry package at execution time. The CPython runtime filesystem is stored as a deterministic `FORGEFS1` archive whose exact SHA-256 is recorded in the toolchain manifest and content identity. Browser and server runners include that digest in the cache identity and verify every cache hit and fresh export before structural decoding. A corrupt or oversized cached archive is removed and reported, then handled as a normal cache miss; the replacement must match the pinned digest before it is decoded. A corrupt fresh export fails closed. On the server the same verified archive is stored in the configured cache directory with a 64 MiB read boundary. Browser persistent-storage permission is requested through the coordinator at startup. Solved-problem IDs use a validated, collection-scoped localStorage record separate from build artifacts. The judge editor debounces build-identity changes for 900 ms and then calls the same compile coordinator in the background. A Run or Judge action for that exact identity joins the request or uses the persisted result. Editing source, target, profile, entry, or toolchain identity supersedes the old speculative intent and invalidates its artifact identity. If the superseded build is already running, cancellation replaces its complete compiler Worker tree; otherwise the retained C/C++ or Rust generation may serve the new serialized build within its stage budget. Runtime-only input changes do not invalidate a valid artifact. ## Security and privacy boundaries -- The production response sets `Cross-Origin-Opener-Policy: same-origin`, `Cross-Origin-Embedder-Policy: credentialless`, and `Cross-Origin-Resource-Policy: same-origin`, plus the documented referrer, content-type, and permissions policies. A Content Security Policy must allow `worker-src 'self' blob:`. +- The production response sets `Cross-Origin-Opener-Policy: same-origin`, `Cross-Origin-Embedder-Policy: require-corp`, and `Cross-Origin-Resource-Policy: same-origin`, plus the documented referrer, content-type, and permissions policies. A Content Security Policy must allow `worker-src 'self' blob:`. - Guest programs see only explicit in-memory mounts and configured stdin, arguments, and environment variables. - Source paths are normalized and cannot escape the project mount. - User-controlled code runs only inside Wasmer's WASI/WASIX sandbox in a disposable Worker or native child process. diff --git a/docs/conformance-report.md b/docs/conformance-report.md index 8ba9285..c728539 100644 --- a/docs/conformance-report.md +++ b/docs/conformance-report.md @@ -6,7 +6,7 @@ judge, and library behavior. The current preregistered evidence is maintained under the single [contract 1 conformance experiment](../experiments/forge-contract-1-conformance/). -This report records real local server and browser runs on 2026-07-19 +This report records real local server and browser runs on 2026-07-20 (Asia/Taipei). The canonical matrix is generated from independent append-only evidence records under `wasm-oj-forge-v1`; it is not a synthetic estimate. @@ -46,27 +46,27 @@ compatibility. | Case | Artifact | Bytes | Net / raw / baseline | Server compile 1 / 2 | Browser compile 1 / 2 | Median run server / browser | | --- | --- | ---: | ---: | ---: | ---: | ---: | -| C / wasip1 | `b195a678…f952b` | 45,625 | 5,445 / 5,591 / 146 | 1,490 ms / 1,520 ms | 1,358 ms / 1 ms | 34 ms / 9 ms | -| C / wasip1 / filesystem metadata | `856e2fe9…c013e` | 33,056 | 15,427 / 15,573 / 146 | 1,493 ms / 1,489 ms | 176 ms / 1 ms | 27 ms / 5 ms | -| C / wasip1 / multi-file IO | `334dab5d…3bf97` | 49,908 | 16,883 / 17,029 / 146 | 1,483 ms / 1,482 ms | 204 ms / 767 ms | 31 ms / 10 ms | -| C / wasip1 / filesystem write limit | `b3d8825f…4f79a` | 18,945 | 6,219 / 6,365 / 146 | 1,678 ms / 1,473 ms | 338 ms / 1 ms | 17 ms / 3 ms | -| C / WASIX | `c3928999…8cd19` | 4,064 | 1,138 / 1,284 / 146 | 1,466 ms / 1,460 ms | 340 ms / 1 ms | 8 ms / 1 ms | -| C / WASIX / denied thread_spawn | `432af0c8…210a7` | 1,072 | 0 / 133 / 146 | 1,459 ms / 1,460 ms | 192 ms / 766 ms | 6 ms / 1 ms | -| C++ / wasip1 | `db897e4f…bb50d` | 4,059 | 934 / 1,080 / 146 | 1,467 ms / 1,520 ms | 567 ms / 1 ms | 8 ms / 1 ms | -| C++ / WASIX | `e5f96539…40e11` | 4,059 | 934 / 1,080 / 146 | 1,513 ms / 1,504 ms | 82 ms / 1 ms | 8 ms / 1 ms | -| Rust / wasip1 | `05fcf6e0…6fac0` | 142,818 | 14,761 / 24,243 / 9,482 | 2,952 ms / 2,895 ms | 2,724 ms / 607 ms | 37 ms / 13 ms | -| Python / wasip1 | `98561f95…ac712` | 1,851 | 4,632,241 / 2,424,466,250 / 2,419,834,009 | 16,381 ms / 16,395 ms | 1,488 ms / 479 ms | 1,049 ms / 800 ms | -| JavaScript / wasip1 | `673f1db6…927a7` | 1,902 | 4,489,846 / 14,074,831 / 9,584,985 | 2,118 ms / 1,849 ms | 2,091 ms / 2,134 ms | 226 ms / 176 ms | -| TypeScript / wasip1 | `8cc8d4b3…83ae4` | 1,925 | 4,514,568 / 14,099,553 / 9,584,985 | 1,789 ms / 1,783 ms | 1,573 ms / 1,548 ms | 228 ms / 177 ms | -| Go / wasip1 | `39d6cb9e…596fb` | 2,550,145 | 429,396 / 2,136,517 / 1,707,121 | 2,918 ms / 2,598 ms | 1,675 ms / 400 ms | 374 ms / 291 ms | -| C / wasip1 / virtual clock | `f72e1525…dc27b` | 18,565 | 8,022 / 8,168 / 146 | 1,499 ms / 1,508 ms | 1,165 ms / 1 ms | 18 ms / 4 ms | -| C / wasip1 / logical time limit | `feae5bbd…e648d` | 1,254 | 51 / 197 / 146 | 1,496 ms / 1,474 ms | 350 ms / 1 ms | 6 ms / 0 ms | -| C++ / wasip1 / virtual sleep | `7ef531ef…2cba1` | 23,327 | 4,985 / 5,131 / 146 | 1,796 ms / 1,531 ms | 246 ms / 769 ms | 21 ms / 4 ms | -| Rust / wasip1 / virtual sleep | `28b9dca7…7e74d` | 168,053 | 16,640 / 26,122 / 9,482 | 2,782 ms / 2,898 ms | 2,622 ms / 594 ms | 39 ms / 14 ms | -| Python / wasip1 / virtual sleep | `3b6e2b1c…5830b` | 2,041 | 4,648,726 / 2,424,482,735 / 2,419,834,009 | 16,367 ms / 16,409 ms | 1,474 ms / 458 ms | 1,047 ms / 825 ms | -| JavaScript / wasip1 / virtual clock | `77fedb77…d488f` | 1,948 | 28,374,535 / 37,959,520 / 9,584,985 | 1,793 ms / 1,786 ms | 1,509 ms / 1,644 ms | 225 ms / 181 ms | -| TypeScript / wasip1 / virtual clock | `3cd0cb23…bcab5` | 1,948 | 28,374,535 / 37,959,520 / 9,584,985 | 2,142 ms / 2,217 ms | 2,012 ms / 1,930 ms | 247 ms / 174 ms | -| Go / wasip1 / virtual sleep | `8a7e09d7…3c07f` | 2,561,512 | 589,026 / 2,296,147 / 1,707,121 | 2,812 ms / 2,904 ms | 881 ms / 415 ms | 414 ms / 293 ms | +| C / wasip1 | `b195a678…f952b` | 45,625 | 5,445 / 5,591 / 146 | 1,549 ms / 1,575 ms | 1,236 ms / 1 ms | 37 ms / 8 ms | +| C / wasip1 / filesystem metadata | `856e2fe9…c013e` | 33,056 | 15,427 / 15,573 / 146 | 1,656 ms / 1,575 ms | 184 ms / 1 ms | 27 ms / 6 ms | +| C / wasip1 / multi-file IO | `334dab5d…3bf97` | 49,908 | 16,883 / 17,029 / 146 | 1,557 ms / 1,509 ms | 174 ms / 777 ms | 37 ms / 9 ms | +| C / wasip1 / filesystem write limit | `b3d8825f…4f79a` | 18,945 | 6,219 / 6,365 / 146 | 1,803 ms / 1,511 ms | 328 ms / 1 ms | 18 ms / 3 ms | +| C / WASIX | `c3928999…8cd19` | 4,064 | 1,138 / 1,284 / 146 | 1,520 ms / 1,775 ms | 162 ms / 1 ms | 9 ms / 1 ms | +| C / WASIX / denied thread_spawn | `432af0c8…210a7` | 1,072 | 0 / 133 / 146 | 1,538 ms / 1,524 ms | 174 ms / 760 ms | 7 ms / 1 ms | +| C++ / wasip1 | `db897e4f…bb50d` | 4,059 | 934 / 1,080 / 146 | 1,586 ms / 1,520 ms | 536 ms / 1 ms | 8 ms / 1 ms | +| C++ / WASIX | `e5f96539…40e11` | 4,059 | 934 / 1,080 / 146 | 1,584 ms / 1,596 ms | 93 ms / 1 ms | 9 ms / 1 ms | +| Rust / wasip1 | `05fcf6e0…6fac0` | 142,818 | 14,761 / 24,243 / 9,482 | 3,114 ms / 3,097 ms | 2,652 ms / 586 ms | 43 ms / 13 ms | +| Python / wasip1 | `98561f95…ac712` | 1,851 | 4,632,241 / 2,424,466,250 / 2,419,834,009 | 8,269 ms / 8,266 ms | 1,449 ms / 429 ms | 1,080 ms / 775 ms | +| JavaScript / wasip1 | `673f1db6…927a7` | 1,902 | 4,489,846 / 14,074,831 / 9,584,985 | 2,150 ms / 1,869 ms | 1,728 ms / 2,183 ms | 232 ms / 168 ms | +| TypeScript / wasip1 | `8cc8d4b3…83ae4` | 1,925 | 4,514,568 / 14,099,553 / 9,584,985 | 1,875 ms / 1,876 ms | 1,656 ms / 1,541 ms | 235 ms / 167 ms | +| Go / wasip1 | `39d6cb9e…596fb` | 2,550,145 | 429,396 / 2,136,517 / 1,707,121 | 3,301 ms / 2,710 ms | 1,648 ms / 397 ms | 393 ms / 273 ms | +| C / wasip1 / virtual clock | `f72e1525…dc27b` | 18,565 | 8,022 / 8,168 / 146 | 1,842 ms / 1,561 ms | 1,095 ms / 2 ms | 19 ms / 3 ms | +| C / wasip1 / logical time limit | `feae5bbd…e648d` | 1,254 | 51 / 197 / 146 | 1,714 ms / 1,514 ms | 328 ms / 1 ms | 6 ms / 0 ms | +| C++ / wasip1 / virtual sleep | `7ef531ef…2cba1` | 23,327 | 4,985 / 5,131 / 146 | 1,995 ms / 1,940 ms | 223 ms / 744 ms | 22 ms / 4 ms | +| Rust / wasip1 / virtual sleep | `28b9dca7…7e74d` | 168,053 | 16,640 / 26,122 / 9,482 | 3,031 ms / 3,022 ms | 2,589 ms / 600 ms | 40 ms / 15 ms | +| Python / wasip1 / virtual sleep | `3b6e2b1c…5830b` | 2,041 | 4,648,726 / 2,424,482,735 / 2,419,834,009 | 16,386 ms / 8,293 ms | 1,505 ms / 490 ms | 1,106 ms / 819 ms | +| JavaScript / wasip1 / virtual clock | `77fedb77…d488f` | 1,948 | 28,374,535 / 37,959,520 / 9,584,985 | 1,932 ms / 1,920 ms | 1,509 ms / 1,485 ms | 231 ms / 167 ms | +| TypeScript / wasip1 / virtual clock | `3cd0cb23…bcab5` | 1,948 | 28,374,535 / 37,959,520 / 9,584,985 | 1,793 ms / 2,215 ms | 1,664 ms / 1,563 ms | 241 ms / 164 ms | +| Go / wasip1 / virtual sleep | `8a7e09d7…3c07f` | 2,561,512 | 589,026 / 2,296,147 / 1,707,121 | 2,735 ms / 2,761 ms | 885 ms / 396 ms | 380 ms / 276 ms | The default panel contains all 21 execution cases shown above: the nine diff --git a/docs/integration-guide.md b/docs/integration-guide.md index 4efd868..5d6fe46 100644 --- a/docs/integration-guide.md +++ b/docs/integration-guide.md @@ -43,8 +43,8 @@ const forge = await Forge.create({ ``` The page must be cross-origin isolated. Its responses need COOP -`same-origin`, COEP `credentialless` (or an equivalently valid isolation -policy), and CORP `same-origin`; CSP must permit `worker-src 'self' blob:`. +`same-origin`, COEP `require-corp`, and CORP `same-origin`; CSP must permit +`worker-src 'self' blob:`. Toolchain requests are static, digest-pinned GETs and contain no source code, stdin, diagnostics, or artifacts. diff --git a/docs/library-contract.md b/docs/library-contract.md index 2bfc011..17baad3 100644 --- a/docs/library-contract.md +++ b/docs/library-contract.md @@ -287,6 +287,6 @@ resource, and calibrated-cost contract. Forge starts its emitted module Workers through same-origin `blob:` bootstraps. Every Wasmer SDK initialization supplies Forge's secondary-worker asset through the official `workerUrl` protocol. That worker validates the SDK initialization envelope (including `sdkUrl`), disables registry access, calls `initSync` with the transferred module and memory plus a page-aligned 1 MiB stack, installs the validated `sdkUrl`, and constructs the official `ThreadPoolWorker`. The packed build emits the facade, SDK/runtime Wasm, and nested Workers as external content-hashed assets rather than library-mode data URLs. This is host compiler/runtime scheduling policy and never grants guest thread-spawn capability. -A production host must serve `Cross-Origin-Opener-Policy: same-origin`, `Cross-Origin-Embedder-Policy: credentialless`, and `Cross-Origin-Resource-Policy: same-origin`; a Content Security Policy must allow `worker-src 'self' blob:`. Packed deployments must retain the emitted compiler, runner, Python-stage, Rust-stage, Go-stage, and Wasmer secondary-worker assets at URLs reachable from their parent bundles. Toolchain and cross-origin assets still require the CORS and Cross-Origin-Resource-Policy behavior imposed by the page's COEP policy. +A production host must serve `Cross-Origin-Opener-Policy: same-origin`, `Cross-Origin-Embedder-Policy: require-corp`, and `Cross-Origin-Resource-Policy: same-origin`; a Content Security Policy must allow `worker-src 'self' blob:`. Packed deployments must retain the emitted compiler, runner, Python-stage, Rust-stage, Go-stage, and Wasmer secondary-worker assets at URLs reachable from their parent bundles. Toolchain and cross-origin assets still require the CORS and Cross-Origin-Resource-Policy behavior imposed by the page's COEP policy. Judge code remains unchanged. Any incompatible judge, artifact, normalization, metering, compiler, runner, extension, or conformance change increments the one Forge contract; artifacts and requests from older contracts are rejected explicitly. See [the versioning policy](versioning.md). diff --git a/docs/problem-bank/CONTRACT.md b/docs/problem-bank/CONTRACT.md new file mode 100644 index 0000000..16c57e2 --- /dev/null +++ b/docs/problem-bank/CONTRACT.md @@ -0,0 +1,115 @@ +# 題庫契約 + +## 範圍 + +本 repository 固定收錄 45 題。題號、slug 與目錄一經建立即為穩定識別; +題意可以修正,但不得以隱藏 fallback 或相容分支保留錯誤契約。 + +根目錄 `catalog.json` 是唯一 discovery entry point,依序明列 45 份 `problem.json`。 +Consumer 不得先列出目錄再猜 manifest path。 + +每題必須具備以下檔案: + +```text +problems/NNN-slug/ +├── problem.json +├── statement.zh-TW.md +├── statement.en.md +├── editorial.zh-TW.md +├── editorial.en.md +├── validator.py +├── generator.py +├── oracle.py +├── tests/ +│ ├── sample-01.in +│ ├── sample-01.out +│ └── ... +└── solutions/ + ├── c/main.c + ├── cpp/main.cpp + ├── rust/main.rs + ├── go/main.go + ├── python/main.py + ├── javascript/main.js + └── typescript/main.ts +``` + +上圖是目前 repository layout,不是 consumer contract。`problem.json.files` 必須明列 +各 locale 的 statement/editorial、validator、generator、oracle、七語言 solution, +以及每個 test 的 input/output path。所有 path 均相對於 manifest 目錄,且必須是 +normalized POSIX relative path。 + +## 題目設計 + +1. 輸入與輸出必須是 deterministic UTF-8 text,不依賴 host locale、clock、 + filesystem 或 network。 +2. `statement.zh-TW.md` 與 `statement.en.md` 必須定義完全相同的 tie-break、錯誤狀態、 + 整數範圍、indexing 與空集合行為;sample 不得替代規格。 +3. 每題至少要存在兩種有實質複雜度差異的解法。完整限制必須排除直覺解, + 而最佳解必須有可證明的漸進複雜度。 +4. `editorial.zh-TW.md` 與 `editorial.en.md` 都至少包含:直覺解、最佳解、正確性證明、 + 時間複雜度、空間複雜度、常見錯誤,且兩個 locale 的演算法宣稱必須一致。 +5. 不把 SHA-256 實作本身當成無關門檻。題意中的 digest 是已計算完成、 + 不碰撞的 lowercase hexadecimal token,除非該題明確是在考 encoding。 +6. 所有容量、成本及 timestamp 都必須能以帶號或無號 64-bit integer 表示。 + 若乘加可能超出,題目必須定義更寬範圍或保證不溢位。 + +## Reference solutions + +- C:C17。 +- C++:C++20。 +- Rust:edition 2024,可使用標準函式庫。 +- Go:Go 1.26。 +- Python:Python 3.14。 +- JavaScript/TypeScript:Forge `std` 輸入輸出介面;整數超過 + `Number.MAX_SAFE_INTEGER` 時必須使用 `bigint`。 +- 七份 solution 必須實作同一個最佳演算法,不得以較寬鬆的語言 timeout + 偷渡次佳解法。 +- Solution 只輸出題目要求的內容,不得包含提示、debug log 或 fallback。 + +## Tests and independent review + +- `validator.py` 對任意輸入 fail closed。 +- `oracle.py` 是與最佳解結構不同的直接解,只供小型測資 differential test。 +- `generator.py SEED INDEX` 必須在 stdout 產生**恰好一個**完整測試輸入; + 同一組參數必須 byte-identical,`INDEX` 用來選擇不同形狀/規模。generator + 的輸出必須落在 oracle 可承受的範圍。 +- 每個 sample output 由 oracle 產生或再次核對。 +- 每個 reference solution 都必須通過 samples、固定 adversarial cases 與 seeded + oracle differential tests。 +- 獨立 reviewer 僅讀 statement,先自行推導解法,再檢查 editorial、solutions + 與 constraints 是否一致,並確認宣稱的時間/空間複雜度為可達最佳解。 + +## Resource policies and scoring + +- 計算量的主要限制是 Forge baseline-normalized weighted `instructionBudget`,不是 + host wall time。 +- `scoring.costContract` 固定為 `wasm-oj-forge-v1`;judge 必須使用該 contract 驗證過的 + artifact cost profile 與 `RunResult.metrics.cost`,遇到 contract/profile/calibration + mismatch 時 fail closed。 +- `scoring.calibration.profiles` 明列七語言的 exact Forge cost profile;execution 必須帶 + submission language,且 metrics profile 必須與該語言校準值 byte-identical。 +- 本 catalog 固定使用依 relaxed-to-strict 排列的 `baseline`、`efficient`、`optimal` + 三個 cumulative policies;每層至少收緊 instruction cost、memory 或 deterministic + logical time 之一。缺少、重複或重新排序任何 policy 都是無效 manifest。 +- `scoring.caseSet=all-manifest-tests`:所有 policies 都使用 `files.tests` 明列的完整 + case set。每個 case 在最寬鬆 hard limits 下執行一次,再以同一份正確性結果及 + metrics 判斷通過哪些 policies。 +- Policy `points` 是增量分數且合計 100;總分採 equal-case average。答案錯誤或 + runtime failure 的 case 不通過任何 policy。 +- `memoryLimitBytes` 指 guest peak linear memory。`logicalTimeLimitMs` 若存在才是 + deterministic policy metric。 +- `safetyLimits.wallTimeLimitMs` 只負責終止失控 host execution,不參與計分,也不得 + 作為跨 host 的演算法效率指標。 +- `calibration.status=measured` 必須能由固定 Forge contract/toolchain、完整 tests 與 + `calibration/forge-v1/` 下的證據重算;solution、test 或 runtime identity 改變時必須 + fail closed 並重新量測,不得沿用舊 budget。 + +## Metadata + +`catalog.json` 必須符合 `tools/catalog.schema.json`,並宣告唯一 default locale 與有序的 +supported locale 清單;目前固定為 `zh-TW`、`en`。`problem.json` 必須符合 +`tools/problem.schema.json`,所有 localized title/name 與 statement/editorial map 必須完整 +覆蓋 catalog locales。`complexities` 記錄 editorial 所分析的主要路徑,最後一筆必須是 +reference solutions 使用的最佳解。完整 API discovery、path resolution 與計分公式見 +`docs/MANIFEST.md`。 diff --git a/docs/problem-bank/MANIFEST.md b/docs/problem-bank/MANIFEST.md new file mode 100644 index 0000000..a5dca04 --- /dev/null +++ b/docs/problem-bank/MANIFEST.md @@ -0,0 +1,229 @@ +# Catalog、manifest 與計分契約 + +## GitHub API discovery + +Repository consumer 必須從根目錄的 `catalog.json` 開始,不得列出 `problems/` +後猜測目錄名稱。Catalog 依題號排序,並為每題提供 manifest 的 repository-relative +POSIX path: + +```json +{ + "schema": "wasm-oj-catalog-v2", + "problemSchema": "wasm-oj-problem-v3", + "localization": { + "defaultLocale": "zh-TW", + "supportedLocales": ["zh-TW", "en"] + }, + "problems": [ + { + "id": 1, + "slug": "weighted-opcode-scale", + "manifest": "problems/001-weighted-opcode-scale/problem.json" + } + ] +} +``` + +取得 `problem.json` 後,所有內容檔都由 `files` 明確列出。路徑相對於該 +`problem.json` 所在目錄,而不是 process cwd 或 repository root。Consumer 不得自行 +拼接 `statement.zh-TW.md`、`solutions//main.*` 或 `tests/*.in`: + +```json +{ + "title": { + "zh-TW": "操作碼秤重站", + "en": "Weighted Opcode Scale" + }, + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + } + ] + } +} +``` + +`catalog.localization.supportedLocales` 是 locale discovery 的唯一來源,順序同時是 UI +建議顯示順序。`defaultLocale` 必須是其中一員。每份 manifest 的 `title`、policy +`title`、complexity `name`、`files.statements` 與 `files.editorials` 都必須完整覆蓋同一組 +locale;consumer 不得在缺檔時靜默退回其他語言。若使用者指定不支援的 locale,應先由 +catalog contract 拒絕,而不是猜測最接近的語言。 + +所有 manifest path 都必須是 case-sensitive、normalized POSIX relative path;禁止 +absolute path、反斜線、NUL、空 segment、`.`、`..` 與重複 `/`。GitHub Contents API、 +Git Trees API 或 raw-content client 都可以把 manifest 所在目錄與此 path 做 URL path +resolution,不需要模擬 host filesystem。 + +## Cost-first cumulative policies + +`scoring.mode` 固定為 `per-case-cumulative-policies`,`scoring.caseSet` 固定為 +`all-manifest-tests`。計分 case set 就是 `files.tests` 依 manifest 順序列出的所有 cases; +所有 policy 使用完全相同的 case set,judge 不為不同分數層級準備不同測資。 + +`scoring.costContract` 固定為 `wasm-oj-forge-v1`。這個 ID 綁定 Forge contract 1 的 +compiler/runner、weighted opcode table、meter placement、artifact cost-profile validation +與 empty-program baseline normalization;不能只看 `costModel=weighted` 後自行選另一套 +weights。權威契約固定引用校準證據所記錄的 Forge commit +`baac61a2d3734b8689bc19e6871fef1c4f63ce8d` 的 +[verdict and metrics contract](https://github.com/wasm-oj/forge/blob/baac61a2d3734b8689bc19e6871fef1c4f63ce8d/docs/library-contract.md#verdict-and-metrics-contract) +、[weighted instruction metering](https://github.com/wasm-oj/forge/blob/baac61a2d3734b8689bc19e6871fef1c4f63ce8d/docs/architecture.md#weighted-instruction-metering) +及 [versioning policy](https://github.com/wasm-oj/forge/blob/baac61a2d3734b8689bc19e6871fef1c4f63ce8d/docs/versioning.md)。Judge +遇到不同 Forge contract、artifact profile 不符、缺少 calibration 或 metric 不可用時必須 +fail closed,不得猜測或換算。 + +每個 case 只需在最寬鬆 policy 的 hard limits 下執行一次。若答案正確且正常完成,judge +把該次執行的 metrics 同時套用到每個 policy: + +- `instructionBudget` 比對 Forge `RunResult.metrics.cost` 回報的 baseline-normalized net + weighted cost; +- `memoryLimitBytes` 比對 guest peak linear memory,不是 browser/Node process RSS; +- `logicalTimeLimitMs` 若存在,才比對 deterministic virtual elapsed time。 + +各限制都是 inclusive upper bound:metric 小於或等於對應 limit 才通過;未宣告 +`logicalTimeLimitMs` 的 policy 不限制 logical time。換言之,policy pass 當且僅當答案 +正確、execution 正常完成,而且該 policy 宣告的每個 metric 都 `metric <= limit`。 +`logicalTimeLimitMs` 以整數方式比對 +`RunResult.metrics.logicalTimeNs <= logicalTimeLimitMs × 1,000,000`,不做浮點換算或四捨五入。 + +答案錯誤、runtime failure,或超過最寬鬆 policy 時,該 case 的所有 policy 都不通過。 +Policies 必須由寬到嚴排列,而且每一層至少收緊一個資源;因此通過較嚴格 policy 必然也 +通過其前面的寬鬆 policies。 +本 catalog 的有序 policy ID 固定為 `baseline`、`efficient`、`optimal`;缺少、重複或 +重新排序任何一層都不符合 calibration contract。 + +Forge contract 1 會在所有函式及 start section 注入 weighted meter。Runner 依 submission +artifact 的 exact contract、language、target、optimization、compiler/runtime content 與 +meter model 找到已校準的 empty-program baseline,並套用: + +```text +raw instruction budget = baseline + manifest instructionBudget +reported metrics.cost = max(0, observed rawCost - baseline) +``` + +Baseline 只扣除該 runtime profile 的固定啟動成本;載入/解析 user module、imports、 +stdin/arguments/environment、deterministic API 初始化、I/O、allocation 與 user code 仍然 +計費。Host 端在進入 guest 前的 compilation、package extraction 與 preparation 不屬於此 +instruction metric。 + +Reference scorer 會要求成功 execution 同時提供整數 `metrics.rawCost`、 +`metrics.baselineCost`、非空 `metrics.costProfile`,並重新驗證上式;只提供 `metrics.cost` +不足以計分。缺少 manifest calibration、Forge cost profile 或任何必要 metric 是 judge +configuration/error,整份 score 不成立;不得靜默把它當成 contestant 的 0 分 case。 + +Execution identity 另須提供 submission `language`。Scorer 會要求 +`metrics.costProfile === scoring.calibration.profiles[language]`;只要 language 未校準、profile +為空,或 toolchain/runtime profile 與本次校準不完全相同,就 fail closed。Profile 不是由 +contestant 自行宣告;judge 必須從 Forge 驗證過的 artifact 與 run result 傳入。 + +假設共有 `C` 個 cases,policy `p` 的增量分數為 `points[p]`,在其中 `passed[p]` 個 +cases 通過,總分以精確有理數計算: + +```text +scoreNumerator = Σ points[p] × passed[p] +scoreDenominator = C +score = scoreNumerator / scoreDenominator +``` + +所有 policy 的 `points` 合計必須等於 `maximumPoints=100`。這讓同一 case 可以依序貢獻 +20、50 或 100 分層級的比例,而不重跑或複製測資。上述 fraction 是 canonical score; +UI 如何顯示或四捨五入不屬於 judging contract,且不得回頭影響 pass/fail 或 numerator。 + +`safetyLimits.wallTimeLimitMs` 是停止失控 engine 的 host safety boundary,不參與 policy +分數,也不得用來比較不同機器上的演算法效率。計算量的主要且可攜式限制永遠是 +`instructionBudget`。 + +## Measured multi-language policies + +45 題使用三層 measured policy: + +| Policy | Incremental points | Instruction budget | Memory budget | +| --- | ---: | ---: | ---: | +| `baseline` | 20 | 七語言 worst-case 的最大值 + 5% | declared-max review ceiling | +| `efficient` | 30 | C/C++/Rust/Go worst-case 的最大值 + 5% | declared-max review ceiling | +| `optimal` | 50 | C/C++/Rust/Go worst-case 的算術平均 + 5% | declared-max review ceiling | + +校準固定 Forge binary、library、toolchain、`release/wasip1` target 與 deterministic +configuration,逐一執行每題 `all-manifest-tests` 中的全部 case。對題目 `p` 與語言 `l`: + +```text +languageWorst[p,l] = max(cost[p,l,case]) +compiled[p] = [languageWorst[p,C], languageWorst[p,C++], + languageWorst[p,Rust], languageWorst[p,Go]] +rawOptimal[p] = ceil(sum(compiled[p]) × 105 / (4 × 100)) +rawEfficient[p] = ceil(max(compiled[p]) × 105 / 100) +rawBaseline[p] = ceil(max(languageWorst[p,*]) × 105 / 100) +quantum(x) = 5 × 10^(decimalDigits(x) - 2) when decimalDigits(x) >= 3 +quantum(x) = 1 otherwise +budget(x) = ceil(x / quantum(x)) × quantum(x) +optimal[p] = budget(rawOptimal[p]) +efficient[p] = budget(rawEfficient[p]) +baseline[p] = budget(rawBaseline[p]) +``` + +因此 `optimal` 不由單一最快語言決定,而是由四種編譯式 reference 的 worst-case cost +算術平均決定;`efficient` 保證 C、C++、Rust、Go 四種官方最佳解至少取得 50 分, +`baseline` 則保證七種官方最佳解至少取得 20 分。這同時避免單一 runtime 特性壟斷 +滿分門檻,並維持 `baseline >= efficient >= optimal` 的 relaxed-to-strict 順序。 +5% 是同一 cost contract 下容納等價實作差異的唯一 headroom; +之後只做單向向上取整,讓第三位起全部為 `0`,且使用 5 倍 decimal quantum,例: +`28,995 → 30,000`、`10,170,535 → 15,000,000`。取整絕不降低安全下限。 +因 cost 在固定 deterministic profile 下可重現,不加入 wall-time variance。Memory ceiling +沿用各題 declared-max review,不參與 instruction budget 推導。 + +Manifest 以 + +```json +"calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-...:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-...:weighted" + } +} +``` + +實際 manifest 的 `profiles` 必須完整明列七種語言;上例為節省篇幅只展示兩個 key。 + +原始逐案 metrics、source/test digest 與 runtime content digest 位於 +`calibration/forge-v1/reference-costs.json`;機器推導結果位於 +`calibration/forge-v1/derived-policies.json`。`node tools/derive_cost_policies.mjs` 會重新 +雜湊所有 solution 與 test、要求完整 45 × 7 records、重算三層 multi-language derivation,並 +核對 45 份 manifest。任何輸入或證據改變都 fail closed;要套用經人工審閱的新證據,使用 +`node tools/derive_cost_policies.mjs --write`。 + +## Validation + +- `tools/catalog.schema.json` 定義 localized root catalog v2。 +- `tools/problem.schema.json` 定義 localized problem manifest v3。 +- `tools/verify.py` 從 `catalog.json` discovery,並只依 manifest path 讀取內容、編譯 + solutions、執行 validator/oracle/generator 與 stored tests。 +- `tools/scoring.py` 是 cumulative policy 計分的 executable specification; + `python3 -m unittest tools.test_scoring` 驗證 inclusive boundaries、partial points、 + logical time、wall-safety 分離,以及缺少或不相容 metrics 時 fail closed。 +- Verifier 也檢查 path normalization、檔案存在性、test inventory、policy points、 + 64 KiB memory page alignment,以及 policy limits 的 relaxed-to-strict 單調性。 diff --git a/docs/problem-bank/independent-041-045.md b/docs/problem-bank/independent-041-045.md new file mode 100644 index 0000000..d95d79a --- /dev/null +++ b/docs/problem-bank/independent-041-045.md @@ -0,0 +1,247 @@ +# Problems 041–045 independent review + +- 審查日期:2026-07-20(Asia/Taipei) +- 範圍:`problems/041-*` 至 `problems/045-*` +- 最終 disposition:**PASS**。五題目前沒有未解的 statement ambiguity、sample、 + correctness、complexity、integer-range、validator、generator、oracle、resource-policy + 或七語 reference blocker。 + +## Blind protocol + +審查分成兩個不可逆的階段。 + +第一階段只讀 `catalog.json`、五份 `problem.json` 中的 identity/statement/validator/ +test paths、雙語 statements、validators 與 stored tests;刻意略過 complexities、scoring、 +editorials、官方 solutions、oracles 與 generators。Reviewer 從題意自行推導直覺、進階與 +最佳解,並在 repository 外的 +`/tmp/forge-blind-review-041-045.VkVSWE/` 寫五份 C++20 solver 及一份獨立 Python brute +cross-checker。五份 solver 先通過四個 stored cases,再各跑 1,000 組固定 seed 的隨機 +小 case;expected output 由直接定義計算,不使用 repo oracle 或 reference consensus。 + +第二階段才讀 `AGENTS.md`、完整 `docs/CONTRACT.md`、雙語 editorials、35 份官方 +solutions、oracles、generators、完整 manifests 與 calibration evidence。這一階段逐一比對 +實際 loops、allocations、整數範圍、tie-break、oracle 結構及 metadata,並編譯/執行七語 +references。 + +Blind solver SHA-256: + +```text +041 cd31cae2c02bb72962790076fa4b88caba6f89ceb7da61ce879d15d035c2ade3 +042 4e87e670c9b1a4465384696dcb3b5a8f08aa2f682812a42807d67043beb2222f +043 2168ff9b350a1697b120bf164a2a07141115347e41d28b73e6f396436d520120 +044 2f123e5a069364179b9a6d717b03ed6832bd72839891cfea95373e17e5510f51 +045 6df122c0d3e2f6732852cc7b5534bc3c81525b12efde3c861641f9bd0d9319d6 +random_crosscheck.py 978fce56a8ad2cdedc7d39d61fbca46773c08933f240b38680be57886aeadd49 +``` + +## Blind finding that changed problem 045 + +最初的 045 是離線輸出全體 top `K`。它把 fixed-size heap 的 `O(N log K)` 稱為 +optimal,但離線 comparison model 可先用 selection 找到 top-`K` 集合,再只排序輸出, +達到 `O(N + K log K)`;所以原宣稱不是漸近最佳。Reviewer 在尚未讀官方內容前回報此 +問題,沒有把「reference 答對 samples」誤當成演算法已最佳。 + +題目因此重設為目前的「持續追蹤第 K 慢測試」:每個 prefix `i >= K` 都必須輸出當時 +第 `K` 名。Reviewer 對新版重新執行第一階段,重寫 045 solver 與 brute expected,並再次 +通過 stored cases及 1,000 組隨機 prefix cases,之後才打開新版 editorial/reference。 +在 comparison-based online prefix model 中,每次會進入 top `K` 的新元素要求更新目前 +第 `K` 名,fixed-size heap 是正確的 `O(log K)` update 結構;adversarial case 又令每個 +後續元素都觸發 replacement,避免把 heap repair 當成偶發支出。 + +## Independent derivations and final per-problem audit + +### 041 — progressive-cost-budget + +Blind derivation: + +1. 每個 budget 從 stage 1 重掃,`O(NQ)` time、`O(N)` cost storage。 +2. 建立非遞減 prefix sums,對每個 budget 做 `upper_bound`, + `O(N + Q log N)` time、`O(N)` algorithmic space。 +3. 利用 budgets 不遞減,保存 `completed` 與 `spent`,stage pointer 全程只前進, + `O(N+Q)` time。因 input/output buffering 的七語共同 resident bound 為 `O(N+Q)`。 + +零成本 stage 使 prefix sums 可重複,故二分必須找第一個 `> budget`;雙指標則必須在 +`cost=0` 時繼續前進。`spent <= current budget` 由 budget 單調性維持,因此 unsigned +比較 `cost <= budget-spent` 不會 underflow。總成本與 budget 都不超過 `9e18`,C-family +`uint64` 安全;JavaScript/TypeScript 正確使用 `bigint`。 + +官方 editorial 與此推導一致。Oracle 使用 prefix sums + binary search,與 reference 的 +monotone two pointers 結構不同。Adversarial case 有 `N=Q=200000`、前 10001 個成本為 +`999999999999`、其後 189999 個為零、所有 budgets 等於總成本;直覺解會做 +`40,000,000,000` 次 stage inspections,binary-search 上界約 360 萬次比較,雙指標只前進 +20 萬次,並同時覆蓋相等 budgets、零成本尾段及 64-bit 累計。 + +結論:**PASS**。`O(N+Q)` 亦由讀入 `N+Q` values 及輸出 `Q` 行給出 matching lower +bound。 + +### 042 — first-duplicate-test + +令 `L` 為最長 token、`S` 為所有 token 長度總和。 + +1. 將第 `i` 個 token 與所有前項精確比較,`O(N^2 L)` time、`O(S)` space。 +2. 排序 `(fingerprint,index)` 後掃 equal groups,`O(N log N * L)` time、`O(S)` space。 +3. 由左至右以 first-occurrence map 保存首次 index,第一次 map hit 就是最小 duplicate + index,map value 是最早 matching index;expected `O(S)` time、`O(S)` resident space。 + +Hash 只選 bucket,七語 equality 都會比較完整 token;沒有把 `0` 與 `00` 當成數值相同。 +若要求 deterministic worst-case,也可用固定 16 字母 alphabet 的 trie 達 `O(S)`,所以 +線性漸近界本身可達;manifest/editorial 清楚把目前 hash reference 的時間標成 expected。 + +Oracle 先排序所有 `(token,index)` 並從 equal groups 找最小 second index,結構不同於 +reference 的 early-exit hash scan。Adversarial case 前 199999 個 token 不同,第 200000 +個重複 index 123457,直覺解約做 `19,999,823,458` 次精確比較,並驗證回報的是首次位置 +而非最近位置。 + +結論:**PASS**。 + +### 043 — verdict-range-counts + +1. 每次掃 `[L,R]`,worst-case `O(NQ)` time。 +2. 每種 verdict 保存 sorted positions,兩次 binary search, + `O(N + Q log N)` time、`O(N)` core space。 +3. 建四組 prefix counts,答案為 `pref[V][R]-pref[V][L-1]`, + `O(N+Q)` time、七語 resident `O(N+Q)`。 + +固定四字母 alphabet 使每位置建表與每查詢都是常數工作;讀 input 並輸出 Q 行又給出 +`Omega(N+Q)` lower bound。所有 prefix counters 最大 200000,`uint32` 安全。 + +Oracle 保存四份位置表並用 `bisect_left/right`,與 prefix-table reference 不同。 +Adversarial case `N=100000,Q=80000`,直接掃描需檢查 `2,018,835,761` 個 verdict characters, +而 prefix 解只需線性建表及查詢。閉區間、單點、缺席 verdict 與四種字元亦由 samples/ +random cases 覆蓋。 + +結論:**PASS**。 + +### 044 — recent-submission-reuse + +令 `U` 為 distinct tokens 數量。 + +1. 每筆向前掃至多 K 筆,`O(N K L)` time、queue 為 `O(KL)` space。 +2. Balanced tree 保存每種 token 最近位置,`O(N log N * L)` time、`O(UL)` core space。 +3. Hash map 只保存 `last[f]`;`i-last[f] <= K` 時 count hit,之後更新 last。Expected + `O(S)` time;core map 為 `O(UL)`,七語 input buffering/按 N reserve 的共同 resident + bound 為 `O(S)`。 + +只需最近位置,因最近者若已早於 window,所有更早位置也必然過期。`K=0` 時所有正 index +差都大於 K,不需危險特判。Oracle 將 `(token,index)` 排序,在每個 equal group 檢查相鄰 +index gaps;每個 occurrence 是否 hit 只取決於它的最近相同前項,因此與 hash reference +不同但等價。 + +Adversarial case 為 50000 個 distinct hex tokens 循環四輪、`N=200000,K=50000`;naive +window scan 約做 `8,749,975,000` 次 token comparisons,每個後三輪 hit 又恰在 window +左邊界,能抓 `=K` 更新後輸出 root。 + `O(N log K)` update time,加上必要的 `O(N-K+1)` output,heap core `O(K)`、七語共同 + resident `O(N+K)`。 + +Tie-break 是 `(cost descending,index ascending)`,因此「更差」是成本較低,或同成本時 +index 較大。Blind proof 與 editorial 都以同一 invariant 歸納:每個 prefix 後 heap 恰含 +其最佳 `min(i,K)` 筆,root 是其中最後一名。 + +Oracle 先對全體建立最終 rank,再用 Fenwick tree 依 arrival 啟用 records,對每個 prefix +找 active ranks 的第 K 個;它是 `O(N log N)` 的 offline order-statistic 解,與 fixed heap +結構不同。Adversarial case `N=200000,K=5000` 且 costs 嚴格遞增;從第 5001 筆起每筆都 +比 root 好,迫使約 195000 次完整 heap replacement/repair,同時輸出 195001 行,能排除 +只算最後 prefix 或假設 replacements 很少的實作。 + +結論:**PASS**。原離線版本的非 optimal finding 已由題目重設根治,不是以放寬 budget +掩蓋。 + +## Official execution evidence + +每題最終執行: + +```text +python3 tools/verify.py --problem NNN --fuzz 100 +``` + +每題 7 programs、728 executions:四個 stored cases加 100 個 generated cases,全部由 +C17、C++20、Rust 2024、Go、Python、JavaScript、TypeScript exact-output 通過。 + +| Problem | Programs | Executions | Result | +|---:|---:|---:|---| +| 041 | 7 | 728 | PASS | +| 042 | 7 | 728 | PASS | +| 043 | 7 | 728 | PASS | +| 044 | 7 | 728 | PASS | +| 045 | 7 | 728 | PASS | + +合計 35 programs、3,640 executions。Blind harness 另有五題各 1,000 cases,合計 5,000 +組,與 official generator/oracle 路徑獨立。 + +三組 sample output 逐題重新由 oracle 產生並 byte-compare,全部一致。所有 +`generator.py 0 999999` 都能 byte-exact 重建 manifest adversarial input;一般 generator +另以 `(0,0)`、`(1,1)`、`(123456789,17)`、`(-7,999)` 各執行兩次,結果 byte-identical 且 +validator 接受。 + +## Validator, generator, and oracle audit + +- 041–044 各測 8 組、045 測 9 組 targeted invalid inputs,涵蓋 empty/truncated、leading + zero、out-of-range、decreasing budgets、bad alphabet/verdict、`L>R`、`K>N`、extra token + 與 malformed UTF-8,全部 nonzero exit;合法 sample 全部 zero exit。 +- Validators 先 UTF-8 decode、驗 token grammar/數量,再驗 cross-field constraints,沒有 + permissive fallback;`validator.py` 對任意 participant input 是唯一 fail-closed gate。 +- Generators 嚴格要求兩個 arguments,同 `(SEED,INDEX)` deterministic,輸出恰一個完整且 + validator-accepted case。五個 `INDEX=999999` branches 是 stored adversarial 的明確 + reproduction recipe。 +- Oracles 位於 validator 後方,依 repository contract 只接合法 generated/stored input, + 不重複扮演 participant-input validator。五份 oracle 都與最佳 reference 結構不同: + binary search、sort groups、positions + binary search、sort adjacent gaps、global rank + + Fenwick;沒有 reference consensus fallback。 + +## Resource-policy recomputation + +執行 `node tools/derive_cost_policies.mjs` 得到: + +```text +cost policy derivation and all 45 manifests are current +``` + +Reviewer 另以獨立 Python 程式重新 hash 35 份 source、140 組 stored input/output bindings, +驗證每筆 `cost = rawCost - baselineCost`、artifact/profile exact match,並從 raw evidence 重新 +計算: + +```text +optimal = pretty(ceil((worst[C]+worst[C++]+worst[Rust]+worst[Go]) * 105 / 400)) +efficient = pretty(ceil(max(worst[C],worst[C++],worst[Rust],worst[Go]) * 105 / 100)) +baseline = pretty(ceil(max(worst[all seven languages]) * 105 / 100)) +``` + +`pretty` 只安全向上取整到 `5 * 10^(digits-2)` quantum。獨立重算結果: + +| Problem | C/C++/Rust/Go worst costs | All-language max | optimal | efficient | baseline | Max measured memory | +|---:|---|---:|---:|---:|---:|---:| +| 041 | 1,196,875,261 / 25,360,713,531 / 1,801,887,493 / 27,174,679,021 | 27,174,679,021 | 15,000,000,000 | 30,000,000,000 | 30,000,000,000 | 51,838,976 | +| 042 | 333,427,292 / 3,444,036,654 / 487,436,842 / 7,086,523,868 | 15,597,707,571 | 3,000,000,000 | 7,500,000,000 | 20,000,000,000 | 46,006,272 | +| 043 | 489,062,936 / 7,503,512,402 / 615,950,036 / 9,388,420,980 | 24,511,720,153 | 5,000,000,000 | 10,000,000,000 | 30,000,000,000 | 41,943,040 | +| 044 | 321,896,784 / 3,188,541,104 / 530,896,017 / 6,799,168,221 | 14,791,697,052 | 3,000,000,000 | 7,500,000,000 | 20,000,000,000 | 41,943,040 | +| 045 | 1,522,930,993 / 18,158,141,489 / 1,187,965,236 / 21,435,819,413 | 146,744,584,040 | 15,000,000,000 | 25,000,000,000 | 200,000,000,000 | 49,938,432 | + +五題所有 language/case 的 measured peak guest memory 都低於 strict 64 MiB policy;memory +tiers仍依 128/96/64 MiB 收緊。041 的 baseline 與 efficient instruction budget 相同,但 +memory 仍由 128 MiB 收緊到 96 MiB,符合每層至少收緊一種 deterministic resource 的 +契約。所有 instruction budgets 都符合「只有前兩位可非零」的漂亮數字要求,且沒有一次 +向下 round。 + +## Findings and closure + +1. **原 045 heap 非離線 optimal**:已重設為 running prefix 題並重新 blind review、七語 + verify、adversarial、calibration;closed。 +2. **041/042/044 adversarial 原無 explicit generator reproduction branch**:均新增 + `INDEX=999999`,與 stored input byte-identical;043/045 亦同樣可重建;closed。 +3. **041/043/044/045 final space metadata 原只寫 algorithmic core,低於部分七語 + actual resident allocations**:現分別改為 `O(N+Q)`、`O(N+Q)`、`O(S)`、`O(N+K)`, + editorials 同時保留 core/resident 的區別;closed。 + +最終 metadata validation、sample embedding check、35-program fuzz100、raw calibration +derivation與獨立 hash/formula recomputation 全部通過。 diff --git a/docs/problem-catalog.md b/docs/problem-catalog.md new file mode 100644 index 0000000..c407648 --- /dev/null +++ b/docs/problem-catalog.md @@ -0,0 +1,87 @@ +# Problem collection loading + +Forge's default problem collection is the public +[`wasm-oj/problems`](https://github.com/wasm-oj/problems) repository. The browser never lists +repository directories or guesses statement, editorial, solution, or test paths. + +## Source configuration + +The user-selectable source has exactly four GitHub fields: + +```json +{ + "owner": "wasm-oj", + "repository": "problems", + "ref": "main", + "indexPath": "collection/index.json" +} +``` + +Forge validates every value before constructing a `raw.githubusercontent.com` URL. Repository +paths must be normalized relative POSIX paths and cannot contain absolute paths, empty segments, +backslashes, `.` or `..`. Settings are scoped to the current browser. Project drafts and solved +progress combine the normalized source key with each problem bundle digest. Unchanged problems +keep their state across index updates; a changed problem is isolated automatically even when its +slug stays the same. + +## Lazy loading and integrity + +The `wasm-oj-browser-collection-v4` index is capped at 512 KiB and contains localized list and +learning-track metadata, explicit repository-root-relative statement paths for both locales, and +one bundle descriptor per problem. Forge renders the challenge list after loading +the index and initially downloads only the first problem. Selecting another problem fetches its +`wasm-oj-browser-problem-v3` bundle on demand. + +The learning-assistant button opens ChatGPT in one click with a compact query. It links to the +active locale's public statement Markdown, which includes the samples, and keeps only the selected +language's starter template inline. Forge never guesses a statement path from a slug or bundle +name. This keeps the query URL bounded while preserving an explicit source for the full problem; +the default catalog is regression-tested so every locale and language combination stays below +2,048 URL characters. + +The canonical repository keeps stable manifest IDs and paths for calibration evidence and API +consumers. Its separate `learning-path.json` groups problems by topic and orders each group from +lower prerequisite load to more advanced techniques. The published browser index flattens that +path into contiguous display numbers and includes each stable track ID and localized track name. Forge groups the +catalog by those tracks and searches across display number, slug, both localized titles, both +localized track names, and tags. + +Every descriptor declares the exact byte length and lowercase SHA-256 digest. Forge enforces a +32 MiB per-problem ceiling while streaming the response, verifies the digest over the original +bytes before UTF-8 decoding or JSON parsing, then validates: + +- bundle/index identity, order, title, track ID, localized track, difficulty, tags, and case count; +- both supported locales for titles, statements, editorials, policy names, and complexities; +- unique test identities and supported case kinds; +- exact calibration languages and method; +- the ordered baseline, efficient, and optimal cumulative policies; +- positive safe-integer resource limits and broad-to-strict monotonicity; and +- the accepted optimal complexity path. + +Any HTTP, size, digest, UTF-8, JSON, schema, or identity failure is reported as a collection +configuration error. Forge does not silently switch repositories or use a bundled catalog. + +## Cache behavior + +Verified bundles are stored in the browser Cache API by SHA-256, not request URL or branch name. +Cached bytes are re-hashed before reuse, so unchanged problems survive index revisions safely. +The index is requested again on startup. If and only if the network itself is unavailable, Forge +may load the previously validated index for the exact same source key and labels it `verified +cache` in the interface. HTTP and validation failures never fall back to cached configuration. + +The canonical source repository defines generation and publication of the split collection. +Forge keeps `src/judge/problems.generated.ts` solely as a typed test fixture regenerated from its +development mirror; no problem payload is emitted as a Sites static asset or included in the +server Worker. + +## Scoring + +Instruction policies remain evidence-derived. For each language, Forge takes the maximum net +weighted cost over the complete manifest case set. The optimal tier averages the C, C++, Rust, +and Go maxima and adds 5%; efficient uses the maximum of those four plus 5%; baseline uses the +maximum of all seven reference languages plus 5%. Results are rounded upward by the documented +decimal quantum. + +Each judge case runs once under the broadest hard limits. Forge then evaluates the same normalized +cost, peak linear memory, and optional logical time against each cumulative policy. Artifact +language and exact cost-profile identity must match the problem calibration before judging begins. diff --git a/eslint.config.mjs b/eslint.config.mjs index e3f9106..0c4e799 100644 --- a/eslint.config.mjs +++ b/eslint.config.mjs @@ -12,7 +12,9 @@ export default defineConfig([ "dist/**", "lib/**", "public/toolchains/**", + "problems/**", "src/runner/generated/**", + "src/judge/problems.generated.ts", "next-env.d.ts", ]), ]); diff --git a/experiments/forge-contract-1-conformance/runs/raw/records/2026-07-20T00-11-23.199Z-99a08950-f8c8-44b7-8306-5e9175079016.json b/experiments/forge-contract-1-conformance/runs/raw/records/2026-07-20T00-11-23.199Z-99a08950-f8c8-44b7-8306-5e9175079016.json new file mode 100644 index 0000000..5bebf82 --- /dev/null +++ b/experiments/forge-contract-1-conformance/runs/raw/records/2026-07-20T00-11-23.199Z-99a08950-f8c8-44b7-8306-5e9175079016.json @@ -0,0 +1,3135 @@ +{ + "schema": "wasm-oj-forge-v1/conformance-evidence", + "experimentId": 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"repeatUncachedCompileMs": 2903.6405830000003, - "runMedianMs": 413.60029199998826, + "firstUncachedCompileMs": 2734.5654579999973, + "repeatUncachedCompileMs": 2761.3875830000034, + "runMedianMs": 380.0994580000115, "artifactBytes": 2561512, "netWeightedCost": 589026, "rawWeightedCost": 2296147, @@ -6442,9 +6442,9 @@ { "caseId": "c-wasip1", "host": "browser-wasmer-js", - "firstUncachedCompileMs": 1358.3300000429153, - "repeatUncachedCompileMs": 1.2249999642372131, - "runMedianMs": 8.544999957084656, + "firstUncachedCompileMs": 1236.3450000286102, + "repeatUncachedCompileMs": 1.375, + "runMedianMs": 8.139999985694885, "artifactBytes": 45625, "netWeightedCost": 5445, "rawWeightedCost": 5591, @@ -6454,9 +6454,9 @@ { "caseId": "c-wasip1-filesystem-metadata", "host": "browser-wasmer-js", - "firstUncachedCompileMs": 176.0349999666214, - "repeatUncachedCompileMs": 1.0400000214576721, - "runMedianMs": 5.469999969005585, + "firstUncachedCompileMs": 184.36000001430511, + "repeatUncachedCompileMs": 1.0649999380111694, + "runMedianMs": 5.705000042915344, "artifactBytes": 33056, "netWeightedCost": 15427, "rawWeightedCost": 15573, @@ -6466,9 +6466,9 @@ { "caseId": "c-wasip1-file-io", "host": "browser-wasmer-js", - "firstUncachedCompileMs": 203.6700000166893, - "repeatUncachedCompileMs": 766.6349999904633, - "runMedianMs": 9.754999995231628, + "firstUncachedCompileMs": 174.48499989509583, + "repeatUncachedCompileMs": 776.8600000143051, + "runMedianMs": 8.794999957084656, "artifactBytes": 49908, "netWeightedCost": 16883, "rawWeightedCost": 17029, @@ -6478,9 +6478,9 @@ { "caseId": "c-wasip1-filesystem-limit", "host": "browser-wasmer-js", - "firstUncachedCompileMs": 338.49000000953674, + "firstUncachedCompileMs": 327.960000038147, "repeatUncachedCompileMs": 1.0049999952316284, - "runMedianMs": 3.2300000190734863, + "runMedianMs": 3.2049999237060547, "artifactBytes": 18945, "netWeightedCost": 6219, "rawWeightedCost": 6365, @@ -6490,9 +6490,9 @@ { "caseId": "c-wasix", "host": "browser-wasmer-js", - "firstUncachedCompileMs": 340.19499999284744, - "repeatUncachedCompileMs": 0.9950000047683716, - "runMedianMs": 0.8949999809265137, + "firstUncachedCompileMs": 161.6600000858307, + "repeatUncachedCompileMs": 1.1299999952316284, + "runMedianMs": 0.9649999141693115, "artifactBytes": 4064, "netWeightedCost": 1138, "rawWeightedCost": 1284, @@ -6502,9 +6502,9 @@ { "caseId": "c-wasix-denied-thread-spawn", "host": "browser-wasmer-js", - "firstUncachedCompileMs": 192.2950000166893, - "repeatUncachedCompileMs": 765.7599999904633, - "runMedianMs": 0.6700000166893005, + "firstUncachedCompileMs": 174.0700000524521, + "repeatUncachedCompileMs": 759.7599999904633, + "runMedianMs": 0.6200000047683716, "artifactBytes": 1072, "netWeightedCost": 0, "rawWeightedCost": 133, @@ -6514,9 +6514,9 @@ { "caseId": "cpp-wasip1", "host": "browser-wasmer-js", - "firstUncachedCompileMs": 566.7549999952316, - "repeatUncachedCompileMs": 1.0199999809265137, - "runMedianMs": 0.8849999904632568, + "firstUncachedCompileMs": 535.6899999380112, + "repeatUncachedCompileMs": 1.040000081062317, + "runMedianMs": 1.125, "artifactBytes": 4059, "netWeightedCost": 934, "rawWeightedCost": 1080, @@ -6526,9 +6526,9 @@ { "caseId": "cpp-wasix", "host": "browser-wasmer-js", - "firstUncachedCompileMs": 82.3299999833107, - "repeatUncachedCompileMs": 0.9449999928474426, - "runMedianMs": 0.7800000309944153, + "firstUncachedCompileMs": 93.46499991416931, + "repeatUncachedCompileMs": 0.9700000286102295, + "runMedianMs": 0.7949999570846558, "artifactBytes": 4059, "netWeightedCost": 934, "rawWeightedCost": 1080, @@ -6538,9 +6538,9 @@ { "caseId": "rust-wasip1", "host": "browser-wasmer-js", - "firstUncachedCompileMs": 2724.054999947548, - "repeatUncachedCompileMs": 606.5900000333786, - "runMedianMs": 12.840000033378601, + "firstUncachedCompileMs": 2652.0500000715256, + "repeatUncachedCompileMs": 585.7999999523163, + "runMedianMs": 12.730000019073486, "artifactBytes": 142818, "netWeightedCost": 14761, "rawWeightedCost": 24243, @@ -6550,9 +6550,9 @@ { "caseId": "python-wasip1", "host": "browser-wasmer-js", - "firstUncachedCompileMs": 1488.4449999928474, - "repeatUncachedCompileMs": 479.19999998807907, - "runMedianMs": 799.6499999761581, + "firstUncachedCompileMs": 1448.8399999141693, + "repeatUncachedCompileMs": 429.335000038147, + "runMedianMs": 775.2200000286102, "artifactBytes": 1851, "netWeightedCost": 4632241, "rawWeightedCost": 2424466250, @@ -6562,9 +6562,9 @@ { "caseId": "javascript-wasip1", "host": "browser-wasmer-js", - "firstUncachedCompileMs": 2090.5799999833107, - "repeatUncachedCompileMs": 2134.074999988079, - "runMedianMs": 175.97999995946884, + "firstUncachedCompileMs": 1728.4900000095367, + "repeatUncachedCompileMs": 2182.5099999904633, + "runMedianMs": 168.32500004768372, "artifactBytes": 1902, "netWeightedCost": 4489846, "rawWeightedCost": 14074831, @@ -6574,9 +6574,9 @@ { "caseId": "typescript-wasip1", "host": "browser-wasmer-js", - "firstUncachedCompileMs": 1572.5750000476837, - "repeatUncachedCompileMs": 1548.3149999976158, - "runMedianMs": 176.5649999976158, + "firstUncachedCompileMs": 1655.75, + "repeatUncachedCompileMs": 1540.539999961853, + "runMedianMs": 166.88499999046326, "artifactBytes": 1925, "netWeightedCost": 4514568, "rawWeightedCost": 14099553, @@ -6586,9 +6586,9 @@ { "caseId": "go-wasip1", "host": "browser-wasmer-js", - "firstUncachedCompileMs": 1674.5049999952316, - "repeatUncachedCompileMs": 400.05000001192093, - "runMedianMs": 291.3600000143051, + "firstUncachedCompileMs": 1647.5149999856949, + "repeatUncachedCompileMs": 396.9800000190735, + "runMedianMs": 273.2000000476837, "artifactBytes": 2550145, "netWeightedCost": 429396, "rawWeightedCost": 2136517, @@ -6598,9 +6598,9 @@ { "caseId": "c-wasip1-virtual-clock", "host": "browser-wasmer-js", - "firstUncachedCompileMs": 1164.925000011921, - "repeatUncachedCompileMs": 1.050000011920929, - "runMedianMs": 3.800000011920929, + "firstUncachedCompileMs": 1095.0350000858307, + "repeatUncachedCompileMs": 2.25, + "runMedianMs": 3.0800000429153442, "artifactBytes": 18565, "netWeightedCost": 8022, "rawWeightedCost": 8168, @@ -6610,9 +6610,9 @@ { "caseId": "c-wasip1-logical-time-limit", "host": "browser-wasmer-js", - "firstUncachedCompileMs": 350.4050000309944, - "repeatUncachedCompileMs": 1, - "runMedianMs": 0.3799999952316284, + "firstUncachedCompileMs": 327.85000002384186, + "repeatUncachedCompileMs": 0.9199999570846558, + "runMedianMs": 0.375, "artifactBytes": 1254, "netWeightedCost": 51, "rawWeightedCost": 197, @@ -6622,9 +6622,9 @@ { "caseId": "cpp-wasip1-virtual-sleep", "host": "browser-wasmer-js", - "firstUncachedCompileMs": 246.11000001430511, - "repeatUncachedCompileMs": 769.0699999928474, - "runMedianMs": 3.7100000381469727, + "firstUncachedCompileMs": 223.48500001430511, + "repeatUncachedCompileMs": 744.1449999809265, + "runMedianMs": 3.8049999475479126, "artifactBytes": 23327, "netWeightedCost": 4985, "rawWeightedCost": 5131, @@ -6634,9 +6634,9 @@ { "caseId": "rust-wasip1-virtual-sleep", "host": "browser-wasmer-js", - "firstUncachedCompileMs": 2622.0900000333786, - "repeatUncachedCompileMs": 593.9449999928474, - "runMedianMs": 14.305000007152557, + "firstUncachedCompileMs": 2588.7300000190735, + "repeatUncachedCompileMs": 599.5400000810623, + "runMedianMs": 14.620000004768372, "artifactBytes": 168053, "netWeightedCost": 16640, "rawWeightedCost": 26122, @@ -6646,9 +6646,9 @@ { "caseId": "python-wasip1-virtual-sleep", "host": "browser-wasmer-js", - "firstUncachedCompileMs": 1474.0849999785423, - "repeatUncachedCompileMs": 458.2800000309944, - "runMedianMs": 824.7849999666214, + "firstUncachedCompileMs": 1505.1499999761581, + "repeatUncachedCompileMs": 490.04500007629395, + "runMedianMs": 819.0750000476837, "artifactBytes": 2041, "netWeightedCost": 4648726, "rawWeightedCost": 2424482735, @@ -6658,9 +6658,9 @@ { "caseId": "javascript-wasip1-virtual-clock", "host": "browser-wasmer-js", - "firstUncachedCompileMs": 1509.3100000023842, - "repeatUncachedCompileMs": 1643.9300000071526, - "runMedianMs": 181.17500001192093, + "firstUncachedCompileMs": 1509.3949999809265, + "repeatUncachedCompileMs": 1484.585000038147, + "runMedianMs": 166.88999998569489, "artifactBytes": 1948, "netWeightedCost": 28374535, "rawWeightedCost": 37959520, @@ -6670,9 +6670,9 @@ { "caseId": "typescript-wasip1-virtual-clock", "host": "browser-wasmer-js", - "firstUncachedCompileMs": 2011.6049999594688, - "repeatUncachedCompileMs": 1930.300000011921, - "runMedianMs": 173.6899999976158, + "firstUncachedCompileMs": 1664.1099998950958, + "repeatUncachedCompileMs": 1562.7900000810623, + "runMedianMs": 163.81500005722046, "artifactBytes": 1948, "netWeightedCost": 28374535, "rawWeightedCost": 37959520, @@ -6682,9 +6682,9 @@ { "caseId": "go-wasip1-virtual-sleep", "host": "browser-wasmer-js", - "firstUncachedCompileMs": 880.714999973774, - "repeatUncachedCompileMs": 414.8100000023842, - "runMedianMs": 292.6050000190735, + "firstUncachedCompileMs": 885.1749999523163, + "repeatUncachedCompileMs": 396.3049999475479, + "runMedianMs": 276.03000009059906, "artifactBytes": 2561512, "netWeightedCost": 589026, "rawWeightedCost": 2296147, diff --git a/learning-path.json b/learning-path.json new file mode 100644 index 0000000..57db733 --- /dev/null +++ b/learning-path.json @@ -0,0 +1,111 @@ +{ + "schema": "wasm-oj-learning-path-v1", + "localization": { + "defaultLocale": "zh-TW", + "supportedLocales": [ + "zh-TW", + "en" + ] + }, + "tracks": [ + { + "id": "foundations", + "title": { + "zh-TW": "入門基礎", + "en": "Foundations" + }, + "problems": [ + "progressive-cost-budget", + "verdict-range-counts", + "first-duplicate-test", + "recent-submission-reuse", + "slowest-k-cases" + ] + }, + { + "id": "resource-limits", + "title": { + "zh-TW": "計量與資源限制", + "en": "Metering & Resource Limits" + }, + "problems": [ + "weighted-opcode-scale", + "baseline-calibration", + "memory-gate", + "shared-output-pool", + "transactional-vfs-quota", + "sparse-file-quota", + "storage-evacuation" + ] + }, + { + "id": "filesystem-packaging", + "title": { + "zh-TW": "檔案系統與封裝", + "en": "Filesystems & Packaging" + }, + "problems": [ + "guest-path-firewall", + "mounted-directory-baseline", + "mount-tree-conflicts", + "bounded-tar-stream", + "all-or-nothing-output-collection", + "build-fingerprint", + "runtime-bundle-encoding", + "source-tree-evidence", + "canonical-replay-bundle" + ] + }, + { + "id": "build-scheduling-cache", + "title": { + "zh-TW": "編譯、排程與快取", + "en": "Build, Scheduling & Caching" + }, + "problems": [ + "reproducible-build-order", + "dirty-build-nodes", + "compile-critical-path", + "worker-generations", + "compiler-race", + "submission-conveyor", + "offline-dependency-bundle", + "exact-dependency-cache", + "graph-blob-lru", + "judge-ledger", + "seven-matchers", + "bidirectional-pipes", + "logical-poll-clock", + "chunk-independent-random", + "cross-host-matrix" + ] + }, + { + "id": "graph-algorithms", + "title": { + "zh-TW": "圖論演算法", + "en": "Graph Algorithms" + }, + "problems": [ + "toolchain-mirror-network", + "wait-for-cycles", + "conflict-package-cover", + "capability-cut" + ] + }, + { + "id": "knapsack-selection", + "title": { + "zh-TW": "背包與集合最佳化", + "en": "Knapsack & Selection" + }, + "problems": [ + "artifact-cache-knapsack", + "calibration-multiple-choice-knapsack", + "dependency-tree-knapsack", + "dual-quota-output-knapsack", + "conformance-feature-coverage" + ] + } + ] +} diff --git a/package.json b/package.json index ee7a343..08f44d9 100644 --- a/package.json +++ b/package.json @@ -89,12 +89,15 @@ }, "scripts": { "dev": "WRANGLER_LOG_PATH=.wrangler/wrangler.log vinext dev", - "build": "node --experimental-strip-types --disable-warning=ExperimentalWarning scripts/build-site.ts", + "build": "pnpm run problems:verify && node --experimental-strip-types --disable-warning=ExperimentalWarning scripts/build-site.ts", "start": "WRANGLER_LOG_PATH=.wrangler/wrangler.log node scripts/start-production.mjs", - "test": "vitest run --config vitest.config.ts", + "test": "pnpm run problems:verify && vitest run --config vitest.config.ts", "typecheck": "node node_modules/typescript/lib/tsc.js --noEmit", "lint": "eslint .", "assets:og": "node scripts/render-og.mjs", + "problems:generate": "node scripts/generate-judge-problems.mjs", + "problems:verify": "node --test tools/derive_cost_policies.test.mjs scripts/problem-schema.test.mjs scripts/learning-path.test.mjs && node tools/derive_cost_policies.mjs && node scripts/generate-judge-problems.mjs --check", + "problems:remote:verify": "FORGE_RUN_PROBLEM_COLLECTION_INTEGRATION=1 vitest run --config vitest.config.ts src/judge/problem-collection.integration.test.ts --reporter=verbose", "library:build": "node scripts/build-library.mjs", "library:verify": "pnpm run contract:verify && pnpm run package-manager:verify && pnpm run docs:verify && pnpm run github:verify && pnpm run conformance:verify && pnpm run licenses:verify && pnpm run runtime:licenses:verify && pnpm run toolchain:verify && pnpm run wasmer-sdk:verify && node scripts/verify-library.mjs && node scripts/verify-library-nodenext.mjs", "prepack": "pnpm run library:build && pnpm run library:verify", @@ -118,7 +121,7 @@ "release:verify": "node scripts/verify-release.mjs", "release:artifacts:verify": "node scripts/verify-release-artifacts.mjs", "release:artifacts:test": "node scripts/verify-release-artifacts-self-test.mjs", - "ci:verify": "pnpm run github:verify && pnpm run conformance:verify && pnpm run typecheck && pnpm run lint && pnpm test && pnpm run library:build && pnpm run library:verify && pnpm run build && pnpm run runtime:test && pnpm run runtime:check-web", + "ci:verify": "pnpm run github:verify && pnpm run conformance:verify && pnpm run problems:verify && pnpm run typecheck && pnpm run lint && pnpm test && pnpm run library:build && pnpm run library:verify && pnpm run build && pnpm run runtime:test && pnpm run runtime:check-web", "judge:integration": "FORGE_RUN_JUDGE_INTEGRATION=1 vitest run --config vitest.config.ts src/server/judge.integration.test.ts --reporter=verbose", "cost-baseline:calibrate": "FORGE_RUN_COST_BASELINE=1 vitest run --config vitest.config.ts src/server/cost-baseline.integration.test.ts --reporter=verbose", "cost-baseline:transform": "node --experimental-strip-types --disable-warning=ExperimentalWarning scripts/transform-cost-baselines.mjs", @@ -146,6 +149,7 @@ "@vitejs/plugin-react": "6.0.3", "@vitejs/plugin-rsc": "0.5.28", "@vitest/coverage-v8": "4.1.10", + "ajv": "8.20.0", "eslint": "9.39.4", "eslint-config-next": "16.2.10", "fake-indexeddb": "6.2.5", diff --git a/pnpm-lock.yaml b/pnpm-lock.yaml index 94dc164..93aa529 100644 --- a/pnpm-lock.yaml +++ b/pnpm-lock.yaml @@ -42,6 +42,9 @@ importers: '@vitest/coverage-v8': specifier: 4.1.10 version: 4.1.10(vitest@4.1.10) + ajv: + specifier: 8.20.0 + version: 8.20.0 eslint: specifier: 9.39.4 version: 9.39.4 @@ -4640,7 +4643,7 @@ snapshots: eslint: 9.39.4 eslint-import-resolver-node: 0.3.10 eslint-import-resolver-typescript: 3.10.1(eslint-plugin-import@2.32.0(@typescript-eslint/parser@8.64.0(eslint@9.39.4)(typescript@5.9.3))(eslint@9.39.4))(eslint@9.39.4) - eslint-plugin-import: 2.32.0(@typescript-eslint/parser@8.64.0(eslint@9.39.4)(typescript@5.9.3))(eslint-import-resolver-typescript@3.10.1)(eslint@9.39.4) + eslint-plugin-import: 2.32.0(@typescript-eslint/parser@8.64.0(eslint@9.39.4)(typescript@5.9.3))(eslint-import-resolver-typescript@3.10.1(eslint-plugin-import@2.32.0(@typescript-eslint/parser@8.64.0(eslint@9.39.4)(typescript@5.9.3))(eslint@9.39.4))(eslint@9.39.4))(eslint@9.39.4) eslint-plugin-jsx-a11y: 6.10.2(eslint@9.39.4) eslint-plugin-react: 7.37.5(eslint@9.39.4) eslint-plugin-react-hooks: 7.1.1(eslint@9.39.4) @@ -4673,7 +4676,7 @@ snapshots: tinyglobby: 0.2.17 unrs-resolver: 1.12.2 optionalDependencies: - eslint-plugin-import: 2.32.0(@typescript-eslint/parser@8.64.0(eslint@9.39.4)(typescript@5.9.3))(eslint-import-resolver-typescript@3.10.1)(eslint@9.39.4) + eslint-plugin-import: 2.32.0(@typescript-eslint/parser@8.64.0(eslint@9.39.4)(typescript@5.9.3))(eslint-import-resolver-typescript@3.10.1(eslint-plugin-import@2.32.0(@typescript-eslint/parser@8.64.0(eslint@9.39.4)(typescript@5.9.3))(eslint@9.39.4))(eslint@9.39.4))(eslint@9.39.4) transitivePeerDependencies: - supports-color @@ -4688,7 +4691,7 @@ snapshots: transitivePeerDependencies: - supports-color - eslint-plugin-import@2.32.0(@typescript-eslint/parser@8.64.0(eslint@9.39.4)(typescript@5.9.3))(eslint-import-resolver-typescript@3.10.1)(eslint@9.39.4): + eslint-plugin-import@2.32.0(@typescript-eslint/parser@8.64.0(eslint@9.39.4)(typescript@5.9.3))(eslint-import-resolver-typescript@3.10.1(eslint-plugin-import@2.32.0(@typescript-eslint/parser@8.64.0(eslint@9.39.4)(typescript@5.9.3))(eslint@9.39.4))(eslint@9.39.4))(eslint@9.39.4): dependencies: '@rtsao/scc': 1.1.0 array-includes: 3.1.9 diff --git a/problems/001-weighted-opcode-scale/editorial.en.md b/problems/001-weighted-opcode-scale/editorial.en.md new file mode 100644 index 0000000..41fde5c --- /dev/null +++ b/problems/001-weighted-opcode-scale/editorial.en.md @@ -0,0 +1,35 @@ +# Editorial + +## Intuitive Approach + +Let `T` be the number of instructions after expanding all runs. Simulating from the first instruction for every budget takes `O(QT)` time. Even retaining the run-length encoding but subtracting one run at a time still takes `O(QR)`, which is too slow for `R,Q=200000`. + +## Optimal Approach: Run Prefix Sums + +Initialize `weight[1..K]` to `1000`, then overwrite the explicitly listed weights. For run `i`, compute: + +- `prefixCost[i]`: the cost of the first `i` complete runs; +- `prefixCount[i]`: the number of instructions in the first `i` complete runs. + +Both arrays start with zero at index `0`. For a budget `B`, use `upper_bound(prefixCost, B)-1` to find the largest number `i` of complete runs that fit. If `i +#include +#include +int main(void) { + int K, W, R, Q; + if (scanf("%d%d%d%d", &K, &W, &R, &Q) != 4) + return 0; + uint64_t *wt = malloc((K + 1) * sizeof(*wt)); + for (int i = 0; i <= K; i++) + wt[i] = 1000; + for (int j = 0; j < W; j++) { + int id; + unsigned long long x; + scanf("%d%llu", &id, &x); + wt[id] = x; + } + uint64_t *pc = calloc(R + 1, sizeof(*pc)), *pn = calloc(R + 1, sizeof(*pn)); + uint64_t *rw = malloc(R * sizeof(*rw)), *rc = malloc(R * sizeof(*rc)); + for (int i = 0; i < R; i++) { + int id; + unsigned long long c; + scanf("%d%llu", &id, &c); + rw[i] = wt[id]; + rc[i] = c; + pc[i + 1] = pc[i] + rw[i] * rc[i]; + pn[i + 1] = pn[i] + rc[i]; + } + while (Q--) { + unsigned long long b; + scanf("%llu", &b); + int lo = 0, hi = R + 1; + while (lo + 1 < hi) { + int m = lo + (hi - lo) / 2; + if (pc[m] <= b) + lo = m; + else + hi = m; + } + uint64_t done = pn[lo], cost = pc[lo]; + if (lo < R) { + uint64_t take = (b - cost) / rw[lo]; + if (take > rc[lo]) + take = rc[lo]; + done += take; + cost += take * rw[lo]; + } + printf("%llu %llu\n", (unsigned long long)done, (unsigned long long)cost); + } + free(wt); + free(pc); + free(pn); + free(rw); + free(rc); + return 0; +} diff --git a/problems/001-weighted-opcode-scale/solutions/cpp/main.cpp b/problems/001-weighted-opcode-scale/solutions/cpp/main.cpp new file mode 100644 index 0000000..bfc30da --- /dev/null +++ b/problems/001-weighted-opcode-scale/solutions/cpp/main.cpp @@ -0,0 +1,36 @@ +#include +#include +#include +using namespace std; +int main() { + ios::sync_with_stdio(false); + cin.tie(nullptr); + int K, W, R, Q; + if (!(cin >> K >> W >> R >> Q)) + return 0; + vector w(K + 1, 1000); + for (int i = 0, id; i < W; i++) { + unsigned long long x; + cin >> id >> x; + w[id] = x; + } + vector pc(R + 1), pn(R + 1), rw(R), rc(R); + for (int i = 0, id; i < R; i++) { + cin >> id >> rc[i]; + rw[i] = w[id]; + pc[i + 1] = pc[i] + rw[i] * rc[i]; + pn[i + 1] = pn[i] + rc[i]; + } + while (Q--) { + unsigned long long b; + cin >> b; + int i = int(upper_bound(pc.begin(), pc.end(), b) - pc.begin()) - 1; + auto cost = pc[i], done = pn[i]; + if (i < R) { + auto take = min(rc[i], (b - cost) / rw[i]); + done += take; + cost += take * rw[i]; + } + cout << done << ' ' << cost << '\n'; + } +} diff --git a/problems/001-weighted-opcode-scale/solutions/go/main.go b/problems/001-weighted-opcode-scale/solutions/go/main.go new file mode 100644 index 0000000..90cb3eb --- /dev/null +++ b/problems/001-weighted-opcode-scale/solutions/go/main.go @@ -0,0 +1,54 @@ +package main + +import ( + "bufio" + "fmt" + "os" + "sort" +) + +func main() { + in := bufio.NewReader(os.Stdin) + out := bufio.NewWriter(os.Stdout) + defer out.Flush() + var k, wn, r, q int + if _, e := fmt.Fscan(in, &k, &wn, &r, &q); e != nil { + return + } + w := make([]uint64, k+1) + for i := range w { + w[i] = 1000 + } + for i := 0; i < wn; i++ { + var id int + var x uint64 + fmt.Fscan(in, &id, &x) + w[id] = x + } + pc := make([]uint64, r+1) + pn := make([]uint64, r+1) + rw := make([]uint64, r) + rc := make([]uint64, r) + for i := 0; i < r; i++ { + var id int + fmt.Fscan(in, &id, &rc[i]) + rw[i] = w[id] + pc[i+1] = pc[i] + rw[i]*rc[i] + pn[i+1] = pn[i] + rc[i] + } + for ; q > 0; q-- { + var b uint64 + fmt.Fscan(in, &b) + i := sort.Search(len(pc), func(j int) bool { return pc[j] > b }) - 1 + done, cost := pn[i], pc[i] + if i < r { + take := (b - cost) / rw[i] + if take > rc[i] { + take = rc[i] + } + done += take + cost += take * rw[i] + } + fmt.Fprintln(out, done, cost) + } +} diff --git a/problems/001-weighted-opcode-scale/solutions/javascript/main.js b/problems/001-weighted-opcode-scale/solutions/javascript/main.js new file mode 100644 index 0000000..dfe2032 --- /dev/null +++ b/problems/001-weighted-opcode-scale/solutions/javascript/main.js @@ -0,0 +1,59 @@ +import * as std from "std"; +/** @type {string} */ +const input = std.in.readAsString(); +let cursor = 0; +/** @returns {string} */ +function nextToken() { + while (cursor < input.length && input.charCodeAt(cursor) <= 32) cursor++; + const start = cursor; + while (cursor < input.length && input.charCodeAt(cursor) > 32) cursor++; + return input.slice(start, cursor); +} +const K = Number(nextToken()), + W = Number(nextToken()), + R = Number(nextToken()), + Q = Number(nextToken()); +/** @type {bigint[]} */ +const w = Array(K + 1).fill(1000n); +for (let i = 0; i < W; i++) { + const id = Number(nextToken()); + w[id] = BigInt(nextToken()); +} +const pc = /** @type {bigint[]} */ ([0n]), + pn = /** @type {bigint[]} */ ([0n]), + rw = /** @type {bigint[]} */ ([]), + rc = /** @type {bigint[]} */ ([]); +for (let i = 0; i < R; i++) { + const id = Number(nextToken()), c = BigInt(nextToken()); + rw.push(w[id]); + rc.push(c); + pc.push(pc[i] + w[id] * c); + pn.push(pn[i] + c); +} +let output = ""; +/** @param {string} line */ +function emit(line) { + if (output.length + line.length > 65536) { + std.out.puts(output); + output = ""; + } + output += line; +} +for (let z = 0; z < Q; z++) { + const b = BigInt(nextToken()); + let lo = 0, hi = R + 1; + while (lo + 1 < hi) { + const m = (lo + hi) >> 1; + if (pc[m] <= b) lo = m; + else hi = m; + } + let done = pn[lo], cost = pc[lo]; + if (lo < R) { + let take = (b - cost) / rw[lo]; + if (take > rc[lo]) take = rc[lo]; + done += take; + cost += take * rw[lo]; + } + emit(`${done} ${cost}\n`); +} +if (output.length) std.out.puts(output); diff --git a/problems/001-weighted-opcode-scale/solutions/python/main.py b/problems/001-weighted-opcode-scale/solutions/python/main.py new file mode 100644 index 0000000..0108d57 --- /dev/null +++ b/problems/001-weighted-opcode-scale/solutions/python/main.py @@ -0,0 +1,31 @@ +import sys +from bisect import bisect_right + +t = list(map(int, sys.stdin.buffer.read().split())) +it = iter(t) +K, W, R, Q = next(it), next(it), next(it), next(it) +weight = [1000] * (K + 1) +for _ in range(W): + op = next(it) + weight[op] = next(it) +pc = [0] +pn = [0] +rw = [] +rc = [] +for _ in range(R): + op, c = next(it), next(it) + rw.append(weight[op]) + rc.append(c) + pc.append(pc[-1] + c * weight[op]) + pn.append(pn[-1] + c) +out = [] +for _ in range(Q): + b = next(it) + i = bisect_right(pc, b) - 1 + done, cost = pn[i], pc[i] + if i < R: + take = min(rc[i], (b - cost) // rw[i]) + done += take + cost += take * rw[i] + out.append(f"{done} {cost}") +print("\n".join(out)) diff --git a/problems/001-weighted-opcode-scale/solutions/rust/main.rs b/problems/001-weighted-opcode-scale/solutions/rust/main.rs new file mode 100644 index 0000000..fd24606 --- /dev/null +++ b/problems/001-weighted-opcode-scale/solutions/rust/main.rs @@ -0,0 +1,46 @@ +use std::io::{self, Read}; +fn main() { + let mut s = String::new(); + io::stdin().read_to_string(&mut s).unwrap(); + let mut it = s.split_whitespace(); + let k: usize = it.next().unwrap().parse().unwrap(); + let w_n: usize = it.next().unwrap().parse().unwrap(); + let r: usize = it.next().unwrap().parse().unwrap(); + let q: usize = it.next().unwrap().parse().unwrap(); + let mut w = vec![1000u64; k + 1]; + for _ in 0..w_n { + let id: usize = it.next().unwrap().parse().unwrap(); + w[id] = it.next().unwrap().parse().unwrap(); + } + let (mut pc, mut pn, mut rw, mut rc) = ( + vec![0u64; r + 1], + vec![0u64; r + 1], + vec![0u64; r], + vec![0u64; r], + ); + for i in 0..r { + let id: usize = it.next().unwrap().parse().unwrap(); + rc[i] = it.next().unwrap().parse().unwrap(); + rw[i] = w[id]; + pc[i + 1] = pc[i] + rw[i] * rc[i]; + pn[i + 1] = pn[i] + rc[i]; + } + let mut out = String::new(); + for _ in 0..q { + let b: u64 = it.next().unwrap().parse().unwrap(); + let mut lo = 0usize; + let mut hi = r + 1; + while lo + 1 < hi { + let m = (lo + hi) / 2; + if pc[m] <= b { lo = m } else { hi = m } + } + let (mut done, mut cost) = (pn[lo], pc[lo]); + if lo < r { + let take = rc[lo].min((b - cost) / rw[lo]); + done += take; + cost += take * rw[lo]; + } + out += &format!("{} {}\n", done, cost); + } + print!("{}", out); +} diff --git a/problems/001-weighted-opcode-scale/solutions/typescript/main.ts b/problems/001-weighted-opcode-scale/solutions/typescript/main.ts new file mode 100644 index 0000000..d5ad944 --- /dev/null +++ b/problems/001-weighted-opcode-scale/solutions/typescript/main.ts @@ -0,0 +1,55 @@ +import * as std from "std"; +const input: string = std.in.readAsString(); +let cursor = 0; +function nextToken(): string { + while (cursor < input.length && input.charCodeAt(cursor) <= 32) cursor++; + const start = cursor; + while (cursor < input.length && input.charCodeAt(cursor) > 32) cursor++; + return input.slice(start, cursor); +} +const K = Number(nextToken()), + W = Number(nextToken()), + R = Number(nextToken()), + Q = Number(nextToken()); +const w: bigint[] = Array(K + 1).fill(1000n); +for (let i = 0; i < W; i++) { + const id = Number(nextToken()); + w[id] = BigInt(nextToken()); +} +const pc: bigint[] = [0n], + pn: bigint[] = [0n], + rw: bigint[] = [], + rc: bigint[] = []; +for (let i = 0; i < R; i++) { + const id = Number(nextToken()), c = BigInt(nextToken()); + rw.push(w[id]); + rc.push(c); + pc.push(pc[i] + w[id] * c); + pn.push(pn[i] + c); +} +let output = ""; +function emit(line: string): void { + if (output.length + line.length > 65536) { + std.out.puts(output); + output = ""; + } + output += line; +} +for (let z = 0; z < Q; z++) { + const b = BigInt(nextToken()); + let lo = 0, hi = R + 1; + while (lo + 1 < hi) { + const m = (lo + hi) >> 1; + if (pc[m] <= b) lo = m; + else hi = m; + } + let done = pn[lo], cost = pc[lo]; + if (lo < R) { + let take = (b - cost) / rw[lo]; + if (take > rc[lo]) take = rc[lo]; + done += take; + cost += take * rw[lo]; + } + emit(`${done} ${cost}\n`); +} +if (output.length) std.out.puts(output); diff --git a/problems/001-weighted-opcode-scale/statement.en.md b/problems/001-weighted-opcode-scale/statement.en.md new file mode 100644 index 0000000..eae719e --- /dev/null +++ b/problems/001-weighted-opcode-scale/statement.en.md @@ -0,0 +1,120 @@ +# Weighted Opcode Scale + +While designing compute limits for a WASM OJ, we cannot merely count how many instructions a program executes. Different WebAssembly opcodes do different amounts of work; treating them all as equally expensive would place the same unreasonable limit on simple operations and costly ones. We therefore assign weights to opcodes that have been characterized and use a conservative cost for opcodes that have not yet been calibrated individually. + +Opcodes are represented by integer IDs from `1` through `K`. Exactly `W` IDs have explicitly specified weights, and every unlisted ID has weight `1000`. Because an execution trace can be long, the measured trace has already compressed consecutive occurrences of the same opcode into `R` runs. Each run records an opcode ID and its consecutive occurrence count. + +When tuning the cost budget, we evaluate the same trace under several candidate budgets. Every query is independent: execution restarts at the beginning of the trace, and an instruction may only be executed in full. It is not possible to pay part of its cost and leave a partially completed instruction. + +For each budget, output the maximum number of instructions that can be completed in order and the actual total cost of those completed instructions. + +## Input + +The first line contains `K W R Q`. + +The next `W` lines each contain `id weight`. These `id` values are distinct. Every ID not listed has weight `1000`. + +The next `R` lines each contain `id count`, describing the execution trace in order. + +The final `Q` lines each contain one `budget`. + +## Output + +For each query, output one line containing `instructions cost`. + +`instructions` is the length of the longest trace prefix whose total cost does not exceed `budget`; `cost` is the cost of that prefix. A prefix may stop partway through a run, but every included instruction is charged in full. The empty prefix is valid and has cost `0`. + +## Constraints + +- `1 ≤ K,R,Q ≤ 200000` +- `0 ≤ W ≤ K` +- `1 ≤ id ≤ K` +- `1 ≤ weight ≤ 10^6` +- `1 ≤ count ≤ 10^12` +- `0 ≤ budget ≤ 9×10^18` +- The total instruction count and total cost of the entire trace are each at most `9×10^18`. +- All integers are decimal. Every multiplication and addition required by the problem fits in an unsigned 64-bit integer. + +Under the full constraints, rescanning every run for every query is too slow. + +## Examples + + + +### Example One + +Input: + +```text +5 3 4 5 +1 2 +2 5 +3 20 +1 3 +5 2 +2 4 +3 1 +0 +6 +10 +2010 +2040 +``` + +Output: + +```text +0 0 +3 6 +3 6 +5 2006 +9 2026 +``` + +### Example Two + +Input: + +```text +1 0 1 3 +1 10 +999 +1000 +9999 +``` + +Output: + +```text +0 0 +1 1000 +9 9000 +``` + +### Example Three + +Input: + +```text +2 2 3 4 +1 7 +2 3 +1 2 +2 3 +1 1 +13 +14 +22 +30 +``` + +Output: + +```text +1 7 +2 14 +4 20 +6 30 +``` + + diff --git a/problems/001-weighted-opcode-scale/statement.zh-TW.md b/problems/001-weighted-opcode-scale/statement.zh-TW.md new file mode 100644 index 0000000..3e94bb1 --- /dev/null +++ b/problems/001-weighted-opcode-scale/statement.zh-TW.md @@ -0,0 +1,120 @@ +# 操作碼秤重站 + +在設計 WASM OJ 的計算資源限制時,我們不能只計算程式執行了幾條指令。不同 WebAssembly 操作碼的工作量並不相同;如果全部視為相同成本,簡單運算與昂貴操作就會受到不合理的同一種限制。因此,我們替部分已知操作碼指定權重,並讓尚未個別校準的操作碼採用保守成本。 + +操作碼以 `1..K` 的整數 ID 表示。其中 `W` 種 ID 有明訂權重,其餘 ID 的權重固定為 `1000`。執行期間收集到的指令軌跡可能很長,所以量測資料已把連續相同的操作碼壓縮成 `R` 個 run;每個 run 記錄操作碼 ID 與連續出現次數。 + +在調整 cost budget 時,我們會用多個候選 budget 評估同一段軌跡。每個查詢都是一次獨立評估,程式會從軌跡開頭重新執行,而且一條指令只能完整執行,不能只支付部分成本後留下半條指令。 + +對每個 budget,請輸出能依序完成的最大指令數,以及這些已完成指令的實際總成本。 + +## 輸入 + +第一行為 `K W R Q`。 + +接下來 `W` 行各為 `id weight`。這些 `id` 互不相同;沒有列出的 ID 權重為 `1000`。 + +接下來 `R` 行各為 `id count`,依序描述執行軌跡。 + +最後 `Q` 行各有一個 `budget`。 + +## 輸出 + +對每個查詢輸出一行 `instructions cost`。 + +`instructions` 是在總成本不超過 `budget` 時能完成的最長軌跡前綴長度;`cost` 是該前綴的成本。即使同一 run 尚可執行一部分,也必須逐條完整計費。空前綴合法,成本為 `0`。 + +## 限制 + +- `1 ≤ K,R,Q ≤ 200000` +- `0 ≤ W ≤ K` +- `1 ≤ id ≤ K` +- `1 ≤ weight ≤ 10^6` +- `1 ≤ count ≤ 10^12` +- `0 ≤ budget ≤ 9×10^18` +- 整條軌跡的指令數與成本都不超過 `9×10^18` +- 所有整數皆為十進位;題目中的乘加保證可存入無號 64-bit integer + +完整限制下,對每個查詢重新掃描所有 run 會超時。 + +## 範例 + + + +### 範例一 + +輸入: + +```text +5 3 4 5 +1 2 +2 5 +3 20 +1 3 +5 2 +2 4 +3 1 +0 +6 +10 +2010 +2040 +``` + +輸出: + +```text +0 0 +3 6 +3 6 +5 2006 +9 2026 +``` + +### 範例二 + +輸入: + +```text +1 0 1 3 +1 10 +999 +1000 +9999 +``` + +輸出: + +```text +0 0 +1 1000 +9 9000 +``` + +### 範例三 + +輸入: + +```text +2 2 3 4 +1 7 +2 3 +1 2 +2 3 +1 1 +13 +14 +22 +30 +``` + +輸出: + +```text +1 7 +2 14 +4 20 +6 30 +``` + + diff --git a/problems/001-weighted-opcode-scale/tests/adversarial-01.in b/problems/001-weighted-opcode-scale/tests/adversarial-01.in new file mode 100644 index 0000000..65a7a47 --- /dev/null +++ b/problems/001-weighted-opcode-scale/tests/adversarial-01.in @@ -0,0 +1,11 @@ +2 1 2 7 +1 1000000 +1 1000000000000 +2 1000000000000 +0 +999999 +1000000 +1000000000000000000 +1000000000000000500 +1000999999999999999 +1001000000000000000 diff --git a/problems/001-weighted-opcode-scale/tests/adversarial-01.out b/problems/001-weighted-opcode-scale/tests/adversarial-01.out new file mode 100644 index 0000000..c42344e --- /dev/null +++ b/problems/001-weighted-opcode-scale/tests/adversarial-01.out @@ -0,0 +1,7 @@ +0 0 +0 0 +1 1000000 +1000000000000 1000000000000000000 +1000000000000 1000000000000000000 +1999999999999 1000999999999999000 +2000000000000 1001000000000000000 diff --git a/problems/001-weighted-opcode-scale/tests/sample-01.in b/problems/001-weighted-opcode-scale/tests/sample-01.in new file mode 100644 index 0000000..f7418e1 --- /dev/null +++ b/problems/001-weighted-opcode-scale/tests/sample-01.in @@ -0,0 +1,13 @@ +5 3 4 5 +1 2 +2 5 +3 20 +1 3 +5 2 +2 4 +3 1 +0 +6 +10 +2010 +2040 diff --git a/problems/001-weighted-opcode-scale/tests/sample-01.out b/problems/001-weighted-opcode-scale/tests/sample-01.out new file mode 100644 index 0000000..6382cde --- /dev/null +++ b/problems/001-weighted-opcode-scale/tests/sample-01.out @@ -0,0 +1,5 @@ +0 0 +3 6 +3 6 +5 2006 +9 2026 diff --git a/problems/001-weighted-opcode-scale/tests/sample-02.in b/problems/001-weighted-opcode-scale/tests/sample-02.in new file mode 100644 index 0000000..2130a2e --- /dev/null +++ b/problems/001-weighted-opcode-scale/tests/sample-02.in @@ -0,0 +1,5 @@ +1 0 1 3 +1 10 +999 +1000 +9999 diff --git a/problems/001-weighted-opcode-scale/tests/sample-02.out b/problems/001-weighted-opcode-scale/tests/sample-02.out new file mode 100644 index 0000000..6499186 --- /dev/null +++ b/problems/001-weighted-opcode-scale/tests/sample-02.out @@ -0,0 +1,3 @@ +0 0 +1 1000 +9 9000 diff --git a/problems/001-weighted-opcode-scale/tests/sample-03.in b/problems/001-weighted-opcode-scale/tests/sample-03.in new file mode 100644 index 0000000..d71f3f4 --- /dev/null +++ b/problems/001-weighted-opcode-scale/tests/sample-03.in @@ -0,0 +1,10 @@ +2 2 3 4 +1 7 +2 3 +1 2 +2 3 +1 1 +13 +14 +22 +30 diff --git a/problems/001-weighted-opcode-scale/tests/sample-03.out b/problems/001-weighted-opcode-scale/tests/sample-03.out new file mode 100644 index 0000000..2a2bfed --- /dev/null +++ b/problems/001-weighted-opcode-scale/tests/sample-03.out @@ -0,0 +1,4 @@ +1 7 +2 14 +4 20 +6 30 diff --git a/problems/001-weighted-opcode-scale/validator.py b/problems/001-weighted-opcode-scale/validator.py new file mode 100644 index 0000000..0856004 --- /dev/null +++ b/problems/001-weighted-opcode-scale/validator.py @@ -0,0 +1,49 @@ +import re, sys + + +def fail(): + raise SystemExit(1) + + +try: + data = sys.stdin.buffer.read().decode("utf-8") + if not data or "\x00" in data: + fail() + t = data.split() + p = 0 + + def ui(lo, hi): + nonlocal_dummy = None + global p + if p >= len(t) or re.fullmatch(r"0|[1-9][0-9]*", t[p]) is None: + fail() + v = int(t[p]) + p += 1 + if not lo <= v <= hi: + fail() + return v + + K, W, R, Q = ui(1, 200000), ui(0, 200000), ui(1, 200000), ui(1, 200000) + if W > K: + fail() + seen = set() + weights = [1000] * (K + 1) + for _ in range(W): + i, w = ui(1, K), ui(1, 10**6) + if i in seen: + fail() + seen.add(i) + weights[i] = w + total_c = total_n = 0 + for _ in range(R): + i, c = ui(1, K), ui(1, 10**12) + total_n += c + total_c += c * weights[i] + if total_n > 9 * 10**18 or total_c > 9 * 10**18: + fail() + for _ in range(Q): + ui(0, 9 * 10**18) + if p != len(t): + fail() +except (UnicodeDecodeError, ValueError, OverflowError): + fail() diff --git a/problems/002-baseline-calibration/editorial.en.md b/problems/002-baseline-calibration/editorial.en.md new file mode 100644 index 0000000..d951b45 --- /dev/null +++ b/problems/002-baseline-calibration/editorial.en.md @@ -0,0 +1,24 @@ +# Editorial + +## Intuitive Approach + +For each query, filter the observations belonging to that profile and check all `S` seeds and costs. This takes `O(NQ)` time. Sorting by `(profile,seed)` once and grouping observations improves the bound to `O(N log N+Q)`. + +## Optimal Approach: Per-Profile Aggregation + +Because `(profile,seed)` pairs are guaranteed to be unique, keep only three values per profile: its observation `count`, `minCost`, and `maxCost`. Update them as each observation is read. A profile is valid if and only if `count=S` and `minCost=maxCost`; the common cost is its baseline. + +## Correctness Proof + +If the algorithm declares a profile valid, it has `S` distinct observed seeds. Every seed lies in the `S`-element set `1..S`, so every required seed appears exactly once. Moreover, `minCost=maxCost` means all observed costs are identical. Thus the publication requirements hold. Conversely, every publishable profile has all `S` observations and identical costs, so it passes both tests. For a valid query, the algorithm then outputs the common cost and `max(0,raw-baseline)`, exactly as defined. + +## Complexity + +Initialization, aggregation, and queries take `O(P)`, `O(N)`, and `O(Q)` time, respectively, for `O(P+N+Q)` total time. Core auxiliary space is `O(P)`. With buffered input/output allocations included, the common worst-case bound of the seven reference implementations is `O(P+N+Q)`. Reading all data already gives an `Ω(P+N+Q)` worst-case lower bound, so the running time is asymptotically optimal. + +## Common Mistakes + +- Comparing costs without verifying that every seed is present. +- Dividing the total by the count; an equal average does not mean all observations are equal. +- Subtracting `raw-baseline` directly in an unsigned type and underflowing. +- Assuming observations are ordered by profile or seed. diff --git a/problems/002-baseline-calibration/editorial.zh-TW.md b/problems/002-baseline-calibration/editorial.zh-TW.md new file mode 100644 index 0000000..d569028 --- /dev/null +++ b/problems/002-baseline-calibration/editorial.zh-TW.md @@ -0,0 +1,24 @@ +# 解題說明 + +## 直覺解 + +每次查詢挑出該 profile 的觀測,再檢查 `S` 個 seed 與成本,需 `O(NQ)` 時間。也可先依 `(profile,seed)` 排序後分組,時間 `O(N log N+Q)`。 + +## 最佳解 + +因輸入保證 `(profile,seed)` 唯一,對每個 profile 只需維護三個量:觀測筆數 `count`、最小成本 `minCost`、最大成本 `maxCost`。讀一筆就更新。最後且僅當 `count=S` 且 `minCost=maxCost` 時有效;baseline 即該共同成本。 + +## 正確性證明 + +若 profile 被判有效,`count=S`;所有 seed 都落在大小恰為 `S` 的集合 `1..S`,又不重複,所以每個 seed 恰出現一次。`minCost=maxCost` 表示全部觀測成本相同,符合發布條件。反之,任何可發布 profile 必有 `S` 筆觀測且成本全同,因此必通過兩項檢查。有效查詢依定義輸出共同成本及 `max(0,raw-baseline)`,所以答案正確。 + +## 複雜度 + +初始化、彙總、回答分別為 `O(P)`、`O(N)`、`O(Q)`,總時間 `O(P+N+Q)`,核心資料結構的輔助空間為 `O(P)`。C、C++、Go reference 串流讀寫;Rust、Python 會保留完整輸入與輸出,JavaScript、TypeScript 保留 Forge `readAsString()` 提供的單一輸入字串,但以固定 64 KiB 分塊輸出。由於每筆觀測、查詢與答案都只有常數個定長整數 token,依實際 resident allocations 計算,七語言 reference 的共同最壞空間上界為 `O(P+N+Q)`。讀取全部資料本身已有 `Ω(P+N+Q)` 的最壞情況下界,因此時間為漸進最佳。 + +## 常見錯誤 + +- 只比較成本卻未檢查 seed 是否完整。 +- 用總和除以筆數;平均相同不代表每筆相同。 +- 將 `raw-baseline` 以無號整數直接相減而 underflow。 +- 誤以為觀測按 profile 或 seed 排序。 diff --git a/problems/002-baseline-calibration/generator.py b/problems/002-baseline-calibration/generator.py new file mode 100644 index 0000000..5fca87a --- /dev/null +++ b/problems/002-baseline-calibration/generator.py @@ -0,0 +1,19 @@ +import random, sys + +if len(sys.argv) != 3: + raise SystemExit("usage: generator.py SEED INDEX") +r = random.Random((int(sys.argv[1]) << 32) ^ int(sys.argv[2])) +idx = int(sys.argv[2]) +P = r.randint(1, 3 + idx % 5) +S = r.randint(1, 3 + idx % 4) +obs = [] +for p in range(1, P + 1): + base = r.randint(0, 30) + for s in range(1, S + 1): + if r.random() < 0.75: + obs.append((p, s, base + (1 if r.random() < 0.15 else 0))) +r.shuffle(obs) +Q = r.randint(1, 8) +out = [f"{P} {S} {len(obs)} {Q}"] + [f"{a} {b} {c}" for a, b, c in obs] +out += [f"{r.randint(1,P)} {r.randint(0,50)}" for _ in range(Q)] +print("\n".join(out)) diff --git a/problems/002-baseline-calibration/oracle.py b/problems/002-baseline-calibration/oracle.py new file mode 100644 index 0000000..59374d0 --- /dev/null +++ b/problems/002-baseline-calibration/oracle.py @@ -0,0 +1,16 @@ +import sys + +t = list(map(int, sys.stdin.buffer.read().split())) +it = iter(t) +P, S, N, Q = next(it), next(it), next(it), next(it) +obs = [(next(it), next(it), next(it)) for _ in range(N)] +out = [] +for _ in range(Q): + p, raw = next(it), next(it) + a = {s: c for x, s, c in obs if x == p} + if len(a) != S or len(set(a.values())) != 1: + out.append("INVALID") + else: + b = next(iter(a.values())) + out.append(f"{b} {max(0,raw-b)}") +print("\n".join(out)) diff --git a/problems/002-baseline-calibration/problem.json b/problems/002-baseline-calibration/problem.json new file mode 100644 index 0000000..44b14ce --- /dev/null +++ b/problems/002-baseline-calibration/problem.json @@ -0,0 +1,155 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 2, + "slug": "baseline-calibration", + "title": { + "zh-TW": "空程式基線校正", + "en": "Empty-Program Baseline Calibration" + }, + "difficulty": "medium", + "tags": [ + "preprocessing", + "grouping", + "resource-metering" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-01", + "kind": "adversarial", + "input": "tests/adversarial-01.in", + "output": "tests/adversarial-01.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 9500000, + "memoryLimitBytes": 536870912 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 2000000, + "memoryLimitBytes": 402653184 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 850000, + "memoryLimitBytes": 268435456 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "每次查詢重掃全部觀測", + "en": "Rescan All Observations per Query" + }, + "time": "O(NQ)", + "space": "O(S)", + "accepted": false + }, + { + "name": { + "zh-TW": "排序後分組", + "en": "Sorting and Grouping" + }, + "time": "O(N log N+Q)", + "space": "O(N+P)", + "accepted": true + }, + { + "name": { + "zh-TW": "依 profile 線性彙總", + "en": "Linear Per-Profile Aggregation" + }, + "time": "O(P+N+Q)", + "space": "O(P) auxiliary; O(P+N+Q) buffered I/O", + "accepted": true + } + ] +} diff --git a/problems/002-baseline-calibration/solutions/c/main.c b/problems/002-baseline-calibration/solutions/c/main.c new file mode 100644 index 0000000..85bd096 --- /dev/null +++ b/problems/002-baseline-calibration/solutions/c/main.c @@ -0,0 +1,34 @@ +#include +#include +#include +int main(void) { + int P, S, N, Q; + if (scanf("%d%d%d%d", &P, &S, &N, &Q) != 4) + return 0; + int *c = calloc(P + 1, sizeof(*c)); + unsigned long long *lo = malloc((P + 1) * sizeof(*lo)), + *hi = calloc(P + 1, sizeof(*hi)); + for (int i = 0; i <= P; i++) + lo[i] = ULLONG_MAX; + for (int i = 0, p, s; i < N; i++) { + unsigned long long x; + scanf("%d%d%llu", &p, &s, &x); + c[p]++; + if (x < lo[p]) + lo[p] = x; + if (x > hi[p]) + hi[p] = x; + } + while (Q--) { + int p; + unsigned long long raw; + scanf("%d%llu", &p, &raw); + if (c[p] != S || lo[p] != hi[p]) + puts("INVALID"); + else + printf("%llu %llu\n", lo[p], raw > lo[p] ? raw - lo[p] : 0ULL); + } + free(c); + free(lo); + free(hi); +} diff --git a/problems/002-baseline-calibration/solutions/cpp/main.cpp b/problems/002-baseline-calibration/solutions/cpp/main.cpp new file mode 100644 index 0000000..f6bea78 --- /dev/null +++ b/problems/002-baseline-calibration/solutions/cpp/main.cpp @@ -0,0 +1,30 @@ +#include +#include +#include +#include +using namespace std; +int main() { + ios::sync_with_stdio(false); + cin.tie(nullptr); + int P, S, N, Q; + if (!(cin >> P >> S >> N >> Q)) + return 0; + vector c(P + 1); + vector lo(P + 1, ULLONG_MAX), hi(P + 1); + for (int i = 0, p, s; i < N; i++) { + unsigned long long x; + cin >> p >> s >> x; + c[p]++; + lo[p] = min(lo[p], x); + hi[p] = max(hi[p], x); + } + while (Q--) { + int p; + unsigned long long x; + cin >> p >> x; + if (c[p] != S || lo[p] != hi[p]) + cout << "INVALID\n"; + else + cout << lo[p] << ' ' << (x > lo[p] ? x - lo[p] : 0) << '\n'; + } +} diff --git a/problems/002-baseline-calibration/solutions/go/main.go b/problems/002-baseline-calibration/solutions/go/main.go new file mode 100644 index 0000000..854168d --- /dev/null +++ b/problems/002-baseline-calibration/solutions/go/main.go @@ -0,0 +1,50 @@ +package main + +import ( + "bufio" + "fmt" + "math" + "os" +) + +func main() { + in := bufio.NewReader(os.Stdin) + out := bufio.NewWriter(os.Stdout) + defer out.Flush() + var p, s, n, q int + if _, e := fmt.Fscan(in, &p, &s, &n, &q); e != nil { + return + } + c := make([]int, p+1) + lo := make([]uint64, p+1) + hi := make([]uint64, p+1) + for i := range lo { + lo[i] = math.MaxUint64 + } + for i := 0; i < n; i++ { + var x, seed int + var v uint64 + fmt.Fscan(in, &x, &seed, &v) + c[x]++ + if v < lo[x] { + lo[x] = v + } + if v > hi[x] { + hi[x] = v + } + } + for ; q > 0; q-- { + var x int + var raw uint64 + fmt.Fscan(in, &x, &raw) + if c[x] != s || lo[x] != hi[x] { + fmt.Fprintln(out, "INVALID") + } else { + var net uint64 + if raw > lo[x] { + net = raw - lo[x] + } + fmt.Fprintln(out, lo[x], net) + } + } +} diff --git a/problems/002-baseline-calibration/solutions/javascript/main.js b/problems/002-baseline-calibration/solutions/javascript/main.js new file mode 100644 index 0000000..b4f5b25 --- /dev/null +++ b/problems/002-baseline-calibration/solutions/javascript/main.js @@ -0,0 +1,44 @@ +import * as std from "std"; +/** @type {string} */ +const input = std.in.readAsString(); +let cursor = 0; +/** @returns {string} */ +function nextToken() { + while (cursor < input.length && input.charCodeAt(cursor) <= 32) cursor++; + const start = cursor; + while (cursor < input.length && input.charCodeAt(cursor) > 32) cursor++; + return input.slice(start, cursor); +} +const P = Number(nextToken()), + S = Number(nextToken()), + N = Number(nextToken()), + Q = Number(nextToken()); +const c = /** @type {number[]} */ (Array(P + 1).fill(0)), + lo = /** @type {(bigint | null)[]} */ (Array(P + 1).fill(null)), + hi = /** @type {bigint[]} */ (Array(P + 1).fill(0n)); +for (let i = 0; i < N; i++) { + const p = Number(nextToken()); + nextToken(); + const v = BigInt(nextToken()); + c[p]++; + if (lo[p] === null || v < /** @type {bigint} */ (lo[p])) lo[p] = v; + if (v > hi[p]) hi[p] = v; +} +let output = ""; +/** @param {string} line */ +function emit(line) { + if (output.length + line.length > 65536) { + std.out.puts(output); + output = ""; + } + output += line; +} +for (let i = 0; i < Q; i++) { + const p = Number(nextToken()), raw = BigInt(nextToken()); + if (c[p] !== S || lo[p] !== hi[p]) emit("INVALID\n"); + else { + const b = /** @type {bigint} */ (lo[p]); + emit(`${b} ${raw > b ? raw - b : 0n}\n`); + } +} +if (output.length) std.out.puts(output); diff --git a/problems/002-baseline-calibration/solutions/python/main.py b/problems/002-baseline-calibration/solutions/python/main.py new file mode 100644 index 0000000..809eff1 --- /dev/null +++ b/problems/002-baseline-calibration/solutions/python/main.py @@ -0,0 +1,22 @@ +import sys + +t = list(map(int, sys.stdin.buffer.read().split())) +it = iter(t) +P, S, N, Q = next(it), next(it), next(it), next(it) +c = [0] * (P + 1) +lo = [10**19] * (P + 1) +hi = [0] * (P + 1) +for _ in range(N): + p = next(it) + next(it) + v = next(it) + c[p] += 1 + lo[p] = min(lo[p], v) + hi[p] = max(hi[p], v) +out = [] +for _ in range(Q): + p, raw = next(it), next(it) + out.append( + "INVALID" if c[p] != S or lo[p] != hi[p] else f"{lo[p]} {max(0,raw-lo[p])}" + ) +print("\n".join(out)) diff --git a/problems/002-baseline-calibration/solutions/rust/main.rs b/problems/002-baseline-calibration/solutions/rust/main.rs new file mode 100644 index 0000000..0fe58a0 --- /dev/null +++ b/problems/002-baseline-calibration/solutions/rust/main.rs @@ -0,0 +1,32 @@ +use std::io::{self, Read}; +fn main() { + let mut s = String::new(); + io::stdin().read_to_string(&mut s).unwrap(); + let mut it = s.split_whitespace(); + let p: usize = it.next().unwrap().parse().unwrap(); + let seeds: usize = it.next().unwrap().parse().unwrap(); + let n: usize = it.next().unwrap().parse().unwrap(); + let q: usize = it.next().unwrap().parse().unwrap(); + let mut c = vec![0usize; p + 1]; + let mut lo = vec![u64::MAX; p + 1]; + let mut hi = vec![0u64; p + 1]; + for _ in 0..n { + let x: usize = it.next().unwrap().parse().unwrap(); + it.next(); + let v: u64 = it.next().unwrap().parse().unwrap(); + c[x] += 1; + lo[x] = lo[x].min(v); + hi[x] = hi[x].max(v); + } + let mut out = String::new(); + for _ in 0..q { + let x: usize = it.next().unwrap().parse().unwrap(); + let raw: u64 = it.next().unwrap().parse().unwrap(); + if c[x] != seeds || lo[x] != hi[x] { + out += "INVALID\n" + } else { + out += &format!("{} {}\n", lo[x], raw.saturating_sub(lo[x])); + } + } + print!("{}", out); +} diff --git a/problems/002-baseline-calibration/solutions/typescript/main.ts b/problems/002-baseline-calibration/solutions/typescript/main.ts new file mode 100644 index 0000000..cce55d4 --- /dev/null +++ b/problems/002-baseline-calibration/solutions/typescript/main.ts @@ -0,0 +1,41 @@ +import * as std from "std"; +const input: string = std.in.readAsString(); +let cursor = 0; +function nextToken(): string { + while (cursor < input.length && input.charCodeAt(cursor) <= 32) cursor++; + const start = cursor; + while (cursor < input.length && input.charCodeAt(cursor) > 32) cursor++; + return input.slice(start, cursor); +} +const P = Number(nextToken()), + S = Number(nextToken()), + N = Number(nextToken()), + Q = Number(nextToken()); +const c: number[] = Array(P + 1).fill(0), + lo: (bigint | null)[] = Array(P + 1).fill(null), + hi: bigint[] = Array(P + 1).fill(0n); +for (let i = 0; i < N; i++) { + const p = Number(nextToken()); + nextToken(); + const v = BigInt(nextToken()); + c[p]++; + if (lo[p] === null || v < (lo[p] as bigint)) lo[p] = v; + if (v > hi[p]) hi[p] = v; +} +let output = ""; +function emit(line: string): void { + if (output.length + line.length > 65536) { + std.out.puts(output); + output = ""; + } + output += line; +} +for (let i = 0; i < Q; i++) { + const p = Number(nextToken()), raw = BigInt(nextToken()); + if (c[p] !== S || lo[p] !== hi[p]) emit("INVALID\n"); + else { + const b = lo[p] as bigint; + emit(`${b} ${raw > b ? raw - b : 0n}\n`); + } +} +if (output.length) std.out.puts(output); diff --git a/problems/002-baseline-calibration/statement.en.md b/problems/002-baseline-calibration/statement.en.md new file mode 100644 index 0000000..01820c4 --- /dev/null +++ b/problems/002-baseline-calibration/statement.en.md @@ -0,0 +1,110 @@ +# Empty-Program Baseline Calibration + +When measuring instruction cost in a WASM OJ, the compiler and execution environment introduce fixed overhead of their own. Charging this overhead directly to the submitted program would make compilation profiles difficult to compare fairly. We therefore run an empty program first and establish a deductible baseline for each profile. + +A baseline may be published only when its measurements are complete and reproducible. The system observes `P` compilation profiles, and each profile is expected to have exactly one result for every seed from `1` through `S`. A profile has a publishable baseline only if every seed is present and all observed costs are identical. + +Measurements may arrive in any order, but the same `(profile, seed)` pair appears at most once in the input. Each later query supplies a profile and a raw cost so that the submitted program's cost can be computed after removing the environmental baseline. + +If the profile has no publishable baseline, output `INVALID`. Otherwise, output the baseline and the net cost. Net cost may not be negative, so it is defined as `max(0, raw-baseline)`. + +## Input + +The first line contains `P S N Q`. The next `N` lines contain `profile seed cost`. The final `Q` lines contain `profile raw`. + +## Output + +Output one line per query. For a valid profile, output `baseline net`. For an invalid profile, output only `INVALID`. Queries do not modify the calibration data. + +## Constraints + +- `1 ≤ P,S,Q ≤ 200000` +- `0 ≤ N ≤ 200000` +- `1 ≤ profile ≤ P`, `1 ≤ seed ≤ S` +- All `(profile,seed)` pairs are distinct. +- `0 ≤ cost,raw ≤ 9×10^18` + +Given the seed range and uniqueness guarantees above, `count=S` is equivalent to saying that the profile has no missing seed. The full constraints rule out rescanning all observations for every query. + +## Examples + + + +### Example One + +Input: + +```text +3 2 5 5 +1 1 10 +2 2 8 +3 2 4 +1 2 10 +2 1 7 +1 6 +1 15 +2 99 +3 4 +1 10 +``` + +Output: + +```text +10 0 +10 5 +INVALID +INVALID +10 0 +``` + +### Example Two + +Input: + +```text +4 1 3 4 +3 1 9 +1 1 0 +4 1 20 +1 5 +2 5 +3 8 +4 25 +``` + +Output: + +```text +0 5 +INVALID +9 0 +20 5 +``` + +### Example Three + +Input: + +```text +2 3 6 3 +2 3 5 +1 2 0 +2 1 5 +1 1 0 +2 2 5 +1 3 0 +1 0 +1 12 +2 4 +``` + +Output: + +```text +0 0 +0 12 +5 0 +``` + + diff --git a/problems/002-baseline-calibration/statement.zh-TW.md b/problems/002-baseline-calibration/statement.zh-TW.md new file mode 100644 index 0000000..22efcb2 --- /dev/null +++ b/problems/002-baseline-calibration/statement.zh-TW.md @@ -0,0 +1,110 @@ +# 空程式基線校正 + +在 WASM OJ 裡量測 instruction cost 時,編譯器與執行環境本身也會產生固定開銷。若直接把這些開銷算進使用者程式的成本,不同編譯 profile 之間便無法公平比較。因此,我們先執行空程式,替每個 profile 建立可扣除的 baseline。 + +一個 baseline 只有在量測完整而且可重現時才能發布。系統對 `P` 個編譯 profile 進行觀測;每個 profile 預期恰有 seed `1..S` 的 `S` 筆結果。只有所有 seed 都有觀測,而且觀測到的成本完全相同,該 profile 才具有可發布的 baseline。 + +量測結果可能以任意順序抵達,但同一組 `(profile, seed)` 在輸入中至多出現一次。之後的每筆查詢會提供一個 profile 與 raw cost,用來計算扣除環境基線後的使用者程式成本。 + +若該 profile 沒有可發布的 baseline,輸出 `INVALID`;否則輸出 baseline 與 net cost。net cost 不得為負,因此定義為 `max(0, raw-baseline)`。 + +## 輸入 + +第一行為 `P S N Q`。接下來 `N` 行為 `profile seed cost`,最後 `Q` 行為 `profile raw`。 + +## 輸出 + +每個查詢一行。有效時輸出 `baseline net`,無效時只輸出 `INVALID`。查詢不會改變校正資料。 + +## 限制 + +- `1 ≤ P,S,Q ≤ 200000` +- `0 ≤ N ≤ 200000` +- `1 ≤ profile ≤ P`,`1 ≤ seed ≤ S` +- 所有 `(profile,seed)` 互不相同 +- `0 ≤ cost,raw ≤ 9×10^18` + +`count=S` 在上述 seed 範圍與唯一性保證下等價於該 profile 沒有缺 seed。完整限制排除每次查詢重掃全部觀測的作法。 + +## 範例 + + + +### 範例一 + +輸入: + +```text +3 2 5 5 +1 1 10 +2 2 8 +3 2 4 +1 2 10 +2 1 7 +1 6 +1 15 +2 99 +3 4 +1 10 +``` + +輸出: + +```text +10 0 +10 5 +INVALID +INVALID +10 0 +``` + +### 範例二 + +輸入: + +```text +4 1 3 4 +3 1 9 +1 1 0 +4 1 20 +1 5 +2 5 +3 8 +4 25 +``` + +輸出: + +```text +0 5 +INVALID +9 0 +20 5 +``` + +### 範例三 + +輸入: + +```text +2 3 6 3 +2 3 5 +1 2 0 +2 1 5 +1 1 0 +2 2 5 +1 3 0 +1 0 +1 12 +2 4 +``` + +輸出: + +```text +0 0 +0 12 +5 0 +``` + + diff --git a/problems/002-baseline-calibration/tests/adversarial-01.in b/problems/002-baseline-calibration/tests/adversarial-01.in new file mode 100644 index 0000000..26eb2e0 --- /dev/null +++ b/problems/002-baseline-calibration/tests/adversarial-01.in @@ -0,0 +1,15 @@ +3 3 8 6 +2 2 7 +1 3 0 +3 1 5 +1 1 0 +3 3 6 +2 1 7 +3 2 5 +1 2 0 +1 0 +1 9000000000000000000 +2 7 +3 5 +2 0 +3 9000000000000000000 diff --git a/problems/002-baseline-calibration/tests/adversarial-01.out b/problems/002-baseline-calibration/tests/adversarial-01.out new file mode 100644 index 0000000..e85e4f9 --- /dev/null +++ b/problems/002-baseline-calibration/tests/adversarial-01.out @@ -0,0 +1,6 @@ +0 0 +0 9000000000000000000 +INVALID +INVALID +INVALID +INVALID diff --git a/problems/002-baseline-calibration/tests/sample-01.in b/problems/002-baseline-calibration/tests/sample-01.in new file mode 100644 index 0000000..8564823 --- /dev/null +++ b/problems/002-baseline-calibration/tests/sample-01.in @@ -0,0 +1,11 @@ +3 2 5 5 +1 1 10 +2 2 8 +3 2 4 +1 2 10 +2 1 7 +1 6 +1 15 +2 99 +3 4 +1 10 diff --git a/problems/002-baseline-calibration/tests/sample-01.out b/problems/002-baseline-calibration/tests/sample-01.out new file mode 100644 index 0000000..a0127ba --- /dev/null +++ b/problems/002-baseline-calibration/tests/sample-01.out @@ -0,0 +1,5 @@ +10 0 +10 5 +INVALID +INVALID +10 0 diff --git a/problems/002-baseline-calibration/tests/sample-02.in b/problems/002-baseline-calibration/tests/sample-02.in new file mode 100644 index 0000000..e433325 --- /dev/null +++ b/problems/002-baseline-calibration/tests/sample-02.in @@ -0,0 +1,8 @@ +4 1 3 4 +3 1 9 +1 1 0 +4 1 20 +1 5 +2 5 +3 8 +4 25 diff --git a/problems/002-baseline-calibration/tests/sample-02.out b/problems/002-baseline-calibration/tests/sample-02.out new file mode 100644 index 0000000..fcca809 --- /dev/null +++ b/problems/002-baseline-calibration/tests/sample-02.out @@ -0,0 +1,4 @@ +0 5 +INVALID +9 0 +20 5 diff --git a/problems/002-baseline-calibration/tests/sample-03.in b/problems/002-baseline-calibration/tests/sample-03.in new file mode 100644 index 0000000..e489483 --- /dev/null +++ b/problems/002-baseline-calibration/tests/sample-03.in @@ -0,0 +1,10 @@ +2 3 6 3 +2 3 5 +1 2 0 +2 1 5 +1 1 0 +2 2 5 +1 3 0 +1 0 +1 12 +2 4 diff --git a/problems/002-baseline-calibration/tests/sample-03.out b/problems/002-baseline-calibration/tests/sample-03.out new file mode 100644 index 0000000..dc05f30 --- /dev/null +++ b/problems/002-baseline-calibration/tests/sample-03.out @@ -0,0 +1,3 @@ +0 0 +0 12 +5 0 diff --git a/problems/002-baseline-calibration/validator.py b/problems/002-baseline-calibration/validator.py new file mode 100644 index 0000000..810145d --- /dev/null +++ b/problems/002-baseline-calibration/validator.py @@ -0,0 +1,37 @@ +import re, sys + + +def fail(): + raise SystemExit(1) + + +try: + d = sys.stdin.buffer.read().decode("utf-8") + t = d.split() + p = 0 + + def u(lo, hi): + global p + if p >= len(t) or re.fullmatch(r"0|[1-9][0-9]*", t[p]) is None: + fail() + v = int(t[p]) + p += 1 + if not lo <= v <= hi: + fail() + return v + + P, S, N, Q = u(1, 200000), u(1, 200000), u(0, 200000), u(1, 200000) + seen = set() + for _ in range(N): + a, b = u(1, P), u(1, S) + u(0, 9 * 10**18) + if (a, b) in seen: + fail() + seen.add((a, b)) + for _ in range(Q): + u(1, P) + u(0, 9 * 10**18) + if p != len(t): + fail() +except (UnicodeDecodeError, ValueError, OverflowError): + fail() diff --git a/problems/003-memory-gate/editorial.en.md b/problems/003-memory-gate/editorial.en.md new file mode 100644 index 0000000..ed659b6 --- /dev/null +++ b/problems/003-memory-gate/editorial.en.md @@ -0,0 +1,26 @@ +# Editorial + +## Intuitive Approach + +Validate declarations and sum page counts by scanning every queried interval. This takes `O(NQ)` in the worst case; even early rejection does not help on large valid intervals. + +## Optimal Approach: Prefix Sums and the Next Invalid Index + +First classify every declaration independently. Build prefix sums for initial pages and effective maximum pages. Then scan from right to left to build `nextBad[i]`, the smallest invalid index at least `i`, or `N+1` if none exists. + +For `[l,r]`, if `nextBad[l]≤r`, it is the required smallest invalid index. Otherwise the interval is entirely valid: obtain both page totals with prefix differences and multiply them by `65536`. + +## Correctness Proof + +In the reverse recurrence, set `nextBad[i]=i` when declaration `i` is invalid; otherwise copy `nextBad[i+1]`. By induction, `nextBad[i]` is exactly the first invalid index not smaller than `i`. Hence `nextBad[l]≤r` holds exactly when the query contains an invalid declaration, and the reported index is minimal. If no invalid declaration exists, every effective maximum is computed by definition, and each prefix difference equals the corresponding interval sum. Multiplication by the fixed page size yields the required byte counts. Therefore both forms of output are correct. + +## Complexity + +Preprocessing takes `O(N)` and each query takes `O(1)`, for total time `O(N+Q)`. Core auxiliary space is `O(N)`; including buffered I/O, the common worst-case space bound of the seven references is `O(N+Q)`. Reading the input and writing all answers already requires `Ω(N+Q)` time, so this is asymptotically optimal. + +## Common Mistakes + +- Treating `maximum=-1` as zero instead of the policy cap `C`. +- Forgetting to cap an explicitly declared maximum at `C`. +- Reporting an arbitrary invalid declaration rather than the smallest index. +- Storing byte totals in 32-bit integers or JavaScript `number`. diff --git a/problems/003-memory-gate/editorial.zh-TW.md b/problems/003-memory-gate/editorial.zh-TW.md new file mode 100644 index 0000000..7e8b0f5 --- /dev/null +++ b/problems/003-memory-gate/editorial.zh-TW.md @@ -0,0 +1,26 @@ +# 解題說明 + +## 直覺解法 + +對每個 `[l,r]` 依序驗證宣告並累加頁數,時間最壞為 `O(NQ)`;即使提早遇到違規,合法的大區間仍會迫使它掃描到底。 + +## 最佳解法 + +先獨立判斷每個索引是否合法。建立 initial 與 effective maximum 的前綴和;再從右向左建立 `nextBad[i]`,代表大於等於 `i` 的最小違規索引,若不存在則為 `N+1`。 + +查詢時若 `nextBad[l]≤r`,它就是規格要求的最小違規索引。否則區間全合法,兩個頁數總和都以一次前綴差取得,再乘 `65536`。 + +## 正確性證明 + +反向遞推時,若 `i` 違規便令 `nextBad[i]=i`,否則沿用 `nextBad[i+1]`;歸納可知它恰為不小於 `i` 的第一個違規索引。因此 `nextBad[l]≤r` 當且僅當查詢區間有違規,且回報者索引最小。若不存在違規,每個宣告都按定義計算 effective maximum;前綴差等於區間逐項總和,乘上固定頁大小即為指定 byte 數。故兩種輸出均正確。 + +## 複雜度 + +前處理 `O(N)`,每個查詢 `O(1)`,總時間 `O(N+Q)`,核心前綴和與 `nextBad` 的輔助空間為 `O(N)`。C、C++、Go reference 串流讀寫;Rust、Python 會保留完整輸入與輸出,JavaScript、TypeScript 保留單一 Forge 輸入字串並以固定 64 KiB 分塊輸出。每筆宣告、查詢與答案的文字長度皆為常數,因此依實際 resident allocations 計算,七語言 reference 的共同最壞空間上界為 `O(N+Q)`。讀取輸入與輸出答案已有 `Ω(N+Q)` 下界,故時間漸進最佳。 + +## 常見錯誤 + +- 把 `maximum=-1` 當成零,而不是政策上限 `C`。 +- 忘記已宣告的 maximum 也要被 `C` 截斷。 +- 回報任意違規索引,而非最小索引。 +- 以 32-bit 或 JavaScript `number` 儲存 byte 總和。 diff --git a/problems/003-memory-gate/generator.py b/problems/003-memory-gate/generator.py new file mode 100644 index 0000000..002ff17 --- /dev/null +++ b/problems/003-memory-gate/generator.py @@ -0,0 +1,21 @@ +import random, sys + +if len(sys.argv) != 3: + raise SystemExit("usage: generator.py SEED INDEX") +r = random.Random((int(sys.argv[1]) << 32) ^ int(sys.argv[2])) +idx = int(sys.argv[2]) +N = r.randint(1, 5 + idx % 8) +Q = r.randint(1, 8) +C = r.randint(1, 20) +a = [] +for _ in range(N): + k = 64 if r.random() < 0.2 else 32 + ini = r.randint(0, C + 5) + mx = -1 if r.random() < 0.3 else r.randint(0, C + 8) + a.append((k, ini, mx)) +out = [f"{N} {Q} {C}"] + [f"{x} {y} {z}" for x, y, z in a] +for _ in range(Q): + l = r.randint(1, N) + rr = r.randint(l, N) + out.append(f"{l} {rr}") +print("\n".join(out)) diff --git a/problems/003-memory-gate/oracle.py b/problems/003-memory-gate/oracle.py new file mode 100644 index 0000000..6e9b4fb --- /dev/null +++ b/problems/003-memory-gate/oracle.py @@ -0,0 +1,22 @@ +import sys + +t = list(map(int, sys.stdin.buffer.read().split())) +it = iter(t) +N, Q, C = next(it), next(it), next(it) +a = [] +for _ in range(N): + a.append((next(it), next(it), next(it))) +out = [] +for _ in range(Q): + l, r = next(it) - 1, next(it) + bad = None + si = sm = 0 + for j in range(l, r): + k, ini, mx = a[j] + if k == 64 or ini > C or (mx != -1 and mx < ini): + bad = j + 1 + break + si += ini + sm += C if mx == -1 else min(C, mx) + out.append(f"REJECT {bad}" if bad is not None else f"ACCEPT {si*65536} {sm*65536}") +print("\n".join(out)) diff --git a/problems/003-memory-gate/problem.json b/problems/003-memory-gate/problem.json new file mode 100644 index 0000000..9da7edf --- /dev/null +++ b/problems/003-memory-gate/problem.json @@ -0,0 +1,146 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 3, + "slug": "memory-gate", + "title": { + "zh-TW": "64 KiB 記憶體閘門", + "en": "64 KiB Memory Gate" + }, + "difficulty": "medium", + "tags": [ + "prefix-sum", + "range-query", + "module-policy" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-01", + "kind": "adversarial", + "input": "tests/adversarial-01.in", + "output": "tests/adversarial-01.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 10000000, + "memoryLimitBytes": 536870912 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 2000000, + "memoryLimitBytes": 402653184 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 750000, + "memoryLimitBytes": 268435456 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "每次查詢掃描區間", + "en": "Scan the Interval per Query" + }, + "time": "O(NQ)", + "space": "O(1)", + "accepted": false + }, + { + "name": { + "zh-TW": "前綴和與下一個違規位置", + "en": "Prefix Sums and Next Invalid Position" + }, + "time": "O(N+Q)", + "space": "O(N) auxiliary; O(N+Q) buffered I/O", + "accepted": true + } + ] +} diff --git a/problems/003-memory-gate/solutions/c/main.c b/problems/003-memory-gate/solutions/c/main.c new file mode 100644 index 0000000..0789134 --- /dev/null +++ b/problems/003-memory-gate/solutions/c/main.c @@ -0,0 +1,43 @@ +#include +#include +#include +int main(void) { + int N, Q; + unsigned long long C; + if (scanf("%d%d%llu", &N, &Q, &C) != 3) + return 0; + uint64_t *pi = calloc(N + 1, sizeof(*pi)), *pm = calloc(N + 1, sizeof(*pm)); + unsigned char *bad = calloc(N + 2, 1); + int *next = malloc((N + 2) * sizeof(*next)); + for (int i = 1, k; i <= N; i++) { + unsigned long long ini; + long long mx; + scanf("%d%llu%lld", &k, &ini, &mx); + bad[i] = (k == 64 || ini > C || (mx >= 0 && (unsigned long long)mx < ini)); + pi[i] = pi[i - 1]; + pm[i] = pm[i - 1]; + if (!bad[i]) { + pi[i] += ini; + pm[i] += mx < 0 + ? C + : ((unsigned long long)mx < C ? (unsigned long long)mx : C); + } + } + next[N + 1] = N + 1; + for (int i = N; i >= 1; i--) + next[i] = bad[i] ? i : next[i + 1]; + while (Q--) { + int l, r; + scanf("%d%d", &l, &r); + if (next[l] <= r) + printf("REJECT %d\n", next[l]); + else + printf("ACCEPT %llu %llu\n", + (unsigned long long)((pi[r] - pi[l - 1]) * 65536ULL), + (unsigned long long)((pm[r] - pm[l - 1]) * 65536ULL)); + } + free(pi); + free(pm); + free(bad); + free(next); +} diff --git a/problems/003-memory-gate/solutions/cpp/main.cpp b/problems/003-memory-gate/solutions/cpp/main.cpp new file mode 100644 index 0000000..db684d8 --- /dev/null +++ b/problems/003-memory-gate/solutions/cpp/main.cpp @@ -0,0 +1,38 @@ +#include +#include +#include +using namespace std; +int main() { + ios::sync_with_stdio(false); + cin.tie(nullptr); + int n, q; + unsigned long long c; + if (!(cin >> n >> q >> c)) + return 0; + vector pi(n + 1), pm(n + 1); + vector bad(n + 2), nxt(n + 2); + for (int i = 1, k; i <= n; i++) { + unsigned long long x; + long long m; + cin >> k >> x >> m; + bad[i] = k == 64 || x > c || (m >= 0 && (unsigned long long)m < x); + pi[i] = pi[i - 1]; + pm[i] = pm[i - 1]; + if (!bad[i]) { + pi[i] += x; + pm[i] += m < 0 ? c : min(c, (unsigned long long)m); + } + } + nxt[n + 1] = n + 1; + for (int i = n; i; i--) + nxt[i] = bad[i] ? i : nxt[i + 1]; + while (q--) { + int l, r; + cin >> l >> r; + if (nxt[l] <= r) + cout << "REJECT " << nxt[l] << '\n'; + else + cout << "ACCEPT " << (pi[r] - pi[l - 1]) * 65536ULL << ' ' + << (pm[r] - pm[l - 1]) * 65536ULL << '\n'; + } +} diff --git a/problems/003-memory-gate/solutions/go/main.go b/problems/003-memory-gate/solutions/go/main.go new file mode 100644 index 0000000..31c188b --- /dev/null +++ b/problems/003-memory-gate/solutions/go/main.go @@ -0,0 +1,58 @@ +package main + +import ( + "bufio" + "fmt" + "os" +) + +func main() { + in := bufio.NewReader(os.Stdin) + out := bufio.NewWriter(os.Stdout) + defer out.Flush() + var n, q int + var c uint64 + if _, e := fmt.Fscan(in, &n, &q, &c); e != nil { + return + } + pi := make([]uint64, n+1) + pm := make([]uint64, n+1) + bad := make([]bool, n+2) + nxt := make([]int, n+2) + for i := 1; i <= n; i++ { + var k int + var x uint64 + var m int64 + fmt.Fscan(in, &k, &x, &m) + bad[i] = k == 64 || x > c || (m >= 0 && uint64(m) < x) + pi[i] = pi[i-1] + pm[i] = pm[i-1] + if !bad[i] { + pi[i] += x + if m < 0 { + pm[i] += c + } else if uint64(m) < c { + pm[i] += uint64(m) + } else { + pm[i] += c + } + } + } + nxt[n+1] = n + 1 + for i := n; i >= 1; i-- { + if bad[i] { + nxt[i] = i + } else { + nxt[i] = nxt[i+1] + } + } + for ; q > 0; q-- { + var l, r int + fmt.Fscan(in, &l, &r) + if nxt[l] <= r { + fmt.Fprintln(out, "REJECT", nxt[l]) + } else { + fmt.Fprintln(out, "ACCEPT", (pi[r]-pi[l-1])*65536, (pm[r]-pm[l-1])*65536) + } + } +} diff --git a/problems/003-memory-gate/solutions/javascript/main.js b/problems/003-memory-gate/solutions/javascript/main.js new file mode 100644 index 0000000..03b1d9e --- /dev/null +++ b/problems/003-memory-gate/solutions/javascript/main.js @@ -0,0 +1,50 @@ +import * as std from "std"; +/** @type {string} */ +const input = std.in.readAsString(); +let cursor = 0; +/** @returns {string} */ +function nextToken() { + while (cursor < input.length && input.charCodeAt(cursor) <= 32) cursor++; + const start = cursor; + while (cursor < input.length && input.charCodeAt(cursor) > 32) cursor++; + return input.slice(start, cursor); +} +const N = Number(nextToken()), Q = Number(nextToken()), C = BigInt(nextToken()); +const pi = /** @type {bigint[]} */ (Array(N + 1).fill(0n)), + pm = /** @type {bigint[]} */ (Array(N + 1).fill(0n)), + bad = /** @type {boolean[]} */ (Array(N + 2).fill(false)), + nxt = /** @type {number[]} */ (Array(N + 2).fill(N + 1)); +for (let i = 1; i <= N; i++) { + const k = Number(nextToken()), + x = BigInt(nextToken()), + ms = nextToken(), + m = ms === "-1" ? null : BigInt(ms); + bad[i] = k === 64 || x > C || (m !== null && m < x); + pi[i] = pi[i - 1]; + pm[i] = pm[i - 1]; + if (!bad[i]) { + pi[i] += x; + pm[i] += m === null ? C : (m < C ? m : C); + } +} +for (let i = N; i >= 1; i--) nxt[i] = bad[i] ? i : nxt[i + 1]; +let output = ""; +/** @param {string} line */ +function emit(line) { + if (output.length + line.length > 65536) { + std.out.puts(output); + output = ""; + } + output += line; +} +for (let z = 0; z < Q; z++) { + const l = Number(nextToken()), r = Number(nextToken()); + emit( + nxt[l] <= r + ? `REJECT ${nxt[l]}\n` + : `ACCEPT ${(pi[r] - pi[l - 1]) * 65536n} ${ + (pm[r] - pm[l - 1]) * 65536n + }\n`, + ); +} +if (output.length) std.out.puts(output); diff --git a/problems/003-memory-gate/solutions/python/main.py b/problems/003-memory-gate/solutions/python/main.py new file mode 100644 index 0000000..8257335 --- /dev/null +++ b/problems/003-memory-gate/solutions/python/main.py @@ -0,0 +1,28 @@ +import sys + +t = list(map(int, sys.stdin.buffer.read().split())) +it = iter(t) +N, Q, C = next(it), next(it), next(it) +pi = [0] * (N + 1) +pm = [0] * (N + 1) +bad = [False] * (N + 2) +for i in range(1, N + 1): + k, x, m = next(it), next(it), next(it) + bad[i] = k == 64 or x > C or (m != -1 and m < x) + pi[i] = pi[i - 1] + pm[i] = pm[i - 1] + if not bad[i]: + pi[i] += x + pm[i] += C if m == -1 else min(C, m) +nxt = [N + 1] * (N + 2) +for i in range(N, 0, -1): + nxt[i] = i if bad[i] else nxt[i + 1] +out = [] +for _ in range(Q): + l, r = next(it), next(it) + out.append( + f"REJECT {nxt[l]}" + if nxt[l] <= r + else f"ACCEPT {(pi[r]-pi[l-1])*65536} {(pm[r]-pm[l-1])*65536}" + ) +print("\n".join(out)) diff --git a/problems/003-memory-gate/solutions/rust/main.rs b/problems/003-memory-gate/solutions/rust/main.rs new file mode 100644 index 0000000..ea7174e --- /dev/null +++ b/problems/003-memory-gate/solutions/rust/main.rs @@ -0,0 +1,43 @@ +use std::io::{self, Read}; +fn main() { + let mut s = String::new(); + io::stdin().read_to_string(&mut s).unwrap(); + let mut it = s.split_whitespace(); + let n: usize = it.next().unwrap().parse().unwrap(); + let q: usize = it.next().unwrap().parse().unwrap(); + let c: u64 = it.next().unwrap().parse().unwrap(); + let mut pi = vec![0u64; n + 1]; + let mut pm = vec![0u64; n + 1]; + let mut bad = vec![false; n + 2]; + for i in 1..=n { + let k: u32 = it.next().unwrap().parse().unwrap(); + let x: u64 = it.next().unwrap().parse().unwrap(); + let m: i64 = it.next().unwrap().parse().unwrap(); + bad[i] = k == 64 || x > c || (m >= 0 && (m as u64) < x); + pi[i] = pi[i - 1]; + pm[i] = pm[i - 1]; + if !bad[i] { + pi[i] += x; + pm[i] += if m < 0 { c } else { c.min(m as u64) }; + } + } + let mut nxt = vec![n + 1; n + 2]; + for i in (1..=n).rev() { + nxt[i] = if bad[i] { i } else { nxt[i + 1] }; + } + let mut out = String::new(); + for _ in 0..q { + let l: usize = it.next().unwrap().parse().unwrap(); + let r: usize = it.next().unwrap().parse().unwrap(); + if nxt[l] <= r { + out += &format!("REJECT {}\n", nxt[l]); + } else { + out += &format!( + "ACCEPT {} {}\n", + (pi[r] - pi[l - 1]) * 65536, + (pm[r] - pm[l - 1]) * 65536 + ); + } + } + print!("{}", out); +} diff --git a/problems/003-memory-gate/solutions/typescript/main.ts b/problems/003-memory-gate/solutions/typescript/main.ts new file mode 100644 index 0000000..a673dc6 --- /dev/null +++ b/problems/003-memory-gate/solutions/typescript/main.ts @@ -0,0 +1,47 @@ +import * as std from "std"; +const input: string = std.in.readAsString(); +let cursor = 0; +function nextToken(): string { + while (cursor < input.length && input.charCodeAt(cursor) <= 32) cursor++; + const start = cursor; + while (cursor < input.length && input.charCodeAt(cursor) > 32) cursor++; + return input.slice(start, cursor); +} +const N = Number(nextToken()), Q = Number(nextToken()), C = BigInt(nextToken()); +const pi: bigint[] = Array(N + 1).fill(0n), + pm: bigint[] = Array(N + 1).fill(0n), + bad: boolean[] = Array(N + 2).fill(false), + nxt: number[] = Array(N + 2).fill(N + 1); +for (let i = 1; i <= N; i++) { + const k = Number(nextToken()), + x = BigInt(nextToken()), + ms = nextToken(), + m: bigint | null = ms === "-1" ? null : BigInt(ms); + bad[i] = k === 64 || x > C || (m !== null && m < x); + pi[i] = pi[i - 1]; + pm[i] = pm[i - 1]; + if (!bad[i]) { + pi[i] += x; + pm[i] += m === null ? C : (m < C ? m : C); + } +} +for (let i = N; i >= 1; i--) nxt[i] = bad[i] ? i : nxt[i + 1]; +let output = ""; +function emit(line: string): void { + if (output.length + line.length > 65536) { + std.out.puts(output); + output = ""; + } + output += line; +} +for (let z = 0; z < Q; z++) { + const l = Number(nextToken()), r = Number(nextToken()); + emit( + nxt[l] <= r + ? `REJECT ${nxt[l]}\n` + : `ACCEPT ${(pi[r] - pi[l - 1]) * 65536n} ${ + (pm[r] - pm[l - 1]) * 65536n + }\n`, + ); +} +if (output.length) std.out.puts(output); diff --git a/problems/003-memory-gate/statement.en.md b/problems/003-memory-gate/statement.en.md new file mode 100644 index 0000000..035f067 --- /dev/null +++ b/problems/003-memory-gate/statement.en.md @@ -0,0 +1,115 @@ +# 64 KiB Memory Gate + +Before a WASM OJ loads a submitted module, it must inspect every linear-memory declaration. The in-browser runtime can accept only controlled 32-bit memories. A module that requests unsupported Memory64, or whose initial capacity already exceeds policy, must be rejected before allocation is attempted. + +A module declares one or more linear memories indexed from `1` through `N`, and every page is exactly `65536` bytes. Policy allows at most `C` pages per memory and does not support Memory64. Each declaration is written as `kind initial maximum`, where `kind` is `32` or `64`. `maximum=-1` means that no maximum was declared; otherwise it is the declared page count. + +A declaration is invalid if any of the following holds: + +1. `kind=64`; +2. a maximum is present and `maximum < initial`; +3. `initial > C`. + +A declaration that passes validation must also be rewritten into a policy-bounded form. Its rewritten maximum is `C` when no maximum was declared, and `min(maximum,C)` otherwise. + +The system performs policy checks on several intervals of declarations. Each query gives `[l,r]`. If the interval contains an invalid declaration, output `REJECT i`, where `i` must be the smallest invalid index in the interval. Otherwise output `ACCEPT initialBytes maximumBytes`: the sums of initial and rewritten-maximum page counts in the interval, respectively, each multiplied by `65536`. + +## Input + +The first line contains `N Q C`. The next `N` lines contain the declarations. The final `Q` lines each contain `l r`. + +## Output + +Output one line per query according to the rules above. Queries are independent, indices are 1-based, and `l≤r`. + +## Constraints + +- `1 ≤ N,Q ≤ 200000` +- `1 ≤ C ≤ 10^12` +- `kind ∈ {32,64}` +- `0 ≤ initial ≤ 10^12` +- `maximum=-1` or `0 ≤ maximum ≤ 10^12` +- Across all valid declarations, the sum of rewritten maximum page counts is at most `137329101562500`; consequently every output byte count is at most `9×10^18`. + +The full constraints rule out scanning an entire interval for each query. + +## Examples + + + +### Example One + +Input: + +```text +5 5 10 +32 2 -1 +32 4 8 +64 1 2 +32 11 -1 +32 3 2 +1 2 +2 2 +1 3 +3 5 +4 5 +``` + +Output: + +```text +ACCEPT 393216 1179648 +ACCEPT 262144 524288 +REJECT 3 +REJECT 3 +REJECT 4 +``` + +### Example Two + +Input: + +```text +3 3 5 +32 0 0 +32 5 -1 +32 2 100 +1 1 +1 3 +2 3 +``` + +Output: + +```text +ACCEPT 0 0 +ACCEPT 458752 655360 +ACCEPT 458752 655360 +``` + +### Example Three + +Input: + +```text +4 4 7 +32 3 3 +32 6 5 +32 8 20 +64 0 -1 +1 1 +1 2 +2 4 +3 4 +``` + +Output: + +```text +ACCEPT 196608 196608 +REJECT 2 +REJECT 2 +REJECT 3 +``` + + diff --git a/problems/003-memory-gate/statement.zh-TW.md b/problems/003-memory-gate/statement.zh-TW.md new file mode 100644 index 0000000..a690016 --- /dev/null +++ b/problems/003-memory-gate/statement.zh-TW.md @@ -0,0 +1,115 @@ +# 64 KiB 記憶體閘門 + +在 WASM OJ 載入使用者模組以前,我們必須先檢查每一份 linear memory 宣告。瀏覽器內的執行環境只能接受受控的 32-bit memory;若模組要求不支援的 Memory64,或初始容量已超過政策限制,就不能等到實際配置時才處理。 + +一個模組依索引 `1..N` 宣告多個 linear memory,每頁恰為 `65536` bytes。政策規定每個 memory 至多 `C` 頁,且不支援 Memory64。每個宣告寫成 `kind initial maximum`:`kind` 是 `32` 或 `64`;`maximum=-1` 表示未宣告 maximum,否則是宣告頁數。 + +單一宣告在下列任一情形違規: + +1. `kind=64`; +2. 有 maximum 且 `maximum < initial`; +3. `initial > C`。 + +通過檢查的宣告還要被重寫成受政策約束的形式:未宣告 maximum 時,重寫後 maximum 為 `C`;有宣告時則為 `min(maximum,C)`。 + +系統會針對多個宣告區間進行政策檢查。每個查詢給定 `[l,r]`;若區間含違規宣告,輸出 `REJECT i`,其中 `i` 必須是區間內最小的違規索引。否則輸出 `ACCEPT initialBytes maximumBytes`,兩者分別是區間內 initial 與重寫後 maximum 的總頁數乘以 `65536`。 + +## 輸入 + +第一行 `N Q C`;接下來 `N` 行為宣告;最後 `Q` 行各為 `l r`。 + +## 輸出 + +依上述規則每個查詢輸出一行。所有查詢互相獨立,索引為 1-based,且 `l≤r`。 + +## 限制 + +- `1 ≤ N,Q ≤ 200000` +- `1 ≤ C ≤ 10^12` +- `kind ∈ {32,64}` +- `0 ≤ initial ≤ 10^12` +- `maximum=-1` 或 `0 ≤ maximum ≤ 10^12` +- 所有合法宣告的重寫後 maximum 總頁數不超過 `137329101562500`,因此任何輸出 byte 數不超過 `9×10^18` + +完整限制排除每次掃描整段區間。 + +## 範例 + + + +### 範例一 + +輸入: + +```text +5 5 10 +32 2 -1 +32 4 8 +64 1 2 +32 11 -1 +32 3 2 +1 2 +2 2 +1 3 +3 5 +4 5 +``` + +輸出: + +```text +ACCEPT 393216 1179648 +ACCEPT 262144 524288 +REJECT 3 +REJECT 3 +REJECT 4 +``` + +### 範例二 + +輸入: + +```text +3 3 5 +32 0 0 +32 5 -1 +32 2 100 +1 1 +1 3 +2 3 +``` + +輸出: + +```text +ACCEPT 0 0 +ACCEPT 458752 655360 +ACCEPT 458752 655360 +``` + +### 範例三 + +輸入: + +```text +4 4 7 +32 3 3 +32 6 5 +32 8 20 +64 0 -1 +1 1 +1 2 +2 4 +3 4 +``` + +輸出: + +```text +ACCEPT 196608 196608 +REJECT 2 +REJECT 2 +REJECT 3 +``` + + diff --git a/problems/003-memory-gate/tests/adversarial-01.in b/problems/003-memory-gate/tests/adversarial-01.in new file mode 100644 index 0000000..48d24eb --- /dev/null +++ b/problems/003-memory-gate/tests/adversarial-01.in @@ -0,0 +1,14 @@ +6 7 7 +32 0 -1 +64 0 0 +32 8 -1 +32 5 4 +32 7 100 +32 3 3 +1 1 +1 6 +2 6 +3 6 +4 6 +5 6 +6 6 diff --git a/problems/003-memory-gate/tests/adversarial-01.out b/problems/003-memory-gate/tests/adversarial-01.out new file mode 100644 index 0000000..e9ac63e --- /dev/null +++ b/problems/003-memory-gate/tests/adversarial-01.out @@ -0,0 +1,7 @@ +ACCEPT 0 458752 +REJECT 2 +REJECT 2 +REJECT 3 +REJECT 4 +ACCEPT 655360 655360 +ACCEPT 196608 196608 diff --git a/problems/003-memory-gate/tests/sample-01.in b/problems/003-memory-gate/tests/sample-01.in new file mode 100644 index 0000000..d29f8de --- /dev/null +++ b/problems/003-memory-gate/tests/sample-01.in @@ -0,0 +1,11 @@ +5 5 10 +32 2 -1 +32 4 8 +64 1 2 +32 11 -1 +32 3 2 +1 2 +2 2 +1 3 +3 5 +4 5 diff --git a/problems/003-memory-gate/tests/sample-01.out b/problems/003-memory-gate/tests/sample-01.out new file mode 100644 index 0000000..d3370a7 --- /dev/null +++ b/problems/003-memory-gate/tests/sample-01.out @@ -0,0 +1,5 @@ +ACCEPT 393216 1179648 +ACCEPT 262144 524288 +REJECT 3 +REJECT 3 +REJECT 4 diff --git a/problems/003-memory-gate/tests/sample-02.in b/problems/003-memory-gate/tests/sample-02.in new file mode 100644 index 0000000..be4448e --- /dev/null +++ b/problems/003-memory-gate/tests/sample-02.in @@ -0,0 +1,7 @@ +3 3 5 +32 0 0 +32 5 -1 +32 2 100 +1 1 +1 3 +2 3 diff --git a/problems/003-memory-gate/tests/sample-02.out b/problems/003-memory-gate/tests/sample-02.out new file mode 100644 index 0000000..110a00b --- /dev/null +++ b/problems/003-memory-gate/tests/sample-02.out @@ -0,0 +1,3 @@ +ACCEPT 0 0 +ACCEPT 458752 655360 +ACCEPT 458752 655360 diff --git a/problems/003-memory-gate/tests/sample-03.in b/problems/003-memory-gate/tests/sample-03.in new file mode 100644 index 0000000..37cc8cb --- /dev/null +++ b/problems/003-memory-gate/tests/sample-03.in @@ -0,0 +1,9 @@ +4 4 7 +32 3 3 +32 6 5 +32 8 20 +64 0 -1 +1 1 +1 2 +2 4 +3 4 diff --git a/problems/003-memory-gate/tests/sample-03.out b/problems/003-memory-gate/tests/sample-03.out new file mode 100644 index 0000000..ccb3494 --- /dev/null +++ b/problems/003-memory-gate/tests/sample-03.out @@ -0,0 +1,4 @@ +ACCEPT 196608 196608 +REJECT 2 +REJECT 2 +REJECT 3 diff --git a/problems/003-memory-gate/validator.py b/problems/003-memory-gate/validator.py new file mode 100644 index 0000000..9300105 --- /dev/null +++ b/problems/003-memory-gate/validator.py @@ -0,0 +1,56 @@ +import re, sys + + +def fail(): + raise SystemExit(1) + + +try: + t = sys.stdin.buffer.read().decode("utf-8").split() + p = 0 + + def tok(): + global p + if p >= len(t): + fail() + x = t[p] + p += 1 + return x + + def u(a, b): + x = tok() + if re.fullmatch(r"0|[1-9][0-9]*", x) is None: + fail() + v = int(x) + if not a <= v <= b: + fail() + return v + + N, Q, C = u(1, 200000), u(1, 200000), u(1, 10**12) + total = 0 + for _ in range(N): + k = u(32, 64) + if k not in (32, 64): + fail() + ini = u(0, 10**12) + m = tok() + if m == "-1": + mx = -1 + elif re.fullmatch(r"0|[1-9][0-9]*", m): + mx = int(m) + else: + fail() + if mx > 10**12: + fail() + if k == 32 and ini <= C and (mx == -1 or mx >= ini): + total += C if mx == -1 else min(C, mx) + if total > 137329101562500: + fail() + for _ in range(Q): + l, r = u(1, N), u(1, N) + if l > r: + fail() + if p != len(t): + fail() +except (UnicodeDecodeError, ValueError, OverflowError): + fail() diff --git a/problems/004-shared-output-pool/editorial.en.md b/problems/004-shared-output-pool/editorial.en.md new file mode 100644 index 0000000..fc8f1e1 --- /dev/null +++ b/problems/004-shared-output-pool/editorial.en.md @@ -0,0 +1,26 @@ +# Editorial + +## Intuitive Approach + +For every budget, restart at the first event, subtract sizes, and maintain three counters. This is `O(NQ)`. Prefix sums plus a binary search for the first overflowing event improve it to `O(N+Q log N)`. + +## Optimal Approach: Monotone Two Pointers + +Because budgets are nondecreasing, the number of completely retained events never decreases. Maintain an index `i`, the total `used` by the first `i` complete events, and their three per-stream totals. For budget `B`, repeatedly include the next event while `used+bytes[i]≤B`. Across all queries, each event is included at most once. + +If `i=N`, output failure `0`. Otherwise event `i+1` fails; add `B-used` only to that event's stream in the temporary answer. Do not commit this partial amount to the shared state, because the event has not yet been retained in full. + +## Correctness Proof + +After processing a budget, the loop condition guarantees that the first `i` events all fit completely. If a next event exists, `used+size>B`, so `i+1` is exactly the first failure. The remaining capacity `B-used` is nonnegative and smaller than that event, and the specification retains exactly that many bytes in its stream. Monotone budgets ensure that every event previously included in full remains valid for later queries, so the pointer never needs to move backward. Partial bytes are not committed and therefore cannot contaminate the next query. By induction over queries, every answer is correct. + +## Complexity + +The event pointer advances at most `N` times in total, and each query does `O(1)` additional work, so total time is `O(N+Q)`. Events precede budgets in the input and must be retained for the later scan, giving `O(N)` core auxiliary space. Including buffered input/output, the common worst-case space bound is `O(N+Q)`. Input and output sizes give an `Ω(N+Q)` time lower bound. + +## Common Mistakes + +- Treating a write as indivisible and omitting the failed event's retained prefix. +- Reporting an event as failed when the budget lands exactly at its end; the next event must be considered instead. +- Committing the partial retained amount, which makes repeated-budget answers grow. +- Giving each stream a separate budget instead of one shared budget. diff --git a/problems/004-shared-output-pool/editorial.zh-TW.md b/problems/004-shared-output-pool/editorial.zh-TW.md new file mode 100644 index 0000000..341e0d0 --- /dev/null +++ b/problems/004-shared-output-pool/editorial.zh-TW.md @@ -0,0 +1,26 @@ +# 解題說明 + +## 直覺解法 + +每個 budget 都從事件一開始扣除並分流計數,最壞 `O(NQ)`。建立總量與三流前綴和後,可對每個 budget 二分第一個超出的前綴,降至 `O(N+Q log N)`。 + +## 最佳解法:單調雙指標 + +budget 非遞減,因此「能完整保留的 event 數」也不會減少。維護指標 `i`、前 `i` 個完整 event 的總量 `used`,以及三流完整保留量。處理 budget `B` 時,不斷完整納入滿足 `used+bytes[i]≤B` 的下一 event;每個 event 全程至多被納入一次。 + +若最後 `i=N`,輸出 failure `0`。否則第 `i+1` 個 event 失敗,並在它所屬流的暫時答案上加 `B-used`;這個部分值不可寫回共同狀態,因為 event 尚未被完整納入。 + +## 正確性證明 + +處理一個 budget 後,while 條件保證前 `i` 個 event 全可完整保留,而若仍有下一 event,`used+size>B`,所以 `i+1` 正是第一次失敗。剩餘容量 `B-used` 非負且小於該 event 大小,依規格恰好全部部分保留到其流。budget 單調使先前完整納入的 event 對後續查詢仍完整合法,故不需回退;未完成 event 的部分量未改動狀態,也不會污染下個查詢。依查詢順序歸納,所有答案正確。 + +## 複雜度 + +事件指標總共前進 `N` 次,每個查詢做 `O(1)` 額外工作,總時間 `O(N+Q)`。事件先於 budget 輸入,必須保留 stream 與 byte 數供後續掃描,所以核心輔助空間為 `O(N)`。C、C++、Go reference 串流讀寫;Rust、Python 保留完整輸入與輸出,JavaScript、TypeScript 保留單一 Forge 輸入字串並以固定 64 KiB 分塊輸出。每筆事件、budget 與答案皆只有常數個定長 token,故依實際 resident allocations 計算,七語言 reference 的共同最壞空間上界為 `O(N+Q)`;讀寫量亦給出 `Ω(N+Q)` 時間下界。 + +## 常見錯誤 + +- 把 write 當成不可分割,漏掉失敗 event 的部分內容。 +- budget 剛好等於 event 結尾時,錯誤地回報該 event 失敗;此時應繼續看下一個。 +- 將部分保留量寫入持久計數,導致重複 budget 答案變大。 +- 忽略三個流共用同一 budget。 diff --git a/problems/004-shared-output-pool/generator.py b/problems/004-shared-output-pool/generator.py new file mode 100644 index 0000000..01620e8 --- /dev/null +++ b/problems/004-shared-output-pool/generator.py @@ -0,0 +1,12 @@ +import random, sys + +if len(sys.argv) != 3: + raise SystemExit("usage: generator.py SEED INDEX") +r = random.Random((int(sys.argv[1]) << 32) ^ int(sys.argv[2])) +idx = int(sys.argv[2]) +N = r.randint(1, 5 + idx % 10) +Q = r.randint(1, 10) +a = [(r.choice("OEF"), r.randint(1, 20)) for _ in range(N)] +total = sum(x for _, x in a) +b = sorted(r.randint(0, total + 15) for _ in range(Q)) +print("\n".join([f"{N} {Q}"] + [f"{s} {x}" for s, x in a] + list(map(str, b)))) diff --git a/problems/004-shared-output-pool/oracle.py b/problems/004-shared-output-pool/oracle.py new file mode 100644 index 0000000..01efa9a --- /dev/null +++ b/problems/004-shared-output-pool/oracle.py @@ -0,0 +1,21 @@ +import sys + +t = sys.stdin.buffer.read().split() +it = iter(t) +N, Q = int(next(it)), int(next(it)) +a = [(next(it).decode(), int(next(it))) for _ in range(N)] +out = [] +for _ in range(Q): + b = int(next(it)) + used = 0 + c = {"O": 0, "E": 0, "F": 0} + fail = 0 + for i, (s, x) in enumerate(a, 1): + take = min(x, b - used) + c[s] += take + used += take + if take < x: + fail = i + break + out.append(f"{fail} {c['O']} {c['E']} {c['F']}") +print("\n".join(out)) diff --git a/problems/004-shared-output-pool/problem.json b/problems/004-shared-output-pool/problem.json new file mode 100644 index 0000000..1f3fa16 --- /dev/null +++ b/problems/004-shared-output-pool/problem.json @@ -0,0 +1,155 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 4, + "slug": "shared-output-pool", + "title": { + "zh-TW": "三流共用輸出池", + "en": "Three-Stream Shared Output Pool" + }, + "difficulty": "medium", + "tags": [ + "two-pointers", + "prefix-sum", + "resource-quota" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-01", + "kind": "adversarial", + "input": "tests/adversarial-01.in", + "output": "tests/adversarial-01.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 9500000, + "memoryLimitBytes": 536870912 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 1500000, + "memoryLimitBytes": 402653184 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 700000, + "memoryLimitBytes": 268435456 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "每個 budget 重播事件", + "en": "Replay Events for Every Budget" + }, + "time": "O(NQ)", + "space": "O(N)", + "accepted": false + }, + { + "name": { + "zh-TW": "前綴和與逐查詢二分", + "en": "Prefix Sums and Per-Query Binary Search" + }, + "time": "O(N+Q log N)", + "space": "O(N)", + "accepted": true + }, + { + "name": { + "zh-TW": "利用 budget 單調性的雙指標", + "en": "Two Pointers Using Monotone Budgets" + }, + "time": "O(N+Q)", + "space": "O(N) auxiliary; O(N+Q) buffered I/O", + "accepted": true + } + ] +} diff --git a/problems/004-shared-output-pool/solutions/c/main.c b/problems/004-shared-output-pool/solutions/c/main.c new file mode 100644 index 0000000..0e95157 --- /dev/null +++ b/problems/004-shared-output-pool/solutions/c/main.c @@ -0,0 +1,40 @@ +#include +#include +#include +int main(void) { + int n, q; + if (scanf("%d%d", &n, &q) != 2) + return 0; + char *s = malloc((size_t)n); + uint64_t *a = malloc((size_t)n * sizeof(*a)); + for (int i = 0; i < n; i++) { + char x[2]; + unsigned long long v; + scanf("%1s%llu", x, &v); + s[i] = x[0]; + a[i] = v; + } + int i = 0; + uint64_t used = 0, c[3] = {0}; + while (q--) { + unsigned long long b; + scanf("%llu", &b); + while (i < n && a[i] <= b - used) { + used += a[i]; + int k = s[i] == 'O' ? 0 : s[i] == 'E' ? 1 : 2; + c[k] += a[i]; + i++; + } + uint64_t d[3] = {c[0], c[1], c[2]}; + int fail = 0; + if (i < n) { + fail = i + 1; + int k = s[i] == 'O' ? 0 : s[i] == 'E' ? 1 : 2; + d[k] += b - used; + } + printf("%d %llu %llu %llu\n", fail, (unsigned long long)d[0], + (unsigned long long)d[1], (unsigned long long)d[2]); + } + free(s); + free(a); +} diff --git a/problems/004-shared-output-pool/solutions/cpp/main.cpp b/problems/004-shared-output-pool/solutions/cpp/main.cpp new file mode 100644 index 0000000..f8d9ede --- /dev/null +++ b/problems/004-shared-output-pool/solutions/cpp/main.cpp @@ -0,0 +1,37 @@ +#include +#include +#include +#include +#include +using namespace std; +int main() { + ios::sync_with_stdio(false); + cin.tie(nullptr); + int n, q; + if (!(cin >> n >> q)) + return 0; + vector s(n); + vector a(n); + for (int i = 0; i < n; i++) + cin >> s[i] >> a[i]; + int i = 0; + uint64_t used = 0; + array c{}; + while (q--) { + uint64_t b; + cin >> b; + while (i < n && a[i] <= b - used) { + used += a[i]; + int k = s[i] == 'O' ? 0 : s[i] == 'E' ? 1 : 2; + c[k] += a[i++]; + } + auto d = c; + int fail = 0; + if (i < n) { + fail = i + 1; + int k = s[i] == 'O' ? 0 : s[i] == 'E' ? 1 : 2; + d[k] += b - used; + } + cout << fail << ' ' << d[0] << ' ' << d[1] << ' ' << d[2] << '\n'; + } +} diff --git a/problems/004-shared-output-pool/solutions/go/main.go b/problems/004-shared-output-pool/solutions/go/main.go new file mode 100644 index 0000000..d608372 --- /dev/null +++ b/problems/004-shared-output-pool/solutions/go/main.go @@ -0,0 +1,53 @@ +package main + +import ( + "bufio" + "fmt" + "os" +) + +func main() { + in := bufio.NewReader(os.Stdin) + out := bufio.NewWriter(os.Stdout) + defer out.Flush() + var n, q int + if _, e := fmt.Fscan(in, &n, &q); e != nil { + return + } + s := make([]string, n) + a := make([]uint64, n) + for j := 0; j < n; j++ { + fmt.Fscan(in, &s[j], &a[j]) + } + i := 0 + var used uint64 + c := [3]uint64{} + for ; q > 0; q-- { + var b uint64 + fmt.Fscan(in, &b) + for i < n && a[i] <= b-used { + used += a[i] + k := 2 + if s[i] == "O" { + k = 0 + } else if s[i] == "E" { + k = 1 + } + c[k] += a[i] + i++ + } + d := c + fail := 0 + if i < n { + fail = i + 1 + k := 2 + if s[i] == "O" { + k = 0 + } else if s[i] == "E" { + k = 1 + } + d[k] += b - used + } + fmt.Fprintln(out, fail, d[0], d[1], d[2]) + } +} diff --git a/problems/004-shared-output-pool/solutions/javascript/main.js b/problems/004-shared-output-pool/solutions/javascript/main.js new file mode 100644 index 0000000..b729f41 --- /dev/null +++ b/problems/004-shared-output-pool/solutions/javascript/main.js @@ -0,0 +1,51 @@ +import * as std from "std"; +/** @type {string} */ +const input = std.in.readAsString(); +let cursor = 0; +/** @returns {string} */ +function nextToken() { + while (cursor < input.length && input.charCodeAt(cursor) <= 32) cursor++; + const start = cursor; + while (cursor < input.length && input.charCodeAt(cursor) > 32) cursor++; + return input.slice(start, cursor); +} +const N = Number(nextToken()), + Q = Number(nextToken()), + s = /** @type {string[]} */ ([]), + a = /** @type {bigint[]} */ ([]); +for (let z = 0; z < N; z++) { + s.push(nextToken()); + a.push(BigInt(nextToken())); +} +let i = 0, used = 0n; +const c = /** @type {bigint[]} */ ([0n, 0n, 0n]); +/** + * @param {string} x + * @returns {number} + */ +const key = (x) => x === "O" ? 0 : x === "E" ? 1 : 2; +let output = ""; +/** @param {string} line */ +function emit(line) { + if (output.length + line.length > 65536) { + std.out.puts(output); + output = ""; + } + output += line; +} +for (let z = 0; z < Q; z++) { + const b = BigInt(nextToken()); + while (i < N && a[i] <= b - used) { + used += a[i]; + c[key(s[i])] += a[i]; + i++; + } + const d = /** @type {bigint[]} */ ([...c]); + let fail = 0; + if (i < N) { + fail = i + 1; + d[key(s[i])] += b - used; + } + emit(`${fail} ${d[0]} ${d[1]} ${d[2]}\n`); +} +if (output.length) std.out.puts(output); diff --git a/problems/004-shared-output-pool/solutions/python/main.py b/problems/004-shared-output-pool/solutions/python/main.py new file mode 100644 index 0000000..bdd9f03 --- /dev/null +++ b/problems/004-shared-output-pool/solutions/python/main.py @@ -0,0 +1,24 @@ +import sys + +t = sys.stdin.buffer.read().split() +it = iter(t) +N, Q = int(next(it)), int(next(it)) +a = [(next(it), int(next(it))) for _ in range(N)] +i = used = 0 +c = {b"O": 0, b"E": 0, b"F": 0} +out = [] +for _ in range(Q): + b = int(next(it)) + while i < N and used + a[i][1] <= b: + s, x = a[i] + used += x + c[s] += x + i += 1 + d = c.copy() + fail = 0 + if i < N: + s, x = a[i] + d[s] += b - used + fail = i + 1 + out.append(f"{fail} {d[b'O']} {d[b'E']} {d[b'F']}") +print("\n".join(out)) diff --git a/problems/004-shared-output-pool/solutions/rust/main.rs b/problems/004-shared-output-pool/solutions/rust/main.rs new file mode 100644 index 0000000..1bbc83b --- /dev/null +++ b/problems/004-shared-output-pool/solutions/rust/main.rs @@ -0,0 +1,47 @@ +use std::io::{self, Read}; +fn main() { + let mut x = String::new(); + io::stdin().read_to_string(&mut x).unwrap(); + let mut t = x.split_whitespace(); + let n: usize = t.next().unwrap().parse().unwrap(); + let q: usize = t.next().unwrap().parse().unwrap(); + let mut s = Vec::with_capacity(n); + let mut a = Vec::with_capacity(n); + for _ in 0..n { + s.push(t.next().unwrap().as_bytes()[0]); + a.push(t.next().unwrap().parse::().unwrap()); + } + let (mut i, mut used, mut c) = (0usize, 0u64, [0u64; 3]); + let mut out = String::new(); + for _ in 0..q { + let b: u64 = t.next().unwrap().parse().unwrap(); + while i < n && a[i] <= b - used { + used += a[i]; + let k = if s[i] == b'O' { + 0 + } else if s[i] == b'E' { + 1 + } else { + 2 + }; + c[k] += a[i]; + i += 1; + } + let mut d = c; + let fail = if i == n { + 0 + } else { + let k = if s[i] == b'O' { + 0 + } else if s[i] == b'E' { + 1 + } else { + 2 + }; + d[k] += b - used; + i + 1 + }; + out += &format!("{} {} {} {}\n", fail, d[0], d[1], d[2]); + } + print!("{}", out); +} diff --git a/problems/004-shared-output-pool/solutions/typescript/main.ts b/problems/004-shared-output-pool/solutions/typescript/main.ts new file mode 100644 index 0000000..1909047 --- /dev/null +++ b/problems/004-shared-output-pool/solutions/typescript/main.ts @@ -0,0 +1,44 @@ +import * as std from "std"; +const input: string = std.in.readAsString(); +let cursor = 0; +function nextToken(): string { + while (cursor < input.length && input.charCodeAt(cursor) <= 32) cursor++; + const start = cursor; + while (cursor < input.length && input.charCodeAt(cursor) > 32) cursor++; + return input.slice(start, cursor); +} +const N = Number(nextToken()), + Q = Number(nextToken()), + s: string[] = [], + a: bigint[] = []; +for (let z = 0; z < N; z++) { + s.push(nextToken()); + a.push(BigInt(nextToken())); +} +let i = 0, used = 0n; +const c: bigint[] = [0n, 0n, 0n], + key = (x: string): number => x === "O" ? 0 : x === "E" ? 1 : 2; +let output = ""; +function emit(line: string): void { + if (output.length + line.length > 65536) { + std.out.puts(output); + output = ""; + } + output += line; +} +for (let z = 0; z < Q; z++) { + const b = BigInt(nextToken()); + while (i < N && a[i] <= b - used) { + used += a[i]; + c[key(s[i])] += a[i]; + i++; + } + const d: bigint[] = [...c]; + let fail = 0; + if (i < N) { + fail = i + 1; + d[key(s[i])] += b - used; + } + emit(`${fail} ${d[0]} ${d[1]} ${d[2]}\n`); +} +if (output.length) std.out.puts(output); diff --git a/problems/004-shared-output-pool/statement.en.md b/problems/004-shared-output-pool/statement.en.md new file mode 100644 index 0000000..6d0c5d7 --- /dev/null +++ b/problems/004-shared-output-pool/statement.en.md @@ -0,0 +1,114 @@ +# Three-Stream Shared Output Pool + +While designing output limits for a WASM OJ, we found that stdout, stderr, and output files cannot have unrelated allowances. Otherwise, a program could use all three streams at once and multiply the intended total output. The three destinations must therefore share one byte budget and consume it in the order in which writes actually occur. + +One execution produces `N` write events in chronological order. Each event writes to `O` (stdout), `E` (stderr), or `F` (the output-file collection). To study the effect of different limits, the system independently replays the same events under several budgets; the output pool starts empty for every query. + +A write may retain only its beginning. If only `x` bytes remain in the pool, retain the first `x` bytes of that event, fill the pool, and record this event as the first failure. Once the output pool is full, no later event is processed. + +The input guarantees that query budgets are nondecreasing. For each budget, output the first event that cannot be retained in full and the number of bytes actually retained for each of the three streams. + +## Input + +The first line contains `N Q`. The next `N` lines each contain `stream bytes`, where `stream` is `O`, `E`, or `F`. The final `Q` lines each contain one `budget`, in nondecreasing order. + +## Output + +For every query, output: + +```text +failure stdoutBytes stderrBytes fileBytes +``` + +`failure` is the 1-based index of the first event that cannot be retained completely. If every event is retained completely, `failure=0`. For a zero budget, the first positive-length event fails immediately and all three counts are zero. Repeated budgets are valid and produce identical answers. + +## Constraints + +- `1 ≤ N,Q ≤ 200000` +- `1 ≤ bytes ≤ 10^12` +- `0 ≤ budget ≤ 9×10^18` +- The sum of bytes over all events is at most `9×10^18`. +- The budget sequence is nondecreasing. + +The full constraints rule out replaying all events for every budget. + +## Examples + + + +### Example One + +Input: + +```text +4 6 +O 5 +E 3 +F 10 +O 4 +0 +5 +7 +8 +20 +30 +``` + +Output: + +```text +1 0 0 0 +2 5 0 0 +2 5 2 0 +3 5 3 0 +4 7 3 10 +0 9 3 10 +``` + +### Example Two + +Input: + +```text +1 3 +F 7 +6 +7 +8 +``` + +Output: + +```text +1 0 0 6 +0 0 0 7 +0 0 0 7 +``` + +### Example Three + +Input: + +```text +3 5 +E 2 +E 2 +O 1 +1 +1 +3 +4 +5 +``` + +Output: + +```text +1 0 1 0 +1 0 1 0 +2 0 3 0 +3 0 4 0 +0 1 4 0 +``` + + diff --git a/problems/004-shared-output-pool/statement.zh-TW.md b/problems/004-shared-output-pool/statement.zh-TW.md new file mode 100644 index 0000000..2e30bc3 --- /dev/null +++ b/problems/004-shared-output-pool/statement.zh-TW.md @@ -0,0 +1,114 @@ +# 三流共用輸出池 + +在設計 WASM OJ 的輸出限制時,我們發現 stdout、stderr 與輸出檔案不能各自擁有互不相關的額度。否則程式可以同時使用三個流,把總輸出量放大到單一限制的數倍。因此,三種輸出必須依實際發生順序,共用同一個 byte budget。 + +一次執行會按時間順序產生 `N` 次 write event。每個事件寫入 `O`(stdout)、`E`(stderr)或 `F`(輸出檔案集合)之一。為了分析不同限制的效果,系統會以多個 budget 獨立重播相同事件;每次查詢的輸出池都從空狀態開始。 + +一次 write 可以只保留前半段。若池中只剩 `x` bytes,就保留該 event 的前 `x` bytes、將池填滿,並把這個 event 記為第一次失敗。輸出池一旦填滿,就不再處理任何後續事件。 + +輸入保證查詢 budget 非遞減。對每個 budget,請輸出第一次無法完整保留的事件,以及三個流實際保留的 byte 數。 + +## 輸入 + +第一行 `N Q`。接下來 `N` 行各為 `stream bytes`,其中 `stream` 為 `O`、`E` 或 `F`。最後 `Q` 行各有一個 `budget`,且依序非遞減。 + +## 輸出 + +每個查詢輸出: + +```text +failure stdoutBytes stderrBytes fileBytes +``` + +`failure` 是第一個無法完整保留的 1-based event 索引。若所有 event 都完整保留,`failure=0`。budget 為零時,第一個正長度 event 立即失敗且三個計數皆為零。重複 budget 合法且答案相同。 + +## 限制 + +- `1 ≤ N,Q ≤ 200000` +- `1 ≤ bytes ≤ 10^12` +- `0 ≤ budget ≤ 9×10^18` +- 全部 event 的 byte 總和不超過 `9×10^18` +- budget 序列非遞減 + +完整限制排除對每個 budget 重播事件的作法。 + +## 範例 + + + +### 範例一 + +輸入: + +```text +4 6 +O 5 +E 3 +F 10 +O 4 +0 +5 +7 +8 +20 +30 +``` + +輸出: + +```text +1 0 0 0 +2 5 0 0 +2 5 2 0 +3 5 3 0 +4 7 3 10 +0 9 3 10 +``` + +### 範例二 + +輸入: + +```text +1 3 +F 7 +6 +7 +8 +``` + +輸出: + +```text +1 0 0 6 +0 0 0 7 +0 0 0 7 +``` + +### 範例三 + +輸入: + +```text +3 5 +E 2 +E 2 +O 1 +1 +1 +3 +4 +5 +``` + +輸出: + +```text +1 0 1 0 +1 0 1 0 +2 0 3 0 +3 0 4 0 +0 1 4 0 +``` + + diff --git a/problems/004-shared-output-pool/tests/adversarial-01.in b/problems/004-shared-output-pool/tests/adversarial-01.in new file mode 100644 index 0000000..271c46e --- /dev/null +++ b/problems/004-shared-output-pool/tests/adversarial-01.in @@ -0,0 +1,11 @@ +3 7 +O 999999999998 +E 1 +F 1 +0 +1 +999999999997 +999999999998 +999999999998 +999999999999 +1000000000000 diff --git a/problems/004-shared-output-pool/tests/adversarial-01.out b/problems/004-shared-output-pool/tests/adversarial-01.out new file mode 100644 index 0000000..509a886 --- /dev/null +++ b/problems/004-shared-output-pool/tests/adversarial-01.out @@ -0,0 +1,7 @@ +1 0 0 0 +1 1 0 0 +1 999999999997 0 0 +2 999999999998 0 0 +2 999999999998 0 0 +3 999999999998 1 0 +0 999999999998 1 1 diff --git a/problems/004-shared-output-pool/tests/sample-01.in b/problems/004-shared-output-pool/tests/sample-01.in new file mode 100644 index 0000000..6a46c3a --- /dev/null +++ b/problems/004-shared-output-pool/tests/sample-01.in @@ -0,0 +1,11 @@ +4 6 +O 5 +E 3 +F 10 +O 4 +0 +5 +7 +8 +20 +30 diff --git a/problems/004-shared-output-pool/tests/sample-01.out b/problems/004-shared-output-pool/tests/sample-01.out new file mode 100644 index 0000000..eafcadd --- /dev/null +++ b/problems/004-shared-output-pool/tests/sample-01.out @@ -0,0 +1,6 @@ +1 0 0 0 +2 5 0 0 +2 5 2 0 +3 5 3 0 +4 7 3 10 +0 9 3 10 diff --git a/problems/004-shared-output-pool/tests/sample-02.in b/problems/004-shared-output-pool/tests/sample-02.in new file mode 100644 index 0000000..749af01 --- /dev/null +++ b/problems/004-shared-output-pool/tests/sample-02.in @@ -0,0 +1,5 @@ +1 3 +F 7 +6 +7 +8 diff --git a/problems/004-shared-output-pool/tests/sample-02.out b/problems/004-shared-output-pool/tests/sample-02.out new file mode 100644 index 0000000..a1475d8 --- /dev/null +++ b/problems/004-shared-output-pool/tests/sample-02.out @@ -0,0 +1,3 @@ +1 0 0 6 +0 0 0 7 +0 0 0 7 diff --git a/problems/004-shared-output-pool/tests/sample-03.in b/problems/004-shared-output-pool/tests/sample-03.in new file mode 100644 index 0000000..e74d003 --- /dev/null +++ b/problems/004-shared-output-pool/tests/sample-03.in @@ -0,0 +1,9 @@ +3 5 +E 2 +E 2 +O 1 +1 +1 +3 +4 +5 diff --git a/problems/004-shared-output-pool/tests/sample-03.out b/problems/004-shared-output-pool/tests/sample-03.out new file mode 100644 index 0000000..c62c3c5 --- /dev/null +++ b/problems/004-shared-output-pool/tests/sample-03.out @@ -0,0 +1,5 @@ +1 0 1 0 +1 0 1 0 +2 0 3 0 +3 0 4 0 +0 1 4 0 diff --git a/problems/004-shared-output-pool/validator.py b/problems/004-shared-output-pool/validator.py new file mode 100644 index 0000000..f21a559 --- /dev/null +++ b/problems/004-shared-output-pool/validator.py @@ -0,0 +1,40 @@ +import re, sys + + +def fail(): + raise SystemExit(1) + + +try: + t = sys.stdin.buffer.read().decode("utf-8").split() + p = 0 + + def u(a, b): + global p + if p >= len(t) or re.fullmatch(r"0|[1-9][0-9]*", t[p]) is None: + fail() + v = int(t[p]) + p += 1 + if not a <= v <= b: + fail() + return v + + N, Q = u(1, 200000), u(1, 200000) + total = 0 + for _ in range(N): + if p >= len(t) or t[p] not in ("O", "E", "F"): + fail() + p += 1 + total += u(1, 10**12) + if total > 9 * 10**18: + fail() + prev = -1 + for _ in range(Q): + b = u(0, 9 * 10**18) + if b < prev: + fail() + prev = b + if p != len(t): + fail() +except (UnicodeDecodeError, ValueError, OverflowError): + fail() diff --git a/problems/005-transactional-vfs-quota/editorial.en.md b/problems/005-transactional-vfs-quota/editorial.en.md new file mode 100644 index 0000000..d063ce8 --- /dev/null +++ b/problems/005-transactional-vfs-quota/editorial.en.md @@ -0,0 +1,27 @@ +# Editorial + +## Intuitive Approach + +Store every path in an array, but rescan all `P` entries before every operation that may change a size or inode count. This makes transaction validation simple but costs `O(PN)` time. + +## Optimal Approach: Incremental Ledger + +Maintain `exists[x]`, `size[x]`, `usedBytes`, and `usedInodes`. `CREATE` and `UNLINK` change the inode count by one. When a file changes from `old` to `new`, inspect only the difference: before growth by `delta=new-old`, check `delta≤B-usedBytes`; shrinking releases `old-new` immediately. This comparison also avoids overflow in `usedBytes+delta`. + +Perform every check before committing any affected field. After a successful commit, update both peaks independently. On a quota error, set the sticky bit but do not modify the file ledger. + +## Correctness Proof + +Induct on the number of processed operations. Initially, the arrays and both usage totals represent the empty VFS. Assume the ledger is correct before an operation. For `CREATE` and `UNLINK`, the algorithm checks existence and inode quota in the prescribed order and, on success, adds or removes exactly that file and its size. For `WRITE` and `TRUNCATE`, the computed `new` is exactly the specified size; its difference from `old` is the only change to total logical bytes, so the quota test is necessary and sufficient. Failure branches commit nothing, while success branches commit every affected field together, establishing transaction semantics. Peaks are updated only from true committed usage, and the sticky bit becomes and remains one exactly after either quota error. Thus all operation results and the final summary are correct. + +## Complexity + +Array initialization takes `O(P)` and each operation takes `O(1)`, for `O(P+N)` total time and `O(P)` core auxiliary space. Including buffered I/O allocations, the common worst-case bound of the seven references is `O(P+N)`. Initialization and reading all operations already impose an `Ω(P+N)` time lower bound. + +## Common Mistakes + +- Changing a file size before a quota check succeeds, breaking atomicity. +- Adding only `length` for a sparse write and ignoring the hole created by `offset`. +- Extending a file to `offset` on a zero-length write. +- Failing to release both bytes and an inode on `UNLINK`. +- Setting sticky on `EXISTS`/`NOENT`, or clearing it after usage shrinks. diff --git a/problems/005-transactional-vfs-quota/editorial.zh-TW.md b/problems/005-transactional-vfs-quota/editorial.zh-TW.md new file mode 100644 index 0000000..328fc94 --- /dev/null +++ b/problems/005-transactional-vfs-quota/editorial.zh-TW.md @@ -0,0 +1,27 @@ +# 解題說明 + +## 直覺解法 + +以陣列保存每個 path,但在每次可能改變 size 或 inode 前,掃描 `P` 個 path 重算目前用量。這很容易確認交易是否合法,卻需 `O(PN)` 時間。 + +## 最佳解法:增量帳本 + +維護 `exists[x]`、`size[x]`、`usedBytes`、`usedInodes`。CREATE/UNLINK 對 inode 加減一;size 從 `old` 改為 `new` 時,只需考慮差值:增長 `delta=new-old` 前檢查 `delta≤B-usedBytes`,縮小則直接釋放 `old-new`。這種寫法也避免計算 `usedBytes+delta` 時溢位。 + +所有檢查先完成,通過後才一次提交相關欄位。提交後分別更新兩個 peak。quota 錯誤時設定 sticky,但不改動檔案帳本。 + +## 正確性證明 + +以已處理操作數歸納。初始陣列與兩個用量皆為零,正確。假設操作前帳本等於 VFS 狀態。對 CREATE/UNLINK,演算法按規定的優先序檢查存在性及 inode quota,成功時恰加入或移除該檔案及其 size。對 WRITE/TRUNCATE,計算的 `new` 正是題目定義;差值等於總 logical bytes 的唯一變化,quota 檢查因此充要。失敗分支不提交任何欄位,成功分支提交全部欄位,故交易語意成立。peak 只在成功後與真實用量取最大,sticky 恰在兩種 quota 錯誤出現後保持為一。歸納得所有逐步輸出與 SUMMARY 正確。 + +## 複雜度 + +初始化陣列 `O(P)`,每個操作 `O(1)`,總時間 `O(P+N)`,檔案狀態的核心輔助空間為 `O(P)`。C、C++、Go reference 串流讀寫;Rust、Python 會保留完整輸入與輸出,JavaScript、TypeScript 保留單一 Forge 輸入字串並以固定 64 KiB 分塊輸出。每筆操作與答案的文字長度皆為常數,因此依實際 resident allocations 計算,七語言 reference 的共同最壞空間上界為 `O(P+N)`;初始化與讀取操作也給出 `Ω(P+N)` 時間下界。 + +## 常見錯誤 + +- quota 失敗後仍先改了 size,破壞原子性。 +- sparse write 只加 `length`,漏算 `offset` 形成的 hole。 +- 零長度 write 錯誤地把檔案延伸到 offset。 +- unlink 忘記同時釋放 bytes 與 inode。 +- EXISTS/NOENT 也設 sticky,或縮小後清除 sticky。 diff --git a/problems/005-transactional-vfs-quota/generator.py b/problems/005-transactional-vfs-quota/generator.py new file mode 100644 index 0000000..ab6bab2 --- /dev/null +++ b/problems/005-transactional-vfs-quota/generator.py @@ -0,0 +1,21 @@ +import random, sys + +if len(sys.argv) != 3: + raise SystemExit("usage: generator.py SEED INDEX") +r = random.Random((int(sys.argv[1]) << 32) ^ int(sys.argv[2])) +idx = int(sys.argv[2]) +P = r.randint(1, 3 + idx % 6) +N = r.randint(1, 8 + idx % 10) +B = r.randint(0, 40) +I = r.randint(0, P) +out = [f"{P} {N} {B} {I}"] +for _ in range(N): + op = r.choice(("CREATE", "WRITE", "TRUNCATE", "UNLINK")) + x = r.randint(1, P) + if op == "WRITE": + out.append(f"{op} {x} {r.randint(0,30)} {r.randint(0,15)}") + elif op == "TRUNCATE": + out.append(f"{op} {x} {r.randint(0,45)}") + else: + out.append(f"{op} {x}") +print("\n".join(out)) diff --git a/problems/005-transactional-vfs-quota/oracle.py b/problems/005-transactional-vfs-quota/oracle.py new file mode 100644 index 0000000..45a6fda --- /dev/null +++ b/problems/005-transactional-vfs-quota/oracle.py @@ -0,0 +1,71 @@ +import sys + +t = sys.stdin.buffer.read().split() +p = 0 + + +def take(): + global p + x = t[p].decode() + p += 1 + return x + + +P, N, B, I = map(int, (take(), take(), take(), take())) +a = [None] * (P + 1) +peak_b = peak_i = 0 +sticky = 0 +out = [] + + +def usage(): + return sum(x is not None for x in a), sum(x or 0 for x in a if x is not None) + + +for _ in range(N): + op = take() + x = int(take()) + code = None + if op == "CREATE": + ino, used = usage() + if a[x] is not None: + code = "EXISTS" + elif ino + 1 > I: + code = "INODES" + else: + a[x] = 0 + elif op == "UNLINK": + if a[x] is None: + code = "NOENT" + else: + a[x] = None + elif op == "TRUNCATE": + new = int(take()) + if a[x] is None: + code = "NOENT" + else: + ino, used = usage() + if used - a[x] + new > B: + code = "BYTES" + else: + a[x] = new + else: + off, length = int(take()), int(take()) + if a[x] is None: + code = "NOENT" + else: + new = a[x] if length == 0 else max(a[x], off + length) + ino, used = usage() + if used - a[x] + new > B: + code = "BYTES" + else: + a[x] = new + if code in ("BYTES", "INODES"): + sticky = 1 + out.append("OK" if code is None else "ERR " + code) + ino, used = usage() + peak_b = max(peak_b, used) + peak_i = max(peak_i, ino) +ino, used = usage() +out.append(f"SUMMARY {used} {ino} {peak_b} {peak_i} {sticky}") +print("\n".join(out)) diff --git a/problems/005-transactional-vfs-quota/problem.json b/problems/005-transactional-vfs-quota/problem.json new file mode 100644 index 0000000..a1d5a61 --- /dev/null +++ b/problems/005-transactional-vfs-quota/problem.json @@ -0,0 +1,146 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 5, + "slug": "transactional-vfs-quota", + "title": { + "zh-TW": "交易式 VFS 配額", + "en": "Transactional VFS Quotas" + }, + "difficulty": "medium", + "tags": [ + "simulation", + "incremental-accounting", + "transaction" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-01", + "kind": "adversarial", + "input": "tests/adversarial-01.in", + "output": "tests/adversarial-01.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 15000000, + "memoryLimitBytes": 536870912 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 2500000, + "memoryLimitBytes": 402653184 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 900000, + "memoryLimitBytes": 268435456 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "每次操作重算所有檔案用量", + "en": "Recompute All File Usage per Operation" + }, + "time": "O(PN)", + "space": "O(P)", + "accepted": false + }, + { + "name": { + "zh-TW": "增量維護 bytes 與 inode", + "en": "Incremental Byte and Inode Accounting" + }, + "time": "O(P+N)", + "space": "O(P) auxiliary; O(P+N) buffered I/O", + "accepted": true + } + ] +} diff --git a/problems/005-transactional-vfs-quota/solutions/c/main.c b/problems/005-transactional-vfs-quota/solutions/c/main.c new file mode 100644 index 0000000..7a06093 --- /dev/null +++ b/problems/005-transactional-vfs-quota/solutions/c/main.c @@ -0,0 +1,77 @@ +#include +#include +#include +#include +int main(void) { + int P, N, I; + if (scanf("%d%d", &P, &N) != 2) + return 0; + unsigned long long B; + scanf("%llu%d", &B, &I); + unsigned char *ex = calloc(P + 1, 1); + uint64_t *sz = calloc(P + 1, sizeof(*sz)); + uint64_t used = 0, peakb = 0; + int ino = 0, peaki = 0, sticky = 0; + for (int z = 0; z < N; z++) { + char op[10]; + int x; + scanf("%9s%d", op, &x); + const char *err = NULL; + if (strcmp(op, "CREATE") == 0) { + if (ex[x]) + err = "EXISTS"; + else if (ino == I) + err = "INODES"; + else { + ex[x] = 1; + sz[x] = 0; + ino++; + } + } else if (strcmp(op, "UNLINK") == 0) { + if (!ex[x]) + err = "NOENT"; + else { + used -= sz[x]; + sz[x] = 0; + ex[x] = 0; + ino--; + } + } else { + uint64_t newsize; + if (strcmp(op, "WRITE") == 0) { + unsigned long long off, len; + scanf("%llu%llu", &off, &len); + newsize = !len ? sz[x] : (off + len > sz[x] ? off + len : sz[x]); + } else { + unsigned long long v; + scanf("%llu", &v); + newsize = v; + } + if (!ex[x]) + err = "NOENT"; + else if (newsize > sz[x] && newsize - sz[x] > B - used) + err = "BYTES"; + else { + if (newsize >= sz[x]) + used += newsize - sz[x]; + else + used -= sz[x] - newsize; + sz[x] = newsize; + } + } + if (err) { + printf("ERR %s\n", err); + if (strcmp(err, "BYTES") == 0 || strcmp(err, "INODES") == 0) + sticky = 1; + } else + puts("OK"); + if (used > peakb) + peakb = used; + if (ino > peaki) + peaki = ino; + } + printf("SUMMARY %llu %d %llu %d %d\n", (unsigned long long)used, ino, + (unsigned long long)peakb, peaki, sticky); + free(ex); + free(sz); +} diff --git a/problems/005-transactional-vfs-quota/solutions/cpp/main.cpp b/problems/005-transactional-vfs-quota/solutions/cpp/main.cpp new file mode 100644 index 0000000..af51669 --- /dev/null +++ b/problems/005-transactional-vfs-quota/solutions/cpp/main.cpp @@ -0,0 +1,67 @@ +#include +#include +#include +#include +#include +using namespace std; +int main() { + ios::sync_with_stdio(false); + cin.tie(nullptr); + int p, n, limit; + if (!(cin >> p >> n)) + return 0; + uint64_t cap; + cin >> cap >> limit; + vector ex(p + 1); + vector sz(p + 1); + uint64_t used = 0, peakb = 0; + int ino = 0, peaki = 0, sticky = 0; + while (n--) { + string op, err; + int x; + cin >> op >> x; + if (op == "CREATE") { + if (ex[x]) + err = "EXISTS"; + else if (ino == limit) + err = "INODES"; + else + ex[x] = 1, sz[x] = 0, ino++; + } else if (op == "UNLINK") { + if (!ex[x]) + err = "NOENT"; + else + used -= sz[x], sz[x] = 0, ex[x] = 0, ino--; + } else { + uint64_t v; + if (op == "WRITE") { + uint64_t off, len; + cin >> off >> len; + v = len ? max(sz[x], off + len) : sz[x]; + } else + cin >> v; + if (!ex[x]) + err = "NOENT"; + else if (v > sz[x] && v - sz[x] > cap - used) + err = "BYTES"; + else { + if (v >= sz[x]) + used += v - sz[x]; + else + used -= sz[x] - v; + sz[x] = v; + } + } + if (err.empty()) + cout << "OK\n"; + else { + cout << "ERR " << err << '\n'; + if (err == "BYTES" || err == "INODES") + sticky = 1; + } + peakb = max(peakb, used); + peaki = max(peaki, ino); + } + cout << "SUMMARY " << used << ' ' << ino << ' ' << peakb << ' ' << peaki + << ' ' << sticky << '\n'; +} diff --git a/problems/005-transactional-vfs-quota/solutions/go/main.go b/problems/005-transactional-vfs-quota/solutions/go/main.go new file mode 100644 index 0000000..c6644a0 --- /dev/null +++ b/problems/005-transactional-vfs-quota/solutions/go/main.go @@ -0,0 +1,86 @@ +package main + +import ( + "bufio" + "fmt" + "os" +) + +func main() { + in := bufio.NewReader(os.Stdin) + out := bufio.NewWriter(os.Stdout) + defer out.Flush() + var p, n, limit int + var cap uint64 + if _, e := fmt.Fscan(in, &p, &n, &cap, &limit); e != nil { + return + } + ex := make([]bool, p+1) + sz := make([]uint64, p+1) + var used, peakb uint64 + ino, peaki, sticky := 0, 0, 0 + for z := 0; z < n; z++ { + var op string + var x int + fmt.Fscan(in, &op, &x) + err := "" + if op == "CREATE" { + if ex[x] { + err = "EXISTS" + } else if ino == limit { + err = "INODES" + } else { + ex[x] = true + ino++ + } + } else if op == "UNLINK" { + if !ex[x] { + err = "NOENT" + } else { + used -= sz[x] + sz[x] = 0 + ex[x] = false + ino-- + } + } else { + var v uint64 + if op == "WRITE" { + var off, length uint64 + fmt.Fscan(in, &off, &length) + v = sz[x] + if length > 0 && off+length > v { + v = off + length + } + } else { + fmt.Fscan(in, &v) + } + if !ex[x] { + err = "NOENT" + } else if v > sz[x] && v-sz[x] > cap-used { + err = "BYTES" + } else { + if v >= sz[x] { + used += v - sz[x] + } else { + used -= sz[x] - v + } + sz[x] = v + } + } + if err == "" { + fmt.Fprintln(out, "OK") + } else { + fmt.Fprintln(out, "ERR", err) + if err == "BYTES" || err == "INODES" { + sticky = 1 + } + } + if used > peakb { + peakb = used + } + if ino > peaki { + peaki = ino + } + } + fmt.Fprintln(out, "SUMMARY", used, ino, peakb, peaki, sticky) +} diff --git a/problems/005-transactional-vfs-quota/solutions/javascript/main.js b/problems/005-transactional-vfs-quota/solutions/javascript/main.js new file mode 100644 index 0000000..a618a50 --- /dev/null +++ b/problems/005-transactional-vfs-quota/solutions/javascript/main.js @@ -0,0 +1,70 @@ +import * as std from "std"; +/** @type {string} */ +const input = std.in.readAsString(); +let cursor = 0; +/** @returns {string} */ +function nextToken() { + while (cursor < input.length && input.charCodeAt(cursor) <= 32) cursor++; + const start = cursor; + while (cursor < input.length && input.charCodeAt(cursor) > 32) cursor++; + return input.slice(start, cursor); +} +const P = Number(nextToken()), + N = Number(nextToken()), + B = BigInt(nextToken()), + I = Number(nextToken()), + a = /** @type {(bigint | null)[]} */ (Array(P + 1).fill(null)); +let used = 0n, ino = 0, peakB = 0n, peakI = 0, sticky = 0; +let output = ""; +/** @param {string} line */ +function emit(line) { + if (output.length + line.length > 65536) { + std.out.puts(output); + output = ""; + } + output += line; +} +for (let z = 0; z < N; z++) { + const op = nextToken(), x = Number(nextToken()); + /** @type {string | null} */ + let err = null; + if (op === "CREATE") { + if (a[x] !== null) err = "EXISTS"; + else if (ino === I) err = "INODES"; + else { + a[x] = 0n; + ino++; + } + } else if (op === "UNLINK") { + if (a[x] === null) err = "NOENT"; + else { + used -= /** @type {bigint} */ (a[x]); + a[x] = null; + ino--; + } + } else { + /** @type {bigint} */ + let v; + if (op === "WRITE") { + const off = BigInt(nextToken()), len = BigInt(nextToken()); + v = len === 0n + ? (a[x] ?? 0n) + : ((a[x] ?? 0n) > off + len ? (a[x] ?? 0n) : off + len); + } else v = BigInt(nextToken()); + if (a[x] === null) err = "NOENT"; + else { + const old = /** @type {bigint} */ (a[x]); + if (v > old && v - old > B - used) err = "BYTES"; + else { + used += v - old; + a[x] = v; + } + } + } + if (err === "BYTES" || err === "INODES") sticky = 1; + emit(err === null ? "OK\n" : `ERR ${err}\n`); + if (used > peakB) peakB = used; + if (ino > peakI) peakI = ino; +} +emit(`SUMMARY ${used} ${ino} ${peakB} ${peakI} ${sticky}\n`); +if (output.length) std.out.puts(output); diff --git a/problems/005-transactional-vfs-quota/solutions/python/main.py b/problems/005-transactional-vfs-quota/solutions/python/main.py new file mode 100644 index 0000000..60dbf32 --- /dev/null +++ b/problems/005-transactional-vfs-quota/solutions/python/main.py @@ -0,0 +1,51 @@ +import sys + +t = sys.stdin.buffer.read().split() +it = iter(t) +P, N, B, I = map(int, (next(it), next(it), next(it), next(it))) +a = [None] * (P + 1) +used = ino = peak_b = peak_i = sticky = 0 +out = [] +for _ in range(N): + op = next(it) + x = int(next(it)) + err = None + if op == b"CREATE": + if a[x] is not None: + err = "EXISTS" + elif ino == I: + err = "INODES" + else: + a[x] = 0 + ino += 1 + elif op == b"UNLINK": + if a[x] is None: + err = "NOENT" + else: + used -= a[x] + a[x] = None + ino -= 1 + else: + if op == b"WRITE": + off, length = int(next(it)), int(next(it)) + new = ( + a[x] + if length == 0 and a[x] is not None + else (0 if length == 0 else max(a[x] or 0, off + length)) + ) + else: + new = int(next(it)) + if a[x] is None: + err = "NOENT" + elif new > a[x] and new - a[x] > B - used: + err = "BYTES" + else: + used += new - a[x] + a[x] = new + if err in ("BYTES", "INODES"): + sticky = 1 + out.append("OK" if err is None else "ERR " + err) + peak_b = max(peak_b, used) + peak_i = max(peak_i, ino) +out.append(f"SUMMARY {used} {ino} {peak_b} {peak_i} {sticky}") +print("\n".join(out)) diff --git a/problems/005-transactional-vfs-quota/solutions/rust/main.rs b/problems/005-transactional-vfs-quota/solutions/rust/main.rs new file mode 100644 index 0000000..0ec8a8c --- /dev/null +++ b/problems/005-transactional-vfs-quota/solutions/rust/main.rs @@ -0,0 +1,75 @@ +use std::io::{self, Read}; +fn main() { + let mut s = String::new(); + io::stdin().read_to_string(&mut s).unwrap(); + let mut t = s.split_whitespace(); + let p: usize = t.next().unwrap().parse().unwrap(); + let n: usize = t.next().unwrap().parse().unwrap(); + let cap: u64 = t.next().unwrap().parse().unwrap(); + let limit: usize = t.next().unwrap().parse().unwrap(); + let mut ex = vec![false; p + 1]; + let mut sz = vec![0u64; p + 1]; + let (mut used, mut peakb, mut ino, mut peaki, mut sticky) = (0u64, 0u64, 0usize, 0usize, 0); + let mut out = String::new(); + for _ in 0..n { + let op = t.next().unwrap(); + let x: usize = t.next().unwrap().parse().unwrap(); + let mut err = ""; + if op == "CREATE" { + if ex[x] { + err = "EXISTS" + } else if ino == limit { + err = "INODES" + } else { + ex[x] = true; + sz[x] = 0; + ino += 1 + } + } else if op == "UNLINK" { + if !ex[x] { + err = "NOENT" + } else { + used -= sz[x]; + sz[x] = 0; + ex[x] = false; + ino -= 1 + } + } else { + let v = if op == "WRITE" { + let off: u64 = t.next().unwrap().parse().unwrap(); + let len: u64 = t.next().unwrap().parse().unwrap(); + if len == 0 { + sz[x] + } else { + sz[x].max(off + len) + } + } else { + t.next().unwrap().parse().unwrap() + }; + if !ex[x] { + err = "NOENT" + } else if v > sz[x] && v - sz[x] > cap - used { + err = "BYTES" + } else { + if v >= sz[x] { + used += v - sz[x] + } else { + used -= sz[x] - v + } + sz[x] = v + } + } + if err.is_empty() { + out += "OK\n" + } else { + out += &format!("ERR {}\n", err); + if err == "BYTES" || err == "INODES" { + sticky = 1 + } + } + peakb = peakb.max(used); + peaki = peaki.max(ino); + } + out += &format!("SUMMARY {} {} {} {} {}\n", used, ino, peakb, peaki, sticky); + print!("{}", out); +} diff --git a/problems/005-transactional-vfs-quota/solutions/typescript/main.ts b/problems/005-transactional-vfs-quota/solutions/typescript/main.ts new file mode 100644 index 0000000..14d28e2 --- /dev/null +++ b/problems/005-transactional-vfs-quota/solutions/typescript/main.ts @@ -0,0 +1,65 @@ +import * as std from "std"; +const input: string = std.in.readAsString(); +let cursor = 0; +function nextToken(): string { + while (cursor < input.length && input.charCodeAt(cursor) <= 32) cursor++; + const start = cursor; + while (cursor < input.length && input.charCodeAt(cursor) > 32) cursor++; + return input.slice(start, cursor); +} +const P = Number(nextToken()), + N = Number(nextToken()), + B = BigInt(nextToken()), + I = Number(nextToken()), + a: (bigint | null)[] = Array(P + 1).fill(null); +let used = 0n, ino = 0, peakB = 0n, peakI = 0, sticky = 0; +let output = ""; +function emit(line: string): void { + if (output.length + line.length > 65536) { + std.out.puts(output); + output = ""; + } + output += line; +} +for (let z = 0; z < N; z++) { + const op = nextToken(), x = Number(nextToken()); + let err: string | null = null; + if (op === "CREATE") { + if (a[x] !== null) err = "EXISTS"; + else if (ino === I) err = "INODES"; + else { + a[x] = 0n; + ino++; + } + } else if (op === "UNLINK") { + if (a[x] === null) err = "NOENT"; + else { + used -= a[x] as bigint; + a[x] = null; + ino--; + } + } else { + let v: bigint; + if (op === "WRITE") { + const off = BigInt(nextToken()), + len = BigInt(nextToken()), + old = a[x] ?? 0n; + v = len === 0n ? old : (old > off + len ? old : off + len); + } else v = BigInt(nextToken()); + if (a[x] === null) err = "NOENT"; + else { + const old = a[x] as bigint; + if (v > old && v - old > B - used) err = "BYTES"; + else { + used += v - old; + a[x] = v; + } + } + } + if (err === "BYTES" || err === "INODES") sticky = 1; + emit(err === null ? "OK\n" : `ERR ${err}\n`); + if (used > peakB) peakB = used; + if (ino > peakI) peakI = ino; +} +emit(`SUMMARY ${used} ${ino} ${peakB} ${peakI} ${sticky}\n`); +if (output.length) std.out.puts(output); diff --git a/problems/005-transactional-vfs-quota/statement.en.md b/problems/005-transactional-vfs-quota/statement.en.md new file mode 100644 index 0000000..94c941d --- /dev/null +++ b/problems/005-transactional-vfs-quota/statement.en.md @@ -0,0 +1,139 @@ +# Transactional VFS Quotas + +While designing the virtual file system for a WASM OJ, we need to limit both the total bytes written and the number of files that can be created. More importantly, a failed quota check must not leave a half-applied operation behind. If a file size changed before an over-limit result was discovered, later judging behavior would no longer be reproducible. Every file operation must therefore commit completely or roll back completely as a transaction. + +The virtual file system has `P` possible canonical guest paths; ID `x` represents `/file/x`, and initially none of them exists. The sum of all logical file sizes may not exceed `B` bytes, and the number of existing files (inodes) may not exceed `I`. Execute `N` operations in order: + +- `CREATE x`: create a zero-length file. +- `WRITE x offset length`: write `length` bytes to the file. If `length>0`, its new logical size is `max(oldSize,offset+length)`; if `length=0`, its size is unchanged. +- `TRUNCATE x size`: set the logical size to exactly `size`, either growing or shrinking it. +- `UNLINK x`: delete the file and release all of its bytes and one inode. + +Every operation is one transaction. If it fails, existence, size, usage, and peak usage must all remain unchanged. To ensure that the same operation always produces the same error, determine results in this order: + +- `CREATE`: return `EXISTS` first if the file exists; otherwise return `INODES` if the inode limit would be exceeded. +- `WRITE`/`TRUNCATE`: return `NOENT` first if the file does not exist; otherwise return `BYTES` if the byte limit would be exceeded. +- `UNLINK`: return `NOENT` if the file does not exist. + +Output `OK` on success and `ERR code` on failure. Any `BYTES` or `INODES` error sets the sticky quota-failure bit to `1`; it is never cleared. `EXISTS` and `NOENT` do not affect it. + +After all operations, output current usage, peak usage among all successfully committed states during execution, and the sticky bit. + +## Input + +The first line contains `P N B I`, followed by the `N` operations above. IDs are 1-based. + +## Output + +Output one result line per operation, followed by: + +```text +SUMMARY usedBytes usedInodes peakBytes peakInodes sticky +``` + +Byte and inode peaks are the separate maxima ever observed; they need not occur at the same time. The initial all-zero state is included. + +## Constraints + +- `1 ≤ P,N ≤ 200000` +- `0 ≤ B ≤ 9×10^18` +- `0 ≤ I ≤ P` +- `1 ≤ x ≤ P` +- `0 ≤ offset,length,size ≤ 9×10^18` +- Every `WRITE` satisfies `offset+length ≤ 9×10^18`. + +A logical hole consumes quota. For example, `WRITE x 10 5` on an empty file gives it size `15`. The full constraints rule out rescanning all paths to recompute usage after every operation. + +## Examples + + + +### Example One + +Input: + +```text +3 8 10 2 +CREATE 1 +WRITE 1 0 6 +CREATE 2 +WRITE 2 0 5 +CREATE 3 +TRUNCATE 1 4 +UNLINK 2 +CREATE 3 +``` + +Output: + +```text +OK +OK +OK +ERR BYTES +ERR INODES +OK +OK +OK +SUMMARY 4 2 6 2 1 +``` + +### Example Two + +Input: + +```text +2 7 0 1 +WRITE 1 0 1 +CREATE 1 +CREATE 1 +TRUNCATE 1 1 +UNLINK 2 +UNLINK 1 +CREATE 2 +``` + +Output: + +```text +ERR NOENT +OK +ERR EXISTS +ERR BYTES +ERR NOENT +OK +OK +SUMMARY 0 1 0 1 1 +``` + +### Example Three + +Input: + +```text +2 8 20 2 +CREATE 1 +WRITE 1 10 5 +TRUNCATE 1 4 +WRITE 1 18 2 +CREATE 2 +TRUNCATE 2 1 +UNLINK 1 +TRUNCATE 2 20 +``` + +Output: + +```text +OK +OK +OK +OK +OK +ERR BYTES +OK +OK +SUMMARY 20 1 20 2 1 +``` + + diff --git a/problems/005-transactional-vfs-quota/statement.zh-TW.md b/problems/005-transactional-vfs-quota/statement.zh-TW.md new file mode 100644 index 0000000..280f858 --- /dev/null +++ b/problems/005-transactional-vfs-quota/statement.zh-TW.md @@ -0,0 +1,139 @@ +# 交易式 VFS 配額 + +在設計 WASM OJ 的虛擬檔案系統時,我們不只要限制寫入的總 bytes,也要限制可建立的檔案數。更重要的是,配額檢查不能讓失敗的操作留下半套狀態:若檔案大小已改變才發現超限,後續判題就不再可重現。因此,每個檔案操作都必須以交易方式完整提交或完全回滾。 + +虛擬檔案系統有 `P` 個可能的 canonical guest path,ID `x` 代表 `/file/x`,初始時全部不存在。所有檔案的 logical bytes 總和不得超過 `B`,存在的檔案數(inode 數)不得超過 `I`。請依序執行 `N` 個操作: + +- `CREATE x`:建立大小為零的檔案。 +- `WRITE x offset length`:在檔案寫入 `length` bytes。若 `length>0`,新 logical size 為 `max(oldSize,offset+length)`;若 `length=0`,size 不變。 +- `TRUNCATE x size`:把 logical size 精確改成 `size`,可增長或縮小。 +- `UNLINK x`:刪除檔案並釋放其全部 bytes 與一個 inode。 + +每個操作都是一筆交易。失敗時,存在狀態、size、用量與 peak 全都不得改變。為了讓相同操作永遠得到相同錯誤,請依下列順序決定結果: + +- `CREATE`:已存在先回 `EXISTS`;否則若 inode 將超限,回 `INODES`。 +- `WRITE`/`TRUNCATE`:不存在先回 `NOENT`;否則若 bytes 將超限,回 `BYTES`。 +- `UNLINK`:不存在回 `NOENT`。 + +成功輸出 `OK`,失敗輸出 `ERR code`。任何一次 `BYTES` 或 `INODES` 錯誤會把 sticky quota failure 設為 `1`,之後永不清除;`EXISTS` 與 `NOENT` 不影響它。 + +所有操作完成後,再輸出目前用量、執行期間所有成功提交狀態中的 peak 用量,以及 sticky bit。 + +## 輸入 + +第一行 `P N B I`,接著 `N` 行為上述操作。ID 為 1-based。 + +## 輸出 + +每個操作一行結果,最後一行: + +```text +SUMMARY usedBytes usedInodes peakBytes peakInodes sticky +``` + +bytes peak 與 inode peak 分別取各自曾出現的最大值,不要求在同一時刻發生;初始零狀態也計入。 + +## 限制 + +- `1 ≤ P,N ≤ 200000` +- `0 ≤ B ≤ 9×10^18` +- `0 ≤ I ≤ P` +- `1 ≤ x ≤ P` +- `0 ≤ offset,length,size ≤ 9×10^18` +- 每個 `WRITE` 都保證 `offset+length ≤ 9×10^18` + +logical hole 也佔配額;例如空檔案執行 `WRITE x 10 5` 後大小為 `15`。完整限制排除每次掃描所有 path 重算用量。 + +## 範例 + + + +### 範例一 + +輸入: + +```text +3 8 10 2 +CREATE 1 +WRITE 1 0 6 +CREATE 2 +WRITE 2 0 5 +CREATE 3 +TRUNCATE 1 4 +UNLINK 2 +CREATE 3 +``` + +輸出: + +```text +OK +OK +OK +ERR BYTES +ERR INODES +OK +OK +OK +SUMMARY 4 2 6 2 1 +``` + +### 範例二 + +輸入: + +```text +2 7 0 1 +WRITE 1 0 1 +CREATE 1 +CREATE 1 +TRUNCATE 1 1 +UNLINK 2 +UNLINK 1 +CREATE 2 +``` + +輸出: + +```text +ERR NOENT +OK +ERR EXISTS +ERR BYTES +ERR NOENT +OK +OK +SUMMARY 0 1 0 1 1 +``` + +### 範例三 + +輸入: + +```text +2 8 20 2 +CREATE 1 +WRITE 1 10 5 +TRUNCATE 1 4 +WRITE 1 18 2 +CREATE 2 +TRUNCATE 2 1 +UNLINK 1 +TRUNCATE 2 20 +``` + +輸出: + +```text +OK +OK +OK +OK +OK +ERR BYTES +OK +OK +SUMMARY 20 1 20 2 1 +``` + + diff --git a/problems/005-transactional-vfs-quota/tests/adversarial-01.in b/problems/005-transactional-vfs-quota/tests/adversarial-01.in new file mode 100644 index 0000000..6f29091 --- /dev/null +++ b/problems/005-transactional-vfs-quota/tests/adversarial-01.in @@ -0,0 +1,16 @@ +3 15 10 2 +CREATE 1 +TRUNCATE 1 10 +CREATE 2 +CREATE 2 +CREATE 3 +WRITE 3 0 20 +WRITE 1 100 0 +WRITE 2 0 1 +TRUNCATE 1 4 +WRITE 2 5 1 +UNLINK 1 +CREATE 3 +TRUNCATE 3 5 +UNLINK 2 +TRUNCATE 3 10 diff --git a/problems/005-transactional-vfs-quota/tests/adversarial-01.out b/problems/005-transactional-vfs-quota/tests/adversarial-01.out new file mode 100644 index 0000000..47f6a62 --- /dev/null +++ b/problems/005-transactional-vfs-quota/tests/adversarial-01.out @@ -0,0 +1,16 @@ +OK +OK +OK +ERR EXISTS +ERR INODES +ERR NOENT +OK +ERR BYTES +OK +OK +OK +OK +ERR BYTES +OK +OK +SUMMARY 10 1 10 2 1 diff --git a/problems/005-transactional-vfs-quota/tests/sample-01.in b/problems/005-transactional-vfs-quota/tests/sample-01.in new file mode 100644 index 0000000..acc3851 --- /dev/null +++ b/problems/005-transactional-vfs-quota/tests/sample-01.in @@ -0,0 +1,9 @@ +3 8 10 2 +CREATE 1 +WRITE 1 0 6 +CREATE 2 +WRITE 2 0 5 +CREATE 3 +TRUNCATE 1 4 +UNLINK 2 +CREATE 3 diff --git a/problems/005-transactional-vfs-quota/tests/sample-01.out b/problems/005-transactional-vfs-quota/tests/sample-01.out new file mode 100644 index 0000000..20a4b57 --- /dev/null +++ b/problems/005-transactional-vfs-quota/tests/sample-01.out @@ -0,0 +1,9 @@ +OK +OK +OK +ERR BYTES +ERR INODES +OK +OK +OK +SUMMARY 4 2 6 2 1 diff --git a/problems/005-transactional-vfs-quota/tests/sample-02.in b/problems/005-transactional-vfs-quota/tests/sample-02.in new file mode 100644 index 0000000..4a63215 --- /dev/null +++ b/problems/005-transactional-vfs-quota/tests/sample-02.in @@ -0,0 +1,8 @@ +2 7 0 1 +WRITE 1 0 1 +CREATE 1 +CREATE 1 +TRUNCATE 1 1 +UNLINK 2 +UNLINK 1 +CREATE 2 diff --git a/problems/005-transactional-vfs-quota/tests/sample-02.out b/problems/005-transactional-vfs-quota/tests/sample-02.out new file mode 100644 index 0000000..34353d2 --- /dev/null +++ b/problems/005-transactional-vfs-quota/tests/sample-02.out @@ -0,0 +1,8 @@ +ERR NOENT +OK +ERR EXISTS +ERR BYTES +ERR NOENT +OK +OK +SUMMARY 0 1 0 1 1 diff --git a/problems/005-transactional-vfs-quota/tests/sample-03.in b/problems/005-transactional-vfs-quota/tests/sample-03.in new file mode 100644 index 0000000..84cf43f --- /dev/null +++ b/problems/005-transactional-vfs-quota/tests/sample-03.in @@ -0,0 +1,9 @@ +2 8 20 2 +CREATE 1 +WRITE 1 10 5 +TRUNCATE 1 4 +WRITE 1 18 2 +CREATE 2 +TRUNCATE 2 1 +UNLINK 1 +TRUNCATE 2 20 diff --git a/problems/005-transactional-vfs-quota/tests/sample-03.out b/problems/005-transactional-vfs-quota/tests/sample-03.out new file mode 100644 index 0000000..0b5066a --- /dev/null +++ b/problems/005-transactional-vfs-quota/tests/sample-03.out @@ -0,0 +1,9 @@ +OK +OK +OK +OK +OK +ERR BYTES +OK +OK +SUMMARY 20 1 20 2 1 diff --git a/problems/005-transactional-vfs-quota/validator.py b/problems/005-transactional-vfs-quota/validator.py new file mode 100644 index 0000000..5d3465a --- /dev/null +++ b/problems/005-transactional-vfs-quota/validator.py @@ -0,0 +1,46 @@ +import re, sys + + +def fail(): + raise SystemExit(1) + + +try: + t = sys.stdin.buffer.read().decode("utf-8").split() + p = 0 + + def u(a, b): + global p + if p >= len(t) or re.fullmatch(r"0|[1-9][0-9]*", t[p]) is None: + fail() + v = int(t[p]) + p += 1 + if not a <= v <= b: + fail() + return v + + P, N, B, I = u(1, 200000), u(1, 200000), u(0, 9 * 10**18), u(0, 200000) + if I > P: + fail() + for _ in range(N): + if p >= len(t): + fail() + op = t[p] + p += 1 + if op in ("CREATE", "UNLINK"): + u(1, P) + elif op == "TRUNCATE": + u(1, P) + u(0, 9 * 10**18) + elif op == "WRITE": + u(1, P) + a = u(0, 9 * 10**18) + b = u(0, 9 * 10**18) + if a + b > 9 * 10**18: + fail() + else: + fail() + if p != len(t): + fail() +except (UnicodeDecodeError, ValueError, OverflowError): + fail() diff --git a/problems/006-logical-poll-clock/editorial.en.md b/problems/006-logical-poll-clock/editorial.en.md new file mode 100644 index 0000000..d5d9e11 --- /dev/null +++ b/problems/006-logical-poll-clock/editorial.en.md @@ -0,0 +1,26 @@ +# Editorial + +## Intuitive Approach + +Keep a table of active timers. On every poll, scan the table once to find the minimum deadline and again to collect expired timers. Interleaved insertions and polls can make this `O(N^2)`. + +## Optimal Approach: Min-Heap with Lazy Cancellation + +Put `(deadline,id)` into a min-heap and track validity separately with `active[id]`. Cancellation only sets the flag to false; a stale heap entry is discarded when it reaches the top. + +For a poll, first remove cancelled entries from the heap top. If `ready=0` and the heap is nonempty, set `clock=max(clock,minDeadline)`. Then repeatedly pop entries with `deadline≤clock`: ignore cancelled entries, and output and deactivate active ones. Because the heap key is exactly `(deadline,id)`, the pop order is the required output order. + +## Correctness Proof + +After entries with `active=false` are ignored, the heap retains the original key of every active timer, so after top cleanup its top is the minimum active `(deadline,id)`. With no ready event, if that deadline lies in the future, advancing to it matches the rule; if it is already due, `max` preserves the clock. The loop removes all and only active timers whose deadlines do not exceed the clock, and heap order emits them increasingly by `(deadline,id)`. Cancelled timers are never output. Therefore every poll has the correct clock, fired set, and order, and removed timers never fire again. + +## Complexity + +Every timer enters and leaves the heap at most once, each in `O(log N)` time. All other command work is `O(1)`, so total time is `O(N log N)` and space is `O(N)`. + +## Common Mistakes + +- Advancing the clock even when at least one fd event is ready. +- Searching linearly through the heap on cancellation, causing quadratic time. +- Moving the clock backward when a newly added deadline is earlier than the current clock; it should fire on the next poll without rewinding time. +- Ordering only by deadline and omitting the ID tie-break. diff --git a/problems/006-logical-poll-clock/editorial.zh-TW.md b/problems/006-logical-poll-clock/editorial.zh-TW.md new file mode 100644 index 0000000..56a6913 --- /dev/null +++ b/problems/006-logical-poll-clock/editorial.zh-TW.md @@ -0,0 +1,26 @@ +# 解題說明 + +## 直覺解法 + +用表保存 active timer;每次 POLL 掃描全部 timer,先找最小 deadline,再掃一次找出到期者。交錯加入與 poll 時會達到 `O(N^2)`。 + +## 最佳解法 + +將 `(deadline,id)` 放入最小堆,另以 `active[id]` 記錄是否仍有效。取消時只把 active 設為 false;當失效項目來到堆頂才丟棄,這是 lazy deletion。 + +POLL 先清掉堆頂已取消項目。若 `ready=0` 且堆非空,clock 更新為 `max(clock,minDeadline)`。之後反覆彈出 `deadline≤clock` 的項目:取消者忽略,active 者輸出並標為不 active。因堆比較鍵正是規定的 `(deadline,id)`,彈出順序就是輸出順序。 + +## 正確性證明 + +忽略 `active=false` 的項目後,堆包含每個 active timer 的原始鍵,所以清理後堆頂是最小 active `(deadline,id)`。在無 ready 事件時,若最小 deadline 在未來,將 clock 快轉至它;若已到期則 `max` 保持 clock,恰符合規則。所有且僅有鍵的 deadline 不大於 clock 的 active 項目會在 while 中被彈出,而堆序保證其 `(deadline,id)` 遞增。取消項目永不輸出。故每次 POLL 的 clock 與觸發集合、順序都正確;移除後不會再次觸發。 + +## 複雜度 + +每個 timer 入堆一次、出堆至多一次,每次 `O(log N)`;其他命令 `O(1)`,總時間 `O(N log N)`、空間 `O(N)`。 + +## 常見錯誤 + +- 有 ready fd 時仍快轉 clock。 +- 取消時在線性堆中搜尋刪除,退化成平方時間。 +- 新加入的 deadline 可能小於目前 clock,下一次 poll 應立即觸發但 clock 不倒退。 +- 只按 deadline 排序,漏掉相同 deadline 的 ID tie-break。 diff --git a/problems/006-logical-poll-clock/generator.py b/problems/006-logical-poll-clock/generator.py new file mode 100644 index 0000000..5587056 --- /dev/null +++ b/problems/006-logical-poll-clock/generator.py @@ -0,0 +1,61 @@ +import random +import sys + + +if len(sys.argv) != 3: + raise SystemExit("usage: generator.py SEED INDEX") + +seed = int(sys.argv[1]) +index = int(sys.argv[2]) +rng = random.Random((seed << 32) ^ index) +target = rng.randint(2, 8 + index % 12) +commands = [] +active = {} +next_id = 1 +clock = 0 + + +def add_timer(timer_id, deadline): + active[timer_id] = deadline + commands.append(f"T {timer_id} {deadline}") + + +def poll(ready): + global clock + commands.append(f"P {ready}") + if ready == 0 and active: + clock = max(clock, min(active.values())) + fired = [timer_id for timer_id, deadline in active.items() if deadline <= clock] + for timer_id in fired: + del active[timer_id] + + +# Every fourth index explicitly covers a timer that survives a poll and is +# canceled afterward. The remaining suffix still varies by seed. +if index % 4 == 0: + target = max(target, 5) + add_timer(1, 5) + add_timer(2, 10) + next_id = 3 + poll(0) + del active[2] + commands.append("C 2") + +while len(commands) < target - 1: + choices = ["P", "T"] + if active: + choices.append("C") + operation = rng.choice(choices) + if operation == "T": + add_timer(next_id, rng.randint(0, 30)) + next_id += 1 + elif operation == "C": + timer_id = rng.choice(list(active)) + del active[timer_id] + commands.append(f"C {timer_id}") + else: + poll(rng.randint(0, 3)) + +poll(rng.randint(0, 2)) +print(len(commands)) +print("\n".join(commands)) diff --git a/problems/006-logical-poll-clock/oracle.py b/problems/006-logical-poll-clock/oracle.py new file mode 100644 index 0000000..34b90ed --- /dev/null +++ b/problems/006-logical-poll-clock/oracle.py @@ -0,0 +1,29 @@ +import sys + +t = sys.stdin.buffer.read().split() +it = iter(t) +N = int(next(it)) +active = {} +clock = 0 +out = [] +for _ in range(N): + op = next(it) + if op == b"T": + x = int(next(it)) + d = int(next(it)) + active[x] = d + elif op == b"C": + del active[int(next(it))] + else: + ready = int(next(it)) + if ready == 0 and active: + clock = max(clock, min(active.values())) + fired = sorted((d, x) for x, d in active.items() if d <= clock) + for _, x in fired: + del active[x] + ids = [str(x) for _, x in fired] + out.append( + " ".join(map(str, (clock, ready, len(ids)))) + + (" " + " ".join(ids) if ids else "") + ) +print("\n".join(out)) diff --git a/problems/006-logical-poll-clock/problem.json b/problems/006-logical-poll-clock/problem.json new file mode 100644 index 0000000..63eb010 --- /dev/null +++ b/problems/006-logical-poll-clock/problem.json @@ -0,0 +1,146 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 6, + "slug": "logical-poll-clock", + "title": { + "zh-TW": "不等待的虛擬時鐘", + "en": "Non-Blocking Logical Clock" + }, + "difficulty": "hard", + "tags": [ + "priority-queue", + "event-simulation", + "lazy-deletion" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-01", + "kind": "adversarial", + "input": "tests/adversarial-01.in", + "output": "tests/adversarial-01.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 150000000, + "memoryLimitBytes": 536870912 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 2000000, + "memoryLimitBytes": 402653184 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 700000, + "memoryLimitBytes": 268435456 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "每次 POLL 掃描全部 active timer", + "en": "Scan All Active Timers per Poll" + }, + "time": "O(N^2)", + "space": "O(N)", + "accepted": false + }, + { + "name": { + "zh-TW": "最小堆與 lazy cancellation", + "en": "Min-Heap with Lazy Cancellation" + }, + "time": "O(N log N)", + "space": "O(N)", + "accepted": true + } + ] +} diff --git a/problems/006-logical-poll-clock/solutions/c/main.c b/problems/006-logical-poll-clock/solutions/c/main.c new file mode 100644 index 0000000..735ae07 --- /dev/null +++ b/problems/006-logical-poll-clock/solutions/c/main.c @@ -0,0 +1,82 @@ +#include +#include +#include +#include +typedef struct { + uint64_t d; + int id; +} Item; +static int less(Item a, Item b) { + return a.d < b.d || (a.d == b.d && a.id < b.id); +} +static void push(Item *h, int *n, Item x) { + int i = (*n)++; + while (i && less(x, h[(i - 1) / 2])) { + h[i] = h[(i - 1) / 2]; + i = (i - 1) / 2; + } + h[i] = x; +} +static Item pop(Item *h, int *n) { + Item r = h[0], x = h[--*n]; + int i = 0; + while (i * 2 + 1 < *n) { + int c = i * 2 + 1; + if (c + 1 < *n && less(h[c + 1], h[c])) + c++; + if (!less(h[c], x)) + break; + h[i] = h[c]; + i = c; + } + if (*n) + h[i] = x; + return r; +} +int main(void) { + int N; + if (scanf("%d", &N) != 1) + return 0; + Item *h = malloc((size_t)N * sizeof(*h)); + int *ids = malloc((size_t)N * sizeof(*ids)); + unsigned char *active = calloc(N + 1, 1); + int hn = 0; + uint64_t clock = 0; + for (int z = 0; z < N; z++) { + char op[2]; + scanf("%1s", op); + if (op[0] == 'T') { + int id; + unsigned long long d; + scanf("%d%llu", &id, &d); + active[id] = 1; + push(h, &hn, (Item){d, id}); + } else if (op[0] == 'C') { + int id; + scanf("%d", &id); + active[id] = 0; + } else { + int ready; + scanf("%d", &ready); + while (hn && !active[h[0].id]) + pop(h, &hn); + if (!ready && hn && h[0].d > clock) + clock = h[0].d; + int k = 0; + while (hn && h[0].d <= clock) { + Item x = pop(h, &hn); + if (active[x.id]) { + active[x.id] = 0; + ids[k++] = x.id; + } + } + printf("%llu %d %d", (unsigned long long)clock, ready, k); + for (int i = 0; i < k; i++) + printf(" %d", ids[i]); + putchar('\n'); + } + } + free(h); + free(ids); + free(active); +} diff --git a/problems/006-logical-poll-clock/solutions/cpp/main.cpp b/problems/006-logical-poll-clock/solutions/cpp/main.cpp new file mode 100644 index 0000000..c98c2f6 --- /dev/null +++ b/problems/006-logical-poll-clock/solutions/cpp/main.cpp @@ -0,0 +1,54 @@ +#include +#include +#include +#include +#include +#include +using namespace std; +int main() { + ios::sync_with_stdio(false); + cin.tie(nullptr); + int n; + if (!(cin >> n)) + return 0; + priority_queue, vector>, + greater>> + h; + vector a(n + 1); + uint64_t clock = 0; + while (n--) { + char op; + cin >> op; + if (op == 'T') { + int id; + uint64_t d; + cin >> id >> d; + a[id] = 1; + h.push({d, id}); + } else if (op == 'C') { + int id; + cin >> id; + a[id] = 0; + } else { + int ready; + cin >> ready; + while (!h.empty() && !a[h.top().second]) + h.pop(); + if (!ready && !h.empty()) + clock = max(clock, h.top().first); + vector f; + while (!h.empty() && h.top().first <= clock) { + auto [d, id] = h.top(); + h.pop(); + if (a[id]) { + a[id] = 0; + f.push_back(id); + } + } + cout << clock << ' ' << ready << ' ' << f.size(); + for (int id : f) + cout << ' ' << id; + cout << '\n'; + } + } +} diff --git a/problems/006-logical-poll-clock/solutions/go/main.go b/problems/006-logical-poll-clock/solutions/go/main.go new file mode 100644 index 0000000..6e9c2e6 --- /dev/null +++ b/problems/006-logical-poll-clock/solutions/go/main.go @@ -0,0 +1,70 @@ +package main + +import ( + "bufio" + "container/heap" + "fmt" + "os" +) + +type item struct { + d uint64 + id int +} +type pq []item + +func (h pq) Len() int { return len(h) } +func (h pq) Less(i, j int) bool { return h[i].d < h[j].d || (h[i].d == h[j].d && h[i].id < h[j].id) } +func (h pq) Swap(i, j int) { h[i], h[j] = h[j], h[i] } +func (h *pq) Push(x any) { *h = append(*h, x.(item)) } +func (h *pq) Pop() any { o := *h; x := o[len(o)-1]; *h = o[:len(o)-1]; return x } +func main() { + in := bufio.NewReader(os.Stdin) + out := bufio.NewWriter(os.Stdout) + defer out.Flush() + var n int + if _, e := fmt.Fscan(in, &n); e != nil { + return + } + h := &pq{} + heap.Init(h) + active := make([]bool, n+1) + var clock uint64 + for z := 0; z < n; z++ { + var op string + fmt.Fscan(in, &op) + if op == "T" { + var id int + var d uint64 + fmt.Fscan(in, &id, &d) + active[id] = true + heap.Push(h, item{d, id}) + } else if op == "C" { + var id int + fmt.Fscan(in, &id) + active[id] = false + } else { + var ready int + fmt.Fscan(in, &ready) + for h.Len() > 0 && !active[(*h)[0].id] { + heap.Pop(h) + } + if ready == 0 && h.Len() > 0 && (*h)[0].d > clock { + clock = (*h)[0].d + } + f := []int{} + for h.Len() > 0 && (*h)[0].d <= clock { + x := heap.Pop(h).(item) + if active[x.id] { + active[x.id] = false + f = append(f, x.id) + } + } + fmt.Fprint(out, clock, " ", ready, " ", len(f)) + for _, id := range f { + fmt.Fprint(out, " ", id) + } + fmt.Fprintln(out) + } + } +} diff --git a/problems/006-logical-poll-clock/solutions/javascript/main.js b/problems/006-logical-poll-clock/solutions/javascript/main.js new file mode 100644 index 0000000..df932f6 --- /dev/null +++ b/problems/006-logical-poll-clock/solutions/javascript/main.js @@ -0,0 +1,92 @@ +import * as std from "std"; +/** @typedef {[bigint, number]} Item */ +/** @type {string} */ +const input = std.in.readAsString(); +let cursor = 0; +/** @returns {string} */ +function nextToken() { + while (cursor < input.length && input.charCodeAt(cursor) <= 32) cursor++; + const start = cursor; + while (cursor < input.length && input.charCodeAt(cursor) > 32) cursor++; + return input.slice(start, cursor); +} +const N = Number(nextToken()); +/** @type {Item[]} */ +const h = []; +/** @type {boolean[]} */ +const active = Array(N + 1).fill(false); +/** + * @param {Item} a + * @param {Item} b + * @returns {boolean} + */ +const less = (a, b) => a[0] < b[0] || (a[0] === b[0] && a[1] < b[1]); +/** @param {Item} x */ +function push(x) { + let i = h.length; + h.push(x); + while (i) { + let q = (i - 1) >> 1; + if (!less(x, h[q])) break; + h[i] = h[q]; + i = q; + } + h[i] = x; +} +/** @returns {Item} */ +function pop() { + const r = h[0], x = /** @type {Item} */ (h.pop()); + if (h.length) { + let i = 0; + while (i * 2 + 1 < h.length) { + let c = i * 2 + 1; + if (c + 1 < h.length && less(h[c + 1], h[c])) c++; + if (!less(h[c], x)) break; + h[i] = h[c]; + i = c; + } + h[i] = x; + } + return r; +} +let clock = 0n; +let output = ""; +/** @param {string} text */ +function emit(text) { + if (text.length >= 65536) { + if (output.length) std.out.puts(output); + std.out.puts(text); + output = ""; + return; + } + if (output.length + text.length > 65536) { + std.out.puts(output); + output = ""; + } + output += text; +} +for (let z = 0; z < N; z++) { + const op = nextToken(); + if (op === "T") { + const id = Number(nextToken()), d = BigInt(nextToken()); + active[id] = true; + push([d, id]); + } else if (op === "C") active[Number(nextToken())] = false; + else { + const ready = Number(nextToken()); + while (h.length && !active[h[0][1]]) pop(); + if (ready === 0 && h.length && h[0][0] > clock) clock = h[0][0]; + const f = /** @type {number[]} */ ([]); + while (h.length && h[0][0] <= clock) { + const x = pop(); + if (active[x[1]]) { + active[x[1]] = false; + f.push(x[1]); + } + } + emit(`${clock} ${ready} ${f.length}`); + for (const id of f) emit(` ${id}`); + emit("\n"); + } +} +if (output.length) std.out.puts(output); diff --git a/problems/006-logical-poll-clock/solutions/python/main.py b/problems/006-logical-poll-clock/solutions/python/main.py new file mode 100644 index 0000000..8160953 --- /dev/null +++ b/problems/006-logical-poll-clock/solutions/python/main.py @@ -0,0 +1,33 @@ +import heapq, sys + +t = sys.stdin.buffer.read().split() +it = iter(t) +N = int(next(it)) +h = [] +active = [False] * (N + 1) +clock = 0 +out = [] +for _ in range(N): + op = next(it) + if op == b"T": + x, d = int(next(it)), int(next(it)) + active[x] = True + heapq.heappush(h, (d, x)) + elif op == b"C": + active[int(next(it))] = False + else: + ready = int(next(it)) + while h and not active[h[0][1]]: + heapq.heappop(h) + if ready == 0 and h: + clock = max(clock, h[0][0]) + f = [] + while h and h[0][0] <= clock: + d, x = heapq.heappop(h) + if active[x]: + active[x] = False + f.append(x) + out.append( + f"{clock} {ready} {len(f)}" + (" " + " ".join(map(str, f)) if f else "") + ) +print("\n".join(out)) diff --git a/problems/006-logical-poll-clock/solutions/rust/main.rs b/problems/006-logical-poll-clock/solutions/rust/main.rs new file mode 100644 index 0000000..2aadf9b --- /dev/null +++ b/problems/006-logical-poll-clock/solutions/rust/main.rs @@ -0,0 +1,58 @@ +use std::cmp::Reverse; +use std::collections::BinaryHeap; +use std::io::{self, Read}; +fn main() { + let mut s = String::new(); + io::stdin().read_to_string(&mut s).unwrap(); + let mut t = s.split_whitespace(); + let n: usize = t.next().unwrap().parse().unwrap(); + let mut h = BinaryHeap::>::new(); + let mut active = vec![false; n + 1]; + let mut clock = 0u64; + let mut out = String::new(); + for _ in 0..n { + match t.next().unwrap() { + "T" => { + let id: usize = t.next().unwrap().parse().unwrap(); + let d: u64 = t.next().unwrap().parse().unwrap(); + active[id] = true; + h.push(Reverse((d, id))); + } + "C" => { + let id: usize = t.next().unwrap().parse().unwrap(); + active[id] = false; + } + _ => { + let ready: u64 = t.next().unwrap().parse().unwrap(); + while let Some(Reverse((_, id))) = h.peek() { + if active[*id] { + break; + } + h.pop(); + } + if ready == 0 { + if let Some(Reverse((d, _))) = h.peek() { + clock = clock.max(*d); + } + } + let mut f = Vec::new(); + while let Some(Reverse((d, id))) = h.peek().copied() { + if d > clock { + break; + } + h.pop(); + if active[id] { + active[id] = false; + f.push(id); + } + } + out += &format!("{} {} {}", clock, ready, f.len()); + for id in f { + out += &format!(" {}", id); + } + out.push('\n'); + } + } + } + print!("{}", out); +} diff --git a/problems/006-logical-poll-clock/solutions/typescript/main.ts b/problems/006-logical-poll-clock/solutions/typescript/main.ts new file mode 100644 index 0000000..a539f2d --- /dev/null +++ b/problems/006-logical-poll-clock/solutions/typescript/main.ts @@ -0,0 +1,81 @@ +import * as std from "std"; +type Item = [bigint, number]; +const input: string = std.in.readAsString(); +let cursor = 0; +function nextToken(): string { + while (cursor < input.length && input.charCodeAt(cursor) <= 32) cursor++; + const start = cursor; + while (cursor < input.length && input.charCodeAt(cursor) > 32) cursor++; + return input.slice(start, cursor); +} +const N = Number(nextToken()), + h: Item[] = [], + active: boolean[] = Array(N + 1).fill(false), + less = (a: Item, b: Item): boolean => + a[0] < b[0] || (a[0] === b[0] && a[1] < b[1]); +function push(x: Item) { + let i = h.length; + h.push(x); + while (i) { + const q = (i - 1) >> 1; + if (!less(x, h[q])) break; + h[i] = h[q]; + i = q; + } + h[i] = x; +} +function pop(): Item { + const r = h[0], x = h.pop() as Item; + if (h.length) { + let i = 0; + while (i * 2 + 1 < h.length) { + let c = i * 2 + 1; + if (c + 1 < h.length && less(h[c + 1], h[c])) c++; + if (!less(h[c], x)) break; + h[i] = h[c]; + i = c; + } + h[i] = x; + } + return r; +} +let clock = 0n; +let output = ""; +function emit(text: string): void { + if (text.length >= 65536) { + if (output.length) std.out.puts(output); + std.out.puts(text); + output = ""; + return; + } + if (output.length + text.length > 65536) { + std.out.puts(output); + output = ""; + } + output += text; +} +for (let z = 0; z < N; z++) { + const op = nextToken(); + if (op === "T") { + const id = Number(nextToken()), d = BigInt(nextToken()); + active[id] = true; + push([d, id]); + } else if (op === "C") active[Number(nextToken())] = false; + else { + const ready = Number(nextToken()); + while (h.length && !active[h[0][1]]) pop(); + if (ready === 0 && h.length && h[0][0] > clock) clock = h[0][0]; + const f: number[] = []; + while (h.length && h[0][0] <= clock) { + const x = pop(); + if (active[x[1]]) { + active[x[1]] = false; + f.push(x[1]); + } + } + emit(`${clock} ${ready} ${f.length}`); + for (const id of f) emit(` ${id}`); + emit("\n"); + } +} +if (output.length) std.out.puts(output); diff --git a/problems/006-logical-poll-clock/statement.en.md b/problems/006-logical-poll-clock/statement.en.md new file mode 100644 index 0000000..daafc0b --- /dev/null +++ b/problems/006-logical-poll-clock/statement.en.md @@ -0,0 +1,118 @@ +# Non-Blocking Logical Clock + +While designing a deterministic runtime for a WASM OJ, polling cannot depend on how much time passes on the host. If the same program observed different timer behavior because of machine speed or system load, judging would not be reproducible. We therefore use a logical clock and, when no event is immediately ready, advance it directly to the next deadline. + +The logical clock is initially `0`. The system never waits in real time and instead processes `N` commands in order: + +- `T id deadline`: add a timer with an absolute deadline. Each `id` is added only once in the entire input. +- `C id`: cancel a timer that is currently active. +- `P ready`: perform one poll; `ready` is the current number of ready file-descriptor events. + +Every poll must follow these rules: + +1. If `ready>0`, the clock does not advance. +2. If `ready=0`, no active timer has deadline at most the current clock, and at least one active timer exists, immediately fast-forward the clock to the minimum active deadline. +3. Then fire and remove every active timer with `deadline≤clock`. +4. If `ready=0` and there is no active timer, the clock is unchanged. The clock never moves backward. + +Simulate this policy so that timer firing depends only on the commands and the logical clock, never on any real waiting time. + +## Input + +The first line contains `N`, followed by `N` command lines. Every `C` names a timer that is currently active, and there is at least one `P` command. + +## Output + +For each `P`, output one line: + +```text +clock ready fired id1 id2 ... +``` + +The first three fields are always present. If `fired=0`, the line ends immediately after `fired`. Fired IDs must be ordered increasingly by `(deadline,id)`, comparing both components numerically. This also defines the tie-break for equal deadlines. + +## Constraints + +- `1 ≤ N ≤ 200000` +- `1 ≤ id ≤ N` +- `0 ≤ deadline ≤ 9×10^18` +- `0 ≤ ready ≤ 10^9` + +The full constraints rule out scanning every active timer on every poll. + +## Examples + + + +### Example One + +Input: + +```text +8 +T 1 5 +T 2 3 +P 0 +P 2 +T 3 1 +P 1 +C 1 +P 0 +``` + +Output: + +```text +3 0 1 2 +3 2 0 +3 1 1 3 +3 0 0 +``` + +### Example Two + +Input: + +```text +5 +T 3 10 +T 1 10 +T 2 10 +P 0 +P 0 +``` + +Output: + +```text +10 0 3 1 2 3 +10 0 0 +``` + +### Example Three + +Input: + +```text +9 +T 1 8 +T 2 4 +C 2 +P 0 +T 4 8 +T 3 7 +P 5 +P 0 +P 0 +``` + +Output: + +```text +8 0 1 1 +8 5 2 3 4 +8 0 0 +8 0 0 +``` + + diff --git a/problems/006-logical-poll-clock/statement.zh-TW.md b/problems/006-logical-poll-clock/statement.zh-TW.md new file mode 100644 index 0000000..428e966 --- /dev/null +++ b/problems/006-logical-poll-clock/statement.zh-TW.md @@ -0,0 +1,118 @@ +# 不等待的虛擬時鐘 + +在設計 WASM OJ 的確定性執行環境時,poll 不能真的依賴主機經過了多少時間。同一份程式若因電腦速度或系統負載不同而看到不同的 timer 結果,判題便無法重現。因此,我們使用 logical clock,並在沒有立即可處理的事件時直接推進到下一個 deadline。 + +logical clock 初始為 `0`。系統不會實際等待,而是依序處理 `N` 個命令: + +- `T id deadline`:加入絕對 deadline 的 timer。每個 `id` 在整份輸入只加入一次。 +- `C id`:取消目前仍 active 的 timer。 +- `P ready`:執行一次 poll;`ready` 是當下已 ready 的 fd 事件數。 + +每次 poll 必須遵守以下規則: + +1. 若 `ready>0`,clock 不前進。 +2. 若 `ready=0`、沒有 deadline 不大於目前 clock 的 active timer、但仍有 active timer,clock 立刻快轉到最小 active deadline。 +3. 接著觸發並移除所有 `deadline≤clock` 的 active timer。 +4. 若 `ready=0` 且沒有 active timer,clock 不變。clock 永不倒退。 + +請模擬這套規則,讓 timer 的觸發只由命令與 logical clock 決定,而不依賴任何實際等待時間。 + +## 輸入 + +第一行 `N`,接著 `N` 行命令。輸入保證 `C` 指向目前 active 的 timer,且至少有一個 `P` 命令。 + +## 輸出 + +每個 `P` 輸出一行: + +```text +clock ready fired id1 id2 ... +``` + +前三個欄位必定存在;若 `fired=0`,行在 `fired` 後結束。觸發 ID 依 `(deadline,id)` 遞增排列,兩者皆以數值比較。這也定義了相同 deadline 的 tie-break。 + +## 限制 + +- `1 ≤ N ≤ 200000` +- `1 ≤ id ≤ N` +- `0 ≤ deadline ≤ 9×10^18` +- `0 ≤ ready ≤ 10^9` + +完整限制排除每次 POLL 掃描全部 active timer。 + +## 範例 + + + +### 範例一 + +輸入: + +```text +8 +T 1 5 +T 2 3 +P 0 +P 2 +T 3 1 +P 1 +C 1 +P 0 +``` + +輸出: + +```text +3 0 1 2 +3 2 0 +3 1 1 3 +3 0 0 +``` + +### 範例二 + +輸入: + +```text +5 +T 3 10 +T 1 10 +T 2 10 +P 0 +P 0 +``` + +輸出: + +```text +10 0 3 1 2 3 +10 0 0 +``` + +### 範例三 + +輸入: + +```text +9 +T 1 8 +T 2 4 +C 2 +P 0 +T 4 8 +T 3 7 +P 5 +P 0 +P 0 +``` + +輸出: + +```text +8 0 1 1 +8 5 2 3 4 +8 0 0 +8 0 0 +``` + + diff --git a/problems/006-logical-poll-clock/tests/adversarial-01.in b/problems/006-logical-poll-clock/tests/adversarial-01.in new file mode 100644 index 0000000..2288bdc --- /dev/null +++ b/problems/006-logical-poll-clock/tests/adversarial-01.in @@ -0,0 +1,14 @@ +13 +T 1 5 +T 2 10 +P 0 +C 2 +T 3 3 +P 4 +T 4 8 +T 5 8 +P 1 +C 4 +T 6 8 +P 0 +P 0 diff --git a/problems/006-logical-poll-clock/tests/adversarial-01.out b/problems/006-logical-poll-clock/tests/adversarial-01.out new file mode 100644 index 0000000..8257a0e --- /dev/null +++ b/problems/006-logical-poll-clock/tests/adversarial-01.out @@ -0,0 +1,5 @@ +5 0 1 1 +5 4 1 3 +5 1 0 +8 0 2 5 6 +8 0 0 diff --git a/problems/006-logical-poll-clock/tests/sample-01.in b/problems/006-logical-poll-clock/tests/sample-01.in new file mode 100644 index 0000000..8120976 --- /dev/null +++ b/problems/006-logical-poll-clock/tests/sample-01.in @@ -0,0 +1,9 @@ +8 +T 1 5 +T 2 3 +P 0 +P 2 +T 3 1 +P 1 +C 1 +P 0 diff --git a/problems/006-logical-poll-clock/tests/sample-01.out b/problems/006-logical-poll-clock/tests/sample-01.out new file mode 100644 index 0000000..7d8b95a --- /dev/null +++ b/problems/006-logical-poll-clock/tests/sample-01.out @@ -0,0 +1,4 @@ +3 0 1 2 +3 2 0 +3 1 1 3 +3 0 0 diff --git a/problems/006-logical-poll-clock/tests/sample-02.in b/problems/006-logical-poll-clock/tests/sample-02.in new file mode 100644 index 0000000..4267ae6 --- /dev/null +++ b/problems/006-logical-poll-clock/tests/sample-02.in @@ -0,0 +1,6 @@ +5 +T 3 10 +T 1 10 +T 2 10 +P 0 +P 0 diff --git a/problems/006-logical-poll-clock/tests/sample-02.out b/problems/006-logical-poll-clock/tests/sample-02.out new file mode 100644 index 0000000..d694f51 --- /dev/null +++ b/problems/006-logical-poll-clock/tests/sample-02.out @@ -0,0 +1,2 @@ +10 0 3 1 2 3 +10 0 0 diff --git a/problems/006-logical-poll-clock/tests/sample-03.in b/problems/006-logical-poll-clock/tests/sample-03.in new file mode 100644 index 0000000..b5e373a --- /dev/null +++ b/problems/006-logical-poll-clock/tests/sample-03.in @@ -0,0 +1,10 @@ +9 +T 1 8 +T 2 4 +C 2 +P 0 +T 4 8 +T 3 7 +P 5 +P 0 +P 0 diff --git a/problems/006-logical-poll-clock/tests/sample-03.out b/problems/006-logical-poll-clock/tests/sample-03.out new file mode 100644 index 0000000..437a41b --- /dev/null +++ b/problems/006-logical-poll-clock/tests/sample-03.out @@ -0,0 +1,4 @@ +8 0 1 1 +8 5 2 3 4 +8 0 0 +8 0 0 diff --git a/problems/006-logical-poll-clock/validator.py b/problems/006-logical-poll-clock/validator.py new file mode 100644 index 0000000..f7d3c1a --- /dev/null +++ b/problems/006-logical-poll-clock/validator.py @@ -0,0 +1,61 @@ +import heapq, re, sys + + +def fail(): + raise SystemExit(1) + + +try: + t = sys.stdin.buffer.read().decode("utf-8").split() + p = 0 + + def u(a, b): + global p + if p >= len(t) or re.fullmatch(r"0|[1-9][0-9]*", t[p]) is None: + fail() + v = int(t[p]) + p += 1 + if not a <= v <= b: + fail() + return v + + N = u(1, 200000) + seen = set() + active = set() + h = [] + clock = 0 + polls = 0 + for _ in range(N): + if p >= len(t): + fail() + op = t[p] + p += 1 + if op == "T": + x = u(1, N) + deadline = u(0, 9 * 10**18) + if x in seen: + fail() + seen.add(x) + active.add(x) + heapq.heappush(h, (deadline, x)) + elif op == "C": + x = u(1, N) + if x not in active: + fail() + active.remove(x) + elif op == "P": + ready = u(0, 10**9) + polls += 1 + while h and h[0][1] not in active: + heapq.heappop(h) + if ready == 0 and h: + clock = max(clock, h[0][0]) + while h and h[0][0] <= clock: + _, x = heapq.heappop(h) + active.discard(x) + else: + fail() + if polls == 0 or p != len(t): + fail() +except (UnicodeDecodeError, ValueError, OverflowError): + fail() diff --git a/problems/007-guest-path-firewall/editorial.en.md b/problems/007-guest-path-firewall/editorial.en.md new file mode 100644 index 0000000..080817d --- /dev/null +++ b/problems/007-guest-path-firewall/editorial.en.md @@ -0,0 +1,26 @@ +# Editorial + +## Intuitive Approach + +Repeatedly search the string for `//`, `/./`, and `name/..`, rebuilding it after each match. Every rewrite can move `Θ(L)` characters, and inputs such as `/a/a/.../../..` can trigger linearly many rewrites, for `O(L^2)` worst-case time. + +## Optimal Approach: Segment Stack + +Split on `/` while maintaining a stack of ordinary segments. Do nothing for an empty segment or `.`; push an ordinary segment; for `..`, pop if possible and otherwise immediately mark the path invalid. Finally join the stack with `/`; an empty stack represents the root. + +An implementation may store the segments themselves or just their starting positions and lengths in the original string. The latter is the same algorithm but avoids copying intermediate substrings. + +## Correctness Proof + +Induct from left to right over processed segments. After every prefix, the stack, in order, equals the ordinary segments remaining after lexical normalization of that prefix. Empty segments and `.` do not change the path; an ordinary segment is appended, matching a push; and `..` removes the most recent ordinary segment, matching a pop. If the stack is empty, the specification defines this as escaping the root, which the algorithm correctly rejects. After all segments, the stack is exactly the canonical path's segment sequence, and joining it with single slashes yields the unique required output. + +## Complexity + +Every character is scanned a constant number of times, and every segment is pushed and popped at most once. Total time is `O(L)` and additional space is `O(L)` across all input (or the maximum single-path length when storage is reused). Reading and writing already require `Ω(L)` time. + +## Common Mistakes + +- Treating `...`, `.config`, or `..hidden` as special segments. +- Silently ignoring `..` at the root; this problem requires `INVALID`. +- Continuing after an escape and allowing later segments to "repair" it. +- Printing the root as an empty string or retaining a trailing slash. diff --git a/problems/007-guest-path-firewall/editorial.zh-TW.md b/problems/007-guest-path-firewall/editorial.zh-TW.md new file mode 100644 index 0000000..6155220 --- /dev/null +++ b/problems/007-guest-path-firewall/editorial.zh-TW.md @@ -0,0 +1,26 @@ +# 解題說明 + +## 直覺解法 + +可反覆在字串中搜尋 `//`、`/./` 與 `name/..` 再建立新字串。每次重寫可能搬動 `Θ(L)` 字元,而 `/a/a/.../../..` 類輸入可觸發線性次重寫,最壞 `O(L^2)`。 + +## 最佳解法 + +以 `/` 切出 segment,維護普通 segment stack。空字串與 `.` 不動作;普通 segment push;`..` 在 stack 非空時 pop,否則立刻標記 INVALID。最後用 `/` 串接 stack;空 stack 輸出 root。 + +實作可儲存 segment 本身,或只記錄原字串中的起點與長度。後者仍是同一演算法且避免複製中間字串。 + +## 正確性證明 + +從左到右歸納:處理任意前綴後,stack 依序等於該前綴 lexical normalization 後仍存在的普通 segments。空 segment 與 `.` 不改變路徑;普通 segment 應追加,對應 push;`..` 應移除最近的普通 segment,對應 pop。若 stack 空,規格定義為穿越 root,演算法正確回報 INVALID。全部處理後,stack 因而恰是 canonical path 的 segments,以單一斜線串接即得唯一答案。 + +## 複雜度 + +每個字元被掃描常數次,每個 segment push、pop 至多一次;所有輸入總時間 `O(L)`、額外空間 `O(L)`(逐 path 重用時為最大單一路徑長度)。讀取與輸出已有 `Ω(L)` 下界。 + +## 常見錯誤 + +- 將 `...`、`.config` 或 `..hidden` 誤認為特殊 segment。 +- 把 root 上的 `..` 靜默忽略;本題必須 INVALID。 +- 在發生穿越後繼續處理並讓後續 segment「補回來」。 +- 輸出 root 為空字串或保留尾斜線。 diff --git a/problems/007-guest-path-firewall/generator.py b/problems/007-guest-path-firewall/generator.py new file mode 100644 index 0000000..28f558e --- /dev/null +++ b/problems/007-guest-path-firewall/generator.py @@ -0,0 +1,16 @@ +import random, sys + +if len(sys.argv) != 3: + raise SystemExit("usage: generator.py SEED INDEX") +r = random.Random((int(sys.argv[1]) << 32) ^ int(sys.argv[2])) +idx = int(sys.argv[2]) +n = r.randint(1, 5 + idx % 8) +paths = [] +for _ in range(n): + seg = [ + r.choice(("", ".", "..", "a", "b2", "x_y", "...", "..hidden")) + for _ in range(r.randint(0, 10)) + ] + paths.append("/" + "/".join(seg) + ("/" if r.random() < 0.3 else "")) +print(n) +print("\n".join(paths)) diff --git a/problems/007-guest-path-firewall/oracle.py b/problems/007-guest-path-firewall/oracle.py new file mode 100644 index 0000000..35af279 --- /dev/null +++ b/problems/007-guest-path-firewall/oracle.py @@ -0,0 +1,26 @@ +import sys + +lines = sys.stdin.buffer.read().decode().splitlines() +out = [] +for path in lines[1:]: + seg = path.split("/") + removed = [False] * len(seg) + bad = False + for i, x in enumerate(seg): + if x in ("", "."): + removed[i] = True + elif x == "..": + removed[i] = True + j = i - 1 + while j >= 0 and removed[j]: + j -= 1 + if j < 0: + bad = True + break + removed[j] = True + out.append( + "INVALID" + if bad + else "/" + ("/".join(x for i, x in enumerate(seg) if not removed[i])) + ) +print("\n".join(out)) diff --git a/problems/007-guest-path-firewall/problem.json b/problems/007-guest-path-firewall/problem.json new file mode 100644 index 0000000..e056fb3 --- /dev/null +++ b/problems/007-guest-path-firewall/problem.json @@ -0,0 +1,146 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 7, + "slug": "guest-path-firewall", + "title": { + "zh-TW": "Guest Path 防火牆", + "en": "Guest Path Firewall" + }, + "difficulty": "medium", + "tags": [ + "stack", + "string", + "path-normalization" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-01", + "kind": "adversarial", + "input": "tests/adversarial-01.in", + "output": "tests/adversarial-01.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 8500000, + "memoryLimitBytes": 536870912 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 1500000, + "memoryLimitBytes": 402653184 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 450000, + "memoryLimitBytes": 268435456 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "反覆搜尋並重寫可約簡片段", + "en": "Repeated Search and String Rewriting" + }, + "time": "O(L^2)", + "space": "O(L)", + "accepted": false + }, + { + "name": { + "zh-TW": "單趟 segment stack", + "en": "Single-Pass Segment Stack" + }, + "time": "O(L)", + "space": "O(L)", + "accepted": true + } + ] +} diff --git a/problems/007-guest-path-firewall/solutions/c/main.c b/problems/007-guest-path-firewall/solutions/c/main.c new file mode 100644 index 0000000..f985157 --- /dev/null +++ b/problems/007-guest-path-firewall/solutions/c/main.c @@ -0,0 +1,47 @@ +#include +#include +#include +int main(void) { + int n; + if (scanf("%d", &n) != 1) + return 0; + char *s = malloc(200001); + int *st = malloc(200001 * sizeof(*st)), *ln = malloc(200001 * sizeof(*ln)); + while (n--) { + scanf("%200000s", s); + int top = 0, bad = 0, L = (int)strlen(s), start = 1; + for (int i = 1; i <= L; i++) + if (i == L || s[i] == '/') { + int len = i - start; + if (len == 0 || (len == 1 && s[start] == '.')) { + } else if (len == 2 && s[start] == '.' && s[start + 1] == '.') { + if (!top) { + bad = 1; + break; + } + top--; + } else { + st[top] = start; + ln[top] = len; + top++; + } + start = i + 1; + } + if (bad) + puts("INVALID"); + else { + if (!top) + puts("/"); + else { + for (int i = 0; i < top; i++) { + putchar('/'); + fwrite(s + st[i], 1, (size_t)ln[i], stdout); + } + putchar('\n'); + } + } + } + free(s); + free(st); + free(ln); +} diff --git a/problems/007-guest-path-firewall/solutions/cpp/main.cpp b/problems/007-guest-path-firewall/solutions/cpp/main.cpp new file mode 100644 index 0000000..2ef0920 --- /dev/null +++ b/problems/007-guest-path-firewall/solutions/cpp/main.cpp @@ -0,0 +1,42 @@ +#include +#include +#include +#include +using namespace std; +int main() { + ios::sync_with_stdio(false); + cin.tie(nullptr); + int n; + if (!(cin >> n)) + return 0; + while (n--) { + string s; + cin >> s; + vector st; + bool bad = false; + size_t b = 1; + for (size_t i = 1; i <= s.size(); i++) + if (i == s.size() || s[i] == '/') { + string_view x(s.data() + b, i - b); + if (x.empty() || x == ".") { + } else if (x == "..") { + if (st.empty()) { + bad = true; + break; + } + st.pop_back(); + } else + st.push_back(x); + b = i + 1; + } + if (bad) + cout << "INVALID\n"; + else if (st.empty()) + cout << "/\n"; + else { + for (auto x : st) + cout << '/' << x; + cout << '\n'; + } + } +} diff --git a/problems/007-guest-path-firewall/solutions/go/main.go b/problems/007-guest-path-firewall/solutions/go/main.go new file mode 100644 index 0000000..e6a022b --- /dev/null +++ b/problems/007-guest-path-firewall/solutions/go/main.go @@ -0,0 +1,45 @@ +package main + +import ( + "bufio" + "fmt" + "os" + "strings" +) + +func main() { + in := bufio.NewReader(os.Stdin) + out := bufio.NewWriter(os.Stdout) + defer out.Flush() + var n int + if _, e := fmt.Fscan(in, &n); e != nil { + return + } + for ; n > 0; n-- { + var path string + fmt.Fscan(in, &path) + st := []string{} + bad := false + for _, x := range strings.Split(path, "/") { + if x == "" || x == "." { + continue + } + if x == ".." { + if len(st) == 0 { + bad = true + break + } + st = st[:len(st)-1] + } else { + st = append(st, x) + } + } + if bad { + fmt.Fprintln(out, "INVALID") + } else if len(st) == 0 { + fmt.Fprintln(out, "/") + } else { + fmt.Fprintln(out, "/"+strings.Join(st, "/")) + } + } +} diff --git a/problems/007-guest-path-firewall/solutions/javascript/main.js b/problems/007-guest-path-firewall/solutions/javascript/main.js new file mode 100644 index 0000000..71fe1d9 --- /dev/null +++ b/problems/007-guest-path-firewall/solutions/javascript/main.js @@ -0,0 +1,43 @@ +import * as std from "std"; +/** @type {string} */ +const input = std.in.readAsString(); +let cursor = 0; +/** @returns {string} */ +function nextToken() { + while (cursor < input.length && input.charCodeAt(cursor) <= 32) cursor++; + const start = cursor; + while (cursor < input.length && input.charCodeAt(cursor) > 32) cursor++; + return input.slice(start, cursor); +} +let output = ""; +/** @param {string} line */ +function emit(line) { + if (line.length >= 65536) { + if (output.length) std.out.puts(output); + std.out.puts(line); + output = ""; + return; + } + if (output.length + line.length > 65536) { + std.out.puts(output); + output = ""; + } + output += line; +} +const N = Number(nextToken()); +for (let i = 0; i < N; i++) { + const st = /** @type {string[]} */ ([]); + let bad = false; + for (const x of nextToken().split("/")) { + if (x === "" || x === ".") continue; + if (x === "..") { + if (!st.length) { + bad = true; + break; + } + st.pop(); + } else st.push(x); + } + emit((bad ? "INVALID" : "/" + st.join("/")) + "\n"); +} +if (output.length) std.out.puts(output); diff --git a/problems/007-guest-path-firewall/solutions/python/main.py b/problems/007-guest-path-firewall/solutions/python/main.py new file mode 100644 index 0000000..c5e246d --- /dev/null +++ b/problems/007-guest-path-firewall/solutions/python/main.py @@ -0,0 +1,19 @@ +import sys + +lines = sys.stdin.buffer.read().split() +out = [] +for path in lines[1:]: + st = [] + bad = False + for x in path.split(b"/"): + if not x or x == b".": + continue + if x == b"..": + if not st: + bad = True + break + st.pop() + else: + st.append(x) + out.append(b"INVALID" if bad else b"/" + b"/".join(st)) +sys.stdout.buffer.write(b"\n".join(out) + b"\n") diff --git a/problems/007-guest-path-firewall/solutions/rust/main.rs b/problems/007-guest-path-firewall/solutions/rust/main.rs new file mode 100644 index 0000000..4d39ef7 --- /dev/null +++ b/problems/007-guest-path-firewall/solutions/rust/main.rs @@ -0,0 +1,38 @@ +use std::io::{self, Read}; +fn main() { + let mut s = String::new(); + io::stdin().read_to_string(&mut s).unwrap(); + let mut t = s.split_whitespace(); + let n: usize = t.next().unwrap().parse().unwrap(); + let mut out = String::new(); + for _ in 0..n { + let path = t.next().unwrap(); + let mut st = Vec::new(); + let mut bad = false; + for x in path.split('/') { + if x.is_empty() || x == "." { + continue; + } + if x == ".." { + if st.pop().is_none() { + bad = true; + break; + } + } else { + st.push(x) + } + } + if bad { + out += "INVALID\n" + } else if st.is_empty() { + out += "/\n" + } else { + for x in st { + out.push('/'); + out += x; + } + out.push('\n'); + } + } + print!("{}", out); +} diff --git a/problems/007-guest-path-firewall/solutions/typescript/main.ts b/problems/007-guest-path-firewall/solutions/typescript/main.ts new file mode 100644 index 0000000..be89403 --- /dev/null +++ b/problems/007-guest-path-firewall/solutions/typescript/main.ts @@ -0,0 +1,40 @@ +import * as std from "std"; +const input: string = std.in.readAsString(); +let cursor = 0; +function nextToken(): string { + while (cursor < input.length && input.charCodeAt(cursor) <= 32) cursor++; + const start = cursor; + while (cursor < input.length && input.charCodeAt(cursor) > 32) cursor++; + return input.slice(start, cursor); +} +let output = ""; +function emit(line: string): void { + if (line.length >= 65536) { + if (output.length) std.out.puts(output); + std.out.puts(line); + output = ""; + return; + } + if (output.length + line.length > 65536) { + std.out.puts(output); + output = ""; + } + output += line; +} +const N = Number(nextToken()); +for (let i = 0; i < N; i++) { + const st: string[] = []; + let bad = false; + for (const x of nextToken().split("/")) { + if (x === "" || x === ".") continue; + if (x === "..") { + if (!st.length) { + bad = true; + break; + } + st.pop(); + } else st.push(x); + } + emit((bad ? "INVALID" : "/" + st.join("/")) + "\n"); +} +if (output.length) std.out.puts(output); diff --git a/problems/007-guest-path-firewall/statement.en.md b/problems/007-guest-path-firewall/statement.en.md new file mode 100644 index 0000000..0c5fd16 --- /dev/null +++ b/problems/007-guest-path-firewall/statement.en.md @@ -0,0 +1,108 @@ +# Guest Path Firewall + +A WASM OJ lets submitted programs access an isolated guest file system, but paths supplied by those programs cannot be passed directly to the host. Repeated separators, `.`, and `..` can make different-looking strings refer to the same place or even attempt to cross the guest root. To obtain a consistent result before any real file access, we first perform purely lexical normalization. + +You receive `N` untrusted absolute guest paths. Process the segments of each path from left to right using these POSIX-like rules: + +- Ignore empty segments, which arise from repeated `/` or the leading or trailing `/`. +- Ignore a segment equal to `.`. +- A segment equal to `..` removes the preceding ordinary segment that has not already been removed. +- If no ordinary segment can be removed when `..` is encountered, the path has attempted to escape the guest root and is `INVALID`. Once this happens, the path remains invalid even if later segments would return it to the root. +- Every other segment, including `...`, is ordinary. Case is not converted. + +For a valid path, output its unique canonical absolute form: use a single `/` between segments, contain neither `.` nor `..` segments, and have no trailing slash. If there are no ordinary segments, output `/`. + +The result is determined entirely by the input string; the host file system is neither needed nor consulted. + +## Input + +The first line contains `N`. Each of the next `N` lines contains one path token. Every path begins with `/` and contains no whitespace. + +## Output + +For each path, output its canonical form if valid, or `INVALID` otherwise. + +## Constraints + +- `1 ≤ N ≤ 200000` +- Each path has length from `1` through `200000`. +- The sum `L` of all path lengths is at most `2000000`. +- Paths contain only lowercase ASCII letters, digits, `_`, `-`, `.`, and `/`. +- There is no separate length limit on an ordinary segment. + +This is purely lexical processing: do not query the host filesystem, resolve symlinks, or perform percent decoding. The full constraints rule out quadratic algorithms that repeatedly rewrite an entire string. + +## Examples + + + +### Example One + +Input: + +```text +6 +/a/b +/a/./b//c/ +/a/b/../../c +/../secret +/a/.../b +//// +``` + +Output: + +```text +/a/b +/a/b/c +/c +INVALID +/a/.../b +/ +``` + +### Example Two + +Input: + +```text +4 +/ +/././ +/x/../ +/x/../../x +``` + +Output: + +```text +/ +/ +/ +INVALID +``` + +### Example Three + +Input: + +```text +5 +/a//b///c +/a-b/c_d/9 +/.../../z +/a/..hidden/.. +/a/../..x +``` + +Output: + +```text +/a/b/c +/a-b/c_d/9 +/z +/a +/..x +``` + + diff --git a/problems/007-guest-path-firewall/statement.zh-TW.md b/problems/007-guest-path-firewall/statement.zh-TW.md new file mode 100644 index 0000000..20981eb --- /dev/null +++ b/problems/007-guest-path-firewall/statement.zh-TW.md @@ -0,0 +1,108 @@ +# Guest Path 防火牆 + +WASM OJ 允許使用者程式存取受隔離的 guest 檔案系統,但它提供的 path 不能直接交給主機處理。重複分隔符、`.` 與 `..` 可能讓表面不同的字串指向同一位置,甚至嘗試越過 guest root。為了在任何實際檔案存取前得到一致結果,我們先做純 lexical normalization。 + +你會收到 `N` 個不可信的 absolute guest path。對每個 path,由左到右依序處理 segment,套用以下 POSIX 式規則: + +- 空 segment(重複 `/` 或開頭、結尾的 `/`)忽略; +- segment `.` 忽略; +- segment `..` 移除前一個尚未移除的普通 segment; +- 若遇到 `..` 時沒有普通 segment 可移除,path 曾嘗試穿越 guest root,結果為 `INVALID`。一旦發生,即使後面又回到 root 也仍為無效。 +- 其他 segment(包含 `...`)都是普通 segment,大小寫不做轉換。 + +對合法 path,輸出唯一的 canonical absolute path:segment 之間只使用單一 `/`,不含 `.`、`..` 或尾斜線;若沒有普通 segment,輸出 `/`。 + +這個結果只由輸入字串決定,不需要也不得查詢主機檔案系統。 + +## 輸入 + +第一行 `N`,接下來 `N` 行各有一個 path token。每個 path 都以 `/` 開頭且不含空白。 + +## 輸出 + +每個 path 一行:合法時輸出 canonical path,否則輸出 `INVALID`。 + +## 限制 + +- `1 ≤ N ≤ 200000` +- 每個 path 長度 `1..200000` +- 所有 path 長度總和 `L ≤ 2000000` +- path 只含 ASCII 小寫字母、數字、`_`、`-`、`.`、`/` +- 普通 segment 不另設長度限制 + +這是純 lexical 處理,不查詢 host filesystem、不解析 symlink,也不做 percent decoding。完整限制排除反覆修改整條字串的平方作法。 + +## 範例 + + + +### 範例一 + +輸入: + +```text +6 +/a/b +/a/./b//c/ +/a/b/../../c +/../secret +/a/.../b +//// +``` + +輸出: + +```text +/a/b +/a/b/c +/c +INVALID +/a/.../b +/ +``` + +### 範例二 + +輸入: + +```text +4 +/ +/././ +/x/../ +/x/../../x +``` + +輸出: + +```text +/ +/ +/ +INVALID +``` + +### 範例三 + +輸入: + +```text +5 +/a//b///c +/a-b/c_d/9 +/.../../z +/a/..hidden/.. +/a/../..x +``` + +輸出: + +```text +/a/b/c +/a-b/c_d/9 +/z +/a +/..x +``` + + diff --git a/problems/007-guest-path-firewall/tests/adversarial-01.in b/problems/007-guest-path-firewall/tests/adversarial-01.in new file mode 100644 index 0000000..6cc15c7 --- /dev/null +++ b/problems/007-guest-path-firewall/tests/adversarial-01.in @@ -0,0 +1,9 @@ +8 +/../a +/a/../../a +/a/.../../b +/a/..hidden/.. +//// +/./ +/a//b/./c/../ +/..x/../... diff --git a/problems/007-guest-path-firewall/tests/adversarial-01.out b/problems/007-guest-path-firewall/tests/adversarial-01.out new file mode 100644 index 0000000..1712cc8 --- /dev/null +++ b/problems/007-guest-path-firewall/tests/adversarial-01.out @@ -0,0 +1,8 @@ +INVALID +INVALID +/a/b +/a +/ +/ +/a/b +/... diff --git a/problems/007-guest-path-firewall/tests/sample-01.in b/problems/007-guest-path-firewall/tests/sample-01.in new file mode 100644 index 0000000..42b8c9b --- /dev/null +++ b/problems/007-guest-path-firewall/tests/sample-01.in @@ -0,0 +1,7 @@ +6 +/a/b +/a/./b//c/ +/a/b/../../c +/../secret +/a/.../b +//// diff --git a/problems/007-guest-path-firewall/tests/sample-01.out b/problems/007-guest-path-firewall/tests/sample-01.out new file mode 100644 index 0000000..62f2e9d --- /dev/null +++ b/problems/007-guest-path-firewall/tests/sample-01.out @@ -0,0 +1,6 @@ +/a/b +/a/b/c +/c +INVALID +/a/.../b +/ diff --git a/problems/007-guest-path-firewall/tests/sample-02.in b/problems/007-guest-path-firewall/tests/sample-02.in new file mode 100644 index 0000000..37af05e --- /dev/null +++ b/problems/007-guest-path-firewall/tests/sample-02.in @@ -0,0 +1,5 @@ +4 +/ +/././ +/x/../ +/x/../../x diff --git a/problems/007-guest-path-firewall/tests/sample-02.out b/problems/007-guest-path-firewall/tests/sample-02.out new file mode 100644 index 0000000..9177127 --- /dev/null +++ b/problems/007-guest-path-firewall/tests/sample-02.out @@ -0,0 +1,4 @@ +/ +/ +/ +INVALID diff --git a/problems/007-guest-path-firewall/tests/sample-03.in b/problems/007-guest-path-firewall/tests/sample-03.in new file mode 100644 index 0000000..6db41d8 --- /dev/null +++ b/problems/007-guest-path-firewall/tests/sample-03.in @@ -0,0 +1,6 @@ +5 +/a//b///c +/a-b/c_d/9 +/.../../z +/a/..hidden/.. +/a/../..x diff --git a/problems/007-guest-path-firewall/tests/sample-03.out b/problems/007-guest-path-firewall/tests/sample-03.out new file mode 100644 index 0000000..032cf68 --- /dev/null +++ b/problems/007-guest-path-firewall/tests/sample-03.out @@ -0,0 +1,5 @@ +/a/b/c +/a-b/c_d/9 +/z +/a +/..x diff --git a/problems/007-guest-path-firewall/validator.py b/problems/007-guest-path-firewall/validator.py new file mode 100644 index 0000000..cda4025 --- /dev/null +++ b/problems/007-guest-path-firewall/validator.py @@ -0,0 +1,28 @@ +import re, sys + + +def fail(): + raise SystemExit(1) + + +try: + data = sys.stdin.buffer.read().decode("ascii") + lines = data.splitlines() + if not lines or re.fullmatch(r"[1-9][0-9]*", lines[0]) is None: + fail() + n = int(lines[0]) + if not 1 <= n <= 200000 or len(lines) != n + 1: + fail() + total = 0 + for s in lines[1:]: + if ( + not 1 <= len(s) <= 200000 + or not s.startswith("/") + or re.fullmatch(r"[a-z0-9_./-]+", s) is None + ): + fail() + total += len(s) + if total > 2000000: + fail() +except (UnicodeDecodeError, ValueError, OverflowError): + fail() diff --git a/problems/008-mounted-directory-baseline/editorial.en.md b/problems/008-mounted-directory-baseline/editorial.en.md new file mode 100644 index 0000000..e75384d --- /dev/null +++ b/problems/008-mounted-directory-baseline/editorial.en.md @@ -0,0 +1,39 @@ +# Editorial + +## Intuitive Approach + +Enumerate every parent-directory prefix of every path, then compare it linearly with an array of known directories. With `Θ(S)` distinct directories, searches cost `O(S^2)` in the worst case. Constructing full prefix tuples may also repeatedly copy long prefixes. + +## Advanced Approach: Segment Trie + +Let trie node 0 be the root and initialize the directory count to one. For each file path, insert only its first `k-1` segments. The current node and segment label identify a unique child; create it and increment the directory count if absent. The last segment is a filename and is not inserted. Baseline inodes equal the number of directory nodes plus `M+O`, while baseline bytes can be summed as mounted files are read. + +Children may be stored in a per-node map or in a global hash map keyed by `(node,label)`. Both represent the same segment trie. Hashing is fast on average, but predictable seeds and table layouts can allow legal segments to collide, so this does not provide a deterministic worst-case bound. + +## Optimal Approach: Sorting and Longest Common Prefixes + +Sort all `P=M+O` segment sequences lexicographically. Count the root once. For each path in order, its first `k-1` segments are its parent directories. Let `lcp` be its longest common prefix length with the preceding path. The number of new directories contributed by this path is + +```text +(k-1) - min(k-1, lcp) +``` + +Treat the first path as having `lcp=0`. This avoids an adversarial hash table and is the strategy used by all seven reference solutions. + +## Correctness Proof + +The root uniquely represents `/`. In lexicographic order, all paths sharing a prefix form a contiguous interval. Therefore, if one of the current path's directory prefixes has appeared before, the last previous path having it is the current path's lexicographic predecessor. Conversely, every prefix shared with that predecessor has already appeared. Thus `min(k-1,lcp)` is exactly the number of already-counted parent directories, and every remaining parent directory is new. By induction over sorted paths, the root plus all contributions equals the number of distinct directories. + +Every file consumes one additional inode, and mounted sizes are summed directly, so both baselines are correct. `ACCEPT`, remaining values, and missing values then follow directly from their definitions. + +## Complexity + +Let `P=M+O`. Comparison sorting performs `O(P log P)` path comparisons. Accounting for compared segments in common prefixes gives `O(S log P)` time. The adjacent-LCP scan after sorting totals `O(S)`, and reading and storing paths uses `O(S+P)` space. This is a deterministic portable comparison-model bound; the hash-trie alternative is `O(S)` expected time but lacks the same worst-case guarantee. + +## Common Mistakes + +- Forgetting that the root itself consumes one inode. +- Inserting the filename as a directory, or omitting the pre-created output-file inodes. +- Counting the same parent directory more than once. +- Using a fixed-seed linear-probing hash table that adversarial input can force into quadratic probing. +- Computing unsigned `quota-baseline` on rejection and underflowing. diff --git a/problems/008-mounted-directory-baseline/editorial.zh-TW.md b/problems/008-mounted-directory-baseline/editorial.zh-TW.md new file mode 100644 index 0000000..0b51215 --- /dev/null +++ b/problems/008-mounted-directory-baseline/editorial.zh-TW.md @@ -0,0 +1,39 @@ +# 解題說明 + +## 直覺解法 + +對每條 path 列出所有父目錄 prefix,再與已知目錄陣列逐一比較。若有 `Θ(S)` 個不同目錄,每次搜尋也線性,最壞 `O(S^2)`;建立完整 prefix tuple 也可能重複複製長前綴。 + +## 進階解法:segment trie + +root 是 trie 節點 0,目錄數初始為 1。對每條檔案 path,只插入前 `k-1` 個 segment:目前節點與 segment label 共同決定唯一 child;不存在就建立並把目錄數加一。最後一個 segment 是檔名,不插入目錄 trie。baseline inode 等於目錄節點數加 `M+O`,bytes 則在讀取 mounted file 時直接加總。 + +child 可用每節點 map,或以 `(node,label)` 為 key 的全域 hash map;兩者是同一棵 segment trie。雜湊表平均很快,但若 hash seed 與 table layout 可由測資預測,合法 segment 仍可能全部落在同一 bucket,無法提供 worst-case 保證。 + +## 最佳解法:排序與最長共同前綴 + +把全部 `P=M+O` 條 segment 序列依字典序排序。root 先計一次。依序處理每條 path 時,它的前 `k-1` 個 segment 是父目錄;令它與前一條 path 的最長共同前綴長度為 `lcp`,則本條新增的目錄數為 + +```text +(k-1) - min(k-1, lcp) +``` + +第一條 path 視為 `lcp=0`。這個作法不依賴可被攻擊的 hash table,且所有七份 reference solution 都使用同一策略。 + +## 正確性證明 + +root 唯一對應 `/`。字典序中,具有同一 prefix 的 path 必形成連續區間。因此處理目前 path 時,某個父目錄 prefix 若先前出現過,具有該 prefix 的最後一條先前 path 就是目前 path 的字典序前驅;反之,前驅與目前 path 共同的前綴都已出現。故 `min(k-1,lcp)` 恰是已計數的父目錄數,其餘父目錄各新增一次。歸納處理全部 path 後,root 加上各次新增數正好是不同目錄數。 + +每個檔案另外各占一個 inode,mounted size 直接加總,所以 baseline 正確;ACCEPT、remaining 與 missing 再依定義計算。 + +## 複雜度 + +令 `P=M+O`。comparison sort 至多進行 `O(P log P)` 次 path 比較;把共同前綴的 segment 比較成本計入後,時間上界為 `O(S log P)`。排序後的相鄰 LCP 掃描合計 `O(S)`,讀入與儲存 path 使用 `O(S+P)` 空間。這是 portable comparison model 下的 deterministic bound;hash trie 則為 `O(S) expected`,但不具同等 worst-case 保證。 + +## 常見錯誤 + +- 忘記 root 本身也佔一個 inode。 +- 把檔名 segment 插成目錄,或漏掉預建輸出檔 inode。 +- 將相同父目錄重複計數。 +- 只寫固定 seed 的線性探測或 deterministic hash,讓對抗測資造成平方 probing。 +- REJECT 時直接做無號 `quota-baseline` 而 underflow。 diff --git a/problems/008-mounted-directory-baseline/generator.py b/problems/008-mounted-directory-baseline/generator.py new file mode 100644 index 0000000..9de481a --- /dev/null +++ b/problems/008-mounted-directory-baseline/generator.py @@ -0,0 +1,25 @@ +import random, sys + +if len(sys.argv) != 3: + raise SystemExit("usage: generator.py SEED INDEX") +r = random.Random((int(sys.argv[1]) << 32) ^ int(sys.argv[2])) +idx = int(sys.argv[2]) +cnt = r.randint(1, 5 + idx % 7) +paths = [] +while len(paths) < cnt: + x = tuple( + [r.randint(1, 3) for _ in range(r.randint(1, 4) - 1)] + [100 + len(paths)] + ) + if x not in paths: + paths.append(x) +M = r.randint(0, cnt) +O = cnt - M +sizes = [r.randint(0, 30) for _ in range(M)] +B = r.randint(0, sum(sizes) + 20) +I = r.randint(0, 20) +out = [f"{M} {O} {B} {I}"] +for x, z in zip(paths[:M], sizes): + out.append(f"{len(x)} {' '.join(map(str,x))} {z}") +for x in paths[M:]: + out.append(f"{len(x)} {' '.join(map(str,x))}") +print("\n".join(out)) diff --git a/problems/008-mounted-directory-baseline/oracle.py b/problems/008-mounted-directory-baseline/oracle.py new file mode 100644 index 0000000..294f27a --- /dev/null +++ b/problems/008-mounted-directory-baseline/oracle.py @@ -0,0 +1,19 @@ +import sys + +t = list(map(int, sys.stdin.buffer.read().split())) +it = iter(t) +M, O, B, I = next(it), next(it), next(it), next(it) +dirs = {()} +total = 0 +for j in range(M + O): + k = next(it) + x = tuple(next(it) for _ in range(k)) + for q in range(k): + dirs.add(x[:q]) + if j < M: + total += next(it) +ino = len(dirs) + M + O +if total <= B and ino <= I: + print("ACCEPT", total, ino, B - total, I - ino) +else: + print("REJECT", total, ino, max(0, total - B), max(0, ino - I)) diff --git a/problems/008-mounted-directory-baseline/problem.json b/problems/008-mounted-directory-baseline/problem.json new file mode 100644 index 0000000..6a47237 --- /dev/null +++ b/problems/008-mounted-directory-baseline/problem.json @@ -0,0 +1,155 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 8, + "slug": "mounted-directory-baseline", + "title": { + "zh-TW": "目錄樹的掛載基線", + "en": "Mounted Directory-Tree Baseline" + }, + "difficulty": "medium", + "tags": [ + "sorting", + "longest-common-prefix", + "quota-accounting" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-01", + "kind": "adversarial", + "input": "tests/adversarial-01.in", + "output": "tests/adversarial-01.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 15000000, + "memoryLimitBytes": 536870912 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 2000000, + "memoryLimitBytes": 402653184 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 650000, + "memoryLimitBytes": 268435456 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "逐 prefix 線性搜尋既有目錄", + "en": "Linear Search for Every Directory Prefix" + }, + "time": "O(S^2)", + "space": "O(S)", + "accepted": false + }, + { + "name": { + "zh-TW": "hash segment trie", + "en": "Hashed Segment Trie" + }, + "time": "O(S) expected", + "space": "O(S)", + "accepted": true + }, + { + "name": { + "zh-TW": "字典序排序與相鄰 LCP", + "en": "Lexicographic Sorting and Adjacent LCP" + }, + "time": "O(S log (M+O)) deterministic", + "space": "O(S+M+O)", + "accepted": true + } + ] +} diff --git a/problems/008-mounted-directory-baseline/solutions/c/main.c b/problems/008-mounted-directory-baseline/solutions/c/main.c new file mode 100644 index 0000000..ce33013 --- /dev/null +++ b/problems/008-mounted-directory-baseline/solutions/c/main.c @@ -0,0 +1,120 @@ +#include +#include +#include +#include + +typedef struct { + uint32_t offset; + uint32_t length; +} Path; + +static const uint32_t *segments; + +static int compare_paths(const void *left_ptr, const void *right_ptr) { + const Path *left = left_ptr; + const Path *right = right_ptr; + uint32_t common = left->length < right->length ? left->length : right->length; + + for (uint32_t i = 0; i < common; ++i) { + uint32_t a = segments[left->offset + i]; + uint32_t b = segments[right->offset + i]; + if (a < b) { + return -1; + } + if (a > b) { + return 1; + } + } + return (left->length > right->length) - (left->length < right->length); +} + +static uint32_t common_prefix(const Path *left, const Path *right) { + uint32_t common = left->length < right->length ? left->length : right->length; + uint32_t i = 0; + while (i < common && + segments[left->offset + i] == segments[right->offset + i]) { + ++i; + } + return i; +} + +int main(void) { + int mounted_count; + int output_count; + uint64_t byte_quota; + uint64_t inode_quota; + if (scanf("%d%d%" SCNu64 "%" SCNu64, &mounted_count, &output_count, + &byte_quota, &inode_quota) != 4) { + return 0; + } + + int path_count = mounted_count + output_count; + Path *paths = malloc((size_t)path_count * sizeof(*paths)); + uint32_t *all_segments = malloc(200000U * sizeof(*all_segments)); + if (paths == NULL || all_segments == NULL) { + free(paths); + free(all_segments); + return 1; + } + segments = all_segments; + + uint32_t segment_count = 0; + uint64_t baseline_bytes = 0; + for (int i = 0; i < path_count; ++i) { + int length; + if (scanf("%d", &length) != 1) { + free(paths); + free(all_segments); + return 1; + } + paths[i].offset = segment_count; + paths[i].length = (uint32_t)length; + for (int j = 0; j < length; ++j) { + if (scanf("%u", &all_segments[segment_count++]) != 1) { + free(paths); + free(all_segments); + return 1; + } + } + if (i < mounted_count) { + unsigned long long size; + if (scanf("%llu", &size) != 1) { + free(paths); + free(all_segments); + return 1; + } + baseline_bytes += (uint64_t)size; + } + } + + qsort(paths, (size_t)path_count, sizeof(*paths), compare_paths); + + uint64_t directory_count = 1; + for (int i = 0; i < path_count; ++i) { + uint32_t parent_length = paths[i].length - 1U; + uint32_t already_present = 0; + if (i > 0) { + already_present = common_prefix(&paths[i - 1], &paths[i]); + if (already_present > parent_length) { + already_present = parent_length; + } + } + directory_count += parent_length - already_present; + } + + uint64_t baseline_inodes = directory_count + (uint64_t)path_count; + if (baseline_bytes <= byte_quota && baseline_inodes <= inode_quota) { + printf("ACCEPT %" PRIu64 " %" PRIu64 " %" PRIu64 " %" PRIu64 "\n", + baseline_bytes, baseline_inodes, byte_quota - baseline_bytes, + inode_quota - baseline_inodes); + } else { + printf("REJECT %" PRIu64 " %" PRIu64 " %" PRIu64 " %" PRIu64 "\n", + baseline_bytes, baseline_inodes, + baseline_bytes > byte_quota ? baseline_bytes - byte_quota : 0, + baseline_inodes > inode_quota ? baseline_inodes - inode_quota : 0); + } + + free(paths); + free(all_segments); + return 0; +} diff --git a/problems/008-mounted-directory-baseline/solutions/cpp/main.cpp b/problems/008-mounted-directory-baseline/solutions/cpp/main.cpp new file mode 100644 index 0000000..647ce42 --- /dev/null +++ b/problems/008-mounted-directory-baseline/solutions/cpp/main.cpp @@ -0,0 +1,68 @@ +#include +#include +#include +#include + +int main() { + std::ios::sync_with_stdio(false); + std::cin.tie(nullptr); + + int mounted_count; + int output_count; + std::uint64_t byte_quota; + std::uint64_t inode_quota; + if (!(std::cin >> mounted_count >> output_count >> byte_quota >> + inode_quota)) { + return 0; + } + + const int path_count = mounted_count + output_count; + std::vector> paths(path_count); + std::uint64_t baseline_bytes = 0; + for (int i = 0; i < path_count; ++i) { + int length; + std::cin >> length; + paths[i].resize(static_cast(length)); + for (std::uint32_t &segment : paths[i]) { + std::cin >> segment; + } + if (i < mounted_count) { + std::uint64_t size; + std::cin >> size; + baseline_bytes += size; + } + } + + std::sort(paths.begin(), paths.end()); + + std::uint64_t directory_count = 1; + for (int i = 0; i < path_count; ++i) { + const std::size_t parent_length = paths[i].size() - 1; + std::size_t already_present = 0; + if (i > 0) { + const std::size_t common_limit = + std::min(paths[i - 1].size(), paths[i].size()); + while (already_present < common_limit && + paths[i - 1][already_present] == paths[i][already_present]) { + ++already_present; + } + already_present = std::min(already_present, parent_length); + } + directory_count += parent_length - already_present; + } + + const std::uint64_t baseline_inodes = + directory_count + static_cast(path_count); + if (baseline_bytes <= byte_quota && baseline_inodes <= inode_quota) { + std::cout << "ACCEPT " << baseline_bytes << ' ' << baseline_inodes << ' ' + << byte_quota - baseline_bytes << ' ' + << inode_quota - baseline_inodes << '\n'; + } else { + std::cout << "REJECT " << baseline_bytes << ' ' << baseline_inodes << ' ' + << (baseline_bytes > byte_quota ? baseline_bytes - byte_quota : 0) + << ' ' + << (baseline_inodes > inode_quota ? baseline_inodes - inode_quota + : 0) + << '\n'; + } +} diff --git a/problems/008-mounted-directory-baseline/solutions/go/main.go b/problems/008-mounted-directory-baseline/solutions/go/main.go new file mode 100644 index 0000000..435ef46 --- /dev/null +++ b/problems/008-mounted-directory-baseline/solutions/go/main.go @@ -0,0 +1,85 @@ +package main + +import ( + "bufio" + "fmt" + "os" + "sort" +) + +func pathLess(a, b []uint32) bool { + limit := len(a) + if len(b) < limit { + limit = len(b) + } + for i := 0; i < limit; i++ { + if a[i] != b[i] { + return a[i] < b[i] + } + } + return len(a) < len(b) +} + +func main() { + in := bufio.NewReader(os.Stdin) + out := bufio.NewWriter(os.Stdout) + defer out.Flush() + + var mountedCount, outputCount int + var byteQuota, inodeQuota uint64 + if _, err := fmt.Fscan(in, &mountedCount, &outputCount, &byteQuota, &inodeQuota); err != nil { + return + } + + pathCount := mountedCount + outputCount + paths := make([][]uint32, pathCount) + var baselineBytes uint64 + for i := 0; i < pathCount; i++ { + var length int + fmt.Fscan(in, &length) + paths[i] = make([]uint32, length) + for j := range paths[i] { + fmt.Fscan(in, &paths[i][j]) + } + if i < mountedCount { + var size uint64 + fmt.Fscan(in, &size) + baselineBytes += size + } + } + + sort.Slice(paths, func(i, j int) bool { return pathLess(paths[i], paths[j]) }) + directoryCount := uint64(1) + for i, path := range paths { + parentLength := len(path) - 1 + alreadyPresent := 0 + if i > 0 { + limit := len(paths[i-1]) + if len(path) < limit { + limit = len(path) + } + for alreadyPresent < limit && paths[i-1][alreadyPresent] == path[alreadyPresent] { + alreadyPresent++ + } + if alreadyPresent > parentLength { + alreadyPresent = parentLength + } + } + directoryCount += uint64(parentLength - alreadyPresent) + } + + baselineInodes := directoryCount + uint64(pathCount) + if baselineBytes <= byteQuota && baselineInodes <= inodeQuota { + fmt.Fprintln(out, "ACCEPT", baselineBytes, baselineInodes, + byteQuota-baselineBytes, inodeQuota-baselineInodes) + } else { + var missingBytes, missingInodes uint64 + if baselineBytes > byteQuota { + missingBytes = baselineBytes - byteQuota + } + if baselineInodes > inodeQuota { + missingInodes = baselineInodes - inodeQuota + } + fmt.Fprintln(out, "REJECT", baselineBytes, baselineInodes, missingBytes, missingInodes) + } +} diff --git a/problems/008-mounted-directory-baseline/solutions/javascript/main.js b/problems/008-mounted-directory-baseline/solutions/javascript/main.js new file mode 100644 index 0000000..99c3cd5 --- /dev/null +++ b/problems/008-mounted-directory-baseline/solutions/javascript/main.js @@ -0,0 +1,64 @@ +import * as std from "std"; + +/** @type {string} */ +const input = std.in.readAsString(); +let cursor = 0; +/** @returns {string} */ +function nextToken() { + while (cursor < input.length && input.charCodeAt(cursor) <= 32) cursor++; + const start = cursor; + while (cursor < input.length && input.charCodeAt(cursor) > 32) cursor++; + return input.slice(start, cursor); +} +const mountedCount = Number(nextToken()); +const outputCount = Number(nextToken()); +const byteQuota = BigInt(nextToken()); +const inodeQuota = BigInt(nextToken()); + +const pathCount = mountedCount + outputCount; +const paths = /** @type {number[][]} */ ([]); +let baselineBytes = 0n; +for (let i = 0; i < pathCount; i++) { + const length = Number(nextToken()); + const path = /** @type {number[]} */ ([]); + for (let j = 0; j < length; j++) path.push(Number(nextToken())); + paths.push(path); + if (i < mountedCount) baselineBytes += BigInt(nextToken()); +} + +paths.sort((a, b) => { + const limit = Math.min(a.length, b.length); + for (let i = 0; i < limit; i++) { + if (a[i] !== b[i]) return a[i] - b[i]; + } + return a.length - b.length; +}); + +let directoryCount = 1n; +for (let i = 0; i < pathCount; i++) { + const parentLength = paths[i].length - 1; + let alreadyPresent = 0; + if (i > 0) { + const limit = Math.min(paths[i - 1].length, paths[i].length); + while ( + alreadyPresent < limit && + paths[i - 1][alreadyPresent] === paths[i][alreadyPresent] + ) { + alreadyPresent++; + } + alreadyPresent = Math.min(alreadyPresent, parentLength); + } + directoryCount += BigInt(parentLength - alreadyPresent); +} + +const baselineInodes = directoryCount + BigInt(pathCount); +const accepted = baselineBytes <= byteQuota && baselineInodes <= inodeQuota; +const missingBytes = baselineBytes > byteQuota ? baselineBytes - byteQuota : 0n; +const missingInodes = baselineInodes > inodeQuota + ? baselineInodes - inodeQuota + : 0n; +std.out.puts( + `${accepted ? "ACCEPT" : "REJECT"} ${baselineBytes} ${baselineInodes} ` + + `${accepted ? byteQuota - baselineBytes : missingBytes} ` + + `${accepted ? inodeQuota - baselineInodes : missingInodes}\n`, +); diff --git a/problems/008-mounted-directory-baseline/solutions/python/main.py b/problems/008-mounted-directory-baseline/solutions/python/main.py new file mode 100644 index 0000000..7b034b4 --- /dev/null +++ b/problems/008-mounted-directory-baseline/solutions/python/main.py @@ -0,0 +1,52 @@ +import sys + + +tokens = iter(map(int, sys.stdin.buffer.read().split())) +mounted_count = next(tokens) +output_count = next(tokens) +byte_quota = next(tokens) +inode_quota = next(tokens) + +path_count = mounted_count + output_count +paths: list[tuple[int, ...]] = [] +baseline_bytes = 0 +for index in range(path_count): + length = next(tokens) + paths.append(tuple(next(tokens) for _ in range(length))) + if index < mounted_count: + baseline_bytes += next(tokens) + +paths.sort() +directory_count = 1 +for index, path in enumerate(paths): + parent_length = len(path) - 1 + already_present = 0 + if index > 0: + previous = paths[index - 1] + limit = min(len(previous), len(path)) + while ( + already_present < limit + and previous[already_present] == path[already_present] + ): + already_present += 1 + already_present = min(already_present, parent_length) + directory_count += parent_length - already_present + +baseline_inodes = directory_count + path_count +accepted = baseline_bytes <= byte_quota and baseline_inodes <= inode_quota +if accepted: + print( + "ACCEPT", + baseline_bytes, + baseline_inodes, + byte_quota - baseline_bytes, + inode_quota - baseline_inodes, + ) +else: + print( + "REJECT", + baseline_bytes, + baseline_inodes, + max(0, baseline_bytes - byte_quota), + max(0, baseline_inodes - inode_quota), + ) diff --git a/problems/008-mounted-directory-baseline/solutions/rust/main.rs b/problems/008-mounted-directory-baseline/solutions/rust/main.rs new file mode 100644 index 0000000..2a219d8 --- /dev/null +++ b/problems/008-mounted-directory-baseline/solutions/rust/main.rs @@ -0,0 +1,63 @@ +use std::io::{self, Read}; + +fn main() { + let mut input = String::new(); + io::stdin().read_to_string(&mut input).unwrap(); + let mut tokens = input.split_whitespace(); + + let mounted_count: usize = tokens.next().unwrap().parse().unwrap(); + let output_count: usize = tokens.next().unwrap().parse().unwrap(); + let byte_quota: u64 = tokens.next().unwrap().parse().unwrap(); + let inode_quota: u64 = tokens.next().unwrap().parse().unwrap(); + + let path_count = mounted_count + output_count; + let mut paths = Vec::>::with_capacity(path_count); + let mut baseline_bytes = 0_u64; + for i in 0..path_count { + let length: usize = tokens.next().unwrap().parse().unwrap(); + let mut path = Vec::with_capacity(length); + for _ in 0..length { + path.push(tokens.next().unwrap().parse().unwrap()); + } + paths.push(path); + if i < mounted_count { + baseline_bytes += tokens.next().unwrap().parse::().unwrap(); + } + } + + paths.sort(); + let mut directory_count = 1_u64; + for i in 0..path_count { + let parent_length = paths[i].len() - 1; + let already_present = if i == 0 { + 0 + } else { + paths[i - 1] + .iter() + .zip(&paths[i]) + .take_while(|(a, b)| a == b) + .count() + .min(parent_length) + }; + directory_count += (parent_length - already_present) as u64; + } + + let baseline_inodes = directory_count + path_count as u64; + if baseline_bytes <= byte_quota && baseline_inodes <= inode_quota { + println!( + "ACCEPT {} {} {} {}", + baseline_bytes, + baseline_inodes, + byte_quota - baseline_bytes, + inode_quota - baseline_inodes + ); + } else { + println!( + "REJECT {} {} {} {}", + baseline_bytes, + baseline_inodes, + baseline_bytes.saturating_sub(byte_quota), + baseline_inodes.saturating_sub(inode_quota) + ); + } +} diff --git a/problems/008-mounted-directory-baseline/solutions/typescript/main.ts b/problems/008-mounted-directory-baseline/solutions/typescript/main.ts new file mode 100644 index 0000000..5d64cdb --- /dev/null +++ b/problems/008-mounted-directory-baseline/solutions/typescript/main.ts @@ -0,0 +1,62 @@ +import * as std from "std"; + +const input: string = std.in.readAsString(); +let cursor = 0; +function nextToken(): string { + while (cursor < input.length && input.charCodeAt(cursor) <= 32) cursor++; + const start = cursor; + while (cursor < input.length && input.charCodeAt(cursor) > 32) cursor++; + return input.slice(start, cursor); +} +const mountedCount = Number(nextToken()); +const outputCount = Number(nextToken()); +const byteQuota = BigInt(nextToken()); +const inodeQuota = BigInt(nextToken()); + +const pathCount = mountedCount + outputCount; +const paths: number[][] = []; +let baselineBytes = 0n; +for (let i = 0; i < pathCount; i++) { + const length = Number(nextToken()); + const path: number[] = []; + for (let j = 0; j < length; j++) path.push(Number(nextToken())); + paths.push(path); + if (i < mountedCount) baselineBytes += BigInt(nextToken()); +} + +paths.sort((a: number[], b: number[]): number => { + const limit = Math.min(a.length, b.length); + for (let i = 0; i < limit; i++) { + if (a[i] !== b[i]) return a[i] - b[i]; + } + return a.length - b.length; +}); + +let directoryCount = 1n; +for (let i = 0; i < pathCount; i++) { + const parentLength = paths[i].length - 1; + let alreadyPresent = 0; + if (i > 0) { + const limit = Math.min(paths[i - 1].length, paths[i].length); + while ( + alreadyPresent < limit && + paths[i - 1][alreadyPresent] === paths[i][alreadyPresent] + ) { + alreadyPresent++; + } + alreadyPresent = Math.min(alreadyPresent, parentLength); + } + directoryCount += BigInt(parentLength - alreadyPresent); +} + +const baselineInodes = directoryCount + BigInt(pathCount); +const accepted = baselineBytes <= byteQuota && baselineInodes <= inodeQuota; +const missingBytes = baselineBytes > byteQuota ? baselineBytes - byteQuota : 0n; +const missingInodes = baselineInodes > inodeQuota + ? baselineInodes - inodeQuota + : 0n; +std.out.puts( + `${accepted ? "ACCEPT" : "REJECT"} ${baselineBytes} ${baselineInodes} ` + + `${accepted ? byteQuota - baselineBytes : missingBytes} ` + + `${accepted ? inodeQuota - baselineInodes : missingInodes}\n`, +); diff --git a/problems/008-mounted-directory-baseline/statement.en.md b/problems/008-mounted-directory-baseline/statement.en.md new file mode 100644 index 0000000..8b8025b --- /dev/null +++ b/problems/008-mounted-directory-baseline/statement.en.md @@ -0,0 +1,102 @@ +# Mounted Directory-Tree Baseline + +Before each isolated WASM OJ execution starts, the system mounts test inputs and creates the output files that the problem permits. These initialization resources already occupy VFS quota before the submitted program begins, so they must not be mistaken for usage added during execution. We need to establish a reproducible mount baseline first. + +The environment mounts `M` read-only input files and pre-creates `O` zero-length output files. To keep the task focused on directory-tree resource accounting, a canonical absolute path is represented by positive integer segments: `k s1 ... sk` denotes `/s1/.../sk`. The last segment is the filename, and all preceding segments are parent directories. + +During mounting, every required parent directory is created automatically, but the same directory is counted only once no matter how many files share it. The guest root `/` always exists and consumes one inode, and every file consumes one inode of its own. Baseline bytes include only the logical sizes of read-only input files; pre-created output files have size zero. + +The system will seal this baseline under byte quota `B` and inode quota `I`. Compute its byte and inode usage and determine whether it can be sealed under both quotas. + +## Input + +The first line contains `M O B I`. + +The next `M` lines each contain `k s1 ... sk size`; the following `O` lines each contain `k s1 ... sk`. + +All file paths are distinct, and no file path is a strict prefix of another file path, so no file/directory kind conflict can occur. + +## Output + +If both baseline values are within quota, output: + +```text +ACCEPT baselineBytes baselineInodes remainingBytes remainingInodes +``` + +Otherwise output: + +```text +REJECT baselineBytes baselineInodes missingBytes missingInodes +``` + +Each missing value is `max(0,baseline-quota)`. Even when only one resource is insufficient, output `0` for the other. + +## Constraints + +- `0 ≤ M,O ≤ 200000`, `1 ≤ M+O ≤ 200000` +- Every path has `1 ≤ k`; the total number `S` of segment occurrences over all paths is at most `200000`. +- `1 ≤ si ≤ 10^9` +- `0 ≤ size ≤ 9×10^18`, and the sum of all input-file sizes is at most `9×10^18`. +- `0 ≤ B,I ≤ 9×10^18` + +The full constraints rule out comparing every new directory prefix linearly against a list of existing prefixes. + +## Examples + + + +### Example One + +Input: + +```text +2 2 100 10 +3 1 2 3 40 +2 1 4 20 +3 1 2 5 +1 6 +``` + +Output: + +```text +ACCEPT 60 7 40 3 +``` + +### Example Two + +Input: + +```text +1 1 4 2 +2 9 1 5 +2 9 2 +``` + +Output: + +```text +REJECT 5 4 1 2 +``` + +### Example Three + +Input: + +```text +3 2 30 8 +4 1 2 3 10 7 +4 1 2 3 11 8 +3 1 2 12 9 +3 1 5 13 +1 14 +``` + +Output: + +```text +REJECT 24 10 0 2 +``` + + diff --git a/problems/008-mounted-directory-baseline/statement.zh-TW.md b/problems/008-mounted-directory-baseline/statement.zh-TW.md new file mode 100644 index 0000000..f344189 --- /dev/null +++ b/problems/008-mounted-directory-baseline/statement.zh-TW.md @@ -0,0 +1,102 @@ +# 目錄樹的掛載基線 + +每次啟動 WASM OJ 的隔離執行環境前,我們都要先掛載測試輸入,並建立題目允許產生的輸出檔。這些初始化資源在使用者程式開始執行前就已占用 VFS 配額,因此不能把它們誤算成程式執行期間才增加的用量。我們需要先建立一份可重現的掛載 baseline。 + +環境會掛載 `M` 個唯讀輸入檔,並預先建立 `O` 個大小為零的輸出檔。為了把問題集中在目錄樹的資源計算,canonical absolute path 以正整數 segment 表示:`k s1 ... sk` 代表 `/s1/.../sk`;最後一個 segment 是檔名,前面都是父目錄。 + +掛載時,所有必要父目錄都要自動建立,但同一個目錄無論被多少檔案共用都只計一次。guest root `/` 永遠存在並消耗一個 inode,每個檔案也各消耗一個 inode。baseline bytes 只包含唯讀輸入檔的 logical size;預建輸出檔的大小為零。 + +系統準備以 byte quota `B` 與 inode quota `I` 封存這個 baseline。請計算 baseline 的 bytes 與 inode 用量,並判斷它能否在兩種配額下完成封存。 + +## 輸入 + +第一行 `M O B I`。 + +接下來 `M` 行各為 `k s1 ... sk size`;再接下來 `O` 行各為 `k s1 ... sk`。 + +所有檔案 path 互不相同,且任一檔案 path 都不是另一檔案 path 的嚴格 prefix,因此不會發生 file/directory 種類衝突。 + +## 輸出 + +若兩種 baseline 都不超過 quota,輸出: + +```text +ACCEPT baselineBytes baselineInodes remainingBytes remainingInodes +``` + +否則輸出: + +```text +REJECT baselineBytes baselineInodes missingBytes missingInodes +``` + +其中 missing 分別是 `max(0,baseline-quota)`;即使只缺一種,另一種仍輸出 `0`。 + +## 限制 + +- `0 ≤ M,O ≤ 200000`,`1 ≤ M+O ≤ 200000` +- 每條 path 的 `1 ≤ k`;所有 path 的 segment 出現總數 `S ≤ 200000` +- `1 ≤ si ≤ 10^9` +- `0 ≤ size ≤ 9×10^18`,所有輸入檔 size 總和不超過 `9×10^18` +- `0 ≤ B,I ≤ 9×10^18` + +完整限制排除把每個新目錄 prefix 與既有清單逐一比較的平方作法。 + +## 範例 + + + +### 範例一 + +輸入: + +```text +2 2 100 10 +3 1 2 3 40 +2 1 4 20 +3 1 2 5 +1 6 +``` + +輸出: + +```text +ACCEPT 60 7 40 3 +``` + +### 範例二 + +輸入: + +```text +1 1 4 2 +2 9 1 5 +2 9 2 +``` + +輸出: + +```text +REJECT 5 4 1 2 +``` + +### 範例三 + +輸入: + +```text +3 2 30 8 +4 1 2 3 10 7 +4 1 2 3 11 8 +3 1 2 12 9 +3 1 5 13 +1 14 +``` + +輸出: + +```text +REJECT 24 10 0 2 +``` + + diff --git a/problems/008-mounted-directory-baseline/tests/adversarial-01.in b/problems/008-mounted-directory-baseline/tests/adversarial-01.in new file mode 100644 index 0000000..95cd86c --- /dev/null +++ b/problems/008-mounted-directory-baseline/tests/adversarial-01.in @@ -0,0 +1,7 @@ +3 3 14 12 +4 1 2 3 10 5 +4 1 2 4 11 6 +2 9 1 4 +4 1 2 3 12 +3 1 5 13 +1 20 diff --git a/problems/008-mounted-directory-baseline/tests/adversarial-01.out b/problems/008-mounted-directory-baseline/tests/adversarial-01.out new file mode 100644 index 0000000..cc8dfb6 --- /dev/null +++ b/problems/008-mounted-directory-baseline/tests/adversarial-01.out @@ -0,0 +1 @@ +REJECT 15 13 1 1 diff --git a/problems/008-mounted-directory-baseline/tests/sample-01.in b/problems/008-mounted-directory-baseline/tests/sample-01.in new file mode 100644 index 0000000..f33b3ff --- /dev/null +++ b/problems/008-mounted-directory-baseline/tests/sample-01.in @@ -0,0 +1,5 @@ +2 2 100 10 +3 1 2 3 40 +2 1 4 20 +3 1 2 5 +1 6 diff --git a/problems/008-mounted-directory-baseline/tests/sample-01.out b/problems/008-mounted-directory-baseline/tests/sample-01.out new file mode 100644 index 0000000..b6c2353 --- /dev/null +++ b/problems/008-mounted-directory-baseline/tests/sample-01.out @@ -0,0 +1 @@ +ACCEPT 60 7 40 3 diff --git a/problems/008-mounted-directory-baseline/tests/sample-02.in b/problems/008-mounted-directory-baseline/tests/sample-02.in new file mode 100644 index 0000000..79aa178 --- /dev/null +++ b/problems/008-mounted-directory-baseline/tests/sample-02.in @@ -0,0 +1,3 @@ +1 1 4 2 +2 9 1 5 +2 9 2 diff --git a/problems/008-mounted-directory-baseline/tests/sample-02.out b/problems/008-mounted-directory-baseline/tests/sample-02.out new file mode 100644 index 0000000..773cdbb --- /dev/null +++ b/problems/008-mounted-directory-baseline/tests/sample-02.out @@ -0,0 +1 @@ +REJECT 5 4 1 2 diff --git a/problems/008-mounted-directory-baseline/tests/sample-03.in b/problems/008-mounted-directory-baseline/tests/sample-03.in new file mode 100644 index 0000000..8e5b492 --- /dev/null +++ b/problems/008-mounted-directory-baseline/tests/sample-03.in @@ -0,0 +1,6 @@ +3 2 30 8 +4 1 2 3 10 7 +4 1 2 3 11 8 +3 1 2 12 9 +3 1 5 13 +1 14 diff --git a/problems/008-mounted-directory-baseline/tests/sample-03.out b/problems/008-mounted-directory-baseline/tests/sample-03.out new file mode 100644 index 0000000..0540449 --- /dev/null +++ b/problems/008-mounted-directory-baseline/tests/sample-03.out @@ -0,0 +1 @@ +REJECT 24 10 0 2 diff --git a/problems/008-mounted-directory-baseline/validator.py b/problems/008-mounted-directory-baseline/validator.py new file mode 100644 index 0000000..60d63a8 --- /dev/null +++ b/problems/008-mounted-directory-baseline/validator.py @@ -0,0 +1,44 @@ +import re, sys + + +def fail(): + raise SystemExit(1) + + +try: + t = sys.stdin.buffer.read().decode("utf-8").split() + p = 0 + + def u(a, b): + global p + if p >= len(t) or re.fullmatch(r"0|[1-9][0-9]*", t[p]) is None: + fail() + v = int(t[p]) + p += 1 + if not a <= v <= b: + fail() + return v + + M, O, B, I = u(0, 200000), u(0, 200000), u(0, 9 * 10**18), u(0, 9 * 10**18) + if not 1 <= M + O <= 200000: + fail() + paths = [] + segments = 0 + total = 0 + for j in range(M + O): + k = u(1, 200000) + segments += k + path = tuple(u(1, 10**9) for _ in range(k)) + paths.append(path) + if j < M: + total += u(0, 9 * 10**18) + if total > 9 * 10**18: + fail() + if segments > 200000 or p != len(t): + fail() + paths.sort() + for a, b in zip(paths, paths[1:]): + if len(a) <= len(b) and a == b[: len(a)]: + fail() +except (UnicodeDecodeError, ValueError, OverflowError): + fail() diff --git a/problems/009-sparse-file-quota/editorial.en.md b/problems/009-sparse-file-quota/editorial.en.md new file mode 100644 index 0000000..7c779a4 --- /dev/null +++ b/problems/009-sparse-file-quota/editorial.en.md @@ -0,0 +1,26 @@ +# Editorial + +## Intuitive Approach + +Representing each file as a byte array forces a write after a huge seek to allocate the entire hole, requiring `O(E)` time and space even though `E` may be `9×10^18`. Storing only sizes still takes `O(FN)` if every quota check rescans all `F` files. + +## Optimal Approach: Incremental Size Accounting + +Store only `size[x]` and `cursor[x]` for each file, and globally maintain `used=sum(size)`. After computing candidate `newSize`, let `delta=newSize-oldSize`. If it is positive and `delta>B-used`, reject; otherwise update `used` and `size` by the difference. Shrinking releases the difference directly. Testing `delta>B-used` instead of `used+delta>B` avoids unsigned overflow. + +Advance the write cursor only after a successful nonzero write. A zero-length write and every failed transaction leave it unchanged. `TRUNCATE` never changes the cursor. Update the peak after every success. + +## Correctness Proof + +Assume inductively that before an operation, `used` equals the sum of all sizes. `SEEK` changes only one cursor, so the sum is preserved. A `WRITE` candidate is the maximum of the old EOF and the write endpoint; a `TRUNCATE` candidate is the specified size. In either case, only one file's size can change, so `new-old` is the exact change in the global total. The quota test is therefore necessary and sufficient. On success the algorithm commits the correct size, total, and prescribed cursor simultaneously; on failure it commits none of them, preserving the invariant. The peak is updated only from correct committed states. Thus every state line and the final summary are correct. + +## Complexity + +Initialization takes `O(F)` and every operation takes `O(1)`, for total time `O(F+N)`. The core state uses `O(F)` auxiliary space and is independent of the largest offset. Including buffered input/output, the common worst-case space bound of the seven references is `O(F+N)`. + +## Common Mistakes + +- Adding only `length` for a sparse write and ignoring the hole before the cursor. +- Clamping the cursor to EOF when truncating downward; it must remain unchanged. +- Advancing a `WRITE` cursor after a quota failure. +- Extending to the cursor or advancing it on a zero-length `WRITE`. diff --git a/problems/009-sparse-file-quota/editorial.zh-TW.md b/problems/009-sparse-file-quota/editorial.zh-TW.md new file mode 100644 index 0000000..2618348 --- /dev/null +++ b/problems/009-sparse-file-quota/editorial.zh-TW.md @@ -0,0 +1,29 @@ +# 解題說明 + +## 直覺解法 + +若以 byte array 表示檔案,SEEK 到巨大 offset 後的一次 write 就要配置整個 hole,時間/空間 `O(E)`,而 `E` 可達 `9×10^18`。即使只存 size,若每次 quota 檢查都掃描 `F` 個檔案,也會是 `O(FN)`。 + +## 最佳解法 + +每個檔案只需 `size[x]` 與 `cursor[x]`,全域維護 `used=sum(size)`。求出候選 `newSize` 後:若增長量 `delta=newSize-oldSize` 大於 `B-used` 就失敗;否則以差值更新 used 與 size。縮小直接釋放差值。使用 `delta>B-used` 而非 `used+delta>B` 可避免無號加法溢位。 + +WRITE 的 cursor 僅在非零且成功時前進;零長度 write 與失敗交易都不動。TRUNCATE 永不改 cursor。成功後更新 peak。 + +## 正確性證明 + +歸納假設操作前 `used` 等於所有 size 總和。SEEK 只改指定 cursor,總和不變。WRITE 的候選 size 依定義為舊 EOF 與寫入結尾較大者,TRUNCATE 的候選即指定值;兩者只有該檔案 size 可能改變,所以全域總和的唯一差值就是 `new-old`。演算法的 quota 判斷因此充要。成功時同時提交正確 size、used 與規定的 cursor,失敗時不提交,維持歸納不變量。peak 只在正確成功狀態取最大,故逐行狀態與 SUMMARY 全部正確。 + +## 複雜度 + +初始化 `O(F)`,每個操作 `O(1)`,總時間 `O(F+N)`,核心狀態的輔助空間為 +`O(F)`,且不依賴最大 offset。C、C++、Go reference 串流讀寫;Rust、Python +會保留完整輸入與輸出,JavaScript、TypeScript 保留單一輸入字串並以固定大小分塊輸出, +因此依實際 resident allocations 計算的共同最壞空間上界為 `O(F+N)`。 + +## 常見錯誤 + +- sparse write 只增加 `length`,漏算 cursor 前的 hole。 +- truncate 縮小時把 cursor 一併截到 EOF;本題明定不改。 +- quota 失敗後仍前進 WRITE cursor。 +- 零長度 WRITE 延伸到 cursor,或錯誤地前進 cursor。 diff --git a/problems/009-sparse-file-quota/generator.py b/problems/009-sparse-file-quota/generator.py new file mode 100644 index 0000000..c4c7a80 --- /dev/null +++ b/problems/009-sparse-file-quota/generator.py @@ -0,0 +1,15 @@ +import random, sys + +if len(sys.argv) != 3: + raise SystemExit("usage: generator.py SEED INDEX") +r = random.Random((int(sys.argv[1]) << 32) ^ int(sys.argv[2])) +idx = int(sys.argv[2]) +F = r.randint(1, 3 + idx % 5) +N = r.randint(1, 8 + idx % 10) +B = r.randint(0, 50) +out = [f"{F} {N} {B}"] +for _ in range(N): + out.append( + f"{r.choice(('SEEK','WRITE','TRUNCATE'))} {r.randint(1,F)} {r.randint(0,45)}" + ) +print("\n".join(out)) diff --git a/problems/009-sparse-file-quota/oracle.py b/problems/009-sparse-file-quota/oracle.py new file mode 100644 index 0000000..aa40ca7 --- /dev/null +++ b/problems/009-sparse-file-quota/oracle.py @@ -0,0 +1,30 @@ +import sys + +t = sys.stdin.buffer.read().split() +it = iter(t) +F, N, B = map(int, (next(it), next(it), next(it))) +size = [0] * (F + 1) +cur = [0] * (F + 1) +peak = 0 +out = [] +for _ in range(N): + op = next(it) + x = int(next(it)) + v = int(next(it)) + err = False + if op == b"SEEK": + cur[x] = v + else: + new = (size[x] if v == 0 else max(size[x], cur[x] + v)) if op == b"WRITE" else v + used = sum(size) + if used - size[x] + new > B: + err = True + else: + size[x] = new + if op == b"WRITE" and v: + cur[x] += v + used = sum(size) + peak = max(peak, used) + out.append(("ERR QUOTA" if err else "OK") + f" {size[x]} {cur[x]} {used}") +out.append(f"SUMMARY {sum(size)} {peak}") +print("\n".join(out)) diff --git a/problems/009-sparse-file-quota/problem.json b/problems/009-sparse-file-quota/problem.json new file mode 100644 index 0000000..4ee8097 --- /dev/null +++ b/problems/009-sparse-file-quota/problem.json @@ -0,0 +1,155 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 9, + "slug": "sparse-file-quota", + "title": { + "zh-TW": "稀疏檔案不是免費的", + "en": "Sparse Files Are Not Free" + }, + "difficulty": "medium", + "tags": [ + "simulation", + "sparse-file", + "incremental-accounting" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-01", + "kind": "adversarial", + "input": "tests/adversarial-01.in", + "output": "tests/adversarial-01.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 10000000, + "memoryLimitBytes": 536870912 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 2000000, + "memoryLimitBytes": 402653184 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 850000, + "memoryLimitBytes": 268435456 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "實體配置到 cursor 的每個 byte", + "en": "Materialize Every Byte up to the Cursor" + }, + "time": "O(N+E)", + "space": "O(E)", + "accepted": false + }, + { + "name": { + "zh-TW": "每次操作重算所有 logical size", + "en": "Recompute All Logical Sizes per Operation" + }, + "time": "O(FN)", + "space": "O(F)", + "accepted": false + }, + { + "name": { + "zh-TW": "size/cursor 狀態與增量 quota", + "en": "Size/Cursor State with Incremental Quota Accounting" + }, + "time": "O(F+N)", + "space": "O(F) auxiliary; O(F+N) buffered I/O", + "accepted": true + } + ] +} diff --git a/problems/009-sparse-file-quota/solutions/c/main.c b/problems/009-sparse-file-quota/solutions/c/main.c new file mode 100644 index 0000000..b5a8ae2 --- /dev/null +++ b/problems/009-sparse-file-quota/solutions/c/main.c @@ -0,0 +1,47 @@ +#include +#include +#include +#include +int main(void) { + int F, N; + unsigned long long B; + if (scanf("%d%d%llu", &F, &N, &B) != 3) + return 0; + uint64_t *sz = calloc(F + 1, sizeof(*sz)), *cur = calloc(F + 1, sizeof(*cur)); + uint64_t used = 0, peak = 0; + while (N--) { + char op[9]; + int x; + unsigned long long v; + scanf("%8s%d%llu", op, &x, &v); + int err = 0; + if (strcmp(op, "SEEK") == 0) + cur[x] = v; + else { + uint64_t newsize = + strcmp(op, "WRITE") == 0 + ? (v ? (cur[x] + v > sz[x] ? cur[x] + v : sz[x]) : sz[x]) + : v; + if (newsize > sz[x] && newsize - sz[x] > B - used) + err = 1; + else { + if (newsize >= sz[x]) + used += newsize - sz[x]; + else + used -= sz[x] - newsize; + sz[x] = newsize; + if (strcmp(op, "WRITE") == 0 && v) + cur[x] += v; + } + } + if (used > peak) + peak = used; + printf("%s %llu %llu %llu\n", err ? "ERR QUOTA" : "OK", + (unsigned long long)sz[x], (unsigned long long)cur[x], + (unsigned long long)used); + } + printf("SUMMARY %llu %llu\n", (unsigned long long)used, + (unsigned long long)peak); + free(sz); + free(cur); +} diff --git a/problems/009-sparse-file-quota/solutions/cpp/main.cpp b/problems/009-sparse-file-quota/solutions/cpp/main.cpp new file mode 100644 index 0000000..0e9fa8f --- /dev/null +++ b/problems/009-sparse-file-quota/solutions/cpp/main.cpp @@ -0,0 +1,43 @@ +#include +#include +#include +#include +#include +using namespace std; +int main() { + ios::sync_with_stdio(false); + cin.tie(nullptr); + int f, n; + uint64_t cap; + if (!(cin >> f >> n >> cap)) + return 0; + vector sz(f + 1), cur(f + 1); + uint64_t used = 0, peak = 0; + while (n--) { + string op; + int x; + uint64_t v; + cin >> op >> x >> v; + bool err = false; + if (op == "SEEK") + cur[x] = v; + else { + uint64_t ns = op == "WRITE" ? (v ? max(sz[x], cur[x] + v) : sz[x]) : v; + if (ns > sz[x] && ns - sz[x] > cap - used) + err = true; + else { + if (ns >= sz[x]) + used += ns - sz[x]; + else + used -= sz[x] - ns; + sz[x] = ns; + if (op == "WRITE" && v) + cur[x] += v; + } + } + peak = max(peak, used); + cout << (err ? "ERR QUOTA" : "OK") << ' ' << sz[x] << ' ' << cur[x] << ' ' + << used << '\n'; + } + cout << "SUMMARY " << used << ' ' << peak << '\n'; +} diff --git a/problems/009-sparse-file-quota/solutions/go/main.go b/problems/009-sparse-file-quota/solutions/go/main.go new file mode 100644 index 0000000..41e9e70 --- /dev/null +++ b/problems/009-sparse-file-quota/solutions/go/main.go @@ -0,0 +1,62 @@ +package main + +import ( + "bufio" + "fmt" + "os" +) + +func main() { + in := bufio.NewReader(os.Stdin) + out := bufio.NewWriter(os.Stdout) + defer out.Flush() + var f, n int + var cap uint64 + if _, e := fmt.Fscan(in, &f, &n, &cap); e != nil { + return + } + size := make([]uint64, f+1) + cur := make([]uint64, f+1) + var used, peak uint64 + for ; n > 0; n-- { + var op string + var x int + var v uint64 + fmt.Fscan(in, &op, &x, &v) + err := false + if op == "SEEK" { + cur[x] = v + } else { + ns := v + if op == "WRITE" { + ns = size[x] + if v > 0 && cur[x]+v > ns { + ns = cur[x] + v + } + } + if ns > size[x] && ns-size[x] > cap-used { + err = true + } else { + if ns >= size[x] { + used += ns - size[x] + } else { + used -= size[x] - ns + } + size[x] = ns + if op == "WRITE" && v > 0 { + cur[x] += v + } + } + } + if used > peak { + peak = used + } + if err { + fmt.Fprint(out, "ERR QUOTA") + } else { + fmt.Fprint(out, "OK") + } + fmt.Fprintln(out, "", size[x], cur[x], used) + } + fmt.Fprintln(out, "SUMMARY", used, peak) +} diff --git a/problems/009-sparse-file-quota/solutions/javascript/main.js b/problems/009-sparse-file-quota/solutions/javascript/main.js new file mode 100644 index 0000000..453e217 --- /dev/null +++ b/problems/009-sparse-file-quota/solutions/javascript/main.js @@ -0,0 +1,46 @@ +import * as std from "std"; +/** @type {string} */ +const input = std.in.readAsString(); +let cursor = 0; +/** @returns {string} */ +function nextToken() { + while (cursor < input.length && input.charCodeAt(cursor) <= 32) cursor++; + const start = cursor; + while (cursor < input.length && input.charCodeAt(cursor) > 32) cursor++; + return input.slice(start, cursor); +} +const F = Number(nextToken()), + N = Number(nextToken()), + B = BigInt(nextToken()), + size = /** @type {bigint[]} */ (Array(F + 1).fill(0n)), + cur = /** @type {bigint[]} */ (Array(F + 1).fill(0n)); +let output = ""; +/** @param {string} line */ +function emit(line) { + if (output.length + line.length > 65536) { + std.out.puts(output); + output = ""; + } + output += line; +} +let used = 0n, peak = 0n; +for (let z = 0; z < N; z++) { + const op = nextToken(), x = Number(nextToken()), v = BigInt(nextToken()); + let err = false; + if (op === "SEEK") cur[x] = v; + else { + let ns = op === "WRITE" + ? (v === 0n ? size[x] : (size[x] > cur[x] + v ? size[x] : cur[x] + v)) + : v; + if (ns > size[x] && ns - size[x] > B - used) err = true; + else { + used += ns - size[x]; + size[x] = ns; + if (op === "WRITE" && v > 0n) cur[x] += v; + } + } + if (used > peak) peak = used; + emit(`${err ? "ERR QUOTA" : "OK"} ${size[x]} ${cur[x]} ${used}\n`); +} +emit(`SUMMARY ${used} ${peak}\n`); +if (output.length) std.out.puts(output); diff --git a/problems/009-sparse-file-quota/solutions/python/main.py b/problems/009-sparse-file-quota/solutions/python/main.py new file mode 100644 index 0000000..b71af38 --- /dev/null +++ b/problems/009-sparse-file-quota/solutions/python/main.py @@ -0,0 +1,29 @@ +import sys + +t = sys.stdin.buffer.read().split() +it = iter(t) +F, N, B = map(int, (next(it), next(it), next(it))) +size = [0] * (F + 1) +cur = [0] * (F + 1) +used = peak = 0 +out = [] +for _ in range(N): + op = next(it) + x = int(next(it)) + v = int(next(it)) + err = False + if op == b"SEEK": + cur[x] = v + else: + ns = (size[x] if v == 0 else max(size[x], cur[x] + v)) if op == b"WRITE" else v + if ns > size[x] and ns - size[x] > B - used: + err = True + else: + used += ns - size[x] + size[x] = ns + if op == b"WRITE" and v: + cur[x] += v + peak = max(peak, used) + out.append(("ERR QUOTA" if err else "OK") + f" {size[x]} {cur[x]} {used}") +out.append(f"SUMMARY {used} {peak}") +print("\n".join(out)) diff --git a/problems/009-sparse-file-quota/solutions/rust/main.rs b/problems/009-sparse-file-quota/solutions/rust/main.rs new file mode 100644 index 0000000..715e2cb --- /dev/null +++ b/problems/009-sparse-file-quota/solutions/rust/main.rs @@ -0,0 +1,55 @@ +use std::io::{self, Read}; +fn main() { + let mut s = String::new(); + io::stdin().read_to_string(&mut s).unwrap(); + let mut t = s.split_whitespace(); + let f: usize = t.next().unwrap().parse().unwrap(); + let n: usize = t.next().unwrap().parse().unwrap(); + let cap: u64 = t.next().unwrap().parse().unwrap(); + let mut size = vec![0u64; f + 1]; + let mut cur = vec![0u64; f + 1]; + let (mut used, mut peak) = (0u64, 0u64); + let mut out = String::new(); + for _ in 0..n { + let op = t.next().unwrap(); + let x: usize = t.next().unwrap().parse().unwrap(); + let v: u64 = t.next().unwrap().parse().unwrap(); + let mut err = false; + if op == "SEEK" { + cur[x] = v + } else { + let ns = if op == "WRITE" { + if v == 0 { + size[x] + } else { + size[x].max(cur[x] + v) + } + } else { + v + }; + if ns > size[x] && ns - size[x] > cap - used { + err = true + } else { + if ns >= size[x] { + used += ns - size[x] + } else { + used -= size[x] - ns + } + size[x] = ns; + if op == "WRITE" && v > 0 { + cur[x] += v + } + } + } + peak = peak.max(used); + out += &format!( + "{} {} {} {}\n", + if err { "ERR QUOTA" } else { "OK" }, + size[x], + cur[x], + used + ); + } + out += &format!("SUMMARY {} {}\n", used, peak); + print!("{}", out); +} diff --git a/problems/009-sparse-file-quota/solutions/typescript/main.ts b/problems/009-sparse-file-quota/solutions/typescript/main.ts new file mode 100644 index 0000000..9e458f3 --- /dev/null +++ b/problems/009-sparse-file-quota/solutions/typescript/main.ts @@ -0,0 +1,43 @@ +import * as std from "std"; +const input: string = std.in.readAsString(); +let cursor = 0; +function nextToken(): string { + while (cursor < input.length && input.charCodeAt(cursor) <= 32) cursor++; + const start = cursor; + while (cursor < input.length && input.charCodeAt(cursor) > 32) cursor++; + return input.slice(start, cursor); +} +const F = Number(nextToken()), + N = Number(nextToken()), + B = BigInt(nextToken()), + size: bigint[] = Array(F + 1).fill(0n), + cur: bigint[] = Array(F + 1).fill(0n); +let output = ""; +function emit(line: string): void { + if (output.length + line.length > 65536) { + std.out.puts(output); + output = ""; + } + output += line; +} +let used = 0n, peak = 0n; +for (let z = 0; z < N; z++) { + const op = nextToken(), x = Number(nextToken()), v = BigInt(nextToken()); + let err = false; + if (op === "SEEK") cur[x] = v; + else { + const ns = op === "WRITE" + ? (v === 0n ? size[x] : (size[x] > cur[x] + v ? size[x] : cur[x] + v)) + : v; + if (ns > size[x] && ns - size[x] > B - used) err = true; + else { + used += ns - size[x]; + size[x] = ns; + if (op === "WRITE" && v > 0n) cur[x] += v; + } + } + if (used > peak) peak = used; + emit(`${err ? "ERR QUOTA" : "OK"} ${size[x]} ${cur[x]} ${used}\n`); +} +emit(`SUMMARY ${used} ${peak}\n`); +if (output.length) std.out.puts(output); diff --git a/problems/009-sparse-file-quota/statement.en.md b/problems/009-sparse-file-quota/statement.en.md new file mode 100644 index 0000000..0d1f51f --- /dev/null +++ b/problems/009-sparse-file-quota/statement.en.md @@ -0,0 +1,125 @@ +# Sparse Files Are Not Free + +When implementing a VFS byte quota for a WASM OJ, counting only payload bytes actually written is unsafe. A program can move its cursor far ahead and then write a small amount of data, creating a large sparse hole. Even though the intervening range is not physically written, it still expands the file's logical size and must consume the same quota. + +The VFS contains `F` existing empty files. Each file has a logical size and a cursor, both initially `0`, and the sum of all logical file sizes may not exceed byte quota `B`. Execute `N` operations in order: + +- `SEEK x position`: set file `x`'s cursor to an absolute position. It may be beyond EOF and does not change the size. +- `WRITE x length`: if `length>0`, the candidate new size is `max(oldSize,cursor+length)`; if `length=0`, both size and cursor remain unchanged. After a successful nonzero write, advance the cursor by `length`. +- `TRUNCATE x size`: the candidate new size is exactly `size`. The cursor is unchanged, even if it lies beyond the new EOF. + +`SEEK` always succeeds. A `WRITE` or `TRUNCATE` must first check the candidate sum of logical sizes across all files. If that sum would exceed `B`, output a quota error and leave size, cursor, and peak usage entirely unchanged. Only an operation that passes the quota check commits all of its changes atomically. + +## Input + +The first line contains `F N B`, followed by `N` operation lines. File IDs are 1-based. + +## Output + +For each operation, output one line. On success: + +```text +OK fileSize cursor usedBytes +``` + +On quota failure: + +```text +ERR QUOTA fileSize cursor usedBytes +``` + +Every field describes the state after that operation. Finally output `SUMMARY usedBytes peakBytes`. The peak considers global `usedBytes` only after successful commits and includes the initial zero state. + +## Constraints + +- `1 ≤ F,N ≤ 200000` +- `0 ≤ B ≤ 9×10^18` +- `1 ≤ x ≤ F` +- `0 ≤ position,length,size ≤ 9×10^18` +- Every `cursor+length` encountered during execution is guaranteed not to exceed `9×10^18`. + +Let `E` be the largest offset ever touched. It can reach `9×10^18`, so a solution may not materialize holes. The full constraints also rule out recomputing the sum of all file sizes after every operation. + +## Examples + + + +### Example One + +Input: + +```text +2 6 10 +SEEK 1 7 +WRITE 1 3 +SEEK 2 5 +WRITE 2 1 +TRUNCATE 1 4 +WRITE 2 1 +``` + +Output: + +```text +OK 0 7 0 +OK 10 10 10 +OK 0 5 10 +ERR QUOTA 0 5 10 +OK 4 10 4 +OK 6 6 10 +SUMMARY 10 10 +``` + +### Example Two + +Input: + +```text +1 5 0 +SEEK 1 100 +WRITE 1 0 +TRUNCATE 1 0 +WRITE 1 1 +SEEK 1 0 +``` + +Output: + +```text +OK 0 100 0 +OK 0 100 0 +OK 0 100 0 +ERR QUOTA 0 100 0 +OK 0 0 0 +SUMMARY 0 0 +``` + +### Example Three + +Input: + +```text +1 7 20 +TRUNCATE 1 12 +SEEK 1 3 +WRITE 1 4 +SEEK 1 18 +WRITE 1 2 +TRUNCATE 1 5 +WRITE 1 1 +``` + +Output: + +```text +OK 12 0 12 +OK 12 3 12 +OK 12 7 12 +OK 12 18 12 +OK 20 20 20 +OK 5 20 5 +ERR QUOTA 5 20 5 +SUMMARY 5 20 +``` + + diff --git a/problems/009-sparse-file-quota/statement.zh-TW.md b/problems/009-sparse-file-quota/statement.zh-TW.md new file mode 100644 index 0000000..45d78c1 --- /dev/null +++ b/problems/009-sparse-file-quota/statement.zh-TW.md @@ -0,0 +1,125 @@ +# 稀疏檔案不是免費的 + +替 WASM OJ 實作 VFS byte quota 時,只計算實際寫入的 payload 並不安全。程式可以先把 cursor 移到很遠的位置,再寫入少量資料,形成很大的 sparse hole。即使中間沒有真正寫入,這段範圍仍會擴張檔案的 logical size,因此必須占用相同的 quota。 + +VFS 中有 `F` 個已存在的空檔案。每個檔案都有 logical size 與 cursor,兩者初始皆為 `0`;所有檔案的 logical size 總和不得超過 byte quota `B`。請依序執行 `N` 個操作: + +- `SEEK x position`:將檔案 `x` 的 cursor 設為絕對位置;可超過 EOF,且不改變 size。 +- `WRITE x length`:若 `length>0`,候選新 size 是 `max(oldSize,cursor+length)`;若 `length=0`,size 與 cursor 都不變。非零 write 成功後 cursor 增加 `length`。 +- `TRUNCATE x size`:候選新 size 精確等於 `size`;cursor 不變,即使它落在新 EOF 之後。 + +`SEEK` 永遠成功。`WRITE` 或 `TRUNCATE` 必須先以候選狀態檢查全體檔案的 logical size 總和;若總和超過 `B`,輸出 quota error,且該操作對 size、cursor 與 peak 都完全沒有影響。只有通過配額檢查時,所有變更才一次提交。 + +## 輸入 + +第一行 `F N B`,接下來 `N` 行為操作。檔案 ID 為 1-based。 + +## 輸出 + +每個操作輸出一行。成功時: + +```text +OK fileSize cursor usedBytes +``` + +quota 失敗時: + +```text +ERR QUOTA fileSize cursor usedBytes +``` + +各欄位皆是該操作結束後的狀態。最後輸出 `SUMMARY usedBytes peakBytes`。peak 只看成功提交後的全域 usedBytes,初始零也計入。 + +## 限制 + +- `1 ≤ F,N ≤ 200000` +- `0 ≤ B ≤ 9×10^18` +- `1 ≤ x ≤ F` +- `0 ≤ position,length,size ≤ 9×10^18` +- 執行序列中每個 `cursor+length` 都保證不超過 `9×10^18` + +令 `E` 為最大曾觸及 offset;它可達 `9×10^18`,所以不可 materialize hole。完整限制也排除每次重算所有檔案 size。 + +## 範例 + + + +### 範例一 + +輸入: + +```text +2 6 10 +SEEK 1 7 +WRITE 1 3 +SEEK 2 5 +WRITE 2 1 +TRUNCATE 1 4 +WRITE 2 1 +``` + +輸出: + +```text +OK 0 7 0 +OK 10 10 10 +OK 0 5 10 +ERR QUOTA 0 5 10 +OK 4 10 4 +OK 6 6 10 +SUMMARY 10 10 +``` + +### 範例二 + +輸入: + +```text +1 5 0 +SEEK 1 100 +WRITE 1 0 +TRUNCATE 1 0 +WRITE 1 1 +SEEK 1 0 +``` + +輸出: + +```text +OK 0 100 0 +OK 0 100 0 +OK 0 100 0 +ERR QUOTA 0 100 0 +OK 0 0 0 +SUMMARY 0 0 +``` + +### 範例三 + +輸入: + +```text +1 7 20 +TRUNCATE 1 12 +SEEK 1 3 +WRITE 1 4 +SEEK 1 18 +WRITE 1 2 +TRUNCATE 1 5 +WRITE 1 1 +``` + +輸出: + +```text +OK 12 0 12 +OK 12 3 12 +OK 12 7 12 +OK 12 18 12 +OK 20 20 20 +OK 5 20 5 +ERR QUOTA 5 20 5 +SUMMARY 5 20 +``` + + diff --git a/problems/009-sparse-file-quota/tests/adversarial-01.in b/problems/009-sparse-file-quota/tests/adversarial-01.in new file mode 100644 index 0000000..bdec81c --- /dev/null +++ b/problems/009-sparse-file-quota/tests/adversarial-01.in @@ -0,0 +1,11 @@ +2 10 10 +SEEK 1 9 +WRITE 1 1 +SEEK 2 5 +WRITE 2 1 +TRUNCATE 1 4 +WRITE 2 1 +TRUNCATE 2 0 +WRITE 1 0 +WRITE 1 1 +TRUNCATE 1 10 diff --git a/problems/009-sparse-file-quota/tests/adversarial-01.out b/problems/009-sparse-file-quota/tests/adversarial-01.out new file mode 100644 index 0000000..d292501 --- /dev/null +++ b/problems/009-sparse-file-quota/tests/adversarial-01.out @@ -0,0 +1,11 @@ +OK 0 9 0 +OK 10 10 10 +OK 0 5 10 +ERR QUOTA 0 5 10 +OK 4 10 4 +OK 6 6 10 +OK 0 6 4 +OK 4 10 4 +ERR QUOTA 4 10 4 +OK 10 10 10 +SUMMARY 10 10 diff --git a/problems/009-sparse-file-quota/tests/sample-01.in b/problems/009-sparse-file-quota/tests/sample-01.in new file mode 100644 index 0000000..efd10d0 --- /dev/null +++ b/problems/009-sparse-file-quota/tests/sample-01.in @@ -0,0 +1,7 @@ +2 6 10 +SEEK 1 7 +WRITE 1 3 +SEEK 2 5 +WRITE 2 1 +TRUNCATE 1 4 +WRITE 2 1 diff --git a/problems/009-sparse-file-quota/tests/sample-01.out b/problems/009-sparse-file-quota/tests/sample-01.out new file mode 100644 index 0000000..e7ab54e --- /dev/null +++ b/problems/009-sparse-file-quota/tests/sample-01.out @@ -0,0 +1,7 @@ +OK 0 7 0 +OK 10 10 10 +OK 0 5 10 +ERR QUOTA 0 5 10 +OK 4 10 4 +OK 6 6 10 +SUMMARY 10 10 diff --git a/problems/009-sparse-file-quota/tests/sample-02.in b/problems/009-sparse-file-quota/tests/sample-02.in new file mode 100644 index 0000000..a1dcda0 --- /dev/null +++ b/problems/009-sparse-file-quota/tests/sample-02.in @@ -0,0 +1,6 @@ +1 5 0 +SEEK 1 100 +WRITE 1 0 +TRUNCATE 1 0 +WRITE 1 1 +SEEK 1 0 diff --git a/problems/009-sparse-file-quota/tests/sample-02.out b/problems/009-sparse-file-quota/tests/sample-02.out new file mode 100644 index 0000000..ecaa3e4 --- /dev/null +++ b/problems/009-sparse-file-quota/tests/sample-02.out @@ -0,0 +1,6 @@ +OK 0 100 0 +OK 0 100 0 +OK 0 100 0 +ERR QUOTA 0 100 0 +OK 0 0 0 +SUMMARY 0 0 diff --git a/problems/009-sparse-file-quota/tests/sample-03.in b/problems/009-sparse-file-quota/tests/sample-03.in new file mode 100644 index 0000000..c0975ba --- /dev/null +++ b/problems/009-sparse-file-quota/tests/sample-03.in @@ -0,0 +1,8 @@ +1 7 20 +TRUNCATE 1 12 +SEEK 1 3 +WRITE 1 4 +SEEK 1 18 +WRITE 1 2 +TRUNCATE 1 5 +WRITE 1 1 diff --git a/problems/009-sparse-file-quota/tests/sample-03.out b/problems/009-sparse-file-quota/tests/sample-03.out new file mode 100644 index 0000000..c0429cc --- /dev/null +++ b/problems/009-sparse-file-quota/tests/sample-03.out @@ -0,0 +1,8 @@ +OK 12 0 12 +OK 12 3 12 +OK 12 7 12 +OK 12 18 12 +OK 20 20 20 +OK 5 20 5 +ERR QUOTA 5 20 5 +SUMMARY 5 20 diff --git a/problems/009-sparse-file-quota/validator.py b/problems/009-sparse-file-quota/validator.py new file mode 100644 index 0000000..986f8eb --- /dev/null +++ b/problems/009-sparse-file-quota/validator.py @@ -0,0 +1,52 @@ +import re, sys + + +def fail(): + raise SystemExit(1) + + +try: + t = sys.stdin.buffer.read().decode("utf-8").split() + p = 0 + + def u(a, b): + global p + if p >= len(t) or re.fullmatch(r"0|[1-9][0-9]*", t[p]) is None: + fail() + v = int(t[p]) + p += 1 + if not a <= v <= b: + fail() + return v + + F, N, B = u(1, 200000), u(1, 200000), u(0, 9 * 10**18) + size = [0] * (F + 1) + cur = [0] * (F + 1) + used = 0 + for _ in range(N): + if p >= len(t): + fail() + op = t[p] + p += 1 + x = u(1, F) + v = u(0, 9 * 10**18) + if op == "SEEK": + cur[x] = v + elif op == "WRITE": + if cur[x] + v > 9 * 10**18: + fail() + new = size[x] if v == 0 else max(size[x], cur[x] + v) + if used - size[x] + new <= B: + used += new - size[x] + size[x] = new + cur[x] += v + elif op == "TRUNCATE": + if used - size[x] + v <= B: + used += v - size[x] + size[x] = v + else: + fail() + if p != len(t): + fail() +except (UnicodeDecodeError, ValueError, OverflowError): + fail() diff --git a/problems/010-all-or-nothing-output-collection/editorial.en.md b/problems/010-all-or-nothing-output-collection/editorial.en.md new file mode 100644 index 0000000..4bb2a43 --- /dev/null +++ b/problems/010-all-or-nothing-output-collection/editorial.en.md @@ -0,0 +1,33 @@ +# Editorial + +## Intuitive Approach + +Let `L` be the total path length in bytes and `Z` the actual output size. Copying and sorting all files for every query, then simulating collection, costs `O(QL log N+Z)`. Sorting once but scanning from the beginning for every budget can still cost `O(L log N+NQ+Z)`. Prefix sums with a binary search per query achieve `O(L log N+Q log N+Z)`. + +## Optimal Approach: One Sort and a Monotone Capacity Pointer + +Sort files by path, compute the prefix sums `prefix` of metadata lengths, and record the first mismatch index `m`, using `m=N` if none exists. Because budgets are nondecreasing, maintain `k`, the maximum number of prefix files whose metadata sum fits within `budget-U`. Advance `k` with a while loop; across all queries it advances at most `N` times. + +Check cases in this order after first handling `U>budget`: + +- If `kbudget`. +- Treating the pointer as committed side effects instead of a static affordable prefix, breaking repeated budgets. +- Writing only `O(N log N)` and omitting the byte cost of variable-length path comparisons. diff --git a/problems/010-all-or-nothing-output-collection/editorial.zh-TW.md b/problems/010-all-or-nothing-output-collection/editorial.zh-TW.md new file mode 100644 index 0000000..5dc736f --- /dev/null +++ b/problems/010-all-or-nothing-output-collection/editorial.zh-TW.md @@ -0,0 +1,35 @@ +# 解題說明 + +## 直覺解法 + +令 `L` 為所有 path 的 byte 長度總和,`Z` 為實際輸出的 byte 數。每個查詢都複製並以字串比較排序檔案,再依序模擬,最壞需 `O(QL log N+Z)`。排序只做一次仍可能因每個 budget 從頭掃描而達 `O(L log N+NQ+Z)`。前綴和加二分可做到 `O(L log N+Q log N+Z)`。 + +## 最佳解法 + +先按 path 排序,計算 metadata length 前綴和 `prefix`,並記住第一個 mismatch 索引 `m`(不存在令 `m=N`)。因 budget 非遞減,可維護 `k`:在容量 `budget-U` 下,前綴和不超過容量的最大檔案數。每次查詢只需 while 向右推進 `k`,所有查詢合計至多前進 `N` 次。 + +若 `U>budget` 先輸出特殊 quota。否則依序判斷: + +- `kbudget` 時仍回報某個 path。 +- budget 相同時重複把指標狀態當成已提交交易;指標只代表靜態可容納前綴,不是檔案副作用。 +- 只寫 `O(N log N)` 而漏算 variable-length path comparison 的 byte 成本。 diff --git a/problems/010-all-or-nothing-output-collection/generator.py b/problems/010-all-or-nothing-output-collection/generator.py new file mode 100644 index 0000000..9b8530b --- /dev/null +++ b/problems/010-all-or-nothing-output-collection/generator.py @@ -0,0 +1,20 @@ +import random, sys + +if len(sys.argv) != 3: + raise SystemExit("usage: generator.py SEED INDEX") +r = random.Random((int(sys.argv[1]) << 32) ^ int(sys.argv[2])) +idx = int(sys.argv[2]) +N = r.randint(1, 5 + idx % 8) +Q = r.randint(1, 9) +U = r.randint(0, 15) +a = [] +for i in range(N): + m = r.randint(0, 20) + a.append((f"/p-{i}", m, m + (r.choice((0, 0, 0, 1))))) +r.shuffle(a) +bud = sorted(r.randint(0, U + sum(x[1] for x in a) + 15) for _ in range(Q)) +print( + "\n".join( + [f"{N} {Q} {U}"] + [f"{p} {m} {x}" for p, m, x in a] + list(map(str, bud)) + ) +) diff --git a/problems/010-all-or-nothing-output-collection/oracle.py b/problems/010-all-or-nothing-output-collection/oracle.py new file mode 100644 index 0000000..2b08330 --- /dev/null +++ b/problems/010-all-or-nothing-output-collection/oracle.py @@ -0,0 +1,24 @@ +import sys + +t = sys.stdin.buffer.read().split() +it = iter(t) +N, Q, U = map(int, (next(it), next(it), next(it))) +a = sorted((next(it).decode(), int(next(it)), int(next(it))) for _ in range(N)) +out = [] +for _ in range(Q): + b = int(next(it)) + if U > b: + out.append("ERR QUOTA -") + continue + used = U + ans = None + for path, m, x in a: + if m != x: + ans = f"ERR MISMATCH {path}" + break + if used + m > b: + ans = f"ERR QUOTA {path}" + break + used += m + out.append(ans or f"OK {N} {used}") +print("\n".join(out)) diff --git a/problems/010-all-or-nothing-output-collection/problem.json b/problems/010-all-or-nothing-output-collection/problem.json new file mode 100644 index 0000000..ceda080 --- /dev/null +++ b/problems/010-all-or-nothing-output-collection/problem.json @@ -0,0 +1,156 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 10, + "slug": "all-or-nothing-output-collection", + "title": { + "zh-TW": "全有或全無的輸出蒐集", + "en": "All-or-Nothing Output Collection" + }, + "difficulty": "hard", + "tags": [ + "sorting", + "two-pointers", + "transaction", + "toctou" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-01", + "kind": "adversarial", + "input": "tests/adversarial-01.in", + "output": "tests/adversarial-01.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 9500000, + "memoryLimitBytes": 536870912 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 1500000, + "memoryLimitBytes": 402653184 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 550000, + "memoryLimitBytes": 268435456 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "每次查詢重新排序與蒐集", + "en": "Re-sort and Collect for Every Query" + }, + "time": "O(QL log N+Z)", + "space": "O(L+N+Z)", + "accepted": false + }, + { + "name": { + "zh-TW": "排序一次後逐查詢二分", + "en": "Sort Once with Per-Query Binary Search" + }, + "time": "O(L log N+Q log N+Z)", + "space": "O(L+N+Z)", + "accepted": true + }, + { + "name": { + "zh-TW": "排序一次與單調 quota 指標", + "en": "Sort Once with a Monotone Quota Pointer" + }, + "time": "O(L log N+Q+Z)", + "space": "O(L+N+Z)", + "accepted": true + } + ] +} diff --git a/problems/010-all-or-nothing-output-collection/solutions/c/main.c b/problems/010-all-or-nothing-output-collection/solutions/c/main.c new file mode 100644 index 0000000..2ebf16c --- /dev/null +++ b/problems/010-all-or-nothing-output-collection/solutions/c/main.c @@ -0,0 +1,60 @@ +#include +#include +#include +#include +typedef struct { + char *p; + uint64_t m, a; +} File; +static int cmp(const void *x, const void *y) { + return strcmp(((const File *)x)->p, ((const File *)y)->p); +} +int main(void) { + int N, Q; + unsigned long long U; + if (scanf("%d%d%llu", &N, &Q, &U) != 3) + return 0; + File *f = malloc((size_t)N * sizeof(*f)); + char *buf = malloc(200001); + for (int i = 0; i < N; i++) { + unsigned long long m, a; + scanf("%200000s%llu%llu", buf, &m, &a); + f[i].p = malloc(strlen(buf) + 1); + strcpy(f[i].p, buf); + f[i].m = m; + f[i].a = a; + } + qsort(f, (size_t)N, sizeof(*f), cmp); + uint64_t *pre = calloc(N + 1, sizeof(*pre)); + int mismatch = N; + for (int i = 0; i < N; i++) { + pre[i + 1] = pre[i] + f[i].m; + if (mismatch == N && f[i].m != f[i].a) + mismatch = i; + } + int k = 0; + while (Q--) { + unsigned long long b; + scanf("%llu", &b); + if (b < U) { + puts("ERR QUOTA -"); + continue; + } + uint64_t cap = b - U; + while (k < N && pre[k + 1] <= cap) + k++; + if (k < mismatch) + printf("ERR QUOTA %s\n", f[k].p); + else if (mismatch < N) + printf("ERR MISMATCH %s\n", f[mismatch].p); + else if (k < N) + printf("ERR QUOTA %s\n", f[k].p); + else + printf("OK %d %llu\n", N, (unsigned long long)(U + pre[N])); + } + for (int i = 0; i < N; i++) + free(f[i].p); + free(f); + free(buf); + free(pre); +} diff --git a/problems/010-all-or-nothing-output-collection/solutions/cpp/main.cpp b/problems/010-all-or-nothing-output-collection/solutions/cpp/main.cpp new file mode 100644 index 0000000..48ff13c --- /dev/null +++ b/problems/010-all-or-nothing-output-collection/solutions/cpp/main.cpp @@ -0,0 +1,50 @@ +#include +#include +#include +#include +#include +using namespace std; +struct File { + string p; + uint64_t m, a; +}; +int main() { + ios::sync_with_stdio(false); + cin.tie(nullptr); + int n, q; + uint64_t u; + if (!(cin >> n >> q >> u)) + return 0; + vector f(n); + for (auto &x : f) + cin >> x.p >> x.m >> x.a; + sort(f.begin(), f.end(), + [](const File &a, const File &b) { return a.p < b.p; }); + vector pre(n + 1); + int mismatch = n; + for (int i = 0; i < n; i++) { + pre[i + 1] = pre[i] + f[i].m; + if (mismatch == n && f[i].m != f[i].a) + mismatch = i; + } + int k = 0; + while (q--) { + uint64_t b; + cin >> b; + if (b < u) { + cout << "ERR QUOTA -\n"; + continue; + } + uint64_t cap = b - u; + while (k < n && pre[k + 1] <= cap) + k++; + if (k < mismatch) + cout << "ERR QUOTA " << f[k].p << '\n'; + else if (mismatch < n) + cout << "ERR MISMATCH " << f[mismatch].p << '\n'; + else if (k < n) + cout << "ERR QUOTA " << f[k].p << '\n'; + else + cout << "OK " << n << ' ' << u + pre[n] << '\n'; + } +} diff --git a/problems/010-all-or-nothing-output-collection/solutions/go/main.go b/problems/010-all-or-nothing-output-collection/solutions/go/main.go new file mode 100644 index 0000000..c349f48 --- /dev/null +++ b/problems/010-all-or-nothing-output-collection/solutions/go/main.go @@ -0,0 +1,59 @@ +package main + +import ( + "bufio" + "fmt" + "os" + "sort" +) + +type file struct { + p string + m, a uint64 +} + +func main() { + in := bufio.NewReader(os.Stdin) + out := bufio.NewWriter(os.Stdout) + defer out.Flush() + var n, q int + var u uint64 + if _, e := fmt.Fscan(in, &n, &q, &u); e != nil { + return + } + f := make([]file, n) + for i := range f { + fmt.Fscan(in, &f[i].p, &f[i].m, &f[i].a) + } + sort.Slice(f, func(i, j int) bool { return f[i].p < f[j].p }) + pre := make([]uint64, n+1) + mismatch := n + for i := 0; i < n; i++ { + pre[i+1] = pre[i] + f[i].m + if mismatch == n && f[i].m != f[i].a { + mismatch = i + } + } + k := 0 + for ; q > 0; q-- { + var b uint64 + fmt.Fscan(in, &b) + if b < u { + fmt.Fprintln(out, "ERR QUOTA -") + continue + } + cap := b - u + for k < n && pre[k+1] <= cap { + k++ + } + if k < mismatch { + fmt.Fprintln(out, "ERR QUOTA", f[k].p) + } else if mismatch < n { + fmt.Fprintln(out, "ERR MISMATCH", f[mismatch].p) + } else if k < n { + fmt.Fprintln(out, "ERR QUOTA", f[k].p) + } else { + fmt.Fprintln(out, "OK", n, u+pre[n]) + } + } +} diff --git a/problems/010-all-or-nothing-output-collection/solutions/javascript/main.js b/problems/010-all-or-nothing-output-collection/solutions/javascript/main.js new file mode 100644 index 0000000..27fd70a --- /dev/null +++ b/problems/010-all-or-nothing-output-collection/solutions/javascript/main.js @@ -0,0 +1,50 @@ +import * as std from "std"; +/** @typedef {{ p: string, m: bigint, a: bigint }} File */ +/** @type {string} */ +const input = std.in.readAsString(); +let cursor = 0; +/** @returns {string} */ +function nextToken() { + while (cursor < input.length && input.charCodeAt(cursor) <= 32) cursor++; + const start = cursor; + while (cursor < input.length && input.charCodeAt(cursor) > 32) cursor++; + return input.slice(start, cursor); +} +const N = Number(nextToken()), + Q = Number(nextToken()), + U = BigInt(nextToken()), + a = /** @type {File[]} */ ([]); +for (let i = 0; i < N; i++) { + a.push({ p: nextToken(), m: BigInt(nextToken()), a: BigInt(nextToken()) }); +} +a.sort((x, y) => x.p < y.p ? -1 : x.p > y.p ? 1 : 0); +const pre = /** @type {bigint[]} */ ([0n]); +let mismatch = N; +for (let i = 0; i < N; i++) { + pre.push(pre[i] + a[i].m); + if (mismatch === N && a[i].m !== a[i].a) mismatch = i; +} +let k = 0; +let output = ""; +/** @param {string} line */ +function emit(line) { + if (output.length + line.length > 65536) { + std.out.puts(output); + output = ""; + } + output += line; +} +for (let z = 0; z < Q; z++) { + const b = BigInt(nextToken()); + if (b < U) { + emit("ERR QUOTA -\n"); + continue; + } + const cap = b - U; + while (k < N && pre[k + 1] <= cap) k++; + if (k < mismatch) emit(`ERR QUOTA ${a[k].p}\n`); + else if (mismatch < N) emit(`ERR MISMATCH ${a[mismatch].p}\n`); + else if (k < N) emit(`ERR QUOTA ${a[k].p}\n`); + else emit(`OK ${N} ${U + pre[N]}\n`); +} +if (output.length) std.out.puts(output); diff --git a/problems/010-all-or-nothing-output-collection/solutions/python/main.py b/problems/010-all-or-nothing-output-collection/solutions/python/main.py new file mode 100644 index 0000000..be5bdea --- /dev/null +++ b/problems/010-all-or-nothing-output-collection/solutions/python/main.py @@ -0,0 +1,31 @@ +import sys + +t = sys.stdin.buffer.read().split() +it = iter(t) +N, Q, U = map(int, (next(it), next(it), next(it))) +a = sorted((next(it), int(next(it)), int(next(it))) for _ in range(N)) +pre = [0] +mismatch = N +for i, (_, m, x) in enumerate(a): + pre.append(pre[-1] + m) + if mismatch == N and m != x: + mismatch = i +k = 0 +out = [] +for _ in range(Q): + b = int(next(it)) + if b < U: + out.append("ERR QUOTA -") + continue + cap = b - U + while k < N and pre[k + 1] <= cap: + k += 1 + if k < mismatch: + out.append("ERR QUOTA " + a[k][0].decode()) + elif mismatch < N: + out.append("ERR MISMATCH " + a[mismatch][0].decode()) + elif k < N: + out.append("ERR QUOTA " + a[k][0].decode()) + else: + out.append(f"OK {N} {U+pre[N]}") +print("\n".join(out)) diff --git a/problems/010-all-or-nothing-output-collection/solutions/rust/main.rs b/problems/010-all-or-nothing-output-collection/solutions/rust/main.rs new file mode 100644 index 0000000..9b071c5 --- /dev/null +++ b/problems/010-all-or-nothing-output-collection/solutions/rust/main.rs @@ -0,0 +1,54 @@ +use std::io::{self, Read}; +struct File { + p: String, + m: u64, + a: u64, +} +fn main() { + let mut s = String::new(); + io::stdin().read_to_string(&mut s).unwrap(); + let mut t = s.split_whitespace(); + let n: usize = t.next().unwrap().parse().unwrap(); + let q: usize = t.next().unwrap().parse().unwrap(); + let u: u64 = t.next().unwrap().parse().unwrap(); + let mut f = Vec::with_capacity(n); + for _ in 0..n { + f.push(File { + p: t.next().unwrap().to_string(), + m: t.next().unwrap().parse().unwrap(), + a: t.next().unwrap().parse().unwrap(), + }); + } + f.sort_by(|a, b| a.p.cmp(&b.p)); + let mut pre = vec![0u64; n + 1]; + let mut mismatch = n; + for i in 0..n { + pre[i + 1] = pre[i] + f[i].m; + if mismatch == n && f[i].m != f[i].a { + mismatch = i; + } + } + let mut k = 0usize; + let mut out = String::new(); + for _ in 0..q { + let b: u64 = t.next().unwrap().parse().unwrap(); + if b < u { + out += "ERR QUOTA -\n"; + continue; + } + let cap = b - u; + while k < n && pre[k + 1] <= cap { + k += 1 + } + if k < mismatch { + out += &format!("ERR QUOTA {}\n", f[k].p) + } else if mismatch < n { + out += &format!("ERR MISMATCH {}\n", f[mismatch].p) + } else if k < n { + out += &format!("ERR QUOTA {}\n", f[k].p) + } else { + out += &format!("OK {} {}\n", n, u + pre[n]) + } + } + print!("{}", out); +} diff --git a/problems/010-all-or-nothing-output-collection/solutions/typescript/main.ts b/problems/010-all-or-nothing-output-collection/solutions/typescript/main.ts new file mode 100644 index 0000000..487e655 --- /dev/null +++ b/problems/010-all-or-nothing-output-collection/solutions/typescript/main.ts @@ -0,0 +1,47 @@ +import * as std from "std"; +type File = { p: string; m: bigint; a: bigint }; +const input: string = std.in.readAsString(); +let cursor = 0; +function nextToken(): string { + while (cursor < input.length && input.charCodeAt(cursor) <= 32) cursor++; + const start = cursor; + while (cursor < input.length && input.charCodeAt(cursor) > 32) cursor++; + return input.slice(start, cursor); +} +const N = Number(nextToken()), + Q = Number(nextToken()), + U = BigInt(nextToken()), + a: File[] = []; +for (let i = 0; i < N; i++) { + a.push({ p: nextToken(), m: BigInt(nextToken()), a: BigInt(nextToken()) }); +} +a.sort((x, y) => x.p < y.p ? -1 : x.p > y.p ? 1 : 0); +const pre: bigint[] = [0n]; +let mismatch = N; +for (let i = 0; i < N; i++) { + pre.push(pre[i] + a[i].m); + if (mismatch === N && a[i].m !== a[i].a) mismatch = i; +} +let k = 0; +let output = ""; +function emit(line: string): void { + if (output.length + line.length > 65536) { + std.out.puts(output); + output = ""; + } + output += line; +} +for (let z = 0; z < Q; z++) { + const b = BigInt(nextToken()); + if (b < U) { + emit("ERR QUOTA -\n"); + continue; + } + const cap = b - U; + while (k < N && pre[k + 1] <= cap) k++; + if (k < mismatch) emit(`ERR QUOTA ${a[k].p}\n`); + else if (mismatch < N) emit(`ERR MISMATCH ${a[mismatch].p}\n`); + else if (k < N) emit(`ERR QUOTA ${a[k].p}\n`); + else emit(`OK ${N} ${U + pre[N]}\n`); +} +if (output.length) std.out.puts(output); diff --git a/problems/010-all-or-nothing-output-collection/statement.en.md b/problems/010-all-or-nothing-output-collection/statement.en.md new file mode 100644 index 0000000..274f67c --- /dev/null +++ b/problems/010-all-or-nothing-output-collection/statement.en.md @@ -0,0 +1,116 @@ +# All-or-Nothing Output Collection + +A WASM OJ collects output files after the submitted program exits, but a file's metadata and its actual contents may no longer agree during collection. If quota validation used metadata first and the subsequent read returned a different length, a TOCTOU problem would result. Output files must also share the same byte budget already used by stdout and stderr. + +To keep results independent of file-enumeration order, the `N` output files must be processed in UTF-8 byte lexicographic order of their paths. Every path is ASCII, so this is ordinary bytewise lexicographic order; when one string is a prefix of another, the shorter string comes first. Stdout and stderr have already consumed `U` bytes together. + +Each file record contains `path metadataLength actualLength`. Before processing a file, compare the two lengths. A difference is a TOCTOU mismatch between metadata and the actual read. Only when they match may `metadataLength` be added to the shared byte budget. + +Every budget query independently starts with no files collected but `U` bytes already used, and processes files in canonical order: + +1. If `U>budget` initially, fail immediately for quota without touching any path. +2. For the current file, check mismatch first and fail immediately if one exists. +3. Otherwise, if adding the file would exceed the budget, fail for quota at that path. +4. Otherwise, include the complete file and continue. + +Collection has all-or-nothing semantics: a failure returns no partial file collection. Input budgets are guaranteed to be nondecreasing. + +## Input + +The first line contains `N Q U`. The next `N` lines contain file records in arbitrary order. The final `Q` lines each contain a nondecreasing `budget`. + +## Output + +On success, output `OK N finalUsedBytes`. On failure, output `ERR MISMATCH path` or `ERR QUOTA path`. For the special initial failure `U>budget`, replace the path with `-`: `ERR QUOTA -`. + +For the same file, `MISMATCH` has priority over `QUOTA`. All paths are distinct. + +## Constraints + +- `1 ≤ N,Q ≤ 200000` +- `0 ≤ U,budget ≤ 9×10^18` +- `0 ≤ metadataLength,actualLength ≤ 10^12` +- `U + Σ metadataLength ≤ 9×10^18` +- Each path has length `2..200000`, starts with `/`, contains only lowercase ASCII letters, digits, `-`, and `/`, has no empty segment, and does not end with `/`. +- Total path length is at most `2000000`. +- `Q × (maximum path byte length) ≤ 2000000`, so repeated error messages also have bounded total path output. +- The budget sequence is nondecreasing. + +The full constraints rule out sorting or scanning all files again for every query. + +## Examples + + + +### Example One + +Input: + +```text +4 6 3 +/z 4 4 +/a 2 2 +/m 5 7 +/b 3 3 +2 +3 +4 +5 +8 +100 +``` + +Output: + +```text +ERR QUOTA - +ERR QUOTA /a +ERR QUOTA /a +ERR QUOTA /b +ERR MISMATCH /m +ERR MISMATCH /m +``` + +### Example Two + +Input: + +```text +2 3 0 +/b 5 5 +/a 0 0 +0 +5 +10 +``` + +Output: + +```text +ERR QUOTA /b +OK 2 5 +OK 2 5 +``` + +### Example Three + +Input: + +```text +2 3 1 +/z 1 1 +/a 100 99 +0 +1 +200 +``` + +Output: + +```text +ERR QUOTA - +ERR MISMATCH /a +ERR MISMATCH /a +``` + + diff --git a/problems/010-all-or-nothing-output-collection/statement.zh-TW.md b/problems/010-all-or-nothing-output-collection/statement.zh-TW.md new file mode 100644 index 0000000..05ea955 --- /dev/null +++ b/problems/010-all-or-nothing-output-collection/statement.zh-TW.md @@ -0,0 +1,116 @@ +# 全有或全無的輸出蒐集 + +WASM OJ 在程式結束後會蒐集輸出檔,但蒐集期間檔案的 metadata 與實際內容可能已不一致。若先依 metadata 通過配額檢查,讀取時卻得到不同長度,就會產生 TOCTOU 問題。此外,輸出檔還必須與先前的 stdout、stderr 共用同一份 byte budget。 + +為了讓結果不受檔案列舉順序影響,`N` 個輸出檔必須按 path 的 UTF-8 byte lexicographic order 處理。所有 path 只含 ASCII,所以等同一般逐 byte 字典序;若較短字串是另一字串的 prefix,較短者在前。stdout 與 stderr 已共同使用 `U` bytes。 + +每個檔案記錄 `path metadataLength actualLength`。處理一個檔案時,必須先比較兩種長度:不相同代表 metadata 與實際讀取之間發生 TOCTOU mismatch;只有相同時,才嘗試把 `metadataLength` 加入共用 byte budget。 + +每個 budget 查詢都從「尚未蒐集任何檔案、但已使用 `U` bytes」的狀態獨立開始,並依 canonical 順序處理: + +1. 若一開始 `U>budget`,立即 quota failure,尚未接觸任何 path。 +2. 對目前檔案,先檢查 mismatch;若 mismatch,立即失敗。 +3. 否則若加入該檔會使總量超過 budget,在該 path quota failure。 +4. 否則完整加入並繼續。 + +蒐集採 all-or-nothing 語意:任何失敗都不回傳部分檔案。輸入保證 budget 查詢非遞減。 + +## 輸入 + +第一行 `N Q U`。接下來 `N` 行為檔案記錄,順序任意;最後 `Q` 行各為一個非遞減 `budget`。 + +## 輸出 + +成功時輸出 `OK N finalUsedBytes`。失敗時輸出 `ERR MISMATCH path` 或 `ERR QUOTA path`。初始 `U>budget` 的特殊 quota failure 以 `-` 取代 path:`ERR QUOTA -`。 + +在同一檔案上,MISMATCH 的優先序高於 QUOTA。path 皆互不相同。 + +## 限制 + +- `1 ≤ N,Q ≤ 200000` +- `0 ≤ U,budget ≤ 9×10^18` +- `0 ≤ metadataLength,actualLength ≤ 10^12` +- `U + Σ metadataLength ≤ 9×10^18` +- 每個 path 長度 `2..200000`,以 `/` 開頭,只含 ASCII 小寫字母、數字、`-`、`/` +- path 不含空 segment、不以 `/` 結尾;全部 path 長度總和不超過 `2000000` +- `Q ×(最長 path 的 byte 長度)≤ 2000000`,因此重複錯誤訊息的總 path 輸出量也有界 +- budget 序列非遞減 + +完整限制排除每個查詢重新排序或掃描全部檔案。 + +## 範例 + + + +### 範例一 + +輸入: + +```text +4 6 3 +/z 4 4 +/a 2 2 +/m 5 7 +/b 3 3 +2 +3 +4 +5 +8 +100 +``` + +輸出: + +```text +ERR QUOTA - +ERR QUOTA /a +ERR QUOTA /a +ERR QUOTA /b +ERR MISMATCH /m +ERR MISMATCH /m +``` + +### 範例二 + +輸入: + +```text +2 3 0 +/b 5 5 +/a 0 0 +0 +5 +10 +``` + +輸出: + +```text +ERR QUOTA /b +OK 2 5 +OK 2 5 +``` + +### 範例三 + +輸入: + +```text +2 3 1 +/z 1 1 +/a 100 99 +0 +1 +200 +``` + +輸出: + +```text +ERR QUOTA - +ERR MISMATCH /a +ERR MISMATCH /a +``` + + diff --git a/problems/010-all-or-nothing-output-collection/tests/adversarial-01.in b/problems/010-all-or-nothing-output-collection/tests/adversarial-01.in new file mode 100644 index 0000000..de2ccfb --- /dev/null +++ b/problems/010-all-or-nothing-output-collection/tests/adversarial-01.in @@ -0,0 +1,11 @@ +4 6 9 +/z 1 1 +/b 100 99 +/aa 5 5 +/a 0 0 +8 +9 +13 +14 +200 +9000000000000000000 diff --git a/problems/010-all-or-nothing-output-collection/tests/adversarial-01.out b/problems/010-all-or-nothing-output-collection/tests/adversarial-01.out new file mode 100644 index 0000000..8bb1efb --- /dev/null +++ b/problems/010-all-or-nothing-output-collection/tests/adversarial-01.out @@ -0,0 +1,6 @@ +ERR QUOTA - +ERR QUOTA /aa +ERR QUOTA /aa +ERR MISMATCH /b +ERR MISMATCH /b +ERR MISMATCH /b diff --git a/problems/010-all-or-nothing-output-collection/tests/sample-01.in b/problems/010-all-or-nothing-output-collection/tests/sample-01.in new file mode 100644 index 0000000..c81996d --- /dev/null +++ b/problems/010-all-or-nothing-output-collection/tests/sample-01.in @@ -0,0 +1,11 @@ +4 6 3 +/z 4 4 +/a 2 2 +/m 5 7 +/b 3 3 +2 +3 +4 +5 +8 +100 diff --git a/problems/010-all-or-nothing-output-collection/tests/sample-01.out b/problems/010-all-or-nothing-output-collection/tests/sample-01.out new file mode 100644 index 0000000..5c039c6 --- /dev/null +++ b/problems/010-all-or-nothing-output-collection/tests/sample-01.out @@ -0,0 +1,6 @@ +ERR QUOTA - +ERR QUOTA /a +ERR QUOTA /a +ERR QUOTA /b +ERR MISMATCH /m +ERR MISMATCH /m diff --git a/problems/010-all-or-nothing-output-collection/tests/sample-02.in b/problems/010-all-or-nothing-output-collection/tests/sample-02.in new file mode 100644 index 0000000..cd7e92d --- /dev/null +++ b/problems/010-all-or-nothing-output-collection/tests/sample-02.in @@ -0,0 +1,6 @@ +2 3 0 +/b 5 5 +/a 0 0 +0 +5 +10 diff --git a/problems/010-all-or-nothing-output-collection/tests/sample-02.out b/problems/010-all-or-nothing-output-collection/tests/sample-02.out new file mode 100644 index 0000000..aae1122 --- /dev/null +++ b/problems/010-all-or-nothing-output-collection/tests/sample-02.out @@ -0,0 +1,3 @@ +ERR QUOTA /b +OK 2 5 +OK 2 5 diff --git a/problems/010-all-or-nothing-output-collection/tests/sample-03.in b/problems/010-all-or-nothing-output-collection/tests/sample-03.in new file mode 100644 index 0000000..224a8e8 --- /dev/null +++ b/problems/010-all-or-nothing-output-collection/tests/sample-03.in @@ -0,0 +1,6 @@ +2 3 1 +/z 1 1 +/a 100 99 +0 +1 +200 diff --git a/problems/010-all-or-nothing-output-collection/tests/sample-03.out b/problems/010-all-or-nothing-output-collection/tests/sample-03.out new file mode 100644 index 0000000..16b0e77 --- /dev/null +++ b/problems/010-all-or-nothing-output-collection/tests/sample-03.out @@ -0,0 +1,3 @@ +ERR QUOTA - +ERR MISMATCH /a +ERR MISMATCH /a diff --git a/problems/010-all-or-nothing-output-collection/validator.py b/problems/010-all-or-nothing-output-collection/validator.py new file mode 100644 index 0000000..eb15faa --- /dev/null +++ b/problems/010-all-or-nothing-output-collection/validator.py @@ -0,0 +1,56 @@ +import re, sys + + +def fail(): + raise SystemExit(1) + + +try: + t = sys.stdin.buffer.read().decode("ascii").split() + p = 0 + + def u(a, b): + global p + if p >= len(t) or re.fullmatch(r"0|[1-9][0-9]*", t[p]) is None: + fail() + v = int(t[p]) + p += 1 + if not a <= v <= b: + fail() + return v + + N, Q, U = u(1, 200000), u(1, 200000), u(0, 9 * 10**18) + seen = set() + total = U + length = 0 + max_length = 0 + for _ in range(N): + if p >= len(t): + fail() + path = t[p] + p += 1 + if ( + not 2 <= len(path) <= 200000 + or re.fullmatch(r"/[a-z0-9-]+(?:/[a-z0-9-]+)*", path) is None + or path in seen + ): + fail() + seen.add(path) + length += len(path) + max_length = max(max_length, len(path)) + total += u(0, 10**12) + u(0, 10**12) + if total > 9 * 10**18: + fail() + if length > 2000000 or Q * max_length > 2000000: + fail() + prev = -1 + for _ in range(Q): + b = u(0, 9 * 10**18) + if b < prev: + fail() + prev = b + if p != len(t): + fail() +except (UnicodeDecodeError, ValueError, OverflowError): + fail() diff --git a/problems/011-mount-tree-conflicts/editorial.en.md b/problems/011-mount-tree-conflicts/editorial.en.md new file mode 100644 index 0000000..c5514ee --- /dev/null +++ b/problems/011-mount-tree-conflicts/editorial.en.md @@ -0,0 +1,65 @@ +# Editorial + +## Intuitive Approach + +Insert records in input order. For record `j`, compare it with every earlier record: equal paths conflict, as does a segment-prefix relationship when the ancestor record is `F`. This naturally implements the tie-break but costs `O(NS)` time after accounting for all path bytes, with `O(S)` space. + +## Advanced Approach: Tree-Order Sorting and an Ancestor Stack + +Sort `(path,kind,index)` by **tree order** and group identical paths. When comparing path bytes, treat separator `/` as smaller than every legal segment character while preserving the order of all other bytes. Then a path precedes all strict descendants, and each prefix subtree is contiguous. + +Ordinary ASCII lexicographic order is insufficient: legal `-` (45) and `.` (46) are both smaller than `/` (47), so `/a-` can appear between `/a` and `/a/b`, breaking subtree contiguity. + +- If a group contains at least two records, its two smallest original indices form its best duplicate conflict. +- Scan distinct paths in tree order. Maintain a stack of groups that are strict ancestors of the current path and contain an `F`; pop a group when leaving its prefix subtree. +- Store in each stack entry the minimum original index of any ancestral `F` up to that point. Pair this minimum with the current group's minimum index. +- If the current group contains `F`, push it after processing so descendants can use it. + +Normalize each candidate pair as `i=min(a,b), j=max(a,b)` and compare candidates by `(j,i)` to implement the required tie-break. + +Comparison sorting plus variable-length comparisons takes `O(S log N)` time and `O(N+S)` space. This earns looser policies but is not optimal enough for the strictest policy. + +## Optimal Approach: An Input-Order Character Trie + +Process `j=1,2,...,N` in input order. The first record `j` that conflicts with an earlier one automatically minimizes `j`; only the minimum candidate `i` is needed before returning immediately. + +Each trie node represents a character prefix and stores: + +- `exactMin`: the smallest earlier index ending at exactly this path; +- `fileMin`: the smallest earlier `F` index ending at exactly this path; +- `descMin`: the smallest earlier record index for which this node's canonical path is a **strict ancestor**; +- `firstChild`, `nextSibling`, and the node's character. + +Walk the current `(kind,path)` from root to endpoint: + +1. At every strict canonical-path prefix, consider that node's `fileMin`. For an ordinary path, a boundary occurs when the next character is `/`; root `/` is a special case and is an ancestor of every non-root path. +2. At the endpoint, consider `exactMin`. +3. If the current kind is `F`, also consider endpoint `descMin`, covering the case where the current file is an ancestor of an earlier path. +4. If any candidate exists, its minimum `i` with current `j` is the answer. Otherwise insert record `j`: update endpoint `exactMin`, update `fileMin` for an `F`, and update `descMin` at every strict canonical ancestor of this path. + +Do not update `descMin` at arbitrary character prefixes. Inserting `/ab` must not update the node for `/a`, because `/a` is not its ancestor. Update only root `/` and strict prefixes followed by `/`. + +Do not use a hash map for child lookup. Legal child characters come from a fixed alphabet: `/`, lowercase letters, digits, `.`, `_`, and `-`. Scanning a first-child/next-sibling list therefore checks only a fixed number of children and is worst-case `O(1)`, not merely expected time. + +## Correctness Proof + +**Lemma 1.** Before processing record `j`, endpoint `exactMin` is the smallest prior index having the same path. Every conflict-free insertion takes a minimum at its unique endpoint, so the invariant holds; querying it covers exactly duplicate-path conflicts. + +**Lemma 2.** At every canonical strict-ancestor node traversed by record `j`, `fileMin` is the smallest earlier `F` index at that ancestor path. Taking the minimum of these values covers exactly all conflicts where an earlier file is a strict ancestor of the current path. + +**Lemma 3.** For every node, `descMin` is the smallest earlier index among strict descendants of its canonical path. Inserting a path updates exactly root `/` and strict prefixes followed by `/`, which are precisely its canonical ancestors. Thus when the current record is `F`, endpoint `descMin` covers exactly all conflicts where the current path is a strict ancestor of an earlier path. + +The three lemmas cover every conflict type and introduce no non-conflicting pair. Processing in input order makes the first `j` with a candidate minimal, and taking the minimum candidate index makes `i` minimal for that fixed `j`. Therefore the output obeys the `(j,i)` tie-break. + +## Complexity + +The trie contains at most `S+1` nodes. Every path byte is traversed a constant number of times, and each child search examines at most the fixed alphabet size. Worst-case time is therefore deterministic `O(S)`, and space is `O(S)`. + +## Common Mistakes + +- Using string `startsWith` and treating `/a` as an ancestor of `/ab`. +- Updating `descMin` at every character prefix, causing the same false ancestor relationship. +- Sorting by ordinary ASCII path order and overlooking that `-` and `.` precede separator `/`. +- Treating a directory ancestor as a conflict. +- Stopping at the first ancestor rather than minimizing `i` for a fixed `j`. +- Forgetting the root path `/` special case. diff --git a/problems/011-mount-tree-conflicts/editorial.zh-TW.md b/problems/011-mount-tree-conflicts/editorial.zh-TW.md new file mode 100644 index 0000000..2bb52df --- /dev/null +++ b/problems/011-mount-tree-conflicts/editorial.zh-TW.md @@ -0,0 +1,65 @@ +# 解題說明 + +## 直覺解 + +依輸入順序加入紀錄,對第 `j` 筆逐一檢查前 `j-1` 筆:路徑相等,或其中的 `F` 路徑是另一條路徑的 segment 前綴,即為衝突。這自然得到正確 tie-break,但把所有 path byte 納入後,時間為 `O(NS)`、空間為 `O(S)`。 + +## 次佳解:排序與祖先堆疊 + +把 `(path, kind, index)` 依 **tree order** 排序,將相同 path 組成一組。tree order 比較 path byte 時,把 separator `/` 視為小於任何合法 segment 字元,其餘 byte 維持原順序。於是某個 path 會排在全部嚴格後代之前,而且整棵 prefix 子樹必為連續區間。 + +不能直接使用一般 ASCII 字典序:合法的 `-`(45)與 `.`(46)都小於 `/`(47),例如 `/a-` 會插在 `/a` 與 `/a/b` 之間,破壞 prefix 子樹連續性。 + +- 同組至少兩筆時,原編號最小的兩筆形成該路徑能產生的最佳重複衝突。 +- 字典序掃描不同路徑。維護仍為目前路徑嚴格祖先、且該組含 `F` 的堆疊。離開一個 prefix 子樹時將它彈出。 +- 堆疊項目另存「到此為止所有祖先 `F` 的最小原編號」。目前組只需與此最小編號、以及目前組的最小編號配對。 +- 若目前組含 `F`,掃描完後把它壓入,供後代使用。 + +每當得到候選 `(a,b)`,先排成 `i=min(a,b), j=max(a,b)`,以 `(j,i)` 比較即可實作題目的 tie-break。 + +comparison sort 會做 `O(N log N)` 次比較。把 variable-length path 的 byte 比較也納入後,這個解法的時間為 `O(S log N)`、空間為 `O(N+S)`;它適合較寬鬆的資源政策,但不是最嚴格政策要求的最佳解。 + +## 最佳解:依輸入順序維護字元 trie + +依 `j=1,2,...,N` 的原順序處理。如此只要第 `j` 筆能和先前紀錄衝突,就已經找到最小的 `j`;我們只需在所有先前候選中取最小的 `i`,然後立刻輸出。 + +trie 的每個節點代表一個字元前綴,並維護: + +- `exactMin`:恰好在這個 path 結束的最小先前編號; +- `fileMin`:恰好在這個 path 結束、且種類為 `F` 的最小先前編號; +- `descMin`:以這個節點所代表的 canonical path 為**嚴格祖先**之先前紀錄最小編號; +- `firstChild`、`nextSibling` 與該節點的字元。 + +對目前的 `(kind,path)` 從根走到終點: + +1. 每到一個嚴格 canonical-path 前綴,就用該節點的 `fileMin` 更新候選。一般路徑的 boundary 是「下一個字元為 `/`」;根路徑 `/` 則是特例,它是所有非根路徑的祖先。 +2. 到達終點後,用 `exactMin` 更新候選。 +3. 若目前種類為 `F`,再用終點的 `descMin` 更新候選,涵蓋「目前檔案是先前路徑祖先」的情況。 +4. 若有候選,最小的 `i` 與目前 `j` 就是答案。否則才把第 `j` 筆寫入 trie:更新終點的 `exactMin`、必要時更新 `fileMin`,並在 path 的每個嚴格 canonical 祖先節點更新 `descMin`。 + +`descMin` 不能更新在所有字元前綴。例如插入 `/ab` 時,不可更新 `/a` 節點,否則會把 `/a` 錯當成 `/ab` 的祖先;只有根 `/`,以及下一個字元為 `/` 的 segment boundary 才能更新。 + +不使用 hash map 尋找 child。合法 child 字元只有 `/`、小寫字母、數字、`.`、`_`、`-`,總數是固定常數。以 first-child/next-sibling 掃描某節點的 children,單次轉移至多檢查這個固定 alphabet 的數量,因此是 worst-case `O(1)`,不是 expected-only 的雜湊複雜度。 + +## 正確性證明 + +**引理一:** 處理第 `j` 筆前,終點的 `exactMin` 恰為所有相同先前 path 的最小編號。每筆無衝突紀錄插入時都在其唯一終點取最小值,因此不變量成立;查詢它正好涵蓋 duplicate 衝突。 + +**引理二:** 沿第 `j` 筆 path 經過 canonical 嚴格祖先節點時,其 `fileMin` 恰為該祖先 path 中最小的先前 `F` 編號。因此取這些值的最小值,恰涵蓋所有「先前 `F` 是目前 path 嚴格祖先」的衝突。 + +**引理三:** 任一節點的 `descMin` 恰為其 canonical path 的所有先前嚴格後代中最小的編號。插入 path 時只更新根 `/` 與下一個字元為 `/` 的嚴格前綴,這些且僅這些前綴是其 canonical path 祖先。因此目前種類為 `F` 時,終點的 `descMin` 恰涵蓋所有「目前 path 是先前紀錄嚴格祖先」的衝突。 + +三個引理涵蓋題目定義的所有衝突,而且沒有納入其他 pair。依輸入順序處理使第一個有候選的 `j` 最小;該次取所有候選編號的最小值使 `i` 最小。因此輸出符合 `(j,i)` tie-break。 + +## 複雜度 + +trie 至多建立 `S+1` 個節點。每個 path byte 只走常數次,而每次 first-child/next-sibling 搜尋至多檢查固定 alphabet 的所有字元,因此 worst-case 時間為 `O(S)`。trie 與輸入所需空間為 `O(S)`。 + +## 常見錯誤 + +- 用字串 `startsWith` 便把 `/a` 誤認為 `/ab` 的祖先。 +- 在所有字元前綴更新 `descMin`,同樣會把 `/a` 與 `/ab` 誤判。 +- 直接用 ASCII path 排序,忽略 `-`、`.` 會排在 separator `/` 之前。 +- 把目錄祖先也判為衝突。 +- 找到第一個祖先就停止,沒有在固定的 `j` 中取最小 `i`。 +- 忘記根路徑 `/` 的特殊 prefix 規則。 diff --git a/problems/011-mount-tree-conflicts/generator.py b/problems/011-mount-tree-conflicts/generator.py new file mode 100644 index 0000000..3d763e0 --- /dev/null +++ b/problems/011-mount-tree-conflicts/generator.py @@ -0,0 +1,19 @@ +import random, sys + +seed, index = map(int, sys.argv[1:]) +r = random.Random((seed << 32) ^ index) +n = 8 + index % 18 +paths = [] +for i in range(n): + if paths and r.random() < 0.28: + p = r.choice(paths) + if r.random() < 0.55: + p += "/x" + str(r.randrange(5)) + else: + p = "/" + "/".join( + "p" + str(r.randrange(12)) for _ in range(1 + r.randrange(3)) + ) + paths.append(p) +print(n) +for p in paths: + print(r.choice("FD"), p) diff --git a/problems/011-mount-tree-conflicts/oracle.py b/problems/011-mount-tree-conflicts/oracle.py new file mode 100644 index 0000000..8047b94 --- /dev/null +++ b/problems/011-mount-tree-conflicts/oracle.py @@ -0,0 +1,18 @@ +import sys + + +def anc(a, b): + return a == "/" and b != "/" or b.startswith(a + "/") + + +data = sys.stdin.read().split() +n = int(data[0]) +rows = [(data[i], data[i + 1]) for i in range(1, 2 * n + 1, 2)] +for j in range(n): + for i in range(j): + ki, pi = rows[i] + kj, pj = rows[j] + if pi == pj or (ki == "F" and anc(pi, pj)) or (kj == "F" and anc(pj, pi)): + print("CONFLICT", i + 1, j + 1) + raise SystemExit +print("VALID") diff --git a/problems/011-mount-tree-conflicts/problem.json b/problems/011-mount-tree-conflicts/problem.json new file mode 100644 index 0000000..81f6c06 --- /dev/null +++ b/problems/011-mount-tree-conflicts/problem.json @@ -0,0 +1,156 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 11, + "slug": "mount-tree-conflicts", + "title": { + "zh-TW": "掛載樹衝突檢查", + "en": "Mount-Tree Conflict Detection" + }, + "difficulty": "medium", + "tags": [ + "sorting", + "trie", + "filesystem", + "prefix" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-separator-order", + "kind": "adversarial", + "input": "tests/adversarial-separator-order.in", + "output": "tests/adversarial-separator-order.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 15000000, + "memoryLimitBytes": 536870912 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 700000, + "memoryLimitBytes": 402653184 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 300000, + "memoryLimitBytes": 268435456 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "逐對比較", + "en": "Pairwise Comparison" + }, + "time": "O(N S)", + "space": "O(S)", + "accepted": false + }, + { + "name": { + "zh-TW": "tree-order 排序與祖先堆疊", + "en": "Tree-Order Sorting and Ancestor Stack" + }, + "time": "O(S log N)", + "space": "O(N + S)", + "accepted": false + }, + { + "name": { + "zh-TW": "first-child/next-sibling 字元 trie", + "en": "First-Child/Next-Sibling Character Trie" + }, + "time": "O(S) deterministic worst-case", + "space": "O(S)", + "accepted": true + } + ] +} diff --git a/problems/011-mount-tree-conflicts/solutions/c/main.c b/problems/011-mount-tree-conflicts/solutions/c/main.c new file mode 100644 index 0000000..330cf24 --- /dev/null +++ b/problems/011-mount-tree-conflicts/solutions/c/main.c @@ -0,0 +1,132 @@ +#include +#include +#include + +typedef struct { + int first_child; + int next_sibling; + int exact_min; + int file_min; + int desc_min; + unsigned char ch; +} Node; + +static Node *nodes; +static int node_count; +static int node_capacity; +static int infinity; + +static int new_node(unsigned char ch, int next_sibling) { + if (node_count == node_capacity) { + int next_capacity = node_capacity * 2; + Node *grown = realloc(nodes, (size_t)next_capacity * sizeof(*nodes)); + if (grown == NULL) + exit(1); + nodes = grown; + node_capacity = next_capacity; + } + int index = node_count++; + nodes[index] = (Node){0, next_sibling, infinity, infinity, infinity, ch}; + return index; +} + +static int find_or_create_child(int parent, unsigned char ch) { + for (int child = nodes[parent].first_child; child != 0; + child = nodes[child].next_sibling) { + if (nodes[child].ch == ch) + return child; + } + int child = new_node(ch, nodes[parent].first_child); + nodes[parent].first_child = child; + return child; +} + +static unsigned char input_buffer[1 << 16]; +static size_t input_at; +static size_t input_size; + +static int next_byte(void) { + if (input_at == input_size) { + input_size = fread(input_buffer, 1, sizeof(input_buffer), stdin); + input_at = 0; + if (input_size == 0) + return EOF; + } + return input_buffer[input_at++]; +} + +static int next_token(char *out, int capacity) { + int c; + do { + c = next_byte(); + } while (c != EOF && c <= ' '); + if (c == EOF) + return 0; + int length = 0; + while (c != EOF && c > ' ') { + if (length + 1 < capacity) + out[length++] = (char)c; + c = next_byte(); + } + out[length] = '\0'; + return 1; +} + +int main(void) { + char token[32]; + if (!next_token(token, (int)sizeof(token))) + return 0; + int n = atoi(token); + infinity = n + 1; + node_capacity = 1024; + nodes = calloc((size_t)node_capacity, sizeof(*nodes)); + if (nodes == NULL) + return 1; + node_count = 1; + + for (int j = 1; j <= n; ++j) { + char kind[2]; + char path[201]; + next_token(kind, (int)sizeof(kind)); + next_token(path, (int)sizeof(path)); + size_t length = strlen(path); + int visited[200]; + int current = 0; + int best = infinity; + + for (size_t position = 0; position < length; ++position) { + current = find_or_create_child(current, (unsigned char)path[position]); + visited[position] = current; + if (position + 1 < length && + (position == 0 || path[position + 1] == '/') && + nodes[current].file_min < best) { + best = nodes[current].file_min; + } + } + if (nodes[current].exact_min < best) + best = nodes[current].exact_min; + if (kind[0] == 'F' && nodes[current].desc_min < best) + best = nodes[current].desc_min; + + if (best != infinity) { + printf("CONFLICT %d %d\n", best, j); + free(nodes); + return 0; + } + + for (size_t position = 0; position + 1 < length; ++position) { + if ((position == 0 || path[position + 1] == '/') && + j < nodes[visited[position]].desc_min) { + nodes[visited[position]].desc_min = j; + } + } + if (j < nodes[current].exact_min) + nodes[current].exact_min = j; + if (kind[0] == 'F' && j < nodes[current].file_min) + nodes[current].file_min = j; + } + + puts("VALID"); + free(nodes); + return 0; +} diff --git a/problems/011-mount-tree-conflicts/solutions/cpp/main.cpp b/problems/011-mount-tree-conflicts/solutions/cpp/main.cpp new file mode 100644 index 0000000..c81b43f --- /dev/null +++ b/problems/011-mount-tree-conflicts/solutions/cpp/main.cpp @@ -0,0 +1,77 @@ +#include +#include +#include +#include +using namespace std; + +struct Node { + int first_child; + int next_sibling; + int exact_min; + int file_min; + int desc_min; + unsigned char ch; +}; + +int main() { + ios::sync_with_stdio(false); + cin.tie(nullptr); + + int n; + if (!(cin >> n)) + return 0; + const int infinity = n + 1; + vector nodes(1, {0, 0, infinity, infinity, infinity, 0}); + + auto find_or_create_child = [&](int parent, unsigned char ch) { + for (int child = nodes[parent].first_child; child != 0; + child = nodes[child].next_sibling) { + if (nodes[child].ch == ch) + return child; + } + int child = static_cast(nodes.size()); + int next_sibling = nodes[parent].first_child; + nodes.push_back({0, next_sibling, infinity, infinity, infinity, ch}); + nodes[parent].first_child = child; + return child; + }; + + for (int j = 1; j <= n; ++j) { + char kind; + string path; + cin >> kind >> path; + vector visited; + visited.reserve(path.size()); + int current = 0; + int best = infinity; + + for (size_t position = 0; position < path.size(); ++position) { + current = find_or_create_child( + current, static_cast(path[position])); + visited.push_back(current); + if (position + 1 < path.size() && + (position == 0 || path[position + 1] == '/')) { + best = min(best, nodes[current].file_min); + } + } + best = min(best, nodes[current].exact_min); + if (kind == 'F') + best = min(best, nodes[current].desc_min); + + if (best != infinity) { + cout << "CONFLICT " << best << ' ' << j << '\n'; + return 0; + } + + for (size_t position = 0; position + 1 < path.size(); ++position) { + if (position == 0 || path[position + 1] == '/') + nodes[visited[position]].desc_min = + min(nodes[visited[position]].desc_min, j); + } + nodes[current].exact_min = min(nodes[current].exact_min, j); + if (kind == 'F') + nodes[current].file_min = min(nodes[current].file_min, j); + } + + cout << "VALID\n"; +} diff --git a/problems/011-mount-tree-conflicts/solutions/go/main.go b/problems/011-mount-tree-conflicts/solutions/go/main.go new file mode 100644 index 0000000..b6ac6d7 --- /dev/null +++ b/problems/011-mount-tree-conflicts/solutions/go/main.go @@ -0,0 +1,111 @@ +package main + +import ( + "bufio" + "fmt" + "io" + "os" +) + +type scanner struct { + data []byte + pos int +} + +func (s *scanner) next() []byte { + for s.pos < len(s.data) && s.data[s.pos] <= ' ' { + s.pos++ + } + start := s.pos + for s.pos < len(s.data) && s.data[s.pos] > ' ' { + s.pos++ + } + return s.data[start:s.pos] +} + +func parseInt(token []byte) int32 { + var value int32 + for _, digit := range token { + value = value*10 + int32(digit-'0') + } + return value +} + +type node struct { + firstChild int32 + nextSibling int32 + exactMin int32 + fileMin int32 + descMin int32 + ch byte +} + +func findOrCreateChild(nodes *[]node, parent int32, ch byte, infinity int32) int32 { + for child := (*nodes)[parent].firstChild; child != 0; child = (*nodes)[child].nextSibling { + if (*nodes)[child].ch == ch { + return child + } + } + child := int32(len(*nodes)) + nextSibling := (*nodes)[parent].firstChild + *nodes = append(*nodes, node{0, nextSibling, infinity, infinity, infinity, ch}) + (*nodes)[parent].firstChild = child + return child +} + +func main() { + data, err := io.ReadAll(os.Stdin) + if err != nil { + panic(err) + } + in := scanner{data: data} + n := parseInt(in.next()) + infinity := n + 1 + nodes := []node{{0, 0, infinity, infinity, infinity, 0}} + out := bufio.NewWriter(os.Stdout) + defer out.Flush() + + for j := int32(1); j <= n; j++ { + kind := in.next()[0] + path := in.next() + visited := make([]int32, 0, len(path)) + var current int32 + best := infinity + + for position, ch := range path { + current = findOrCreateChild(&nodes, current, ch, infinity) + visited = append(visited, current) + if position+1 < len(path) && (position == 0 || path[position+1] == '/') && nodes[current].fileMin < best { + best = nodes[current].fileMin + } + } + if nodes[current].exactMin < best { + best = nodes[current].exactMin + } + if kind == 'F' && nodes[current].descMin < best { + best = nodes[current].descMin + } + + if best != infinity { + fmt.Fprintln(out, "CONFLICT", best, j) + return + } + + for position := 0; position+1 < len(path); position++ { + if position == 0 || path[position+1] == '/' { + at := visited[position] + if j < nodes[at].descMin { + nodes[at].descMin = j + } + } + } + if j < nodes[current].exactMin { + nodes[current].exactMin = j + } + if kind == 'F' && j < nodes[current].fileMin { + nodes[current].fileMin = j + } + } + + fmt.Fprintln(out, "VALID") +} diff --git a/problems/011-mount-tree-conflicts/solutions/javascript/main.js b/problems/011-mount-tree-conflicts/solutions/javascript/main.js new file mode 100644 index 0000000..c4425e0 --- /dev/null +++ b/problems/011-mount-tree-conflicts/solutions/javascript/main.js @@ -0,0 +1,74 @@ +import * as std from "std"; + +function main() { + const input = std.in.readAsString(); + const tokens = input.trim().split(/\s+/); + const n = Number(tokens[0]); + const infinity = n + 1; + const capacity = input.length + 1; + const firstChild = new Int32Array(capacity); + const nextSibling = new Int32Array(capacity); + const exactMin = new Int32Array(capacity); + const fileMin = new Int32Array(capacity); + const descMin = new Int32Array(capacity); + const nodeChar = new Uint8Array(capacity); + let nodeCount = 1; + + /** @param {number} parent @param {number} ch @returns {number} */ + const findOrCreateChild = (parent, ch) => { + for (let child = firstChild[parent]; child !== 0; child = nextSibling[child]) { + if (nodeChar[child] === ch) return child; + } + const child = nodeCount++; + firstChild[child] = 0; + nextSibling[child] = firstChild[parent]; + exactMin[child] = infinity; + fileMin[child] = infinity; + descMin[child] = infinity; + nodeChar[child] = ch; + firstChild[parent] = child; + return child; + }; + + let tokenAt = 1; + for (let j = 1; j <= n; j++) { + const kind = tokens[tokenAt++]; + const path = tokens[tokenAt++]; + let current = 0; + let best = infinity; + + for (let position = 0; position < path.length; position++) { + current = findOrCreateChild(current, path.charCodeAt(position)); + if ( + position + 1 < path.length && + (position === 0 || path[position + 1] === "/") + ) { + best = Math.min(best, fileMin[current]); + } + } + best = Math.min(best, exactMin[current]); + if (kind === "F") best = Math.min(best, descMin[current]); + + if (best !== infinity) { + std.out.puts(`CONFLICT ${best} ${j}\n`); + return; + } + + current = 0; + for (let position = 0; position < path.length; position++) { + current = findOrCreateChild(current, path.charCodeAt(position)); + if ( + position + 1 < path.length && + (position === 0 || path[position + 1] === "/") + ) { + descMin[current] = Math.min(descMin[current], j); + } + } + exactMin[current] = Math.min(exactMin[current], j); + if (kind === "F") fileMin[current] = Math.min(fileMin[current], j); + } + + std.out.puts("VALID\n"); +} + +main(); diff --git a/problems/011-mount-tree-conflicts/solutions/python/main.py b/problems/011-mount-tree-conflicts/solutions/python/main.py new file mode 100644 index 0000000..d0c10a5 --- /dev/null +++ b/problems/011-mount-tree-conflicts/solutions/python/main.py @@ -0,0 +1,65 @@ +import sys +from array import array + + +tokens = sys.stdin.buffer.read().split() +n = int(tokens[0]) +infinity = n + 1 +first_child = array("i", [0]) +next_sibling = array("i", [0]) +exact_min = array("i", [infinity]) +file_min = array("i", [infinity]) +desc_min = array("i", [infinity]) +node_char = bytearray(1) + + +def find_or_create_child(parent, char): + child = first_child[parent] + while child: + if node_char[child] == char: + return child + child = next_sibling[child] + child = len(node_char) + first_child.append(0) + next_sibling.append(first_child[parent]) + exact_min.append(infinity) + file_min.append(infinity) + desc_min.append(infinity) + node_char.append(char) + first_child[parent] = child + return child + + +token_at = 1 +for j in range(1, n + 1): + kind = tokens[token_at] + path = tokens[token_at + 1] + token_at += 2 + visited = [] + current = 0 + best = infinity + + for position, char in enumerate(path): + current = find_or_create_child(current, char) + visited.append(current) + if position + 1 < len(path) and ( + position == 0 or path[position + 1] == ord("/") + ): + best = min(best, file_min[current]) + best = min(best, exact_min[current]) + if kind == b"F": + best = min(best, desc_min[current]) + + if best != infinity: + print("CONFLICT", best, j) + raise SystemExit + + for position in range(len(path) - 1): + if position == 0 or path[position + 1] == ord("/"): + at = visited[position] + desc_min[at] = min(desc_min[at], j) + exact_min[current] = min(exact_min[current], j) + if kind == b"F": + file_min[current] = min(file_min[current], j) + +print("VALID") diff --git a/problems/011-mount-tree-conflicts/solutions/rust/main.rs b/problems/011-mount-tree-conflicts/solutions/rust/main.rs new file mode 100644 index 0000000..78f0c15 --- /dev/null +++ b/problems/011-mount-tree-conflicts/solutions/rust/main.rs @@ -0,0 +1,88 @@ +use std::io::{self, Read}; + +#[derive(Clone, Copy)] +struct Node { + first_child: u32, + next_sibling: u32, + exact_min: u32, + file_min: u32, + desc_min: u32, + ch: u8, +} + +fn find_or_create_child(nodes: &mut Vec, parent: u32, ch: u8, infinity: u32) -> u32 { + let mut child = nodes[parent as usize].first_child; + while child != 0 { + if nodes[child as usize].ch == ch { + return child; + } + child = nodes[child as usize].next_sibling; + } + let child = nodes.len() as u32; + let next_sibling = nodes[parent as usize].first_child; + nodes.push(Node { + first_child: 0, + next_sibling, + exact_min: infinity, + file_min: infinity, + desc_min: infinity, + ch, + }); + nodes[parent as usize].first_child = child; + child +} + +fn main() { + let mut input = Vec::new(); + io::stdin().read_to_end(&mut input).unwrap(); + let text = std::str::from_utf8(&input).unwrap(); + let mut tokens = text.split_ascii_whitespace(); + let n: u32 = tokens.next().unwrap().parse().unwrap(); + let infinity = n + 1; + let mut nodes = vec![Node { + first_child: 0, + next_sibling: 0, + exact_min: infinity, + file_min: infinity, + desc_min: infinity, + ch: 0, + }]; + + for j in 1..=n { + let kind = tokens.next().unwrap().as_bytes()[0]; + let path = tokens.next().unwrap().as_bytes(); + let mut visited = Vec::with_capacity(path.len()); + let mut current = 0_u32; + let mut best = infinity; + + for (position, &ch) in path.iter().enumerate() { + current = find_or_create_child(&mut nodes, current, ch, infinity); + visited.push(current); + if position + 1 < path.len() && (position == 0 || path[position + 1] == b'/') { + best = best.min(nodes[current as usize].file_min); + } + } + best = best.min(nodes[current as usize].exact_min); + if kind == b'F' { + best = best.min(nodes[current as usize].desc_min); + } + + if best != infinity { + println!("CONFLICT {best} {j}"); + return; + } + + for position in 0..path.len() - 1 { + if position == 0 || path[position + 1] == b'/' { + let node = visited[position] as usize; + nodes[node].desc_min = nodes[node].desc_min.min(j); + } + } + nodes[current as usize].exact_min = nodes[current as usize].exact_min.min(j); + if kind == b'F' { + nodes[current as usize].file_min = nodes[current as usize].file_min.min(j); + } + } + + println!("VALID"); +} diff --git a/problems/011-mount-tree-conflicts/solutions/typescript/main.ts b/problems/011-mount-tree-conflicts/solutions/typescript/main.ts new file mode 100644 index 0000000..1122f8d --- /dev/null +++ b/problems/011-mount-tree-conflicts/solutions/typescript/main.ts @@ -0,0 +1,73 @@ +import * as std from "std"; + +function main(): void { + const input: string = std.in.readAsString(); + const tokens: string[] = input.trim().split(/\s+/); + const n: number = Number(tokens[0]); + const infinity: number = n + 1; + const capacity: number = input.length + 1; + const firstChild = new Int32Array(capacity); + const nextSibling = new Int32Array(capacity); + const exactMin = new Int32Array(capacity); + const fileMin = new Int32Array(capacity); + const descMin = new Int32Array(capacity); + const nodeChar = new Uint8Array(capacity); + let nodeCount = 1; + + const findOrCreateChild = (parent: number, ch: number): number => { + for (let child = firstChild[parent]; child !== 0; child = nextSibling[child]) { + if (nodeChar[child] === ch) return child; + } + const child = nodeCount++; + firstChild[child] = 0; + nextSibling[child] = firstChild[parent]; + exactMin[child] = infinity; + fileMin[child] = infinity; + descMin[child] = infinity; + nodeChar[child] = ch; + firstChild[parent] = child; + return child; + }; + + let tokenAt = 1; + for (let j = 1; j <= n; j++) { + const kind = tokens[tokenAt++]; + const path = tokens[tokenAt++]; + let current = 0; + let best = infinity; + + for (let position = 0; position < path.length; position++) { + current = findOrCreateChild(current, path.charCodeAt(position)); + if ( + position + 1 < path.length && + (position === 0 || path[position + 1] === "/") + ) { + best = Math.min(best, fileMin[current]); + } + } + best = Math.min(best, exactMin[current]); + if (kind === "F") best = Math.min(best, descMin[current]); + + if (best !== infinity) { + std.out.puts(`CONFLICT ${best} ${j}\n`); + return; + } + + current = 0; + for (let position = 0; position < path.length; position++) { + current = findOrCreateChild(current, path.charCodeAt(position)); + if ( + position + 1 < path.length && + (position === 0 || path[position + 1] === "/") + ) { + descMin[current] = Math.min(descMin[current], j); + } + } + exactMin[current] = Math.min(exactMin[current], j); + if (kind === "F") fileMin[current] = Math.min(fileMin[current], j); + } + + std.out.puts("VALID\n"); +} + +main(); diff --git a/problems/011-mount-tree-conflicts/statement.en.md b/problems/011-mount-tree-conflicts/statement.en.md new file mode 100644 index 0000000..a7d9014 --- /dev/null +++ b/problems/011-mount-tree-conflicts/statement.en.md @@ -0,0 +1,106 @@ +# Mount-Tree Conflict Detection + +When a WASM OJ constructs an isolated file system, it mounts inputs, tools, and working directories into one virtual file tree. Mount settings may come from different parts of the configuration. If two records occupy the same path, or if a regular file is placed at an ancestor of another item, the resulting tree has no valid interpretation. + +The system receives a sequence of directory (`D`) and regular-file (`F`) records. Either condition below makes a pair conflict: + +1. The two records have exactly the same path, regardless of their kinds. +2. One record is a regular file whose path is a **strict ancestor** of the other record's path. + +Ancestry is determined by complete path segments. For example, `/a` is an ancestor of `/a/b`, but not of `/ab`. The root path `/` is an ancestor of every other path. + +Configuration validation must report the earliest conflict that can be established in input order. For conflicting record indices `i < j`, minimize `j` first, then minimize `i` among ties. If no conflict exists, output `VALID`. + +## Input + +The first line contains integer `N`. Each of the next `N` lines contains `kind path`. + +- `kind` is `F` or `D`. +- A path is canonical and absolute. The root is `/`. Every other path starts with `/`, does not end with `/`, and consists of segments containing only lowercase English letters, digits, `.`, `_`, and `-`; a segment is never `.` or `..`. +- Records are numbered from 1. + +## Output + +If there is no conflict, output: + +```text +VALID +``` + +Otherwise output: + +```text +CONFLICT i j +``` + +where `(i,j)` obeys the tie-break above. + +## Constraints + +- `1 ≤ N ≤ 200000` +- Each path has length at most `200`. +- The sum `S` of all path lengths is at most `2000000`. +- Input is UTF-8, but the path restrictions make all compared contents ASCII. + +Checking every pair exceeds every resource policy. An `O(S log N)` tree-order sorting solution can earn the looser-policy points; the strictest instruction-cost policy requires a deterministic `O(S)` solution. + +An expected `O(S)` hash table is not a deterministic worst-case `O(S)` solution. Because the legal path-character alphabet has fixed size, a first-child/next-sibling character trie can examine only a constant number of siblings at each node. + +## Examples + + + +### Example One + +Input: + +```text +4 +D /src +F /src/main.c +D /include +F /include/a.h +``` + +Output: + +```text +VALID +``` + +### Example Two + +Input: + +```text +3 +D /a +F /a/b +D /a/b/c +``` + +Output: + +```text +CONFLICT 2 3 +``` + +### Example Three + +Input: + +```text +4 +D /x +F /x/a +D /x/b +F /x +``` + +Output: + +```text +CONFLICT 1 4 +``` + + diff --git a/problems/011-mount-tree-conflicts/statement.zh-TW.md b/problems/011-mount-tree-conflicts/statement.zh-TW.md new file mode 100644 index 0000000..ea9cf73 --- /dev/null +++ b/problems/011-mount-tree-conflicts/statement.zh-TW.md @@ -0,0 +1,105 @@ +# 掛載樹衝突檢查 + +WASM OJ 在建立隔離檔案系統時,會把輸入檔、工具與工作目錄掛進同一棵虛擬檔案樹。掛載設定可能來自不同部分;如果兩筆設定占用同一路徑,或把一般檔案放在另一個項目的祖先位置,實際建立檔案樹時就會產生無法解釋的結構。 + +系統依序收到一批目錄(`D`)與一般檔案(`F`)紀錄。以下任一情況稱為一對衝突: + +1. 兩筆紀錄的路徑完全相同(種類是否相同不影響); +2. 一筆是一般檔案,且它的路徑是另一筆路徑的**嚴格祖先**。 + +祖先關係以完整 path segment 判斷。例如 `/a` 是 `/a/b` 的祖先,卻不是 `/ab` 的祖先。根路徑 `/` 是所有其他路徑的祖先。 + +設定檢查要回報依輸入順序最早能確定的衝突。對衝突紀錄編號 `i < j`,先最小化 `j`;若仍有多組,再最小化 `i`。若沒有任何衝突,輸出 `VALID`。 + +## 輸入 + +第一行為整數 `N`。接著 `N` 行各為 `kind path`。 + +- `1 <= N <= 200000`。 +- `kind` 為 `F` 或 `D`。 +- 路徑是 canonical absolute path:根路徑為 `/`;其他路徑以 `/` 開頭、不以 `/` 結尾,每個 segment 只含小寫英文字母、數字、`.`、`_`、`-`,且 segment 不得為 `.` 或 `..`。 +- 每條路徑長度至多 200;所有路徑長度總和 `S <= 2000000`。 +- 紀錄採 1-based 編號。 + +## 輸出 + +沒有衝突時輸出: + +```text +VALID +``` + +否則輸出: + +```text +CONFLICT i j +``` + +其中 `(i,j)` 遵守上述 tie-break。 + +## 限制 + +逐對檢查會超出所有資源政策。把路徑依樹序排序的 `O(S log N)` 解法可取得較寬鬆政策的分數;最嚴格的 instruction-cost 政策要求 deterministic `O(S)` 解法。 + +注意:不能把雜湊表的 expected `O(S)` 當成 deterministic worst-case `O(S)`。由於合法路徑字元的 alphabet 大小固定,可以用 first-child/next-sibling 字元 trie,在每個節點至多檢查固定數量的兄弟節點。 + +所有數值與 indexing 如上所列;輸入保證為 UTF-8,而 path 限制使實際比較內容皆為 ASCII。 + +## 範例 + + + +### 範例一 + +輸入: + +```text +4 +D /src +F /src/main.c +D /include +F /include/a.h +``` + +輸出: + +```text +VALID +``` + +### 範例二 + +輸入: + +```text +3 +D /a +F /a/b +D /a/b/c +``` + +輸出: + +```text +CONFLICT 2 3 +``` + +### 範例三 + +輸入: + +```text +4 +D /x +F /x/a +D /x/b +F /x +``` + +輸出: + +```text +CONFLICT 1 4 +``` + + diff --git a/problems/011-mount-tree-conflicts/tests/adversarial-separator-order.in b/problems/011-mount-tree-conflicts/tests/adversarial-separator-order.in new file mode 100644 index 0000000..7f78733 --- /dev/null +++ b/problems/011-mount-tree-conflicts/tests/adversarial-separator-order.in @@ -0,0 +1,4 @@ +3 +F /a +D /a- +D /a/b diff --git a/problems/011-mount-tree-conflicts/tests/adversarial-separator-order.out b/problems/011-mount-tree-conflicts/tests/adversarial-separator-order.out new file mode 100644 index 0000000..83fb1f4 --- /dev/null +++ b/problems/011-mount-tree-conflicts/tests/adversarial-separator-order.out @@ -0,0 +1 @@ +CONFLICT 1 3 diff --git a/problems/011-mount-tree-conflicts/tests/sample-01.in b/problems/011-mount-tree-conflicts/tests/sample-01.in new file mode 100644 index 0000000..be4dac8 --- /dev/null +++ b/problems/011-mount-tree-conflicts/tests/sample-01.in @@ -0,0 +1,5 @@ +4 +D /src +F /src/main.c +D /include +F /include/a.h diff --git a/problems/011-mount-tree-conflicts/tests/sample-01.out b/problems/011-mount-tree-conflicts/tests/sample-01.out new file mode 100644 index 0000000..1d78739 --- /dev/null +++ b/problems/011-mount-tree-conflicts/tests/sample-01.out @@ -0,0 +1 @@ +VALID diff --git a/problems/011-mount-tree-conflicts/tests/sample-02.in b/problems/011-mount-tree-conflicts/tests/sample-02.in new file mode 100644 index 0000000..694e000 --- /dev/null +++ b/problems/011-mount-tree-conflicts/tests/sample-02.in @@ -0,0 +1,4 @@ +3 +D /a +F /a/b +D /a/b/c diff --git a/problems/011-mount-tree-conflicts/tests/sample-02.out b/problems/011-mount-tree-conflicts/tests/sample-02.out new file mode 100644 index 0000000..64da12a --- /dev/null +++ b/problems/011-mount-tree-conflicts/tests/sample-02.out @@ -0,0 +1 @@ +CONFLICT 2 3 diff --git a/problems/011-mount-tree-conflicts/tests/sample-03.in b/problems/011-mount-tree-conflicts/tests/sample-03.in new file mode 100644 index 0000000..85bd613 --- /dev/null +++ b/problems/011-mount-tree-conflicts/tests/sample-03.in @@ -0,0 +1,5 @@ +4 +D /x +F /x/a +D /x/b +F /x diff --git a/problems/011-mount-tree-conflicts/tests/sample-03.out b/problems/011-mount-tree-conflicts/tests/sample-03.out new file mode 100644 index 0000000..6702c8a --- /dev/null +++ b/problems/011-mount-tree-conflicts/tests/sample-03.out @@ -0,0 +1 @@ +CONFLICT 1 4 diff --git a/problems/011-mount-tree-conflicts/validator.py b/problems/011-mount-tree-conflicts/validator.py new file mode 100644 index 0000000..71de655 --- /dev/null +++ b/problems/011-mount-tree-conflicts/validator.py @@ -0,0 +1,31 @@ +import re, sys + + +def ok_path(p: str) -> bool: + if p == "/": + return True + if not p.startswith("/") or p.endswith("/") or len(p) > 200: + return False + return all( + x not in ("", ".", "..") and re.fullmatch(r"[a-z0-9._-]+", x) + for x in p[1:].split("/") + ) + + +def main() -> None: + lines = sys.stdin.read().splitlines() + assert lines and re.fullmatch(r"[1-9][0-9]*", lines[0]) + n = int(lines[0]) + assert n <= 200000 and len(lines) == n + 1 + total = 0 + for line in lines[1:]: + parts = line.split() + assert len(parts) == 2 and parts[0] in ("F", "D") and ok_path(parts[1]) + total += len(parts[1].encode()) + assert total <= 2000000 + + +try: + main() +except (AssertionError, ValueError): + sys.exit(1) diff --git a/problems/012-bounded-tar-stream/editorial.en.md b/problems/012-bounded-tar-stream/editorial.en.md new file mode 100644 index 0000000..ced7db4 --- /dev/null +++ b/problems/012-bounded-tar-stream/editorial.en.md @@ -0,0 +1,32 @@ +# Editorial + +## Intuitive Approach + +Allocate payloads, padding, and the whole archive according to each size, then simulate byte offsets. For archive length `A`, both time and space become `O(A)`. Since `A` may reach `9×10^18`, this is impossible. + +## Optimal Approach: Streaming State Machine + +Maintain only `expectedOffset`, an optional pending metadata path, the file count, and extracted bytes. Check each event in exactly the error order specified. No content is needed for layout: compute + +```text +blocks = (size + 511) // 512 +``` + +and increase the expected offset by `512 + 512*blocks`. A `G/P` stores only one path of at most 200 bytes; clear it immediately after the next `F/D` consumes it. + +Validate a path by splitting on `/`, checking every segment's allowed characters, and rejecting empty segments, `.`, and `..`. + +## Correctness Proof + +Induct on the number of processed events. Initially the expected offset is 0, metadata is absent, and both statistics are zero, matching an empty archive. Assume the state is correct after event `i-1`. Event `i` is checked in the exact priority order from the specification, so rejection reports both the earliest event and its highest-priority error. If it passes, the offset formula skips exactly the header, payload, and padding; metadata state changes uniquely according to the event type; and only `F` updates the two quota statistics. Thus the invariant remains true after event `i`. By induction, after all events the statistics and end offset are correct, and the final pending-metadata check catches exactly an unconsumed metadata record. + +## Complexity + +Let `S` be the total length of all names and `T` the complete textual input size. Time is `O(N+S)`. C, C++, Rust, Go, and Python read line by line, so solver auxiliary space is `O(S_max)`, where `S_max≤200`. Forge's JavaScript/TypeScript API supplies only an immutable full input string through `readAsString()`, so those languages necessarily retain `O(T)` host-provided input; their parser uses a cursor and no all-token array, leaving its additional state at `O(S_max)`. The 256 MiB memory limit includes this runtime/input-contract cost. + +## Common Mistakes + +- Using floor division instead of `ceil(size/512)`. +- Counting metadata as a regular file, or failing to clear it after the next `F/D`. +- Checking type before offset or checksum, producing the wrong error code. +- Using 32-bit integers, or JavaScript `number`. diff --git a/problems/012-bounded-tar-stream/editorial.zh-TW.md b/problems/012-bounded-tar-stream/editorial.zh-TW.md new file mode 100644 index 0000000..9c0d514 --- /dev/null +++ b/problems/012-bounded-tar-stream/editorial.zh-TW.md @@ -0,0 +1,30 @@ +# 解題說明 + +## 直覺解 + +依 size 配置 payload、padding 與整個 archive,再從 byte offset 模擬。若 archive 長度為 `A`,時間與空間都是 `O(A)`;本題 `A` 可達 `9*10^18`,無法執行。 + +## 最佳解 + +只維護 `expectedOffset`、待使用 metadata 路徑、檔案數與解壓 bytes。每筆依題目列出的錯誤優先序檢查。layout 不需要內容;使用 + +`blocks = (size + 511) // 512` + +便可把 expected offset 增加 `512 + 512*blocks`。`G/P` 僅保存一條至多 200 bytes 的路徑;下一筆 `F/D` 使用後立刻清空。 + +路徑以 `/` 分割,逐 segment 檢查允許字元並拒絕空字串、`.`、`..`。 + +## 正確性證明 + +以已處理事件數歸納。初始 expected offset 為 0、狀態與統計皆空,符合空 archive。假設前 `i-1` 筆後狀態正確:第 `i` 筆依規格相同順序檢查所有可能錯誤,因此若拒絕,回報的正是最早事件與該事件最高優先錯誤;若通過,公式精確略過 header、payload 與 padding,metadata 狀態亦依種類唯一更新,只有 `F` 依規格更新兩項 quota。故第 `i` 筆後 invariant 仍成立。歸納可知全部通過時三個統計與 endOffset 正確;最後的 pending 檢查也正好捕捉未被消耗的 metadata。 + +## 複雜度 + +令所有 name 長度總和為 `S`、完整輸入文字 bytes 為 `T`,時間 `O(N+S)`。C、C++、Rust、Go、Python 逐行讀取,solver 額外空間為 `O(S_max)`,此處 `S_max <= 200`。Forge 的 JavaScript/TypeScript 輸入 API 只提供 immutable 完整字串 `readAsString()`,因此這兩語言必須保留 `O(T)` 的 host-provided input string;實作以 cursor 掃描而不建立全量 token array,額外狀態仍為 `O(S_max)`。256 MiB memory limit 包含這項 runtime/input contract 成本。 + +## 常見錯誤 + +- 把 `ceil(size/512)` 寫成 floor。 +- metadata 自己被算成一般檔案,或沒有在下一筆 `F/D` 後清除。 +- 先檢查種類才檢查 offset/checksum,造成錯誤碼不符。 +- 使用 32-bit 整數,或在 JS/TS 使用 `number`。 diff --git a/problems/012-bounded-tar-stream/generator.py b/problems/012-bounded-tar-stream/generator.py new file mode 100644 index 0000000..ac8662c --- /dev/null +++ b/problems/012-bounded-tar-stream/generator.py @@ -0,0 +1,35 @@ +import random, sys + +seed, index = map(int, sys.argv[1:]) +r = random.Random((seed << 24) ^ index) +n = 4 + index % 8 +limf = n +limb = 5000 +rows = [] +off = 0 +pending = False +for i in range(n): + t = r.choices(list("FDGP"), [5, 2, 1, 1])[0] + if pending: + t = r.choice("FD") + name = "d" + str(r.randrange(20)) + ("/f" + str(i) if r.random() < 0.5 else "") + size = 0 if t == "D" else (len(name) + 1 if t in "GP" else r.randrange(40)) + c = r.randrange(1000) + rows.append([off, t, name, size, c, c]) + off += 512 + ((size + 511) // 512) * 512 + pending = t in "GP" +mode = index % 5 +if mode == 1: + rows[r.randrange(n)][4] += 1 +elif mode == 2: + rows[r.randrange(n)][0] += 512 +elif mode == 3: + rows[r.randrange(n)][1] = "X" +elif mode == 4 and n >= 2: + rows[-2][1] = "G" + rows[-2][2] = "meta" + rows[-2][3] = 5 + rows[-1][1] = "P" +print(n, limf, limb) +for x in rows: + print(*x) diff --git a/problems/012-bounded-tar-stream/oracle.py b/problems/012-bounded-tar-stream/oracle.py new file mode 100644 index 0000000..5de4b84 --- /dev/null +++ b/problems/012-bounded-tar-stream/oracle.py @@ -0,0 +1,59 @@ +import re, sys + + +def path_ok(p): + return ( + not p.startswith("/") + and not p.endswith("/") + and all( + x not in ("", ".", "..") and re.fullmatch(r"[a-z0-9._-]+", x) + for x in p.split("/") + ) + ) + + +it = iter(sys.stdin.read().split()) +n, mf, mb = map(int, (next(it), next(it), next(it))) +expected = files = used = 0 +pending = None +for i in range(1, n + 1): + o = int(next(it)) + t = next(it) + name = next(it) + size = int(next(it)) + a = int(next(it)) + b = int(next(it)) + err = None + if o != expected: + err = "OFFSET" + elif a != b: + err = "CHECKSUM" + elif t not in "FDGP": + err = "TYPE" + elif t in "GP" and pending is not None: + err = "STATE" + elif t in "GP" and size != len(name.encode()) + 1: + err = "META_SIZE" + elif t in "GP" and not path_ok(name): + err = "PATH" + elif t in "FD" and not path_ok(pending if pending is not None else name): + err = "PATH" + elif t == "D" and size != 0: + err = "ENTRY_SIZE" + elif t == "F" and (files + 1 > mf or used + size > mb): + err = "LIMIT" + if err: + print("REJECT", i, err) + raise SystemExit + expected += 512 + ((size + 511) // 512) * 512 + if t in "GP": + pending = name + else: + pending = None + if t == "F": + files += 1 + used += size +if pending is not None: + print("REJECT", n + 1, "STATE") +else: + print("ACCEPT", files, used, expected) diff --git a/problems/012-bounded-tar-stream/problem.json b/problems/012-bounded-tar-stream/problem.json new file mode 100644 index 0000000..622afae --- /dev/null +++ b/problems/012-bounded-tar-stream/problem.json @@ -0,0 +1,147 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 12, + "slug": "bounded-tar-stream", + "title": { + "zh-TW": "512-byte 封存檔", + "en": "512-Byte Archive" + }, + "difficulty": "hard", + "tags": [ + "streaming", + "state-machine", + "parsing", + "filesystem" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-bigint-metadata", + "kind": "adversarial", + "input": "tests/adversarial-bigint-metadata.in", + "output": "tests/adversarial-bigint-metadata.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 2000000000, + "memoryLimitBytes": 536870912 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 1500000, + "memoryLimitBytes": 402653184 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 600000, + "memoryLimitBytes": 268435456 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "展開整個封存檔", + "en": "Expand the Entire Archive" + }, + "time": "O(A)", + "space": "O(A)", + "accepted": false + }, + { + "name": { + "zh-TW": "串流狀態機", + "en": "Streaming State Machine" + }, + "time": "O(N + S)", + "space": "O(S_max) auxiliary; O(T) JS/TS input", + "accepted": true + } + ] +} diff --git a/problems/012-bounded-tar-stream/solutions/c/main.c b/problems/012-bounded-tar-stream/solutions/c/main.c new file mode 100644 index 0000000..0d7b70e --- /dev/null +++ b/problems/012-bounded-tar-stream/solutions/c/main.c @@ -0,0 +1,73 @@ +#include +#include +#include +typedef unsigned long long U; +int pathok(const char *s) { + if (!*s || *s == '/' || s[strlen(s) - 1] == '/') + return 0; + const char *p = s, *q; + while (*p) { + q = strchr(p, '/'); + size_t n = q ? (size_t)(q - p) : strlen(p); + if (!n || (n == 1 && p[0] == '.') || (n == 2 && p[0] == '.' && p[1] == '.')) + return 0; + for (size_t i = 0; i < n; i++) + if (!(islower((unsigned char)p[i]) || isdigit((unsigned char)p[i]) || + p[i] == '.' || p[i] == '_' || p[i] == '-')) + return 0; + if (!q) + break; + p = q + 1; + } + return 1; +} +int main(void) { + int n; + U limn, limb; + if (scanf("%d %llu %llu", &n, &limn, &limb) != 3) + return 0; + U off = 0, cnt = 0, used = 0; + char pending[201] = ""; + for (int i = 1; i <= n; i++) { + U got, size, a, b; + char t, name[201], *err = NULL; + scanf("%llu %c %200s %llu %llu %llu", &got, &t, name, &size, &a, &b); + if (got != off) + err = "OFFSET"; + else if (a != b) + err = "CHECKSUM"; + else if (!strchr("FDGP", t)) + err = "TYPE"; + else if ((t == 'G' || t == 'P') && *pending) + err = "STATE"; + else if ((t == 'G' || t == 'P') && size != strlen(name) + 1) + err = "META_SIZE"; + else if ((t == 'G' || t == 'P') && !pathok(name)) + err = "PATH"; + else if ((t == 'F' || t == 'D') && !pathok(*pending ? pending : name)) + err = "PATH"; + else if (t == 'D' && size) + err = "ENTRY_SIZE"; + else if (t == 'F' && (cnt == limn || size > limb - used)) + err = "LIMIT"; + if (err) { + printf("REJECT %d %s\n", i, err); + return 0; + } + off += 512 + ((size + 511) / 512) * 512; + if (t == 'G' || t == 'P') + strcpy(pending, name); + else { + pending[0] = 0; + if (t == 'F') { + cnt++; + used += size; + } + } + } + if (*pending) + printf("REJECT %d STATE\n", n + 1); + else + printf("ACCEPT %llu %llu %llu\n", cnt, used, off); + return 0; +} diff --git a/problems/012-bounded-tar-stream/solutions/cpp/main.cpp b/problems/012-bounded-tar-stream/solutions/cpp/main.cpp new file mode 100644 index 0000000..ca483d8 --- /dev/null +++ b/problems/012-bounded-tar-stream/solutions/cpp/main.cpp @@ -0,0 +1,76 @@ +#include +#include +#include +using namespace std; +using U = unsigned long long; +bool ok(const string &s) { + if (s.empty() || s.front() == '/' || s.back() == '/') + return false; + size_t p = 0; + while (p < s.size()) { + size_t q = s.find('/', p); + if (q == string::npos) + q = s.size(); + string x = s.substr(p, q - p); + if (x.empty() || x == "." || x == "..") + return false; + for (char c : x) + if (!((c >= 'a' && c <= 'z') || (c >= '0' && c <= '9') || c == '.' || + c == '_' || c == '-')) + return false; + p = q + 1; + } + return true; +} +int main() { + ios::sync_with_stdio(false); + cin.tie(nullptr); + int n; + U ln, lb; + if (!(cin >> n >> ln >> lb)) + return 0; + U off = 0, cnt = 0, used = 0; + string pending; + for (int i = 1; i <= n; i++) { + U got, z, a, b; + char t; + string name, err; + cin >> got >> t >> name >> z >> a >> b; + if (got != off) + err = "OFFSET"; + else if (a != b) + err = "CHECKSUM"; + else if (string("FDGP").find(t) == string::npos) + err = "TYPE"; + else if ((t == 'G' || t == 'P') && !pending.empty()) + err = "STATE"; + else if ((t == 'G' || t == 'P') && z != name.size() + 1) + err = "META_SIZE"; + else if ((t == 'G' || t == 'P') && !ok(name)) + err = "PATH"; + else if ((t == 'F' || t == 'D') && !ok(pending.empty() ? name : pending)) + err = "PATH"; + else if (t == 'D' && z) + err = "ENTRY_SIZE"; + else if (t == 'F' && (cnt == ln || z > lb - used)) + err = "LIMIT"; + if (!err.empty()) { + cout << "REJECT " << i << ' ' << err << '\n'; + return 0; + } + off += 512 + ((z + 511) / 512) * 512; + if (t == 'G' || t == 'P') + pending = name; + else { + pending.clear(); + if (t == 'F') { + cnt++; + used += z; + } + } + } + if (!pending.empty()) + cout << "REJECT " << n + 1 << " STATE\n"; + else + cout << "ACCEPT " << cnt << ' ' << used << ' ' << off << '\n'; +} diff --git a/problems/012-bounded-tar-stream/solutions/go/main.go b/problems/012-bounded-tar-stream/solutions/go/main.go new file mode 100644 index 0000000..2e4bd23 --- /dev/null +++ b/problems/012-bounded-tar-stream/solutions/go/main.go @@ -0,0 +1,83 @@ +package main + +import ( + "bufio" + "fmt" + "os" + "strings" +) + +func ok(s string) bool { + if s == "" || s[0] == '/' || s[len(s)-1] == '/' { + return false + } + for _, x := range strings.Split(s, "/") { + if x == "" || x == "." || x == ".." { + return false + } + for _, c := range x { + if !(c >= 'a' && c <= 'z' || c >= '0' && c <= '9' || strings.ContainsRune("._-", c)) { + return false + } + } + } + return true +} +func main() { + in := bufio.NewReader(os.Stdin) + var n int + var ln, lb uint64 + fmt.Fscan(in, &n, &ln, &lb) + var off, cnt, used uint64 + pending := "" + for i := 1; i <= n; i++ { + var got, z, a, b uint64 + var t, name string + fmt.Fscan(in, &got, &t, &name, &z, &a, &b) + meta := t == "G" || t == "P" + actual := t == "F" || t == "D" + eff := name + if pending != "" { + eff = pending + } + err := "" + if got != off { + err = "OFFSET" + } else if a != b { + err = "CHECKSUM" + } else if !strings.Contains("FDGP", t) { + err = "TYPE" + } else if meta && pending != "" { + err = "STATE" + } else if meta && z != uint64(len(name)+1) { + err = "META_SIZE" + } else if meta && !ok(name) { + err = "PATH" + } else if actual && !ok(eff) { + err = "PATH" + } else if t == "D" && z != 0 { + err = "ENTRY_SIZE" + } else if t == "F" && (cnt == ln || z > lb-used) { + err = "LIMIT" + } + if err != "" { + fmt.Println("REJECT", i, err) + return + } + off += 512 + ((z+511)/512)*512 + if meta { + pending = name + } else { + pending = "" + if t == "F" { + cnt++ + used += z + } + } + } + if pending != "" { + fmt.Println("REJECT", n+1, "STATE") + } else { + fmt.Println("ACCEPT", cnt, used, off) + } +} diff --git a/problems/012-bounded-tar-stream/solutions/javascript/main.js b/problems/012-bounded-tar-stream/solutions/javascript/main.js new file mode 100644 index 0000000..982b440 --- /dev/null +++ b/problems/012-bounded-tar-stream/solutions/javascript/main.js @@ -0,0 +1,65 @@ +import * as std from "std"; +const input = std.in.readAsString(); +let p = 0; +const nextToken = () => { + while (p < input.length && input.charCodeAt(p) <= 32) p++; + const start = p; + while (p < input.length && input.charCodeAt(p) > 32) p++; + return input.slice(start, p); +}; +const n = Number(nextToken()), + ln = BigInt(nextToken()), + lb = BigInt(nextToken()); +let off = 0n, cnt = 0n, used = 0n; +/** @type {string | null} */ +let pending = null; +let done = false; +/** @param {string} s @returns {boolean} */ +const ok = (s) => + !s.startsWith("/") && !s.endsWith("/") && + s.split("/").every((x) => + x !== "" && x !== "." && x !== ".." && /^[a-z0-9._-]+$/.test(x) + ); +for (let i = 1; i <= n; i++) { + const got = BigInt(nextToken()), + t = nextToken(), + name = nextToken(), + z = BigInt(nextToken()), + x = BigInt(nextToken()), + y = BigInt(nextToken()); + const meta = t === "G" || t === "P", + actual = t === "F" || t === "D", + eff = pending ?? name; + /** @type {string | null} */ + let e = null; + if (got !== off) e = "OFFSET"; + else if (x !== y) e = "CHECKSUM"; + else if (!"FDGP".includes(t)) e = "TYPE"; + else if (meta && pending !== null) e = "STATE"; + else if (meta && z !== BigInt(name.length + 1)) e = "META_SIZE"; + else if (meta && !ok(name)) e = "PATH"; + else if (actual && !ok(eff)) e = "PATH"; + else if (t === "D" && z !== 0n) e = "ENTRY_SIZE"; + else if (t === "F" && (cnt === ln || z > lb - used)) e = "LIMIT"; + if (e !== null) { + std.out.puts(`REJECT ${i} ${e}\n`); + done = true; + break; + } + off += 512n + ((z + 511n) / 512n) * 512n; + if (meta) pending = name; + else { + pending = null; + if (t === "F") { + cnt++; + used += z; + } + } +} +if (!done) { + std.out.puts( + pending !== null + ? `REJECT ${n + 1} STATE\n` + : `ACCEPT ${cnt} ${used} ${off}\n`, + ); +} diff --git a/problems/012-bounded-tar-stream/solutions/python/main.py b/problems/012-bounded-tar-stream/solutions/python/main.py new file mode 100644 index 0000000..e2696f8 --- /dev/null +++ b/problems/012-bounded-tar-stream/solutions/python/main.py @@ -0,0 +1,63 @@ +import re, sys + + +def ok(p): + return ( + not p.startswith(b"/") + and not p.endswith(b"/") + and all( + x not in (b"", b".", b"..") and re.fullmatch(rb"[a-z0-9._-]+", x) + for x in p.split(b"/") + ) + ) + + +n, limit_n, limit_b = map(int, sys.stdin.buffer.readline().split()) +off = count = used = 0 +pending = None +for i in range(1, n + 1): + ( + given_raw, + typ, + name, + size_raw, + stored_raw, + calc_raw, + ) = sys.stdin.buffer.readline().split() + given = int(given_raw) + size = int(size_raw) + stored = int(stored_raw) + calc = int(calc_raw) + err = None + if given != off: + err = "OFFSET" + elif stored != calc: + err = "CHECKSUM" + elif typ not in (b"F", b"D", b"G", b"P"): + err = "TYPE" + elif typ in (b"G", b"P") and pending is not None: + err = "STATE" + elif typ in (b"G", b"P") and size != len(name) + 1: + err = "META_SIZE" + elif typ in (b"G", b"P") and not ok(name): + err = "PATH" + elif typ in (b"F", b"D") and not ok(pending if pending is not None else name): + err = "PATH" + elif typ == b"D" and size: + err = "ENTRY_SIZE" + elif typ == b"F" and (count == limit_n or used + size > limit_b): + err = "LIMIT" + if err: + print("REJECT", i, err) + sys.exit() + off += 512 + ((size + 511) // 512) * 512 + if typ in (b"G", b"P"): + pending = name + else: + pending = None + if typ == b"F": + count += 1 + used += size +print("REJECT", n + 1, "STATE") if pending is not None else print( + "ACCEPT", count, used, off +) diff --git a/problems/012-bounded-tar-stream/solutions/rust/main.rs b/problems/012-bounded-tar-stream/solutions/rust/main.rs new file mode 100644 index 0000000..e5f0ce5 --- /dev/null +++ b/problems/012-bounded-tar-stream/solutions/rust/main.rs @@ -0,0 +1,75 @@ +use std::io::{self, BufRead}; +fn ok(s: &str) -> bool { + !s.starts_with('/') + && !s.ends_with('/') + && s.split('/').all(|x| { + !x.is_empty() + && x != "." + && x != ".." + && x.bytes() + .all(|c| c.is_ascii_lowercase() || c.is_ascii_digit() || b"._-".contains(&c)) + }) +} +fn main() { + let stdin = io::stdin(); + let mut lines = stdin.lock().lines(); + let header = lines.next().unwrap().unwrap(); + let mut header_tokens = header.split_whitespace(); + let n: usize = header_tokens.next().unwrap().parse().unwrap(); + let ln: u64 = header_tokens.next().unwrap().parse().unwrap(); + let lb: u64 = header_tokens.next().unwrap().parse().unwrap(); + let (mut off, mut cnt, mut used) = (0u64, 0u64, 0u64); + let mut pending: Option = None; + for i in 1..=n { + let line = lines.next().unwrap().unwrap(); + let mut tokens = line.split_whitespace(); + let got: u64 = tokens.next().unwrap().parse().unwrap(); + let t = tokens.next().unwrap().as_bytes()[0]; + let name = tokens.next().unwrap(); + let z: u64 = tokens.next().unwrap().parse().unwrap(); + let a: u64 = tokens.next().unwrap().parse().unwrap(); + let b: u64 = tokens.next().unwrap().parse().unwrap(); + let meta = t == b'G' || t == b'P'; + let actual = t == b'F' || t == b'D'; + let err = if got != off { + Some("OFFSET") + } else if a != b { + Some("CHECKSUM") + } else if !b"FDGP".contains(&t) { + Some("TYPE") + } else if meta && pending.is_some() { + Some("STATE") + } else if meta && z != name.len() as u64 + 1 { + Some("META_SIZE") + } else if meta && !ok(name) { + Some("PATH") + } else if actual && !ok(pending.as_deref().unwrap_or(name)) { + Some("PATH") + } else if t == b'D' && z != 0 { + Some("ENTRY_SIZE") + } else if t == b'F' && (cnt == ln || z > lb - used) { + Some("LIMIT") + } else { + None + }; + if let Some(e) = err { + println!("REJECT {i} {e}"); + return; + } + off += 512 + ((z + 511) / 512) * 512; + if meta { + pending = Some(name.to_string()) + } else { + pending = None; + if t == b'F' { + cnt += 1; + used += z + } + } + } + if pending.is_some() { + println!("REJECT {} STATE", n + 1) + } else { + println!("ACCEPT {cnt} {used} {off}") + } +} diff --git a/problems/012-bounded-tar-stream/solutions/typescript/main.ts b/problems/012-bounded-tar-stream/solutions/typescript/main.ts new file mode 100644 index 0000000..202b221 --- /dev/null +++ b/problems/012-bounded-tar-stream/solutions/typescript/main.ts @@ -0,0 +1,60 @@ +import * as std from "std"; +const input: string = std.in.readAsString(); +let p: number = 0; +const nextToken = (): string => { + while (p < input.length && input.charCodeAt(p) <= 32) p++; + const start = p; + while (p < input.length && input.charCodeAt(p) > 32) p++; + return input.slice(start, p); +}; +const n: number = Number(nextToken()), + ln: bigint = BigInt(nextToken()), + lb: bigint = BigInt(nextToken()); +let off = 0n, cnt = 0n, used = 0n, pending: string | null = null, done = false; +const ok = (s: string): boolean => + !s.startsWith("/") && !s.endsWith("/") && + s.split("/").every((x) => + x !== "" && x !== "." && x !== ".." && /^[a-z0-9._-]+$/.test(x) + ); +for (let i = 1; i <= n; i++) { + const got = BigInt(nextToken()), + t = nextToken(), + name = nextToken(), + z = BigInt(nextToken()), + x = BigInt(nextToken()), + y = BigInt(nextToken()); + const meta = t === "G" || t === "P", + actual = t === "F" || t === "D", + eff = pending ?? name; + let e: string | null = null; + if (got !== off) e = "OFFSET"; + else if (x !== y) e = "CHECKSUM"; + else if (!"FDGP".includes(t)) e = "TYPE"; + else if (meta && pending !== null) e = "STATE"; + else if (meta && z !== BigInt(name.length + 1)) e = "META_SIZE"; + else if (meta && !ok(name)) e = "PATH"; + else if (actual && !ok(eff)) e = "PATH"; + else if (t === "D" && z !== 0n) e = "ENTRY_SIZE"; + else if (t === "F" && (cnt === ln || z > lb - used)) e = "LIMIT"; + if (e !== null) { + std.out.puts(`REJECT ${i} ${e}\n`); + done = true; + break; + } + off += 512n + ((z + 511n) / 512n) * 512n; + if (meta) pending = name; + else { + pending = null; + if (t === "F") { + cnt++; + used += z; + } + } +} +if (!done) { + std.out.puts( + pending !== null + ? `REJECT ${n + 1} STATE\n` + : `ACCEPT ${cnt} ${used} ${off}\n`, + ); +} diff --git a/problems/012-bounded-tar-stream/statement.en.md b/problems/012-bounded-tar-stream/statement.en.md new file mode 100644 index 0000000..31887dd --- /dev/null +++ b/problems/012-bounded-tar-stream/statement.en.md @@ -0,0 +1,117 @@ +# 512-Byte Archive + +A WASM OJ needs to accept dependency archives for problems or programs, but it cannot safely expand unknown contents first and decide whether they were valid afterward. To reject damaged or unsupported structures before allocating extraction space, a low-level parser has already converted the archive into header events. The remaining safety check must be performed **without expanding any payload**. + +Every event occupies one 512-byte header, followed by `size` payload bytes and zero padding to a multiple of 512. Therefore the offset of the next event is: + +`offset + 512 + ceil(size / 512) * 512`. + +Event types and their meanings are: + +- `F`: a regular file; counts toward both the file count and extracted bytes. +- `D`: a directory; `size` must be 0. +- `G`, `P`: GNU long-path or PAX path metadata. `name` overrides the path of the next `F/D`, and `size` must equal the ASCII byte length of `name` plus one. Metadata may not appear while previous metadata is still waiting to be consumed. +- Any other uppercase letter is unsupported. + +Each event also provides a stored checksum and a calculated checksum, which must match. A valid path must be nonempty, relative, and canonical: it neither begins nor ends with `/`; every segment contains only lowercase letters, digits, `.`, `_`, and `-`, and no segment is `.` or `..`. + +When metadata is pending, the next `F/D` uses the metadata `name` as its effective path and ignores its own header `name`. Validate the event stream under these rules without reading or expanding any payload. + +## Input + +The first line contains `N maxFiles maxBytes`. Each of the next `N` lines has: + +```text +offset type name size storedChecksum calculatedChecksum +``` + +All event fields are supplied even if an earlier event would already cause rejection. + +## Output + +Process events in order and stop at the first error, outputting `REJECT i CODE`. If one event has several errors, report only the first according to this priority: + +1. `OFFSET`: `offset` differs from the expected value; the first expected offset is 0. +2. `CHECKSUM`: the two checksums differ. +3. `TYPE`: the type is not `F/D/G/P`. +4. `STATE`: `G/P` appears while metadata is already pending. +5. `META_SIZE`: metadata size is not the path length plus one. +6. `PATH`: the metadata path, or the effective path of an `F/D`, is invalid. +7. `ENTRY_SIZE`: a `D` has nonzero size. +8. `LIMIT`: adding an `F` would exceed `maxFiles` or make cumulative extracted bytes exceed `maxBytes`. + +If metadata remains unused after all events, output `REJECT N+1 STATE`. Otherwise output: + +```text +ACCEPT fileCount extractedBytes endOffset +``` + +All indices are 1-based. An entry that fails a limit check is not included in the output statistics. + +## Constraints + +- `1 ≤ N ≤ 200000` +- `0 ≤ maxFiles ≤ N` +- `0 ≤ maxBytes ≤ 9×10^18` +- Every numeric value is a nonnegative integer at most `9×10^18`. +- `type` is one uppercase letter. +- `name` is a visible ASCII token of length `1..200`. +- The layout endpoint computed from all `size` values is guaranteed not to exceed `9×10^18`. +- A `size` may be far larger than allocatable memory; a full solution must not create payload storage or an array proportional to archive size. + +All names are visible ASCII, so path byte length equals character count. + +## Examples + + + +### Example One + +Input: + +```text +3 3 1000 +0 F a.txt 5 10 10 +1024 D dir 0 11 11 +1536 F dir/b 600 12 12 +``` + +Output: + +```text +ACCEPT 2 605 3072 +``` + +### Example Two + +Input: + +```text +2 1 10 +0 G very/long/path 15 7 7 +1024 F short 3 8 8 +``` + +Output: + +```text +ACCEPT 1 3 2048 +``` + +### Example Three + +Input: + +```text +2 1 10 +0 G a 2 1 1 +1024 P b 2 2 2 +``` + +Output: + +```text +REJECT 2 STATE +``` + + diff --git a/problems/012-bounded-tar-stream/statement.zh-TW.md b/problems/012-bounded-tar-stream/statement.zh-TW.md new file mode 100644 index 0000000..58b71f3 --- /dev/null +++ b/problems/012-bounded-tar-stream/statement.zh-TW.md @@ -0,0 +1,113 @@ +# 512-byte 封存檔 + +WASM OJ 需要接收題目或程式的依賴封存檔,但不能先完整展開未知內容,再判斷它是否安全。為了在配置解壓空間以前拒絕損壞或不受支援的結構,底層解析器已把封存檔轉成 header 事件;現在要在**不展開 payload** 的前提下完成最後一道檢查。 + +每筆事件占一個 512-byte header,之後緊接 `size` bytes payload,再補零到 512 的倍數。因此下一筆事件的 offset 為: + +`offset + 512 + ceil(size / 512) * 512`。 + +事件種類及其語意如下: + +- `F`:一般檔案;計入檔案數與解壓 bytes。 +- `D`:目錄;`size` 必須為 0。 +- `G`、`P`:GNU long-path 或 PAX path metadata。`name` 是下一筆 `F/D` 的覆寫路徑,且 `size` 必須等於 `name` 的 ASCII byte 長度加一。尚有 metadata 等待使用時不得再出現 metadata。 +- 其他大寫字母:不支援。 + +每筆事件另給 stored checksum 與 calculated checksum,兩者必須相等。有效路徑必須非空、相對且 canonical:不得以 `/` 開頭或結尾;每個 segment 只含小寫字母、數字、`.`、`_`、`-`,且不得為 `.` 或 `..`。 + +若有 metadata 等待使用,下一筆 `F/D` 的有效路徑採用 metadata 的 `name`,並忽略該 header 自己的 `name`。請依這些規則驗證事件串流,而不讀取或展開任何 payload。 + +## 輸入 + +第一行為 `N maxFiles maxBytes`。接著 `N` 行: + +```text +offset type name size storedChecksum calculatedChecksum +``` + +- `1 <= N <= 200000`;`0 <= maxFiles <= N`;`0 <= maxBytes <= 9*10^18`。 +- 所有數值均為不超過 `9*10^18` 的非負整數。 +- `type` 是一個大寫英文字母,`name` 是長度 1 到 200 的可見 ASCII token。 +- 依所有 `size` 計算的 layout 結尾保證不超過 `9*10^18`。 + +## 輸出 + +逐筆處理,遇到第一個錯誤立即輸出 `REJECT i CODE`。同一筆依下列順序只回報第一項: + +1. `OFFSET`:offset 不是預期值(第一筆預期 0)。 +2. `CHECKSUM`:兩個 checksum 不同。 +3. `TYPE`:種類不是 `F/D/G/P`。 +4. `STATE`:已有待使用 metadata,卻又讀到 `G/P`。 +5. `META_SIZE`:metadata size 不等於路徑長度加一。 +6. `PATH`:metadata 路徑,或 `F/D` 的有效路徑不合法。 +7. `ENTRY_SIZE`:`D` 的 size 不為 0。 +8. `LIMIT`:加入 `F` 後,檔案數超過 `maxFiles` 或累計 bytes 超過 `maxBytes`。 + +全部事件讀完仍有 metadata 未使用,輸出 `REJECT N+1 STATE`。否則輸出: + +```text +ACCEPT fileCount extractedBytes endOffset +``` + +所有編號為 1-based。限制檢查失敗的那筆不算進輸出統計。 + +## 限制 + +`size` 可遠大於可配置記憶體;完整解不得建立 payload 或長度為 archive size 的陣列。 + +輸入列數、數值範圍、name 長度與 layout 上限均如輸入段落所列;所有 name 是可見 ASCII,故 path byte 長度等於字元數。 + +## 範例 + + + +### 範例一 + +輸入: + +```text +3 3 1000 +0 F a.txt 5 10 10 +1024 D dir 0 11 11 +1536 F dir/b 600 12 12 +``` + +輸出: + +```text +ACCEPT 2 605 3072 +``` + +### 範例二 + +輸入: + +```text +2 1 10 +0 G very/long/path 15 7 7 +1024 F short 3 8 8 +``` + +輸出: + +```text +ACCEPT 1 3 2048 +``` + +### 範例三 + +輸入: + +```text +2 1 10 +0 G a 2 1 1 +1024 P b 2 2 2 +``` + +輸出: + +```text +REJECT 2 STATE +``` + + diff --git a/problems/012-bounded-tar-stream/tests/adversarial-bigint-metadata.in b/problems/012-bounded-tar-stream/tests/adversarial-bigint-metadata.in new file mode 100644 index 0000000..8531f32 --- /dev/null +++ b/problems/012-bounded-tar-stream/tests/adversarial-bigint-metadata.in @@ -0,0 +1,4 @@ +3 1 9007199254740993 +0 G deep/path 10 7 7 +1024 F ignored//bad 9007199254740993 8 8 +9007199254743040 D dir 0 9 9 diff --git a/problems/012-bounded-tar-stream/tests/adversarial-bigint-metadata.out b/problems/012-bounded-tar-stream/tests/adversarial-bigint-metadata.out new file mode 100644 index 0000000..31e8ae2 --- /dev/null +++ b/problems/012-bounded-tar-stream/tests/adversarial-bigint-metadata.out @@ -0,0 +1 @@ +ACCEPT 1 9007199254740993 9007199254743552 diff --git a/problems/012-bounded-tar-stream/tests/sample-01.in b/problems/012-bounded-tar-stream/tests/sample-01.in new file mode 100644 index 0000000..06d9625 --- /dev/null +++ b/problems/012-bounded-tar-stream/tests/sample-01.in @@ -0,0 +1,4 @@ +3 3 1000 +0 F a.txt 5 10 10 +1024 D dir 0 11 11 +1536 F dir/b 600 12 12 diff --git a/problems/012-bounded-tar-stream/tests/sample-01.out b/problems/012-bounded-tar-stream/tests/sample-01.out new file mode 100644 index 0000000..6e56d36 --- /dev/null +++ b/problems/012-bounded-tar-stream/tests/sample-01.out @@ -0,0 +1 @@ +ACCEPT 2 605 3072 diff --git a/problems/012-bounded-tar-stream/tests/sample-02.in b/problems/012-bounded-tar-stream/tests/sample-02.in new file mode 100644 index 0000000..74703fa --- /dev/null +++ b/problems/012-bounded-tar-stream/tests/sample-02.in @@ -0,0 +1,3 @@ +2 1 10 +0 G very/long/path 15 7 7 +1024 F short 3 8 8 diff --git a/problems/012-bounded-tar-stream/tests/sample-02.out b/problems/012-bounded-tar-stream/tests/sample-02.out new file mode 100644 index 0000000..a07cbec --- /dev/null +++ b/problems/012-bounded-tar-stream/tests/sample-02.out @@ -0,0 +1 @@ +ACCEPT 1 3 2048 diff --git a/problems/012-bounded-tar-stream/tests/sample-03.in b/problems/012-bounded-tar-stream/tests/sample-03.in new file mode 100644 index 0000000..7c35066 --- /dev/null +++ b/problems/012-bounded-tar-stream/tests/sample-03.in @@ -0,0 +1,3 @@ +2 1 10 +0 G a 2 1 1 +1024 P b 2 2 2 diff --git a/problems/012-bounded-tar-stream/tests/sample-03.out b/problems/012-bounded-tar-stream/tests/sample-03.out new file mode 100644 index 0000000..2d81d4d --- /dev/null +++ b/problems/012-bounded-tar-stream/tests/sample-03.out @@ -0,0 +1 @@ +REJECT 2 STATE diff --git a/problems/012-bounded-tar-stream/validator.py b/problems/012-bounded-tar-stream/validator.py new file mode 100644 index 0000000..5356f2c --- /dev/null +++ b/problems/012-bounded-tar-stream/validator.py @@ -0,0 +1,33 @@ +import re, sys + +U = 9_000_000_000_000_000_000 + + +def main(): + ls = sys.stdin.read().splitlines() + assert ls + h = ls[0].split() + assert len(h) == 3 and all(re.fullmatch(r"0|[1-9][0-9]*", x) for x in h) + n, f, b = map(int, h) + assert 1 <= n <= 200000 and 0 <= f <= n and b <= U and len(ls) == n + 1 + end = 0 + for line in ls[1:]: + p = line.split() + assert len(p) == 6 + o, t, name, z, c, d = p + assert ( + re.fullmatch(r"[A-Z]", t) + and 1 <= len(name) <= 200 + and all(33 <= ord(x) <= 126 for x in name) + ) + assert all(re.fullmatch(r"0|[1-9][0-9]*", x) for x in (o, z, c, d)) + vals = list(map(int, (o, z, c, d))) + assert all(x <= U for x in vals) + end += 512 + ((vals[1] + 511) // 512) * 512 + assert end <= U + + +try: + main() +except (AssertionError, ValueError): + sys.exit(1) diff --git a/problems/013-build-fingerprint/editorial.en.md b/problems/013-build-fingerprint/editorial.en.md new file mode 100644 index 0000000..8caa4d3 --- /dev/null +++ b/problems/013-build-fingerprint/editorial.en.md @@ -0,0 +1,26 @@ +# Editorial + +## Intuitive Approach + +For each build, start with an empty array and insert every file ID at its correct position by path. A build with `K` files may require `O(K^2)` comparisons and moves, so a large build times out. + +## Optimal Approach: Per-Build Comparison Sort + +After reading the file table, collect each build's file IDs and comparison-sort them using the corresponding path as the key. Output the four metadata fields and `K`, then each sorted `(path,digest)` pair. Because all paths are ASCII, ordinary byte/string lexicographic order in each supported language agrees under these constraints. + +Do not concatenate the tokens into one giant string only to split it again, and do not compute a digest. Stream output tokens directly, or use a fixed-size 64 KiB chunk buffer, to avoid allocating a string as large as the entire output. + +## Correctness Proof + +After sorting, adjacent paths are nondecreasing. Because paths are unique, they are strictly increasing, and sorting is a permutation, so the selected file set is unchanged. The algorithm outputs the four metadata fields and `K` verbatim, then retrieves the unique path and digest for every sorted ID. Each line is therefore exactly the specified canonical preimage. Since the canonical order is unique, the output is correct. + +## Complexity + +Build `i` takes `O(K_i log K_i)` path comparisons and `O(K_i)` temporary space. Let `S` include all text bytes read and written. Total time is `O(sum K_i log K_i + S)`, and peak auxiliary space is `O(K_max)`. The file table and input separately require `O(N+S_input)`; streaming output does not retain `S_output`. + +## Common Mistakes + +- Sorting by file ID or digest instead of path. +- Sorting the metadata fields. +- Printing a placeholder token when `K=0`. +- Using locale-aware collation and obtaining host-dependent order. diff --git a/problems/013-build-fingerprint/editorial.zh-TW.md b/problems/013-build-fingerprint/editorial.zh-TW.md new file mode 100644 index 0000000..24b4a2f --- /dev/null +++ b/problems/013-build-fingerprint/editorial.zh-TW.md @@ -0,0 +1,26 @@ +# 解題說明 + +## 直覺解 + +對每個 build 建立空陣列,再把每個 file ID 依 path 插入正確位置。第 `K` 筆 build 最壞需 `O(K^2)` 次比較與搬移;大 build 會逾時。 + +## 最佳解 + +讀入檔案表後,對每個 build 收集其 file ID,使用比較排序,key 為對應的 path。輸出四個 metadata、`K`,再依排序結果輸出 `(path,digest)`。path 都是 ASCII,所以各語言的 byte/一般字典序在此限制下相同。 + +不應真的把 token 串接後再拆解,也不需要計算 digest;直接串流輸出 token(或使用固定大小的 64 KiB chunk)可避免配置與總輸出等大的字串。 + +## 正確性證明 + +比較排序結束後,所有相鄰 path 非遞減;因 path 唯一,故嚴格遞增,且排序只是置換,所含檔案集合與輸入相同。演算法原樣輸出四個 metadata 與 `K`,再對每個排序後 ID 查回唯一的 path、digest。因此每行恰為題目定義的 canonical preimage。canonical 順序唯一,所以輸出正確。 + +## 複雜度 + +第 `i` 個 build 需 `O(K_i log K_i)` 次 path 比較與 `O(K_i)` 暫存空間;令 `S` 包含全部讀寫文字 bytes,總時間 `O(sum K_i log K_i + S)`,峰值額外空間 `O(K_max)`(檔案表與輸入另需 `O(N+S_input)`,streaming output 不另存 `S_output`)。 + +## 常見錯誤 + +- 依 file ID 或 digest 排序,而不是 path。 +- 把 metadata 也排序。 +- `K=0` 時多印占位 token。 +- 使用 locale-aware collation,造成跨 host 不一致。 diff --git a/problems/013-build-fingerprint/generator.py b/problems/013-build-fingerprint/generator.py new file mode 100644 index 0000000..3bf4053 --- /dev/null +++ b/problems/013-build-fingerprint/generator.py @@ -0,0 +1,14 @@ +import random, sys + +seed, index = map(int, sys.argv[1:]) +r = random.Random(seed * 1000003 + index) +n = 7 + index % 8 +q = 3 + index % 5 +print(n, q) +for i in range(n): + print(f"src/p{i:02d}.c", f"{r.getrandbits(32):08x}") +for j in range(q): + k = r.randrange(n + 1) + ids = r.sample(range(1, n + 1), k) + r.shuffle(ids) + print("cc wasm32 o2", f"{r.getrandbits(32):08x}", k, *ids) diff --git a/problems/013-build-fingerprint/oracle.py b/problems/013-build-fingerprint/oracle.py new file mode 100644 index 0000000..22e189d --- /dev/null +++ b/problems/013-build-fingerprint/oracle.py @@ -0,0 +1,20 @@ +import sys + +it = iter(sys.stdin.read().split()) +n = int(next(it)) +q = int(next(it)) +files = [(next(it), next(it)) for _ in range(n)] +for _ in range(q): + meta = [next(it) for _ in range(4)] + k = int(next(it)) + ids = [] + for _ in range(k): + x = int(next(it)) - 1 + j = len(ids) + while j and files[ids[j - 1]][0] > files[x][0]: + j -= 1 + ids.insert(j, x) + out = meta + [str(k)] + for x in ids: + out.extend(files[x]) + print(*out) diff --git a/problems/013-build-fingerprint/problem.json b/problems/013-build-fingerprint/problem.json new file mode 100644 index 0000000..cee63da --- /dev/null +++ b/problems/013-build-fingerprint/problem.json @@ -0,0 +1,146 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 13, + "slug": "build-fingerprint", + "title": { + "zh-TW": "Build Fingerprint", + "en": "Build Fingerprint" + }, + "difficulty": "medium", + "tags": [ + "sorting", + "canonicalization", + "content-addressing" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-long-metadata", + "kind": "adversarial", + "input": "tests/adversarial-long-metadata.in", + "output": "tests/adversarial-long-metadata.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 8000000, + "memoryLimitBytes": 536870912 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 1500000, + "memoryLimitBytes": 402653184 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 500000, + "memoryLimitBytes": 268435456 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "每次插入排序", + "en": "Per-Build Insertion Sort" + }, + "time": "O(sum K_i^2 + S)", + "space": "O(K_max)", + "accepted": false + }, + { + "name": { + "zh-TW": "每次比較排序", + "en": "Per-Build Comparison Sort" + }, + "time": "O(sum K_i log K_i + S)", + "space": "O(K_max)", + "accepted": true + } + ] +} diff --git a/problems/013-build-fingerprint/solutions/c/main.c b/problems/013-build-fingerprint/solutions/c/main.c new file mode 100644 index 0000000..eaaf638 --- /dev/null +++ b/problems/013-build-fingerprint/solutions/c/main.c @@ -0,0 +1,109 @@ +#include +#include +#include +#include + +typedef struct { + char *path; + char *digest; +} File; + +static File *files; + +static char *read_token(void) { + int ch; + do { + ch = getchar(); + } while (ch != EOF && isspace((unsigned char)ch)); + if (ch == EOF) + return NULL; + + size_t length = 0; + size_t capacity = 32; + char *token = malloc(capacity); + if (token == NULL) + return NULL; + while (ch != EOF && !isspace((unsigned char)ch)) { + if (length + 1 == capacity) { + capacity *= 2; + char *grown = realloc(token, capacity); + if (grown == NULL) { + free(token); + return NULL; + } + token = grown; + } + token[length++] = (char)ch; + ch = getchar(); + } + token[length] = '\0'; + return token; +} + +static int read_int(void) { + char *token = read_token(); + if (token == NULL) + exit(1); + int value = (int)strtol(token, NULL, 10); + free(token); + return value; +} + +static int compare_file_ids(const void *left, const void *right) { + int left_id = *(const int *)left; + int right_id = *(const int *)right; + return strcmp(files[left_id].path, files[right_id].path); +} + +int main(void) { + int file_count = read_int(); + int build_count = read_int(); + files = malloc((size_t)file_count * sizeof(*files)); + if (files == NULL) + return 1; + + for (int i = 0; i < file_count; i++) { + files[i].path = read_token(); + files[i].digest = read_token(); + if (files[i].path == NULL || files[i].digest == NULL) + return 1; + } + + for (int build = 0; build < build_count; build++) { + char *compiler = read_token(); + char *target = read_token(); + char *optimization = read_token(); + char *dependency_digest = read_token(); + int selected_count = read_int(); + if (compiler == NULL || target == NULL || optimization == NULL || + dependency_digest == NULL) + return 1; + + int *ids = malloc((size_t)(selected_count > 0 ? selected_count : 1) * + sizeof(*ids)); + if (ids == NULL) + return 1; + for (int i = 0; i < selected_count; i++) + ids[i] = read_int() - 1; + qsort(ids, (size_t)selected_count, sizeof(*ids), compare_file_ids); + + printf("%s %s %s %s %d", compiler, target, optimization, dependency_digest, + selected_count); + for (int i = 0; i < selected_count; i++) + printf(" %s %s", files[ids[i]].path, files[ids[i]].digest); + putchar('\n'); + + free(ids); + free(compiler); + free(target); + free(optimization); + free(dependency_digest); + } + + for (int i = 0; i < file_count; i++) { + free(files[i].path); + free(files[i].digest); + } + free(files); + return 0; +} diff --git a/problems/013-build-fingerprint/solutions/cpp/main.cpp b/problems/013-build-fingerprint/solutions/cpp/main.cpp new file mode 100644 index 0000000..9246ed1 --- /dev/null +++ b/problems/013-build-fingerprint/solutions/cpp/main.cpp @@ -0,0 +1,31 @@ +#include +#include +#include +#include +using namespace std; +int main() { + ios::sync_with_stdio(false); + cin.tie(nullptr); + int n, q; + if (!(cin >> n >> q)) + return 0; + vector> f(n); + for (auto &x : f) + cin >> x.first >> x.second; + while (q--) { + string a, b, c, d; + int k; + cin >> a >> b >> c >> d >> k; + vector v(k); + for (int &x : v) { + cin >> x; + --x; + } + sort(v.begin(), v.end(), + [&](int x, int y) { return f[x].first < f[y].first; }); + cout << a << ' ' << b << ' ' << c << ' ' << d << ' ' << k; + for (int x : v) + cout << ' ' << f[x].first << ' ' << f[x].second; + cout << '\n'; + } +} diff --git a/problems/013-build-fingerprint/solutions/go/main.go b/problems/013-build-fingerprint/solutions/go/main.go new file mode 100644 index 0000000..0ef619c --- /dev/null +++ b/problems/013-build-fingerprint/solutions/go/main.go @@ -0,0 +1,38 @@ +package main + +import ( + "bufio" + "fmt" + "os" + "sort" +) + +type F struct{ p, d string } + +func main() { + in := bufio.NewReader(os.Stdin) + out := bufio.NewWriter(os.Stdout) + defer out.Flush() + var n, q int + fmt.Fscan(in, &n, &q) + f := make([]F, n) + for i := range f { + fmt.Fscan(in, &f[i].p, &f[i].d) + } + for ; q > 0; q-- { + var a, b, c, d string + var k int + fmt.Fscan(in, &a, &b, &c, &d, &k) + v := make([]int, k) + for i := range v { + fmt.Fscan(in, &v[i]) + v[i]-- + } + sort.Slice(v, func(i, j int) bool { return f[v[i]].p < f[v[j]].p }) + fmt.Fprint(out, a, " ", b, " ", c, " ", d, " ", k) + for _, x := range v { + fmt.Fprint(out, " ", f[x].p, " ", f[x].d) + } + fmt.Fprintln(out) + } +} diff --git a/problems/013-build-fingerprint/solutions/javascript/main.js b/problems/013-build-fingerprint/solutions/javascript/main.js new file mode 100644 index 0000000..f4e6470 --- /dev/null +++ b/problems/013-build-fingerprint/solutions/javascript/main.js @@ -0,0 +1,26 @@ +import * as std from "std"; +const a = std.in.readAsString().trim().split(/\s+/); +let p = 0, n = Number(a[p++]), q = Number(a[p++]); +/** @type {[string, string][]} */ +const f = []; +for (let i = 0; i < n; i++) f.push([a[p++], a[p++]]); +let output = ""; +/** @param {string} text @returns {void} */ +const emit = (text) => { + if (output.length + text.length > 65536) { + std.out.puts(output); + output = ""; + } + output += text; +}; +while (q--) { + const m = [a[p++], a[p++], a[p++], a[p++]], k = Number(a[p++]); + /** @type {number[]} */ + const v = []; + for (let i = 0; i < k; i++) v.push(Number(a[p++]) - 1); + v.sort((x, y) => f[x][0] < f[y][0] ? -1 : f[x][0] > f[y][0] ? 1 : 0); + emit(`${m[0]} ${m[1]} ${m[2]} ${m[3]} ${k}`); + for (const x of v) emit(` ${f[x][0]} ${f[x][1]}`); + emit("\n"); +} +if (output.length) std.out.puts(output); diff --git a/problems/013-build-fingerprint/solutions/python/main.py b/problems/013-build-fingerprint/solutions/python/main.py new file mode 100644 index 0000000..a954af7 --- /dev/null +++ b/problems/013-build-fingerprint/solutions/python/main.py @@ -0,0 +1,22 @@ +import sys + +it = iter(sys.stdin.read().split()) +n = int(next(it)) +q = int(next(it)) +f = [(next(it), next(it)) for _ in range(n)] +output = sys.stdout +for _ in range(q): + meta = [next(it) for _ in range(4)] + k = int(next(it)) + ids = [int(next(it)) - 1 for _ in range(k)] + ids.sort(key=lambda x: f[x][0]) + output.write(meta[0]) + for token in (*meta[1:], str(k)): + output.write(" ") + output.write(token) + for x in ids: + output.write(" ") + output.write(f[x][0]) + output.write(" ") + output.write(f[x][1]) + output.write("\n") diff --git a/problems/013-build-fingerprint/solutions/rust/main.rs b/problems/013-build-fingerprint/solutions/rust/main.rs new file mode 100644 index 0000000..b24f73c --- /dev/null +++ b/problems/013-build-fingerprint/solutions/rust/main.rs @@ -0,0 +1,30 @@ +use std::io::{self, BufWriter, Read, Write}; +fn main() { + let mut s = String::new(); + io::stdin().read_to_string(&mut s).unwrap(); + let mut it = s.split_whitespace(); + let n: usize = it.next().unwrap().parse().unwrap(); + let q: usize = it.next().unwrap().parse().unwrap(); + let mut f = Vec::with_capacity(n); + for _ in 0..n { + f.push(( + it.next().unwrap().to_string(), + it.next().unwrap().to_string(), + )); + } + let stdout = io::stdout(); + let mut out = BufWriter::new(stdout.lock()); + for _ in 0..q { + let meta: [&str; 4] = std::array::from_fn(|_| it.next().unwrap()); + let k: usize = it.next().unwrap().parse().unwrap(); + let mut ids: Vec = (0..k) + .map(|_| it.next().unwrap().parse::().unwrap() - 1) + .collect(); + ids.sort_by(|&a, &b| f[a].0.cmp(&f[b].0)); + write!(out, "{} {} {} {} {}", meta[0], meta[1], meta[2], meta[3], k).unwrap(); + for x in ids { + write!(out, " {} {}", f[x].0, f[x].1).unwrap(); + } + writeln!(out).unwrap(); + } +} diff --git a/problems/013-build-fingerprint/solutions/typescript/main.ts b/problems/013-build-fingerprint/solutions/typescript/main.ts new file mode 100644 index 0000000..5760173 --- /dev/null +++ b/problems/013-build-fingerprint/solutions/typescript/main.ts @@ -0,0 +1,24 @@ +import * as std from "std"; +const a: string[] = std.in.readAsString().trim().split(/\s+/); +let p = 0, n = Number(a[p++]), q = Number(a[p++]); +const f: [string, string][] = []; +for (let i = 0; i < n; i++) f.push([a[p++], a[p++]]); +let output = ""; +const emit = (text: string): void => { + if (output.length + text.length > 65536) { + std.out.puts(output); + output = ""; + } + output += text; +}; +while (q--) { + const m: string[] = [a[p++], a[p++], a[p++], a[p++]], + k = Number(a[p++]), + v: number[] = []; + for (let i = 0; i < k; i++) v.push(Number(a[p++]) - 1); + v.sort((x, y) => f[x][0] < f[y][0] ? -1 : f[x][0] > f[y][0] ? 1 : 0); + emit(`${m[0]} ${m[1]} ${m[2]} ${m[3]} ${k}`); + for (const x of v) emit(` ${f[x][0]} ${f[x][1]}`); + emit("\n"); +} +if (output.length) std.out.puts(output); diff --git a/problems/013-build-fingerprint/statement.en.md b/problems/013-build-fingerprint/statement.en.md new file mode 100644 index 0000000..cbf9c60 --- /dev/null +++ b/problems/013-build-fingerprint/statement.en.md @@ -0,0 +1,96 @@ +# Build Fingerprint + +In a WASM OJ, identical source code and compilation settings should hit the same build cache, while any input that can change the artifact must produce a different identity. If a fingerprint depended on file-enumeration order, the same project could be compiled repeatedly merely because its inputs arrived in another order. We therefore need a unique canonical preimage. + +A real build digest hashes this canonical preimage. This problem does not ask you to implement SHA-256 or make the hash function itself an obstacle. Instead, output a token representation of the canonical preimage. + +A project has `N` files, each with a unique path and a precomputed digest. Every build specifies a compiler, target, optimization level, dependency digest, and an arbitrarily ordered set of file indices. + +The canonical representation preserves the input order of those four metadata fields and orders the file portion by ASCII lexicographic path order. Produce the unique token sequence that would be supplied to the later hashing step. + +## Input + +The first line contains `N Q`. The next `N` lines contain `path digest`. Each of the following `Q` lines has: + +```text +compiler target optimization dependencyDigest K fileId_1 ... fileId_K +``` + +## Output + +For each build, output one line: + +```text +compiler target optimization dependencyDigest K path_1 digest_1 ... path_K digest_K +``` + +The file paths must be strictly increasing. When `K=0`, the line ends immediately after `0`; do not add a sentinel for the empty set. + +## Constraints + +- `1 ≤ N,Q ≤ 200000`; the sum of `K` over all builds is at most `400000`. +- A path is a canonical relative path of length `1..100`, contains only lowercase letters, digits, `.`, `_`, `-`, and `/`, and has no empty, `.`, or `..` segment. All paths are unique. +- A digest is a lowercase hexadecimal token of length `8..64`. Metadata tokens contain only lowercase letters, digits, `.`, `_`, and `-`. +- File IDs within one build are distinct and lie in `1..N`. +- The total input text length is at most 4 MB. Comparison uses ASCII bytes and is locale-independent. + +Quadratic insertion into a sorted array does not pass the full tests. + +## Examples + + + +### Example One + +Input: + +```text +3 1 +src/z.c aaaaaaaa +src/a.c bbbbbbbb +inc/x.h cccccccc +clang wasm32 o2 deadbeef 3 1 3 2 +``` + +Output: + +```text +clang wasm32 o2 deadbeef 3 inc/x.h cccccccc src/a.c bbbbbbbb src/z.c aaaaaaaa +``` + +### Example Two + +Input: + +```text +1 1 +main.c 01234567 +gcc wasi o0 abcdef12 0 +``` + +Output: + +```text +gcc wasi o0 abcdef12 0 +``` + +### Example Three + +Input: + +```text +2 2 +b.c 11111111 +a.c 22222222 +cc x o3 aaaaaaaa 2 1 2 +cc y o1 bbbbbbbb 1 1 +``` + +Output: + +```text +cc x o3 aaaaaaaa 2 a.c 22222222 b.c 11111111 +cc y o1 bbbbbbbb 1 b.c 11111111 +``` + + diff --git a/problems/013-build-fingerprint/statement.zh-TW.md b/problems/013-build-fingerprint/statement.zh-TW.md new file mode 100644 index 0000000..9672acb --- /dev/null +++ b/problems/013-build-fingerprint/statement.zh-TW.md @@ -0,0 +1,96 @@ +# Build Fingerprint + +在 WASM OJ 中,相同的原始碼與編譯設定應該命中同一份 build cache,而任何會改變產物的輸入都必須產生不同的識別。若 fingerprint 取決於檔案被列舉的順序,同一個專案只因輸入順序不同就會重複編譯;因此,我們需要先定義唯一的 canonical preimage。 + +真正的 build digest 會對這份 canonical preimage 做雜湊。本題不要求實作 SHA-256,也不把雜湊函式本身當成門檻;你要輸出的是 canonical preimage 的 token 表示。 + +專案有 `N` 個檔案,每個檔案都有唯一 path 與已算好的 digest。每次 build 會提供 compiler、target、optimization、dependency digest,以及一組順序任意的檔案編號。 + +canonical 表示保留上述四個 metadata 欄位的輸入順序,檔案部分則依 path 的 ASCII 字典序排列。請根據這項規格產生可供後續雜湊的唯一 token 序列。 + +## 輸入 + +第一行 `N Q`。接著 `N` 行為 `path digest`。再接著 `Q` 行: + +```text +compiler target optimization dependencyDigest K fileId_1 ... fileId_K +``` + +## 輸出 + +每個 build 輸出一行: + +```text +compiler target optimization dependencyDigest K path_1 digest_1 ... path_K digest_K +``` + +其中檔案依 path 嚴格遞增。`K=0` 時該行在 `0` 後結束。空集合不另加 sentinel。 + +## 限制 + +- `1 <= N,Q <= 200000`,所有 build 的 `K` 總和不超過 400000。 +- path 是長度 1 到 100 的 canonical relative path,只含小寫字母、數字、`. _ - /`,不得有空 segment、`.` 或 `..`;所有 path 唯一。 +- digest 是長度 8 到 64 的 lowercase hexadecimal token;metadata token 只含小寫字母、數字、`.`、`_`、`-`。 +- 每個 build 內的 file ID 互異且介於 1 到 `N`。 +- 全部文字總長度不超過 4 MB;比較順序按 ASCII bytes,與 locale 無關。 + +逐一把元素插入已排序陣列的二次方解法無法通過完整測資。 + +## 範例 + + + +### 範例一 + +輸入: + +```text +3 1 +src/z.c aaaaaaaa +src/a.c bbbbbbbb +inc/x.h cccccccc +clang wasm32 o2 deadbeef 3 1 3 2 +``` + +輸出: + +```text +clang wasm32 o2 deadbeef 3 inc/x.h cccccccc src/a.c bbbbbbbb src/z.c aaaaaaaa +``` + +### 範例二 + +輸入: + +```text +1 1 +main.c 01234567 +gcc wasi o0 abcdef12 0 +``` + +輸出: + +```text +gcc wasi o0 abcdef12 0 +``` + +### 範例三 + +輸入: + +```text +2 2 +b.c 11111111 +a.c 22222222 +cc x o3 aaaaaaaa 2 1 2 +cc y o1 bbbbbbbb 1 1 +``` + +輸出: + +```text +cc x o3 aaaaaaaa 2 a.c 22222222 b.c 11111111 +cc y o1 bbbbbbbb 1 b.c 11111111 +``` + + diff --git a/problems/013-build-fingerprint/tests/adversarial-long-metadata.in b/problems/013-build-fingerprint/tests/adversarial-long-metadata.in new file mode 100644 index 0000000..ace007f --- /dev/null +++ b/problems/013-build-fingerprint/tests/adversarial-long-metadata.in @@ -0,0 +1,3 @@ +1 1 +p 00000000 +aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa t o d 1 1 diff --git a/problems/013-build-fingerprint/tests/adversarial-long-metadata.out b/problems/013-build-fingerprint/tests/adversarial-long-metadata.out new file mode 100644 index 0000000..495ffaf --- /dev/null +++ b/problems/013-build-fingerprint/tests/adversarial-long-metadata.out @@ -0,0 +1 @@ +aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa t o d 1 p 00000000 diff --git a/problems/013-build-fingerprint/tests/sample-01.in b/problems/013-build-fingerprint/tests/sample-01.in new file mode 100644 index 0000000..9ec0e71 --- /dev/null +++ b/problems/013-build-fingerprint/tests/sample-01.in @@ -0,0 +1,5 @@ +3 1 +src/z.c aaaaaaaa +src/a.c bbbbbbbb +inc/x.h cccccccc +clang wasm32 o2 deadbeef 3 1 3 2 diff --git a/problems/013-build-fingerprint/tests/sample-01.out b/problems/013-build-fingerprint/tests/sample-01.out new file mode 100644 index 0000000..63ac68e --- /dev/null +++ b/problems/013-build-fingerprint/tests/sample-01.out @@ -0,0 +1 @@ +clang wasm32 o2 deadbeef 3 inc/x.h cccccccc src/a.c bbbbbbbb src/z.c aaaaaaaa diff --git a/problems/013-build-fingerprint/tests/sample-02.in b/problems/013-build-fingerprint/tests/sample-02.in new file mode 100644 index 0000000..68bc7a0 --- /dev/null +++ b/problems/013-build-fingerprint/tests/sample-02.in @@ -0,0 +1,3 @@ +1 1 +main.c 01234567 +gcc wasi o0 abcdef12 0 diff --git a/problems/013-build-fingerprint/tests/sample-02.out b/problems/013-build-fingerprint/tests/sample-02.out new file mode 100644 index 0000000..ef1b141 --- /dev/null +++ b/problems/013-build-fingerprint/tests/sample-02.out @@ -0,0 +1 @@ +gcc wasi o0 abcdef12 0 diff --git a/problems/013-build-fingerprint/tests/sample-03.in b/problems/013-build-fingerprint/tests/sample-03.in new file mode 100644 index 0000000..98c5684 --- /dev/null +++ b/problems/013-build-fingerprint/tests/sample-03.in @@ -0,0 +1,5 @@ +2 2 +b.c 11111111 +a.c 22222222 +cc x o3 aaaaaaaa 2 1 2 +cc y o1 bbbbbbbb 1 1 diff --git a/problems/013-build-fingerprint/tests/sample-03.out b/problems/013-build-fingerprint/tests/sample-03.out new file mode 100644 index 0000000..fad68bf --- /dev/null +++ b/problems/013-build-fingerprint/tests/sample-03.out @@ -0,0 +1,2 @@ +cc x o3 aaaaaaaa 2 a.c 22222222 b.c 11111111 +cc y o1 bbbbbbbb 1 b.c 11111111 diff --git a/problems/013-build-fingerprint/validator.py b/problems/013-build-fingerprint/validator.py new file mode 100644 index 0000000..2289258 --- /dev/null +++ b/problems/013-build-fingerprint/validator.py @@ -0,0 +1,48 @@ +import re, sys + +P = re.compile(r"[a-z0-9._/-]+$") +T = re.compile(r"[a-z0-9._-]+$") +D = re.compile(r"[0-9a-f]{8,64}$") + + +def path_ok(p): + return ( + len(p) <= 100 + and not p.startswith("/") + and not p.endswith("/") + and P.fullmatch(p) + and all(x not in ("", ".", "..") for x in p.split("/")) + ) + + +def main(): + ls = sys.stdin.read().splitlines() + assert ls and len("\n".join(ls).encode()) <= 4_000_000 + h = ls[0].split() + assert len(h) == 2 and all( + x.isdigit() and (x == "0" or not x.startswith("0")) for x in h + ) + n, q = map(int, h) + assert 1 <= n <= 200000 and 1 <= q <= 200000 and len(ls) == 1 + n + q + paths = set() + for line in ls[1 : n + 1]: + x = line.split() + assert len(x) == 2 and path_ok(x[0]) and D.fullmatch(x[1]) and x[0] not in paths + paths.add(x[0]) + total = 0 + for line in ls[n + 1 :]: + x = line.split() + assert len(x) >= 5 and all(T.fullmatch(v) for v in x[:4]) + assert x[4].isdigit() and (x[4] == "0" or not x[4].startswith("0")) + k = int(x[4]) + assert len(x) == 5 + k + ids = list(map(int, x[5:])) + assert all(1 <= v <= n for v in ids) and len(ids) == len(set(ids)) + total += k + assert total <= 400000 + + +try: + main() +except (AssertionError, ValueError): + sys.exit(1) diff --git a/problems/014-runtime-bundle-encoding/editorial.en.md b/problems/014-runtime-bundle-encoding/editorial.en.md new file mode 100644 index 0000000..0cb6249 --- /dev/null +++ b/problems/014-runtime-bundle-encoding/editorial.en.md @@ -0,0 +1,26 @@ +# Editorial + +## Intuitive Approach + +Insert records one at a time into an already-sorted path array, then concatenate every field. Sorting takes `O(N^2)` in the worst case, and repeatedly appending to an immutable string can introduce another quadratic copying cost. + +## Optimal Approach: Comparison Sort and Streaming Encoding + +First comparison-sort records by path. Use fixed-width big-endian helpers for u32 and u64 fields. Emit two hex digits for every byte of a path or `T` payload. A `B` payload is already canonical hexadecimal and may be emitted directly. Type, path length, and payload length all precede their contents, so a decoder can determine every field boundary uniquely. + +An implementation may collect hexadecimal fragments in an array and join once, or stream them directly. Do not dump an integer's in-memory representation, because host byte order is not guaranteed to be big-endian. + +## Correctness Proof + +After sorting, record order is uniquely determined by the unique paths. Every integer helper emits exactly the specified fixed-width big-endian bytes, and the conversions of ASCII and binary tokens preserve their contents byte for byte. Thus every segment of the algorithm's output equals the corresponding segment of the format definition. Conversely, a decoder reads the fixed magic and count, then uses the tag and two lengths to consume the path and payload and advance to the next record uniquely. Therefore any change in type, length, path, or payload changes at least one encoded byte, so the bundle is unambiguous and the output is correct. + +## Complexity + +Let `B` be the total number of input path and payload bytes. Time is `O(N log N+B)`. Storing records and the output uses `O(N+B_out)` space; with streaming output, space beyond the sorting data can be reduced to `O(N)`. + +## Common Mistakes + +- Forgetting that a binary token's byte length is half its hexadecimal character length. +- Using little-endian encoding or omitting leading zero bytes. +- Encoding records in input order. +- Treating the empty-payload sentinel `-` as a content byte. diff --git a/problems/014-runtime-bundle-encoding/editorial.zh-TW.md b/problems/014-runtime-bundle-encoding/editorial.zh-TW.md new file mode 100644 index 0000000..da6710a --- /dev/null +++ b/problems/014-runtime-bundle-encoding/editorial.zh-TW.md @@ -0,0 +1,26 @@ +# 解題說明 + +## 直覺解 + +逐筆插入 path 已排序的陣列,再串接所有欄位;排序最壞 `O(N^2)`,且反覆串接 immutable string 還可能造成額外二次方複製。 + +## 最佳解 + +先以標準比較排序按 path 排好。用固定寬度 big-endian helper 輸出 u32/u64;path 與 `T` payload 的每個 ASCII byte輸出兩位 hex,`B` payload 已是 canonical hex,可直接輸出。type、path length、payload length 都在內容之前,因此 decoder 能唯一決定每個欄位邊界。 + +實作可將 hex 片段收在陣列最後 join,或直接串流寫出;不可依 host endian 直接 dump 整數記憶體。 + +## 正確性證明 + +排序後 record 順序依唯一 path 唯一決定。每個整數 helper 依定義產生固定寬度 big-endian bytes;ASCII 與 binary token 的轉換各自逐 byte 保留內容。故演算法輸出的每一段都與格式定義相同。另一方面,decoder 先讀固定 magic/count,再由 type 與兩個長度精確切出 path、payload,能唯一前進到下一 record;因此不同 type、長度、path 或 payload 至少有一個編碼 byte 不同,整體不可混淆。 + +## 複雜度 + +令 `B` 為輸入檔名與 payload byte 數,時間 `O(N log N+B)`,保存 records 與輸出時空間 `O(N+B_out)`;若串流輸出,除排序資料外可降為 `O(N)`。 + +## 常見錯誤 + +- 忘記 binary token 的長度是 hex 字元數除以二。 +- 使用 little-endian 或漏補前導零。 +- 依輸入順序編碼。 +- 把空 payload 的 `-` 當成內容 byte。 diff --git a/problems/014-runtime-bundle-encoding/generator.py b/problems/014-runtime-bundle-encoding/generator.py new file mode 100644 index 0000000..724e858 --- /dev/null +++ b/problems/014-runtime-bundle-encoding/generator.py @@ -0,0 +1,24 @@ +import random, sys + +seed, index = map(int, sys.argv[1:]) +r = random.Random(seed ^ index * 0x9E3779B1) +n = 5 + index % 10 +rows = [] +for i in range(n): + t = r.choice("TB") + path = f"d{r.randrange(5)}/f{i:02d}" + z = r.randrange(10) + payload = ( + "-" + if z == 0 + else ( + "".join(chr(65 + r.randrange(26)) for _ in range(z)) + if t == "T" + else bytes(r.randrange(256) for _ in range(z)).hex() + ) + ) + rows.append((t, path, payload)) +r.shuffle(rows) +print(n) +for x in rows: + print(*x) diff --git a/problems/014-runtime-bundle-encoding/oracle.py b/problems/014-runtime-bundle-encoding/oracle.py new file mode 100644 index 0000000..6311062 --- /dev/null +++ b/problems/014-runtime-bundle-encoding/oracle.py @@ -0,0 +1,28 @@ +import sys + +it = iter(sys.stdin.read().split()) +n = int(next(it)) +a = [] +for _ in range(n): + row = (next(it), next(it), next(it)) + j = len(a) + while j and a[j - 1][1] > row[1]: + j -= 1 + a.insert(j, row) +out = bytearray(b"WOBJ") + n.to_bytes(4, "big") +for t, path, payload in a: + raw = ( + b"" + if payload == "-" + else payload.encode() + if t == "T" + else bytes.fromhex(payload) + ) + out += ( + bytes([1 if t == "T" else 2]) + + len(path).to_bytes(4, "big") + + path.encode() + + len(raw).to_bytes(8, "big") + + raw + ) +print(out.hex()) diff --git a/problems/014-runtime-bundle-encoding/problem.json b/problems/014-runtime-bundle-encoding/problem.json new file mode 100644 index 0000000..9b42a08 --- /dev/null +++ b/problems/014-runtime-bundle-encoding/problem.json @@ -0,0 +1,147 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 14, + "slug": "runtime-bundle-encoding", + "title": { + "zh-TW": "不可混淆的 Runtime Bundle", + "en": "Unambiguous Runtime Bundle" + }, + "difficulty": "medium", + "tags": [ + "encoding", + "sorting", + "binary-format", + "canonicalization" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-punctuation-order", + "kind": "adversarial", + "input": "tests/adversarial-punctuation-order.in", + "output": "tests/adversarial-punctuation-order.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 7500000, + "memoryLimitBytes": 536870912 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 1500000, + "memoryLimitBytes": 402653184 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 500000, + "memoryLimitBytes": 268435456 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "插入排序後編碼", + "en": "Insertion Sort Followed by Encoding" + }, + "time": "O(N^2 + B)", + "space": "O(B)", + "accepted": false + }, + { + "name": { + "zh-TW": "比較排序與串流編碼", + "en": "Comparison Sort and Streaming Encoding" + }, + "time": "O(N log N + B)", + "space": "O(N + B_out)", + "accepted": true + } + ] +} diff --git a/problems/014-runtime-bundle-encoding/solutions/c/main.c b/problems/014-runtime-bundle-encoding/solutions/c/main.c new file mode 100644 index 0000000..6ac9074 --- /dev/null +++ b/problems/014-runtime-bundle-encoding/solutions/c/main.c @@ -0,0 +1,47 @@ +#include +#include +#include +typedef struct { + char t, *p, *v; +} R; +int cmp(const void *a, const void *b) { + return strcmp(((const R *)a)->p, ((const R *)b)->p); +} +void hx(const char *s) { + for (; *s; s++) + printf("%02x", (unsigned char)*s); +} +int main(void) { + int n; + if (scanf("%d", &n) != 1) + return 0; + R *a = malloc(sizeof(R) * (size_t)n); + char *tmp = malloc(400001); + for (int i = 0; i < n; i++) { + char path[101]; + scanf(" %c %100s %400000s", &a[i].t, path, tmp); + a[i].p = malloc(strlen(path) + 1); + a[i].v = malloc(strlen(tmp) + 1); + strcpy(a[i].p, path); + strcpy(a[i].v, tmp); + } + qsort(a, (size_t)n, sizeof(R), cmp); + printf("574f424a%08x", (unsigned)n); + for (int i = 0; i < n; i++) { + size_t z = !strcmp(a[i].v, "-") + ? 0 + : (a[i].t == 'T' ? strlen(a[i].v) : strlen(a[i].v) / 2); + fputs(a[i].t == 'T' ? "01" : "02", stdout); + printf("%08x", (unsigned)strlen(a[i].p)); + hx(a[i].p); + printf("%016llx", (unsigned long long)z); + if (z) { + if (a[i].t == 'T') + hx(a[i].v); + else + printf("%s", a[i].v); + } + } + putchar('\n'); + return 0; +} diff --git a/problems/014-runtime-bundle-encoding/solutions/cpp/main.cpp b/problems/014-runtime-bundle-encoding/solutions/cpp/main.cpp new file mode 100644 index 0000000..6ef6724 --- /dev/null +++ b/problems/014-runtime-bundle-encoding/solutions/cpp/main.cpp @@ -0,0 +1,40 @@ +#include +#include +#include +#include +#include +using namespace std; +struct R { + char t; + string p, v; +}; +void bytes(const string &s) { + for (unsigned char c : s) + cout << setw(2) << (unsigned)c; +} +int main() { + ios::sync_with_stdio(false); + cin.tie(nullptr); + int n; + if (!(cin >> n)) + return 0; + vector a(n); + for (auto &x : a) + cin >> x.t >> x.p >> x.v; + sort(a.begin(), a.end(), [](auto &x, auto &y) { return x.p < y.p; }); + cout << hex << nouppercase << setfill('0') << "574f424a" << setw(8) + << (unsigned)n; + for (auto &x : a) { + size_t z = x.v == "-" ? 0 : (x.t == 'T' ? x.v.size() : x.v.size() / 2); + cout << (x.t == 'T' ? "01" : "02") << setw(8) << (unsigned)x.p.size(); + bytes(x.p); + cout << setw(16) << (unsigned long long)z; + if (z) { + if (x.t == 'T') + bytes(x.v); + else + cout << x.v; + } + } + cout << '\n'; +} diff --git a/problems/014-runtime-bundle-encoding/solutions/go/main.go b/problems/014-runtime-bundle-encoding/solutions/go/main.go new file mode 100644 index 0000000..257c1a1 --- /dev/null +++ b/problems/014-runtime-bundle-encoding/solutions/go/main.go @@ -0,0 +1,54 @@ +package main + +import ( + "bufio" + "fmt" + "os" + "sort" +) + +type R struct{ t, p, v string } + +func ascii(out *bufio.Writer, s string) { + for i := 0; i < len(s); i++ { + fmt.Fprintf(out, "%02x", s[i]) + } +} +func main() { + in := bufio.NewReader(os.Stdin) + out := bufio.NewWriter(os.Stdout) + defer out.Flush() + var n int + fmt.Fscan(in, &n) + a := make([]R, n) + for i := range a { + fmt.Fscan(in, &a[i].t, &a[i].p, &a[i].v) + } + sort.Slice(a, func(i, j int) bool { return a[i].p < a[j].p }) + fmt.Fprintf(out, "574f424a%08x", n) + for _, x := range a { + z := 0 + if x.v != "-" { + z = len(x.v) + if x.t == "B" { + z /= 2 + } + } + if x.t == "T" { + fmt.Fprint(out, "01") + } else { + fmt.Fprint(out, "02") + } + fmt.Fprintf(out, "%08x", len(x.p)) + ascii(out, x.p) + fmt.Fprintf(out, "%016x", z) + if z > 0 { + if x.t == "T" { + ascii(out, x.v) + } else { + fmt.Fprint(out, x.v) + } + } + } + fmt.Fprintln(out) +} diff --git a/problems/014-runtime-bundle-encoding/solutions/javascript/main.js b/problems/014-runtime-bundle-encoding/solutions/javascript/main.js new file mode 100644 index 0000000..a364257 --- /dev/null +++ b/problems/014-runtime-bundle-encoding/solutions/javascript/main.js @@ -0,0 +1,23 @@ +import * as std from "std"; +const z = std.in.readAsString().trim().split(/\s+/); +let p = 0, n = Number(z[p++]); +/** @type {[string, string, string][]} */ +const a = []; +for (let i = 0; i < n; i++) a.push([z[p++], z[p++], z[p++]]); +a.sort((x, y) => x[1] < y[1] ? -1 : x[1] > y[1] ? 1 : 0); +/** @param {number} x @param {number} w @returns {string} */ +const num = (x, w) => x.toString(16).padStart(w, "0"); +/** @param {string} s @returns {string} */ +const ascii = (s) => Array.from(s, (c) => num(c.charCodeAt(0), 2)).join(""); +const out = ["574f424a", num(n, 8)]; +for (const [t, path, v] of a) { + const len = v === "-" ? 0 : t === "T" ? v.length : v.length / 2; + out.push( + t === "T" ? "01" : "02", + num(path.length, 8), + ascii(path), + num(len, 16), + len === 0 ? "" : t === "T" ? ascii(v) : v, + ); +} +std.out.puts(out.join("") + "\n"); diff --git a/problems/014-runtime-bundle-encoding/solutions/python/main.py b/problems/014-runtime-bundle-encoding/solutions/python/main.py new file mode 100644 index 0000000..801e17b --- /dev/null +++ b/problems/014-runtime-bundle-encoding/solutions/python/main.py @@ -0,0 +1,25 @@ +import sys + +it = iter(sys.stdin.read().split()) +n = int(next(it)) +a = [(next(it), next(it), next(it)) for _ in range(n)] +a.sort(key=lambda x: x[1]) +out = ["574f424a", n.to_bytes(4, "big").hex()] +for t, path, payload in a: + raw = ( + b"" + if payload == "-" + else payload.encode() + if t == "T" + else bytes.fromhex(payload) + ) + out.extend( + ( + "01" if t == "T" else "02", + len(path).to_bytes(4, "big").hex(), + path.encode().hex(), + len(raw).to_bytes(8, "big").hex(), + raw.hex(), + ) + ) +print("".join(out)) diff --git a/problems/014-runtime-bundle-encoding/solutions/rust/main.rs b/problems/014-runtime-bundle-encoding/solutions/rust/main.rs new file mode 100644 index 0000000..17d92b4 --- /dev/null +++ b/problems/014-runtime-bundle-encoding/solutions/rust/main.rs @@ -0,0 +1,45 @@ +use std::fmt::Write; +use std::io::{self, Read}; +fn ascii(out: &mut String, s: &str) { + for b in s.bytes() { + write!(out, "{b:02x}").unwrap(); + } +} +fn main() { + let mut s = String::new(); + io::stdin().read_to_string(&mut s).unwrap(); + let mut it = s.split_whitespace(); + let n: usize = it.next().unwrap().parse().unwrap(); + let mut a: Vec<(u8, &str, &str)> = (0..n) + .map(|_| { + ( + it.next().unwrap().as_bytes()[0], + it.next().unwrap(), + it.next().unwrap(), + ) + }) + .collect(); + a.sort_by_key(|x| x.1); + let mut out = format!("574f424a{n:08x}"); + for (t, p, v) in a { + let z = if v == "-" { + 0 + } else if t == b'T' { + v.len() + } else { + v.len() / 2 + }; + out.push_str(if t == b'T' { "01" } else { "02" }); + write!(out, "{:08x}", p.len()).unwrap(); + ascii(&mut out, p); + write!(out, "{z:016x}").unwrap(); + if z > 0 { + if t == b'T' { + ascii(&mut out, v) + } else { + out.push_str(v) + } + } + } + println!("{out}"); +} diff --git a/problems/014-runtime-bundle-encoding/solutions/typescript/main.ts b/problems/014-runtime-bundle-encoding/solutions/typescript/main.ts new file mode 100644 index 0000000..5e5d053 --- /dev/null +++ b/problems/014-runtime-bundle-encoding/solutions/typescript/main.ts @@ -0,0 +1,21 @@ +import * as std from "std"; +const z: string[] = std.in.readAsString().trim().split(/\s+/); +let p = 0, n = Number(z[p++]); +const a: [string, string, string][] = []; +for (let i = 0; i < n; i++) a.push([z[p++], z[p++], z[p++]]); +a.sort((x, y) => x[1] < y[1] ? -1 : x[1] > y[1] ? 1 : 0); +const num = (x: number, w: number): string => x.toString(16).padStart(w, "0"), + ascii = (s: string): string => + Array.from(s, (c) => num(c.charCodeAt(0), 2)).join(""); +const out: string[] = ["574f424a", num(n, 8)]; +for (const [t, path, v] of a) { + const len = v === "-" ? 0 : t === "T" ? v.length : v.length / 2; + out.push( + t === "T" ? "01" : "02", + num(path.length, 8), + ascii(path), + num(len, 16), + len === 0 ? "" : t === "T" ? ascii(v) : v, + ); +} +std.out.puts(out.join("") + "\n"); diff --git a/problems/014-runtime-bundle-encoding/statement.en.md b/problems/014-runtime-bundle-encoding/statement.en.md new file mode 100644 index 0000000..8ea50bf --- /dev/null +++ b/problems/014-runtime-bundle-encoding/statement.en.md @@ -0,0 +1,90 @@ +# Unambiguous Runtime Bundle + +A WASM OJ needs to deliver text source files and binary resources together to an isolated runtime. If paths and payloads were merely concatenated, different field boundaries could produce the same byte stream. If file-enumeration order were unstable, the same contents could also produce different bundles. For reliable storage, transport, and comparison, we need a unique, prefix-free format. + +Given a collection of text and binary files, first sort them by ASCII lexicographic path order, then output these bytes: + +1. the ASCII magic `WOBJ`; +2. the file count as an unsigned 32-bit big-endian integer; +3. each file in order: a one-byte type tag (`T=01`, `B=02`), the path byte length as u32 big-endian, the ASCII path bytes, the payload byte length as u64 big-endian, and the payload bytes. + +The type tag distinguishes text from binary payloads. The fixed-width length prefix before each variable-length field determines where that field ends. Consequently, different file or field boundaries cannot be confused as the same valid encoding. + +Output the complete runtime bundle produced by this specification. + +## Input + +The first line contains `N`. Each of the next `N` lines contains `type path payloadToken`. + +- For `T`, a nonempty `payloadToken` is used directly as visible ASCII bytes. +- For `B`, a nonempty `payloadToken` is lowercase hexadecimal, with every two characters representing one byte. +- For either type, the single token `-` represents an empty payload. Consequently, this problem cannot represent a text file whose entire content is one `-` byte. + +## Output + +Output one line containing the complete bundle bytes as contiguous lowercase hexadecimal, with no whitespace or `0x` prefix. + +## Constraints + +- `1 ≤ N ≤ 50000` +- Every path is unique and is a canonical relative ASCII path of length `1..100`. +- Path segments contain only lowercase letters, digits, `.`, `_`, and `-`, and are never empty, `.`, or `..`. +- A `T` payload token other than `-` contains ASCII bytes 33 through 126 and has length at most `200000`. +- A `B` payload token other than `-` is a positive even-length string over `[0-9a-f]`. +- The sum `B` of all path bytes and decoded payload bytes is at most `200000`. +- Every length field is guaranteed to fit its specified unsigned integer type. + +The full tests rule out `O(N^2)` sorting. + +## Examples + + + +### Example One + +Input: + +```text +2 +T b x +B a ff00 +``` + +Output: + +```text +574f424a000000020200000001610000000000000002ff00010000000162000000000000000178 +``` + +### Example Two + +Input: + +```text +1 +T empty - +``` + +Output: + +```text +574f424a000000010100000005656d7074790000000000000000 +``` + +### Example Three + +Input: + +```text +2 +T x hi +B y 6869 +``` + +Output: + +```text +574f424a000000020100000001780000000000000002686902000000017900000000000000026869 +``` + + diff --git a/problems/014-runtime-bundle-encoding/statement.zh-TW.md b/problems/014-runtime-bundle-encoding/statement.zh-TW.md new file mode 100644 index 0000000..b176221 --- /dev/null +++ b/problems/014-runtime-bundle-encoding/statement.zh-TW.md @@ -0,0 +1,89 @@ +# 不可混淆的 Runtime Bundle + +WASM OJ 需要把文字原始碼與二進位資源一起交給隔離 runtime。若只串接 path 與 payload,不同的欄位切法可能產生完全相同的 byte stream;若檔案列舉順序不固定,同一組內容也可能得到不同 bundle。為了可靠地儲存、傳輸與比對,我們要定義唯一且 prefix-free 的格式。 + +給定一組文字與二進位檔案,先依 path 的 ASCII 字典序排列,再依下列順序輸出 bytes: + +1. magic ASCII `WOBJ`; +2. 檔案數的 unsigned 32-bit big-endian; +3. 每個檔案依序編碼:一 byte type tag(`T=01`、`B=02`)、path byte 長度的 u32 big-endian、path ASCII bytes、payload byte 長度的 u64 big-endian、payload bytes。 + +type tag 區分文字與二進位 payload;每個可變長欄位前的固定寬度長度前綴則界定其終點。因此,不同檔案或欄位切法不能混淆成同一份有效編碼。 + +請輸出依此規格產生的完整 runtime bundle。 + +## 輸入 + +第一行為 `N`,接著 `N` 行為 `type path payloadToken`。 + +- `T` 的非空 payloadToken 直接視為可見 ASCII bytes。 +- `B` 的非空 payloadToken 是 lowercase hexadecimal,每兩個字元代表一 byte。 +- 兩種 type 都以單一 token `-` 表示空 payload;因此本題不表示內容恰為單一 `-` 的文字檔。 + +## 輸出 + +輸出一行:完整 bundle bytes 的連續 lowercase hexadecimal,不含空白或 `0x`。 + +## 限制 + +- `1 <= N <= 50000`,path 唯一且為長度 1 到 100 的 canonical relative ASCII path。 +- path segment 只含小寫字母、數字、`.`、`_`、`-`,不得為空、`.`、`..`。 +- `T` payloadToken 除 `-` 外由 ASCII 33..126 組成,長度至多 200000。 +- `B` payloadToken 除 `-` 外為長度為正偶數的 `[0-9a-f]` 字串。 +- 所有 path 與解碼後 payload 的 bytes 總和 `B <= 200000`。 +- 長度欄位保證可放入其指定的 unsigned 整數型別。 + +完整測資排除 `O(N^2)` 的排序。 + +## 範例 + + + +### 範例一 + +輸入: + +```text +2 +T b x +B a ff00 +``` + +輸出: + +```text +574f424a000000020200000001610000000000000002ff00010000000162000000000000000178 +``` + +### 範例二 + +輸入: + +```text +1 +T empty - +``` + +輸出: + +```text +574f424a000000010100000005656d7074790000000000000000 +``` + +### 範例三 + +輸入: + +```text +2 +T x hi +B y 6869 +``` + +輸出: + +```text +574f424a000000020100000001780000000000000002686902000000017900000000000000026869 +``` + + diff --git a/problems/014-runtime-bundle-encoding/tests/adversarial-punctuation-order.in b/problems/014-runtime-bundle-encoding/tests/adversarial-punctuation-order.in new file mode 100644 index 0000000..21e10fc --- /dev/null +++ b/problems/014-runtime-bundle-encoding/tests/adversarial-punctuation-order.in @@ -0,0 +1,5 @@ +4 +T a/b ~ +B a- 00ff +T a. !# +B a_ - diff --git a/problems/014-runtime-bundle-encoding/tests/adversarial-punctuation-order.out b/problems/014-runtime-bundle-encoding/tests/adversarial-punctuation-order.out new file mode 100644 index 0000000..2131d47 --- /dev/null +++ b/problems/014-runtime-bundle-encoding/tests/adversarial-punctuation-order.out @@ -0,0 +1 @@ +574f424a000000040200000002612d000000000000000200ff0100000002612e000000000000000221230100000003612f6200000000000000017e0200000002615f0000000000000000 diff --git a/problems/014-runtime-bundle-encoding/tests/sample-01.in b/problems/014-runtime-bundle-encoding/tests/sample-01.in new file mode 100644 index 0000000..92b8a9b --- /dev/null +++ b/problems/014-runtime-bundle-encoding/tests/sample-01.in @@ -0,0 +1,3 @@ +2 +T b x +B a ff00 diff --git a/problems/014-runtime-bundle-encoding/tests/sample-01.out b/problems/014-runtime-bundle-encoding/tests/sample-01.out new file mode 100644 index 0000000..b9b4b2c --- /dev/null +++ b/problems/014-runtime-bundle-encoding/tests/sample-01.out @@ -0,0 +1 @@ +574f424a000000020200000001610000000000000002ff00010000000162000000000000000178 diff --git a/problems/014-runtime-bundle-encoding/tests/sample-02.in b/problems/014-runtime-bundle-encoding/tests/sample-02.in new file mode 100644 index 0000000..25c4f6f --- /dev/null +++ b/problems/014-runtime-bundle-encoding/tests/sample-02.in @@ -0,0 +1,2 @@ +1 +T empty - diff --git a/problems/014-runtime-bundle-encoding/tests/sample-02.out b/problems/014-runtime-bundle-encoding/tests/sample-02.out new file mode 100644 index 0000000..d67f114 --- /dev/null +++ b/problems/014-runtime-bundle-encoding/tests/sample-02.out @@ -0,0 +1 @@ +574f424a000000010100000005656d7074790000000000000000 diff --git a/problems/014-runtime-bundle-encoding/tests/sample-03.in b/problems/014-runtime-bundle-encoding/tests/sample-03.in new file mode 100644 index 0000000..0f9c635 --- /dev/null +++ b/problems/014-runtime-bundle-encoding/tests/sample-03.in @@ -0,0 +1,3 @@ +2 +T x hi +B y 6869 diff --git a/problems/014-runtime-bundle-encoding/tests/sample-03.out b/problems/014-runtime-bundle-encoding/tests/sample-03.out new file mode 100644 index 0000000..9c1428d --- /dev/null +++ b/problems/014-runtime-bundle-encoding/tests/sample-03.out @@ -0,0 +1 @@ +574f424a000000020100000001780000000000000002686902000000017900000000000000026869 diff --git a/problems/014-runtime-bundle-encoding/validator.py b/problems/014-runtime-bundle-encoding/validator.py new file mode 100644 index 0000000..e9d538d --- /dev/null +++ b/problems/014-runtime-bundle-encoding/validator.py @@ -0,0 +1,43 @@ +import re, sys + + +def path_ok(p): + return ( + len(p) <= 100 + and not p.startswith("/") + and not p.endswith("/") + and all( + x not in ("", ".", "..") and re.fullmatch(r"[a-z0-9._-]+", x) + for x in p.split("/") + ) + ) + + +def main(): + ls = sys.stdin.read().splitlines() + assert ls and re.fullmatch(r"[1-9][0-9]*", ls[0]) + n = int(ls[0]) + assert n <= 50000 and len(ls) == n + 1 + seen = set() + total = 0 + for line in ls[1:]: + x = line.split() + assert len(x) == 3 and x[0] in ("T", "B") and path_ok(x[1]) and x[1] not in seen + seen.add(x[1]) + p = x[2] + if x[0] == "T": + assert p == "-" or ( + len(p) <= 200000 and all(33 <= ord(c) <= 126 for c in p) and p != "-" + ) + else: + assert p == "-" or ( + len(p) % 2 == 0 and len(p) > 0 and re.fullmatch(r"[0-9a-f]+", p) + ) + total += len(x[1]) + (0 if p == "-" else len(p) if x[0] == "T" else len(p) // 2) + assert total <= 200000 + + +try: + main() +except (AssertionError, ValueError): + sys.exit(1) diff --git a/problems/015-dirty-build-nodes/editorial.en.md b/problems/015-dirty-build-nodes/editorial.en.md new file mode 100644 index 0000000..f5777d1 --- /dev/null +++ b/problems/015-dirty-build-nodes/editorial.en.md @@ -0,0 +1,24 @@ +# Editorial + +## Intuitive Approach + +Run a separate DFS from every changed node and union the results. If `visited` is reset for every source, this takes `O(C(N+M))` in the worst case because shared downstream regions are traversed repeatedly. + +## Optimal Approach: Multi-Source Reachability + +Build the adjacency list in the direction given by the statement. Mark all changed nodes and insert them into one queue. Whenever a node `u` is removed, mark and enqueue each neighbor `v` that is not dirty yet. Finally scan the Boolean array by ID to produce sorted output. This is multi-source BFS; DFS with one shared visited array has the same complexity. + +## Correctness Proof + +Every changed node is initially marked dirty, matching reachability by a path of zero edges. Whenever the search traverses an edge from dirty `u` to `v`, node `v` directly depends on a dirty artifact and is therefore correctly marked. Conversely, for every node `x` that should be dirty, some changed node has a path to `x`. Induction on path length shows that when each predecessor is processed, the next node is marked, so `x` is eventually marked. Thus the marked set is exactly the union of all downstream reachable nodes. Scanning by ID changes only output order, not the set. + +## Complexity + +Every node enters the queue at most once and every edge is examined at most once. Time is `O(N+M)` and space is `O(N+M)`. + +## Common Mistakes + +- Reversing edges and finding dependencies instead of users. +- Forgetting that a changed node itself is dirty. +- Resetting `visited` for every source and losing the benefit of multi-source search. +- Omitting the second newline when `C=0`. diff --git a/problems/015-dirty-build-nodes/editorial.zh-TW.md b/problems/015-dirty-build-nodes/editorial.zh-TW.md new file mode 100644 index 0000000..9bf0dd9 --- /dev/null +++ b/problems/015-dirty-build-nodes/editorial.zh-TW.md @@ -0,0 +1,24 @@ +# 解題說明 + +## 直覺解 + +從每個 changed node 各自做一次 DFS,最後聯集結果。若每次都清空 visited,最壞時間 `O(C(N+M))`,大量共同下游會被反覆走訪。 + +## 最佳解 + +建立題目給定方向的 adjacency list。把所有 changed nodes 一起標記並放進同一個 queue;每次取出 `u`,只把尚未 dirty 的 `v` 標記並入列。最後依 ID 掃描 boolean array 即可得到排序輸出。這是 multi-source BFS;DFS 使用共享 visited 也有相同複雜度。 + +## 正確性證明 + +所有 changed nodes 初始化為 dirty,符合零條邊的可達性。每次從 dirty `u` 沿邊到 `v`,代表 `v` 直接依賴 dirty 產物,所以標記 `v` 正確。反之,任一應 dirty 節點 `x` 都存在某 changed node 到 `x` 的路徑;沿路徑長度歸納,前一節點出列時必會標記下一節點,故 `x` 最終必被標記。因此標記集合恰等於所有下游可達點,遞增掃描只改變輸出順序,不改變集合。 + +## 複雜度 + +每個節點最多入列一次、每條邊最多掃描一次,時間 `O(N+M)`,空間 `O(N+M)`。 + +## 常見錯誤 + +- 把邊反轉,找到依賴項而非使用者。 +- 忘記 changed node 自己也是 dirty。 +- 每個來源重設 visited,失去多源搜尋的效益。 +- `C=0` 時少印第二個換行。 diff --git a/problems/015-dirty-build-nodes/generator.py b/problems/015-dirty-build-nodes/generator.py new file mode 100644 index 0000000..7bf02d0 --- /dev/null +++ b/problems/015-dirty-build-nodes/generator.py @@ -0,0 +1,15 @@ +import random, sys + +seed, index = map(int, sys.argv[1:]) +r = random.Random(seed * 97 + index) +n = 8 + index % 13 +all_edges = [ + (i, j) for i in range(1, n + 1) for j in range(i + 1, n + 1) if r.random() < 0.14 +] +m = len(all_edges) +c = r.randrange(min(5, n) + 1) +changed = r.sample(range(1, n + 1), c) +print(n, m, c) +for e in all_edges: + print(*e) +print(*changed) diff --git a/problems/015-dirty-build-nodes/oracle.py b/problems/015-dirty-build-nodes/oracle.py new file mode 100644 index 0000000..2fd14a3 --- /dev/null +++ b/problems/015-dirty-build-nodes/oracle.py @@ -0,0 +1,23 @@ +import sys + +a = list(map(int, sys.stdin.read().split())) +n, m, c = a[:3] +g = [[] for _ in range(n)] +p = 3 +for _ in range(m): + u, v = a[p] - 1, a[p + 1] - 1 + p += 2 + g[u].append(v) +ans = set() +for s in a[p : p + c]: + st = [s - 1] + seen = {s - 1} + while st: + u = st.pop() + for v in g[u]: + if v not in seen: + seen.add(v) + st.append(v) + ans |= seen +print(len(ans)) +print(" ".join(str(x + 1) for x in sorted(ans))) diff --git a/problems/015-dirty-build-nodes/problem.json b/problems/015-dirty-build-nodes/problem.json new file mode 100644 index 0000000..868cfab --- /dev/null +++ b/problems/015-dirty-build-nodes/problem.json @@ -0,0 +1,147 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 15, + "slug": "dirty-build-nodes", + "title": { + "zh-TW": "標頭改了,誰必須重編?", + "en": "A Header Changed: What Must Be Rebuilt?" + }, + "difficulty": "medium", + "tags": [ + "graph", + "dag", + "bfs", + "reachability" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-nonnumeric-dag", + "kind": "adversarial", + "input": "tests/adversarial-nonnumeric-dag.in", + "output": "tests/adversarial-nonnumeric-dag.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 7500000, + "memoryLimitBytes": 536870912 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 1500000, + "memoryLimitBytes": 402653184 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 600000, + "memoryLimitBytes": 268435456 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "每個變更各做一次搜尋", + "en": "One Search per Changed Node" + }, + "time": "O(C(N+M))", + "space": "O(N)", + "accepted": false + }, + { + "name": { + "zh-TW": "多源反向失效傳播", + "en": "Multi-Source Downstream Invalidation" + }, + "time": "O(N+M)", + "space": "O(N+M)", + "accepted": true + } + ] +} diff --git a/problems/015-dirty-build-nodes/solutions/c/main.c b/problems/015-dirty-build-nodes/solutions/c/main.c new file mode 100644 index 0000000..ef73531 --- /dev/null +++ b/problems/015-dirty-build-nodes/solutions/c/main.c @@ -0,0 +1,53 @@ +#include +#include +int main(void) { + int n, m, c; + if (scanf("%d%d%d", &n, &m, &c) != 3) + return 0; + int *head = malloc(sizeof(int) * (size_t)n), + *to = malloc(sizeof(int) * (size_t)(m ? m : 1)), + *next = malloc(sizeof(int) * (size_t)(m ? m : 1)); + for (int i = 0; i < n; i++) + head[i] = -1; + for (int i = 0; i < m; i++) { + int u; + scanf("%d%d", &u, &to[i]); + u--; + to[i]--; + next[i] = head[u]; + head[u] = i; + } + unsigned char *d = calloc((size_t)n, 1); + int *q = malloc(sizeof(int) * (size_t)n), l = 0, r = 0; + for (int i = 0; i < c; i++) { + int x; + scanf("%d", &x); + x--; + if (!d[x]) { + d[x] = 1; + q[r++] = x; + } + } + while (l < r) { + int u = q[l++]; + for (int e = head[u]; e >= 0; e = next[e]) + if (!d[to[e]]) { + d[to[e]] = 1; + q[r++] = to[e]; + } + } + int k = 0; + for (int i = 0; i < n; i++) + k += d[i] != 0; + printf("%d\n", k); + int first = 1; + for (int i = 0; i < n; i++) + if (d[i]) { + if (!first) + putchar(' '); + printf("%d", i + 1); + first = 0; + } + putchar('\n'); + return 0; +} diff --git a/problems/015-dirty-build-nodes/solutions/cpp/main.cpp b/problems/015-dirty-build-nodes/solutions/cpp/main.cpp new file mode 100644 index 0000000..0167f78 --- /dev/null +++ b/problems/015-dirty-build-nodes/solutions/cpp/main.cpp @@ -0,0 +1,45 @@ +#include +#include +#include +using namespace std; +int main() { + ios::sync_with_stdio(false); + cin.tie(nullptr); + int n, m, c; + if (!(cin >> n >> m >> c)) + return 0; + vector> g(n); + while (m--) { + int u, v; + cin >> u >> v; + g[u - 1].push_back(v - 1); + } + vector d(n); + deque q; + while (c--) { + int x; + cin >> x; + if (!d[--x]) + d[x] = 1, q.push_back(x); + } + while (!q.empty()) { + int u = q.front(); + q.pop_front(); + for (int v : g[u]) + if (!d[v]) + d[v] = 1, q.push_back(v); + } + int k = 0; + for (char x : d) + k += x; + cout << k << '\n'; + bool first = true; + for (int i = 0; i < n; i++) + if (d[i]) { + if (!first) + cout << ' '; + cout << i + 1; + first = false; + } + cout << '\n'; +} diff --git a/problems/015-dirty-build-nodes/solutions/go/main.go b/problems/015-dirty-build-nodes/solutions/go/main.go new file mode 100644 index 0000000..5b9ea19 --- /dev/null +++ b/problems/015-dirty-build-nodes/solutions/go/main.go @@ -0,0 +1,50 @@ +package main + +import ( + "bufio" + "fmt" + "os" + "strconv" + "strings" +) + +func main() { + in := bufio.NewReader(os.Stdin) + var n, m, c int + fmt.Fscan(in, &n, &m, &c) + g := make([][]int, n) + for ; m > 0; m-- { + var u, v int + fmt.Fscan(in, &u, &v) + g[u-1] = append(g[u-1], v-1) + } + d := make([]bool, n) + q := make([]int, 0, n) + for ; c > 0; c-- { + var x int + fmt.Fscan(in, &x) + x-- + if !d[x] { + d[x] = true + q = append(q, x) + } + } + for p := 0; p < len(q); p++ { + for _, v := range g[q[p]] { + if !d[v] { + d[v] = true + q = append(q, v) + } + } + } + ans := []string{} + for i, x := range d { + if x { + ans = append(ans, strconv.Itoa(i+1)) + } + } + out := bufio.NewWriter(os.Stdout) + defer out.Flush() + fmt.Fprintln(out, len(ans)) + fmt.Fprintln(out, strings.Join(ans, " ")) +} diff --git a/problems/015-dirty-build-nodes/solutions/javascript/main.js b/problems/015-dirty-build-nodes/solutions/javascript/main.js new file mode 100644 index 0000000..b0b0405 --- /dev/null +++ b/problems/015-dirty-build-nodes/solutions/javascript/main.js @@ -0,0 +1,34 @@ +import * as std from "std"; +const a = std.in.readAsString().trim().split(/\s+/).map(Number); +let p = 0, + n = a[p++], + m = a[p++], + c = a[p++]; +/** @type {number[][]} */ +const g = Array.from({ length: n }, () => []); +while (m--) { + const u = a[p++] - 1, v = a[p++] - 1; + g[u].push(v); +} +const d = new Uint8Array(n); +/** @type {number[]} */ +const q = []; +while (c--) { + const x = a[p++] - 1; + if (!d[x]) { + d[x] = 1; + q.push(x); + } +} +for (let h = 0; h < q.length; h++) { + for (const v of g[q[h]]) { + if (!d[v]) { + d[v] = 1; + q.push(v); + } + } +} +/** @type {number[]} */ +const ids = []; +for (let i = 0; i < n; i++) if (d[i]) ids.push(i + 1); +std.out.puts(`${ids.length}\n${ids.join(" ")}\n`); diff --git a/problems/015-dirty-build-nodes/solutions/python/main.py b/problems/015-dirty-build-nodes/solutions/python/main.py new file mode 100644 index 0000000..c1a25dd --- /dev/null +++ b/problems/015-dirty-build-nodes/solutions/python/main.py @@ -0,0 +1,24 @@ +import sys, collections + +a = list(map(int, sys.stdin.read().split())) +n, m, c = a[:3] +g = [[] for _ in range(n)] +p = 3 +for _ in range(m): + u, v = a[p] - 1, a[p + 1] - 1 + p += 2 + g[u].append(v) +dirty = [False] * n +q = collections.deque() +for x in a[p : p + c]: + dirty[x - 1] = True + q.append(x - 1) +while q: + u = q.popleft() + for v in g[u]: + if not dirty[v]: + dirty[v] = True + q.append(v) +ids = [str(i + 1) for i, x in enumerate(dirty) if x] +print(len(ids)) +print(" ".join(ids)) diff --git a/problems/015-dirty-build-nodes/solutions/rust/main.rs b/problems/015-dirty-build-nodes/solutions/rust/main.rs new file mode 100644 index 0000000..6a62344 --- /dev/null +++ b/problems/015-dirty-build-nodes/solutions/rust/main.rs @@ -0,0 +1,41 @@ +use std::collections::VecDeque; +use std::io::{self, Read}; +fn main() { + let mut s = String::new(); + io::stdin().read_to_string(&mut s).unwrap(); + let mut it = s.split_whitespace(); + let n: usize = it.next().unwrap().parse().unwrap(); + let m: usize = it.next().unwrap().parse().unwrap(); + let c: usize = it.next().unwrap().parse().unwrap(); + let mut g = vec![vec![]; n]; + for _ in 0..m { + let u: usize = it.next().unwrap().parse::().unwrap() - 1; + let v: usize = it.next().unwrap().parse::().unwrap() - 1; + g[u].push(v); + } + let mut d = vec![false; n]; + let mut q = VecDeque::new(); + for _ in 0..c { + let x = it.next().unwrap().parse::().unwrap() - 1; + if !d[x] { + d[x] = true; + q.push_back(x) + } + } + while let Some(u) = q.pop_front() { + for &v in &g[u] { + if !d[v] { + d[v] = true; + q.push_back(v) + } + } + } + println!("{}", d.iter().filter(|&&x| x).count()); + let ans = d + .iter() + .enumerate() + .filter(|x| *x.1) + .map(|x| (x.0 + 1).to_string()) + .collect::>(); + println!("{}", ans.join(" ")); +} diff --git a/problems/015-dirty-build-nodes/solutions/typescript/main.ts b/problems/015-dirty-build-nodes/solutions/typescript/main.ts new file mode 100644 index 0000000..d6c00c9 --- /dev/null +++ b/problems/015-dirty-build-nodes/solutions/typescript/main.ts @@ -0,0 +1,27 @@ +import * as std from "std"; +const a: number[] = std.in.readAsString().trim().split(/\s+/).map(Number); +let p = 0, n = a[p++], m = a[p++], c = a[p++]; +const g: number[][] = Array.from({ length: n }, () => []); +while (m--) { + const u = a[p++] - 1, v = a[p++] - 1; + g[u].push(v); +} +const d: Uint8Array = new Uint8Array(n), q: number[] = []; +while (c--) { + const x = a[p++] - 1; + if (!d[x]) { + d[x] = 1; + q.push(x); + } +} +for (let h = 0; h < q.length; h++) { + for (const v of g[q[h]]) { + if (!d[v]) { + d[v] = 1; + q.push(v); + } + } +} +const ids: number[] = []; +for (let i = 0; i < n; i++) if (d[i]) ids.push(i + 1); +std.out.puts(`${ids.length}\n${ids.join(" ")}\n`); diff --git a/problems/015-dirty-build-nodes/statement.en.md b/problems/015-dirty-build-nodes/statement.en.md new file mode 100644 index 0000000..cc0b1f7 --- /dev/null +++ b/problems/015-dirty-build-nodes/statement.en.md @@ -0,0 +1,88 @@ +# A Header Changed: What Must Be Rebuilt? + +A WASM OJ build cache avoids rebuilding every intermediate artifact for each submission, but only if it never reuses a stale result. When a shared header, generated file, or other build node changes, every artifact that depends on it must be invalidated. Nodes unrelated to the change should remain available in the cache. + +We represent these relationships as a build graph. The graph is a DAG, and an edge `u v` means that node `v`'s artifact directly depends on node `u`. When a node changes, that node becomes dirty, as does every node that depends on it directly or indirectly. + +One file update may change several nodes at once. Given every node changed in the same batch, output all nodes that must be considered dirty. + +## Input + +The first line contains `N M C`. The next `M` lines each contain `u v`. The final line contains `C` distinct changed-node IDs; when `C=0`, the final line is empty. Node IDs are 1-based. Edges already point from dependencies to their users and must not be reversed. + +## Output + +On the first line, output the number `K` of dirty nodes. On the second line, output every dirty ID in strictly increasing order, separated by single spaces. When `K=0`, the second line must still exist and be empty. + +## Constraints + +- `1 ≤ N ≤ 200000` +- `0 ≤ M ≤ 400000` +- `0 ≤ C ≤ N` +- The input graph is a DAG with no self-loops or duplicate edges. +- Changed IDs are distinct. + +The full constraints rule out running a complete DFS or BFS separately for every changed node. + +## Examples + + + +### Example One + +Input: + +```text +6 5 2 +1 3 +2 4 +3 5 +4 5 +5 6 +1 2 +``` + +Output: + +```text +6 +1 2 3 4 5 6 +``` + +### Example Two + +Input: + +```text +4 2 1 +1 2 +1 3 +4 +``` + +Output: + +```text +1 +4 +``` + +### Example Three + +Input: + +```text +3 2 0 +1 2 +2 3 + +``` + +Output: + +```text +0 + +``` + + diff --git a/problems/015-dirty-build-nodes/statement.zh-TW.md b/problems/015-dirty-build-nodes/statement.zh-TW.md new file mode 100644 index 0000000..5d9955e --- /dev/null +++ b/problems/015-dirty-build-nodes/statement.zh-TW.md @@ -0,0 +1,84 @@ +# 標頭改了,誰必須重編? + +WASM OJ 的編譯快取可以避免每次提交都重建所有中間產物,但前提是不能沿用已經過期的結果。當共用標頭、產生器輸出或其他建置節點改變時,任何依賴它的產物都必須失效;與修改無關的節點則應繼續留在快取中。 + +我們把這些關係表示成一張 build graph。圖是一張 DAG,邊 `u v` 表示節點 `v` 的產物直接依賴節點 `u`。因此,一個節點被修改後,它自己會變成 dirty,所有直接或間接依賴它的節點也都會變成 dirty。 + +一次檔案更新可能同時修改多個節點。給定同一批次中所有被修改的節點,請輸出這次必須視為 dirty 的全部節點。 + +## 輸入 + +第一行 `N M C`。接著 `M` 行各為 `u v`。最後一行含 `C` 個互異的 changed node ID;若 `C=0`,最後一行為空行。節點使用 1-based ID。邊的方向已是「依賴項到使用者」,不需要反轉。 + +## 輸出 + +第一行輸出 dirty 節點數 `K`;第二行輸出所有 dirty ID,嚴格遞增並以單一空白分隔。`K=0` 時第二行仍存在但為空行。 + +## 限制 + +- `1 <= N <= 200000`,`0 <= M <= 400000`,`0 <= C <= N`。 +- 輸入圖是 DAG,沒有 self-loop 或重複邊;changed ID 互異。 +- 完整限制排除為每個 changed node 重做完整 DFS/BFS 的方法。 + +## 範例 + + + +### 範例一 + +輸入: + +```text +6 5 2 +1 3 +2 4 +3 5 +4 5 +5 6 +1 2 +``` + +輸出: + +```text +6 +1 2 3 4 5 6 +``` + +### 範例二 + +輸入: + +```text +4 2 1 +1 2 +1 3 +4 +``` + +輸出: + +```text +1 +4 +``` + +### 範例三 + +輸入: + +```text +3 2 0 +1 2 +2 3 + +``` + +輸出: + +```text +0 + +``` + + diff --git a/problems/015-dirty-build-nodes/tests/adversarial-nonnumeric-dag.in b/problems/015-dirty-build-nodes/tests/adversarial-nonnumeric-dag.in new file mode 100644 index 0000000..f8b8baf --- /dev/null +++ b/problems/015-dirty-build-nodes/tests/adversarial-nonnumeric-dag.in @@ -0,0 +1,11 @@ +10 9 2 +7 2 +2 9 +7 5 +5 9 +1 8 +8 3 +9 4 +3 4 +4 6 +7 1 diff --git a/problems/015-dirty-build-nodes/tests/adversarial-nonnumeric-dag.out b/problems/015-dirty-build-nodes/tests/adversarial-nonnumeric-dag.out new file mode 100644 index 0000000..b1bbd6a --- /dev/null +++ b/problems/015-dirty-build-nodes/tests/adversarial-nonnumeric-dag.out @@ -0,0 +1,2 @@ +9 +1 2 3 4 5 6 7 8 9 diff --git a/problems/015-dirty-build-nodes/tests/sample-01.in b/problems/015-dirty-build-nodes/tests/sample-01.in new file mode 100644 index 0000000..e2e96fe --- /dev/null +++ b/problems/015-dirty-build-nodes/tests/sample-01.in @@ -0,0 +1,7 @@ +6 5 2 +1 3 +2 4 +3 5 +4 5 +5 6 +1 2 diff --git a/problems/015-dirty-build-nodes/tests/sample-01.out b/problems/015-dirty-build-nodes/tests/sample-01.out new file mode 100644 index 0000000..5ee886e --- /dev/null +++ b/problems/015-dirty-build-nodes/tests/sample-01.out @@ -0,0 +1,2 @@ +6 +1 2 3 4 5 6 diff --git a/problems/015-dirty-build-nodes/tests/sample-02.in b/problems/015-dirty-build-nodes/tests/sample-02.in new file mode 100644 index 0000000..d0928fe --- /dev/null +++ b/problems/015-dirty-build-nodes/tests/sample-02.in @@ -0,0 +1,4 @@ +4 2 1 +1 2 +1 3 +4 diff --git a/problems/015-dirty-build-nodes/tests/sample-02.out b/problems/015-dirty-build-nodes/tests/sample-02.out new file mode 100644 index 0000000..2f1b638 --- /dev/null +++ b/problems/015-dirty-build-nodes/tests/sample-02.out @@ -0,0 +1,2 @@ +1 +4 diff --git a/problems/015-dirty-build-nodes/tests/sample-03.in b/problems/015-dirty-build-nodes/tests/sample-03.in new file mode 100644 index 0000000..fbf2bc1 --- /dev/null +++ b/problems/015-dirty-build-nodes/tests/sample-03.in @@ -0,0 +1,4 @@ +3 2 0 +1 2 +2 3 + diff --git a/problems/015-dirty-build-nodes/tests/sample-03.out b/problems/015-dirty-build-nodes/tests/sample-03.out new file mode 100644 index 0000000..77ac542 --- /dev/null +++ b/problems/015-dirty-build-nodes/tests/sample-03.out @@ -0,0 +1,2 @@ +0 + diff --git a/problems/015-dirty-build-nodes/validator.py b/problems/015-dirty-build-nodes/validator.py new file mode 100644 index 0000000..496ae9a --- /dev/null +++ b/problems/015-dirty-build-nodes/validator.py @@ -0,0 +1,42 @@ +import sys + + +def main(): + tok = sys.stdin.read().split() + assert len(tok) >= 3 + n, m, c = map(int, tok[:3]) + assert ( + 1 <= n <= 200000 + and 0 <= m <= 400000 + and 0 <= c <= n + and len(tok) == 3 + 2 * m + c + ) + edges = [] + seen = set() + p = 3 + for _ in range(m): + u, v = map(int, tok[p : p + 2]) + p += 2 + assert 1 <= u <= n and 1 <= v <= n and u != v and (u, v) not in seen + seen.add((u, v)) + edges.append((u, v)) + changed = list(map(int, tok[p:])) + assert len(changed) == len(set(changed)) and all(1 <= x <= n for x in changed) + indeg = [0] * n + g = [[] for _ in range(n)] + for u, v in edges: + g[u - 1].append(v - 1) + indeg[v - 1] += 1 + q = [i for i, x in enumerate(indeg) if x == 0] + for u in q: + for v in g[u]: + indeg[v] -= 1 + if indeg[v] == 0: + q.append(v) + assert len(q) == n + + +try: + main() +except (AssertionError, ValueError): + sys.exit(1) diff --git a/problems/016-exact-dependency-cache/editorial.en.md b/problems/016-exact-dependency-cache/editorial.en.md new file mode 100644 index 0000000..21a3f03 --- /dev/null +++ b/problems/016-exact-dependency-cache/editorial.en.md @@ -0,0 +1,27 @@ +# Editorial + +## Intuitive Approach + +For each round, scan every dependency of every TU and test membership in the changed set, taking `O(QM)` time. Reverse adjacency lists are better, but repeatedly changing the same high-degree header still performs `O(N)` scalar marking operations per round. + +## Optimal Approach: Header-to-TU Bitsets + +Build one length-`N` bitset per header. Bit `s` is set exactly when TU `s` depends on that header. For one round, OR together the bitsets of all changed headers, then popcount the result. Begin every round with a fresh all-zero accumulator, matching the clean baseline after rebuilding. + +In Python, build each row with a mutable `bytearray` and convert it once to an arbitrary-precision integer. Repeatedly performing `mask |= 1 << s` on an immutable large integer may copy the entire bitset for every edge, degrading construction to `O(M ceil(N/w))`. Other languages can use arrays of 32- or 64-bit words. These are implementations of the same word-parallel algorithm. + +## Correctness Proof + +Bit `s` of header `h`'s bitset is one if and only if dependency `(s,h)` appears in the input. A bit is one in the OR if and only if it is one in at least one changed header's bitset, which holds exactly when TU `s` read at least one header changed this round. That is precisely the cache-miss definition. Popcount returns the size of this set. Independent accumulators prevent changes from an earlier round from leaking into the next, so every output is correct. + +## Complexity + +Let `w` be the machine-word width, `R=ceil(N/w)`, and `K` the total number of changed headers over all queries. Allocating and clearing the `H` bitset rows costs `O(HR)`, setting edges costs `O(M)`, and query ORs, accumulator clears, and popcounts total `O((K+Q)R)`. Total time is `O(HR+M+(K+Q)R)`, with `O(HR)` auxiliary bitset space. The Rust, Python, JavaScript, and TypeScript references retain complete input and buffered output, adding `O(M+Q+K)` resident I/O space; when `N=H=1`, this term is not absorbed by `O(HR)`. + +## Common Mistakes + +- Adding popcounts of individual bitsets without ORing first, double-counting TUs. +- Reusing the previous round's accumulator. +- Forgetting `>>> 0` when counting signed 32-bit JavaScript words. +- Allocating `N*H` bytes rather than bits, using eight times the necessary space. +- Building immutable big integers one edge at a time and overlooking full-row copies. diff --git a/problems/016-exact-dependency-cache/editorial.zh-TW.md b/problems/016-exact-dependency-cache/editorial.zh-TW.md new file mode 100644 index 0000000..7dd8a52 --- /dev/null +++ b/problems/016-exact-dependency-cache/editorial.zh-TW.md @@ -0,0 +1,27 @@ +# 解題說明 + +## 直覺解 + +每輪對每個 TU 掃描其所有依賴,檢查是否在 changed set,時間 `O(QM)`。改用 header 的反向 adjacency list,逐 changed header 標記 TU,雖較好,若同一個高 degree header 在很多輪出現仍會反覆做 `O(N)` 個 scalar 操作。 + +## 最佳解 + +為每個 header 建立長度 `N` 的 bitset,第 `s` bit 表示 TU `s` 依賴它。處理一輪時,把所有 changed header 的 bitset 做 OR,最後 popcount。每輪使用新的全零 accumulator,對應「重編完成後回到乾淨 baseline」。 + +在 Python 可先用 mutable `bytearray` 逐邊設 bit,再一次轉成任意精度整數;若直接對 immutable 大整數逐邊做 `mask |= 1 << s`,每次都可能複製整個 bitset,使建表退化為 `O(M ceil(N/w))`。其他語言以 32/64-bit word 陣列實作。這些只是同一個 word-parallel 演算法。 + +## 正確性證明 + +header `h` 的 bitset 第 `s` bit 為 1,若且唯若輸入含依賴 `(s,h)`。OR 的某一 bit 為 1,若且唯若至少一個 changed header 的對應 bit 為 1,亦即 TU `s` 讀過至少一個本輪 changed header;這正是 cache miss 定義。popcount 計算集合元素數,因此每輪輸出正確。輪與輪使用獨立 accumulator,不會錯把上一輪修改帶入下一輪。 + +## 複雜度 + +令 `w` 為 machine word bits、`R=ceil(N/w)`、所有 query 的 changed header 總數為 `K`。配置並清零 `H` 列 bitset 需 `O(HR)`,逐邊設 bit 需 `O(M)`;query OR、清零 accumulator 與 popcount 總時間 `O((K+Q)R)`。總時間為 `O(HR+M+(K+Q)R)`,演算法的 auxiliary bitset 空間為 `O(HR)`。目前 Rust、Python、JavaScript、TypeScript reference 會保留完整輸入並緩衝輸出,因此實際 resident space 另含 `O(M+Q+K)` buffered I/O;這在 `N=H=1` 時不能被 `O(HR)` 吸收。 + +## 常見錯誤 + +- 對各 bitset 的 popcount 相加,沒有先 OR 去除重複 TU。 +- 沿用上一輪 accumulator。 +- JS 用 signed 32-bit 值計數時忘記 `>>> 0`。 +- 配置 `N*H` bytes 而非 bits,造成不必要的八倍空間。 +- 在 immutable big integer 上逐邊 OR,漏算每次複製整列 bitset 的成本。 diff --git a/problems/016-exact-dependency-cache/generator.py b/problems/016-exact-dependency-cache/generator.py new file mode 100644 index 0000000..7830541 --- /dev/null +++ b/problems/016-exact-dependency-cache/generator.py @@ -0,0 +1,14 @@ +import random, sys + +seed, index = map(int, sys.argv[1:]) +r = random.Random(seed * 65537 + index) +n = 10 + index % 15 +h = 8 + index % 12 +edges = [(s, x) for s in range(1, n + 1) for x in range(1, h + 1) if r.random() < 0.22] +q = 5 + index % 7 +print(n, h, len(edges), q) +for e in edges: + print(*e) +for _ in range(q): + k = r.randrange(min(5, h) + 1) + print(k, *r.sample(range(1, h + 1), k)) diff --git a/problems/016-exact-dependency-cache/oracle.py b/problems/016-exact-dependency-cache/oracle.py new file mode 100644 index 0000000..2ed9ecf --- /dev/null +++ b/problems/016-exact-dependency-cache/oracle.py @@ -0,0 +1,18 @@ +import sys + +a = list(map(int, sys.stdin.read().split())) +n, h, m, q = a[:4] +rev = [set() for _ in range(h)] +p = 4 +for _ in range(m): + s, x = a[p] - 1, a[p + 1] - 1 + p += 2 + rev[x].add(s) +for _ in range(q): + k = a[p] + p += 1 + hit = set() + for x in a[p : p + k]: + hit |= rev[x - 1] + p += k + print(len(hit)) diff --git a/problems/016-exact-dependency-cache/problem.json b/problems/016-exact-dependency-cache/problem.json new file mode 100644 index 0000000..739fbc2 --- /dev/null +++ b/problems/016-exact-dependency-cache/problem.json @@ -0,0 +1,156 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 16, + "slug": "exact-dependency-cache", + "title": { + "zh-TW": "精確依賴快取", + "en": "Exact Dependency Cache" + }, + "difficulty": "hard", + "tags": [ + "bitset", + "cache", + "set-union", + "offline-queries" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-word-boundary", + "kind": "adversarial", + "input": "tests/adversarial-word-boundary.in", + "output": "tests/adversarial-word-boundary.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 15000000, + "memoryLimitBytes": 536870912 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 5000000, + "memoryLimitBytes": 402653184 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 2500000, + "memoryLimitBytes": 268435456 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "每輪掃描所有依賴", + "en": "Scan All Dependencies per Round" + }, + "time": "O(QM)", + "space": "O(M)", + "accepted": false + }, + { + "name": { + "zh-TW": "反向表逐點聯集", + "en": "Scalar Union through Reverse Lists" + }, + "time": "O(sum_q sum_{h in q} deg(h))", + "space": "O(N+M)", + "accepted": false + }, + { + "name": { + "zh-TW": "header-to-TU bitset", + "en": "Header-to-TU Bitsets" + }, + "time": "O(H ceil(N/w) + M + (Q+K) ceil(N/w))", + "space": "O(H ceil(N/w)) auxiliary; O(M+Q+K) buffered I/O", + "accepted": true + } + ] +} diff --git a/problems/016-exact-dependency-cache/solutions/c/main.c b/problems/016-exact-dependency-cache/solutions/c/main.c new file mode 100644 index 0000000..8e674a0 --- /dev/null +++ b/problems/016-exact-dependency-cache/solutions/c/main.c @@ -0,0 +1,42 @@ +#include +#include +#include +#include +int pc(uint64_t x) { + int c = 0; + while (x) { + x &= x - 1; + c++; + } + return c; +} +int main(void) { + int n, h, m, q; + if (scanf("%d%d%d%d", &n, &h, &m, &q) != 4) + return 0; + int w = (n + 63) / 64; + uint64_t *b = calloc((size_t)h * w, sizeof(uint64_t)), + *v = malloc(sizeof(uint64_t) * (size_t)w); + for (int i = 0; i < m; i++) { + int s, x; + scanf("%d%d", &s, &x); + b[(size_t)(x - 1) * w + (s - 1) / 64] |= UINT64_C(1) << ((s - 1) % 64); + } + while (q--) { + memset(v, 0, sizeof(uint64_t) * (size_t)w); + int k; + scanf("%d", &k); + while (k--) { + int x; + scanf("%d", &x); + uint64_t *z = b + (size_t)(x - 1) * w; + for (int j = 0; j < w; j++) + v[j] |= z[j]; + } + int ans = 0; + for (int j = 0; j < w; j++) + ans += pc(v[j]); + printf("%d\n", ans); + } + return 0; +} diff --git a/problems/016-exact-dependency-cache/solutions/cpp/main.cpp b/problems/016-exact-dependency-cache/solutions/cpp/main.cpp new file mode 100644 index 0000000..02ddb91 --- /dev/null +++ b/problems/016-exact-dependency-cache/solutions/cpp/main.cpp @@ -0,0 +1,33 @@ +#include +#include +#include +using namespace std; +int main() { + ios::sync_with_stdio(false); + cin.tie(nullptr); + int n, h, m, q; + if (!(cin >> n >> h >> m >> q)) + return 0; + int w = (n + 63) / 64; + vector> b(h, vector(w)); + while (m--) { + int s, x; + cin >> s >> x; + b[x - 1][(s - 1) / 64] |= uint64_t(1) << ((s - 1) % 64); + } + while (q--) { + vector v(w); + int k; + cin >> k; + while (k--) { + int x; + cin >> x; + for (int j = 0; j < w; j++) + v[j] |= b[x - 1][j]; + } + int ans = 0; + for (auto x : v) + ans += __builtin_popcountll(x); + cout << ans << '\n'; + } +} diff --git a/problems/016-exact-dependency-cache/solutions/go/main.go b/problems/016-exact-dependency-cache/solutions/go/main.go new file mode 100644 index 0000000..0f0c1da --- /dev/null +++ b/problems/016-exact-dependency-cache/solutions/go/main.go @@ -0,0 +1,43 @@ +package main + +import ( + "bufio" + "fmt" + "math/bits" + "os" +) + +func main() { + in := bufio.NewReader(os.Stdin) + out := bufio.NewWriter(os.Stdout) + defer out.Flush() + var n, h, m, q int + fmt.Fscan(in, &n, &h, &m, &q) + w := (n + 63) / 64 + b := make([]uint64, h*w) + for ; m > 0; m-- { + var s, x int + fmt.Fscan(in, &s, &x) + s-- + x-- + b[x*w+s/64] |= uint64(1) << uint(s%64) + } + for ; q > 0; q-- { + v := make([]uint64, w) + var k int + fmt.Fscan(in, &k) + for ; k > 0; k-- { + var x int + fmt.Fscan(in, &x) + x-- + for j := 0; j < w; j++ { + v[j] |= b[x*w+j] + } + } + ans := 0 + for _, x := range v { + ans += bits.OnesCount64(x) + } + fmt.Fprintln(out, ans) + } +} diff --git a/problems/016-exact-dependency-cache/solutions/javascript/main.js b/problems/016-exact-dependency-cache/solutions/javascript/main.js new file mode 100644 index 0000000..58c53bc --- /dev/null +++ b/problems/016-exact-dependency-cache/solutions/javascript/main.js @@ -0,0 +1,33 @@ +import * as std from "std"; +const a = std.in.readAsString().trim().split(/\s+/).map(Number); +let p = 0, + n = a[p++], + h = a[p++], + m = a[p++], + q = a[p++], + w = (n + 31) >> 5, + b = new Uint32Array(h * w); +while (m--) { + const s = a[p++] - 1, x = a[p++] - 1; + b[x * w + (s >>> 5)] |= 1 << (s & 31); +} +/** @param {number} x @returns {number} */ +const pop = (x) => { + x >>>= 0; + x -= x >>> 1 & 0x55555555; + x = (x & 0x33333333) + (x >>> 2 & 0x33333333); + return ((x + (x >>> 4) & 0x0f0f0f0f) * 0x01010101) >>> 24; + }; +/** @type {string[]} */ +const out = []; +while (q--) { + const v = new Uint32Array(w), k = a[p++]; + for (let i = 0; i < k; i++) { + const x = a[p++] - 1, o = x * w; + for (let j = 0; j < w; j++) v[j] |= b[o + j]; + } + let ans = 0; + for (const x of v) ans += pop(x); + out.push(String(ans)); +} +std.out.puts(out.join("\n") + "\n"); diff --git a/problems/016-exact-dependency-cache/solutions/python/main.py b/problems/016-exact-dependency-cache/solutions/python/main.py new file mode 100644 index 0000000..6f3a238 --- /dev/null +++ b/problems/016-exact-dependency-cache/solutions/python/main.py @@ -0,0 +1,23 @@ +import sys + +a = list(map(int, sys.stdin.read().split())) +n, h, m, q = a[:4] +byte_width = (n + 7) // 8 +rows = [bytearray(byte_width) for _ in range(h)] +p = 4 +for _ in range(m): + s, x = a[p] - 1, a[p + 1] - 1 + p += 2 + rows[x][s >> 3] |= 1 << (s & 7) +mask = [int.from_bytes(row, "little") for row in rows] +del rows +out = [] +for _ in range(q): + k = a[p] + p += 1 + v = 0 + for x in a[p : p + k]: + v |= mask[x - 1] + p += k + out.append(str(v.bit_count())) +print("\n".join(out)) diff --git a/problems/016-exact-dependency-cache/solutions/rust/main.rs b/problems/016-exact-dependency-cache/solutions/rust/main.rs new file mode 100644 index 0000000..de18f68 --- /dev/null +++ b/problems/016-exact-dependency-cache/solutions/rust/main.rs @@ -0,0 +1,31 @@ +use std::io::{self, Read}; +fn main() { + let mut s = String::new(); + io::stdin().read_to_string(&mut s).unwrap(); + let mut it = s.split_whitespace(); + let n: usize = it.next().unwrap().parse().unwrap(); + let h: usize = it.next().unwrap().parse().unwrap(); + let m: usize = it.next().unwrap().parse().unwrap(); + let q: usize = it.next().unwrap().parse().unwrap(); + let w = n.div_ceil(64); + let mut b = vec![vec![0u64; w]; h]; + for _ in 0..m { + let s = it.next().unwrap().parse::().unwrap() - 1; + let x = it.next().unwrap().parse::().unwrap() - 1; + b[x][s / 64] |= 1u64 << (s % 64); + } + let mut out = String::new(); + for _ in 0..q { + let k: usize = it.next().unwrap().parse().unwrap(); + let mut v = vec![0u64; w]; + for _ in 0..k { + let x = it.next().unwrap().parse::().unwrap() - 1; + for j in 0..w { + v[j] |= b[x][j] + } + } + let ans: u32 = v.iter().map(|x| x.count_ones()).sum(); + out.push_str(&format!("{ans}\n")); + } + print!("{out}"); +} diff --git a/problems/016-exact-dependency-cache/solutions/typescript/main.ts b/problems/016-exact-dependency-cache/solutions/typescript/main.ts new file mode 100644 index 0000000..47f0385 --- /dev/null +++ b/problems/016-exact-dependency-cache/solutions/typescript/main.ts @@ -0,0 +1,26 @@ +import * as std from "std"; +const a: number[] = std.in.readAsString().trim().split(/\s+/).map(Number); +let p = 0, n = a[p++], h = a[p++], m = a[p++], q = a[p++], w = (n + 31) >> 5; +const b: Uint32Array = new Uint32Array(h * w); +while (m--) { + const s = a[p++] - 1, x = a[p++] - 1; + b[x * w + (s >>> 5)] |= 1 << (s & 31); +} +const pop = (v: number): number => { + v >>>= 0; + v -= v >>> 1 & 0x55555555; + v = (v & 0x33333333) + (v >>> 2 & 0x33333333); + return ((v + (v >>> 4) & 0x0f0f0f0f) * 0x01010101) >>> 24; + }, + out: string[] = []; +while (q--) { + const v = new Uint32Array(w), k = a[p++]; + for (let i = 0; i < k; i++) { + const x = a[p++] - 1, o = x * w; + for (let j = 0; j < w; j++) v[j] |= b[o + j]; + } + let ans = 0; + for (const x of v) ans += pop(x); + out.push(String(ans)); +} +std.out.puts(out.join("\n") + "\n"); diff --git a/problems/016-exact-dependency-cache/statement.en.md b/problems/016-exact-dependency-cache/statement.en.md new file mode 100644 index 0000000..b3e3906 --- /dev/null +++ b/problems/016-exact-dependency-cache/statement.en.md @@ -0,0 +1,97 @@ +# Exact Dependency Cache + +The in-browser compilation cache of a WASM OJ must avoid recompiling every translation unit (TU) whenever one header changes. That conservative policy is safe, but it wastes substantial instruction cost and turns a small source edit into a full rebuild. + +Instead, the compiler records exactly which headers each TU actually read during compilation. A TU is a cache miss in a round only if the changed set contains at least one of those headers. If the changed set and its exact dependencies are disjoint, the existing compilation result remains a hit. + +To evaluate a series of independent editing scenarios, assume that every miss has finished rebuilding by the end of its round. The next round therefore starts again from a clean baseline rather than inheriting changes from earlier rounds. + +Given the fixed TU-to-header dependencies and several changed-header sets, output how many TUs are cache misses in each round. + +## Input + +The first line contains `N H M Q`: the number of TUs, headers, dependency edges, and rounds. The next `M` lines contain `s h`, meaning TU `s` read header `h`. Each of the next `Q` lines contains `K h_1 ... h_K`. + +TU IDs and header IDs are each 1-based. Header IDs within a round are distinct. When `K=0`, the line contains only `0`. + +## Output + +Output `Q` lines. Line `i` contains one decimal integer: the number of TUs depending on at least one header changed in round `i`. Output `0` when no TU misses. + +## Constraints + +- `1 ≤ N,H ≤ 6000` +- `0 ≤ M ≤ 200000` +- `1 ≤ Q ≤ 20000` +- Dependency edges are distinct. +- The sum of `K` over all queries is at most `50000`. +- A machine word in the word-RAM model has at least 32 bits. +- Tests repeatedly change high-degree headers; worst-case scalar marking through reverse adjacency lists does not pass. + +## Examples + + + +### Example One + +Input: + +```text +4 3 4 2 +1 1 +2 1 +2 2 +3 2 +2 1 2 +1 3 +``` + +Output: + +```text +3 +0 +``` + +### Example Two + +Input: + +```text +2 2 2 2 +1 1 +2 2 +0 +1 2 +``` + +Output: + +```text +0 +1 +``` + +### Example Three + +Input: + +```text +3 1 3 3 +1 1 +2 1 +3 1 +1 1 +1 1 +0 +``` + +Output: + +```text +3 +3 +0 +``` + + diff --git a/problems/016-exact-dependency-cache/statement.zh-TW.md b/problems/016-exact-dependency-cache/statement.zh-TW.md new file mode 100644 index 0000000..041ea36 --- /dev/null +++ b/problems/016-exact-dependency-cache/statement.zh-TW.md @@ -0,0 +1,94 @@ +# 精確依賴快取 + +WASM OJ 的瀏覽器內編譯快取,首先要避免「只要一個 header 改變,就重新編譯所有 translation unit(TU)」的情況。這種保守作法雖然安全,卻會浪費大量 instruction cost,也會讓只改動一個小檔案的使用者等待完整重建。 + +因此,編譯器會記錄每個 TU 在編譯時**實際讀過**哪些 header。當一輪修改包含某個 TU 讀過的至少一個 header 時,該 TU 才會 cache miss;如果修改集合與它的精確依賴完全沒有交集,就能沿用原本的編譯結果。 + +為了評估一系列獨立的編輯情境,每輪結束後都視為所有 miss 已完成重編,所以下一輪重新從乾淨 baseline 開始,而不是累積前幾輪的修改狀態。 + +給定固定的 TU 與 header 依賴關係,以及多輪 changed-header 集合,請輸出每一輪會 cache miss 的 TU 數量。 + +## 輸入 + +第一行 `N H M Q`:TU 數、header 數、依賴邊數、輪數。接著 `M` 行 `s h`,表示 TU `s` 實際讀過 header `h`。再接 `Q` 行,每行為 `K h_1 ... h_K`。 + +TU 與 header 各自使用 1-based ID。一輪內 header ID 互異;`K=0` 時該行只有 `0`。 + +## 輸出 + +輸出 `Q` 行,第 `i` 行是一個十進位整數:第 `i` 輪至少依賴一個 changed header 的 TU 數。沒有 miss 時輸出 `0`。 + +## 限制 + +- `1 <= N,H <= 6000`,`0 <= M <= 200000`,`1 <= Q <= 20000`。 +- 依賴邊不重複;所有 query 的 `K` 總和不超過 50000。 +- word-RAM 的 machine word 至少 32 bits。 +- 測資包含高 degree header 被反覆修改;逐 adjacency list 標記的最壞情況不能通過。 + +## 範例 + + + +### 範例一 + +輸入: + +```text +4 3 4 2 +1 1 +2 1 +2 2 +3 2 +2 1 2 +1 3 +``` + +輸出: + +```text +3 +0 +``` + +### 範例二 + +輸入: + +```text +2 2 2 2 +1 1 +2 2 +0 +1 2 +``` + +輸出: + +```text +0 +1 +``` + +### 範例三 + +輸入: + +```text +3 1 3 3 +1 1 +2 1 +3 1 +1 1 +1 1 +0 +``` + +輸出: + +```text +3 +3 +0 +``` + + diff --git a/problems/016-exact-dependency-cache/tests/adversarial-word-boundary.in b/problems/016-exact-dependency-cache/tests/adversarial-word-boundary.in new file mode 100644 index 0000000..ef159fa --- /dev/null +++ b/problems/016-exact-dependency-cache/tests/adversarial-word-boundary.in @@ -0,0 +1,69 @@ +65 1 65 3 +1 1 +2 1 +3 1 +4 1 +5 1 +6 1 +7 1 +8 1 +9 1 +10 1 +11 1 +12 1 +13 1 +14 1 +15 1 +16 1 +17 1 +18 1 +19 1 +20 1 +21 1 +22 1 +23 1 +24 1 +25 1 +26 1 +27 1 +28 1 +29 1 +30 1 +31 1 +32 1 +33 1 +34 1 +35 1 +36 1 +37 1 +38 1 +39 1 +40 1 +41 1 +42 1 +43 1 +44 1 +45 1 +46 1 +47 1 +48 1 +49 1 +50 1 +51 1 +52 1 +53 1 +54 1 +55 1 +56 1 +57 1 +58 1 +59 1 +60 1 +61 1 +62 1 +63 1 +64 1 +65 1 +1 1 +1 1 +0 diff --git a/problems/016-exact-dependency-cache/tests/adversarial-word-boundary.out b/problems/016-exact-dependency-cache/tests/adversarial-word-boundary.out new file mode 100644 index 0000000..2e04be1 --- /dev/null +++ b/problems/016-exact-dependency-cache/tests/adversarial-word-boundary.out @@ -0,0 +1,3 @@ +65 +65 +0 diff --git a/problems/016-exact-dependency-cache/tests/sample-01.in b/problems/016-exact-dependency-cache/tests/sample-01.in new file mode 100644 index 0000000..d37e980 --- /dev/null +++ b/problems/016-exact-dependency-cache/tests/sample-01.in @@ -0,0 +1,7 @@ +4 3 4 2 +1 1 +2 1 +2 2 +3 2 +2 1 2 +1 3 diff --git a/problems/016-exact-dependency-cache/tests/sample-01.out b/problems/016-exact-dependency-cache/tests/sample-01.out new file mode 100644 index 0000000..043e571 --- /dev/null +++ b/problems/016-exact-dependency-cache/tests/sample-01.out @@ -0,0 +1,2 @@ +3 +0 diff --git a/problems/016-exact-dependency-cache/tests/sample-02.in b/problems/016-exact-dependency-cache/tests/sample-02.in new file mode 100644 index 0000000..c75c0ae --- /dev/null +++ b/problems/016-exact-dependency-cache/tests/sample-02.in @@ -0,0 +1,5 @@ +2 2 2 2 +1 1 +2 2 +0 +1 2 diff --git a/problems/016-exact-dependency-cache/tests/sample-02.out b/problems/016-exact-dependency-cache/tests/sample-02.out new file mode 100644 index 0000000..0d66ea1 --- /dev/null +++ b/problems/016-exact-dependency-cache/tests/sample-02.out @@ -0,0 +1,2 @@ +0 +1 diff --git a/problems/016-exact-dependency-cache/tests/sample-03.in b/problems/016-exact-dependency-cache/tests/sample-03.in new file mode 100644 index 0000000..4b2f33c --- /dev/null +++ b/problems/016-exact-dependency-cache/tests/sample-03.in @@ -0,0 +1,7 @@ +3 1 3 3 +1 1 +2 1 +3 1 +1 1 +1 1 +0 diff --git a/problems/016-exact-dependency-cache/tests/sample-03.out b/problems/016-exact-dependency-cache/tests/sample-03.out new file mode 100644 index 0000000..f978897 --- /dev/null +++ b/problems/016-exact-dependency-cache/tests/sample-03.out @@ -0,0 +1,3 @@ +3 +3 +0 diff --git a/problems/016-exact-dependency-cache/validator.py b/problems/016-exact-dependency-cache/validator.py new file mode 100644 index 0000000..4b59d3a --- /dev/null +++ b/problems/016-exact-dependency-cache/validator.py @@ -0,0 +1,32 @@ +import sys + + +def main(): + a = list(map(int, sys.stdin.read().split())) + assert len(a) >= 4 + n, h, m, q = a[:4] + assert 1 <= n <= 6000 and 1 <= h <= 6000 and 0 <= m <= 200000 and 1 <= q <= 20000 + p = 4 + seen = set() + for _ in range(m): + s, x = a[p : p + 2] + p += 2 + assert 1 <= s <= n and 1 <= x <= h and (s, x) not in seen + seen.add((s, x)) + total = 0 + for _ in range(q): + assert p < len(a) + k = a[p] + p += 1 + assert 0 <= k <= h and p + k <= len(a) + v = a[p : p + k] + p += k + assert len(v) == len(set(v)) and all(1 <= x <= h for x in v) + total += k + assert p == len(a) and total <= 50000 + + +try: + main() +except (AssertionError, ValueError): + sys.exit(1) diff --git a/problems/017-graph-blob-lru/editorial.en.md b/problems/017-graph-blob-lru/editorial.en.md new file mode 100644 index 0000000..fbd5411 --- /dev/null +++ b/problems/017-graph-blob-lru/editorial.en.md @@ -0,0 +1,28 @@ +# Editorial + +## Intuitive Approach + +Store LRU order in an array, linearly searching and moving entries on every touch. On eviction, scan all `N` nodes for references. This costs `O(Q(N+D))` in the worst case. + +## Optimal Approach: Two Intrusive Doubly Linked Structures + +Digest IDs are dense, so arrays can store `cached` and LRU `prev/next` links. A doubly linked list from `head=LRU` to `tail=MRU` implements touch, insertion, and removal in constant time. + +Each node references at most one digest. For every digest, maintain another doubly linked list of referencing nodes. Per-node `refPrev/refNext` links allow `O(1)` detachment during reassignment. When a digest is evicted, walk its reference list and clear every node mapping. + +One eviction may visit many nodes, but every visited reference was created by an earlier `P` attachment. Once invalidated, it cannot be visited again unless another `P` recreates it. Therefore total reference visits over all evictions are at most `Q`. + +## Correctness Proof + +Maintain three invariants: (1) every cached digest appears exactly once in LRU order, ordered by its most recent successful `P` or hit `G`; (2) node mappings and digest reverse lists agree; and (3) occupancy is the sum of distinct cached blob sizes. Detach, attach, and touch operations preserve their corresponding invariants. Eviction removes the head, exactly the required least-recently-used blob; clearing its complete reverse list invalidates all and only references to that digest, while subtracting its size once preserves occupancy. Repeating stops exactly when occupancy is at most `C`. The oversize branch performs only the required detachment. By induction, all invariants hold after every operation, so each `G` result, digest, and recency update is correct. + +## Complexity + +Every operation except reference invalidation is `O(1)`. Each attached reference is invalidated at most once before another attachment, so total time is `O(Q)` amortized and space is `O(N+D)`. + +## Common Mistakes + +- Using nodes rather than blobs as the LRU unit, breaking digest deduplication. +- Failing to detach a reassigned node from the old digest's reverse list. +- Removing an unreferenced blob immediately; it must remain cached. +- Forgetting to clear the old reference before an oversize `P`. diff --git a/problems/017-graph-blob-lru/editorial.zh-TW.md b/problems/017-graph-blob-lru/editorial.zh-TW.md new file mode 100644 index 0000000..59b175c --- /dev/null +++ b/problems/017-graph-blob-lru/editorial.zh-TW.md @@ -0,0 +1,28 @@ +# 解題說明 + +## 直覺解 + +用陣列保存 LRU,每次 touch 線性尋找/搬移;淘汰時再掃描全部 `N` 節點找引用者。最壞 `O(Q(N+D))`。 + +## 最佳解 + +digest ID 稠密,可用陣列保存 cached、LRU prev/next,以 head=LRU、tail=MRU 的雙向串列做到 `touch/insert/remove` 常數時間。 + +每個 node 只引用一個 digest;再為每個 digest 維護引用 node 的雙向串列。node 的 `refPrev/refNext` 足以在 reassign 時 `O(1)` detach。淘汰 digest 時沿它的引用串列逐一清空 node mapping。 + +雖然一次淘汰可能走很多 node,但每個被走訪的引用必由更早的一次 `P` attach 建立,且失效後不會再被走訪,除非另一次 `P` 重新建立。故所有淘汰走訪總數不超過 `Q`。 + +## 正確性證明 + +維護 invariant:(一)cached digest 恰各出現一次於 LRU,順序為最近成功 `P/HIT G` 的時間;(二)node mapping 與 digest 反向串列互相一致;(三)occupancy 是 cached digest size 的不重複總和。各個 detach/attach/touch helper 顯然保持對應 invariant。新 blob 加入後從 head 淘汰,故每次選到規格要求的 LRU;清空整條引用串列使且只使該 digest 的引用失效,減去一次 size 保持 occupancy。迴圈停止時 occupancy<=C。oversize 分支只做規定的 detach。歸納所有操作後 invariant 成立,因此每個 `G` 的 hit/miss、digest 與更新順序都正確。 + +## 複雜度 + +除淘汰引用外每操作 `O(1)`;每個引用在 attach 後至多被淘汰一次,總時間 `O(Q)` amortized,空間 `O(N+D)`。 + +## 常見錯誤 + +- 以 node 而非 blob 為 LRU 單位,破壞 digest 去重。 +- reassign 時沒從舊 digest 的反向串列 detach。 +- 無引用 blob 立刻刪除;規格要求它留在 cache。 +- oversize `P` 忘記先清除舊引用。 diff --git a/problems/017-graph-blob-lru/generator.py b/problems/017-graph-blob-lru/generator.py new file mode 100644 index 0000000..8374bbd --- /dev/null +++ b/problems/017-graph-blob-lru/generator.py @@ -0,0 +1,19 @@ +import random, sys + +seed, index = map(int, sys.argv[1:]) +r = random.Random(seed * 31337 + index) +n = 5 + index % 8 +d = 4 + index % 6 +q = 15 + index % 15 +cap = r.randrange(4, 15) +sizes = [r.randrange(1, 9) for _ in range(d)] +ops = [] +for i in range(q): + if i == q - 1 or r.random() < 0.4: + ops.append(("G", r.randrange(1, n + 1))) + else: + ops.append(("P", r.randrange(1, n + 1), r.randrange(1, d + 1))) +print(n, d, q, cap) +print(*sizes) +for x in ops: + print(*x) diff --git a/problems/017-graph-blob-lru/oracle.py b/problems/017-graph-blob-lru/oracle.py new file mode 100644 index 0000000..9b20d9d --- /dev/null +++ b/problems/017-graph-blob-lru/oracle.py @@ -0,0 +1,39 @@ +import sys + +it = iter(sys.stdin.read().split()) +n, d, q = int(next(it)), int(next(it)), int(next(it)) +cap = int(next(it)) +size = [int(next(it)) for _ in range(d)] +node = [None] * n +lru = [] +out = [] + + +def touch(x): + if x in lru: + lru.remove(x) + lru.append(x) + + +for _ in range(q): + op = next(it) + u = int(next(it)) - 1 + if op == "G": + if node[u] is None: + out.append("MISS") + else: + touch(node[u]) + out.append(f"HIT {node[u]+1}") + else: + x = int(next(it)) - 1 + node[u] = None + if size[x] > cap: + continue + touch(x) + node[u] = x + while sum(size[v] for v in lru) > cap: + dead = lru.pop(0) + for i in range(n): + if node[i] == dead: + node[i] = None +print("\n".join(out)) diff --git a/problems/017-graph-blob-lru/problem.json b/problems/017-graph-blob-lru/problem.json new file mode 100644 index 0000000..170e5d6 --- /dev/null +++ b/problems/017-graph-blob-lru/problem.json @@ -0,0 +1,147 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 17, + "slug": "graph-blob-lru", + "title": { + "zh-TW": "Graph Blob LRU", + "en": "Graph Blob LRU" + }, + "difficulty": "hard", + "tags": [ + "lru", + "linked-list", + "cache", + "amortized-analysis" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-zero-dedup-eviction", + "kind": "adversarial", + "input": "tests/adversarial-zero-dedup-eviction.in", + "output": "tests/adversarial-zero-dedup-eviction.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 15000000, + "memoryLimitBytes": 536870912 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 2500000, + "memoryLimitBytes": 402653184 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 850000, + "memoryLimitBytes": 268435456 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "陣列搜尋與全節點失效", + "en": "Array Search and Full-Node Invalidation" + }, + "time": "O(Q(N+D))", + "space": "O(N+D)", + "accepted": false + }, + { + "name": { + "zh-TW": "雙向 LRU 與反向引用串列", + "en": "Doubly Linked LRU and Reverse Reference Lists" + }, + "time": "O(Q) amortized", + "space": "O(N+D)", + "accepted": true + } + ] +} diff --git a/problems/017-graph-blob-lru/solutions/c/main.c b/problems/017-graph-blob-lru/solutions/c/main.c new file mode 100644 index 0000000..9f0486e --- /dev/null +++ b/problems/017-graph-blob-lru/solutions/c/main.c @@ -0,0 +1,109 @@ +#include +#include +#include +typedef unsigned long long U; +static int *lp, *ln, *rh, *nb, *rp, *rn, head = -1, tail = -1; +static unsigned char *cached; +void lr(int x) { + if (lp[x] >= 0) + ln[lp[x]] = ln[x]; + else + head = ln[x]; + if (ln[x] >= 0) + lp[ln[x]] = lp[x]; + else + tail = lp[x]; + lp[x] = ln[x] = -1; +} +void touch(int x) { + if (cached[x]) + lr(x); + cached[x] = 1; + lp[x] = tail; + if (tail >= 0) + ln[tail] = x; + else + head = x; + tail = x; +} +void detach(int u) { + int x = nb[u]; + if (x < 0) + return; + if (rp[u] >= 0) + rn[rp[u]] = rn[u]; + else + rh[x] = rn[u]; + if (rn[u] >= 0) + rp[rn[u]] = rp[u]; + nb[u] = rp[u] = rn[u] = -1; +} +void attach(int u, int x) { + nb[u] = x; + rn[u] = rh[x]; + if (rh[x] >= 0) + rp[rh[x]] = u; + rh[x] = u; + rp[u] = -1; +} +int main(void) { + int n, d, q; + U cap; + if (scanf("%d%d%d%llu", &n, &d, &q, &cap) != 4) + return 0; + U *sz = malloc(sizeof(U) * (size_t)d); + for (int i = 0; i < d; i++) + scanf("%llu", &sz[i]); + lp = malloc(sizeof(int) * (size_t)d); + ln = malloc(sizeof(int) * (size_t)d); + rh = malloc(sizeof(int) * (size_t)d); + cached = calloc((size_t)d, 1); + nb = malloc(sizeof(int) * (size_t)n); + rp = malloc(sizeof(int) * (size_t)n); + rn = malloc(sizeof(int) * (size_t)n); + memset(lp, 255, sizeof(int) * (size_t)d); + memset(ln, 255, sizeof(int) * (size_t)d); + memset(rh, 255, sizeof(int) * (size_t)d); + memset(nb, 255, sizeof(int) * (size_t)n); + memset(rp, 255, sizeof(int) * (size_t)n); + memset(rn, 255, sizeof(int) * (size_t)n); + U used = 0; + while (q--) { + char op; + int u; + scanf(" %c%d", &op, &u); + u--; + if (op == 'G') { + if (nb[u] < 0) + puts("MISS"); + else { + touch(nb[u]); + printf("HIT %d\n", nb[u] + 1); + } + continue; + } + int x; + scanf("%d", &x); + x--; + detach(u); + if (sz[x] > cap) + continue; + if (!cached[x]) + used += sz[x]; + touch(x); + attach(u, x); + while (used > cap) { + int dead = head; + lr(dead); + cached[dead] = 0; + used -= sz[dead]; + for (int v = rh[dead]; v >= 0;) { + int z = rn[v]; + nb[v] = rp[v] = rn[v] = -1; + v = z; + } + rh[dead] = -1; + } + } + return 0; +} diff --git a/problems/017-graph-blob-lru/solutions/cpp/main.cpp b/problems/017-graph-blob-lru/solutions/cpp/main.cpp new file mode 100644 index 0000000..dcf1ae4 --- /dev/null +++ b/problems/017-graph-blob-lru/solutions/cpp/main.cpp @@ -0,0 +1,100 @@ +#include +#include +#include +#include +using namespace std; +int main() { + ios::sync_with_stdio(false); + cin.tie(nullptr); + int n, d, q; + uint64_t cap; + if (!(cin >> n >> d >> q >> cap)) + return 0; + vector sz(d); + for (auto &x : sz) + cin >> x; + vector lp(d, -1), ln(d, -1), rh(d, -1), node(n, -1), rp(n, -1), + rn(n, -1); + vector cached(d); + int head = -1, tail = -1; + uint64_t used = 0; + auto remove_lru = [&](int x) { + if (lp[x] >= 0) + ln[lp[x]] = ln[x]; + else + head = ln[x]; + if (ln[x] >= 0) + lp[ln[x]] = lp[x]; + else + tail = lp[x]; + lp[x] = ln[x] = -1; + }; + auto touch = [&](int x) { + if (cached[x]) + remove_lru(x); + cached[x] = 1; + lp[x] = tail; + if (tail >= 0) + ln[tail] = x; + else + head = x; + tail = x; + }; + auto detach = [&](int u) { + int x = node[u]; + if (x < 0) + return; + if (rp[u] >= 0) + rn[rp[u]] = rn[u]; + else + rh[x] = rn[u]; + if (rn[u] >= 0) + rp[rn[u]] = rp[u]; + node[u] = rp[u] = rn[u] = -1; + }; + auto attach = [&](int u, int x) { + node[u] = x; + rn[u] = rh[x]; + if (rh[x] >= 0) + rp[rh[x]] = u; + rh[x] = u; + rp[u] = -1; + }; + while (q--) { + char op; + int u; + cin >> op >> u; + --u; + if (op == 'G') { + if (node[u] < 0) + cout << "MISS\n"; + else { + touch(node[u]); + cout << "HIT " << node[u] + 1 << '\n'; + } + continue; + } + int x; + cin >> x; + --x; + detach(u); + if (sz[x] > cap) + continue; + if (!cached[x]) + used += sz[x]; + touch(x); + attach(u, x); + while (used > cap) { + int dead = head; + remove_lru(dead); + cached[dead] = 0; + used -= sz[dead]; + for (int v = rh[dead]; v >= 0;) { + int z = rn[v]; + node[v] = rp[v] = rn[v] = -1; + v = z; + } + rh[dead] = -1; + } + } +} diff --git a/problems/017-graph-blob-lru/solutions/go/main.go b/problems/017-graph-blob-lru/solutions/go/main.go new file mode 100644 index 0000000..61bba40 --- /dev/null +++ b/problems/017-graph-blob-lru/solutions/go/main.go @@ -0,0 +1,124 @@ +package main + +import ( + "bufio" + "fmt" + "os" +) + +func main() { + in := bufio.NewReader(os.Stdin) + out := bufio.NewWriter(os.Stdout) + defer out.Flush() + var n, d, q int + var cap uint64 + fmt.Fscan(in, &n, &d, &q, &cap) + sz := make([]uint64, d) + for i := range sz { + fmt.Fscan(in, &sz[i]) + } + lp := make([]int, d) + ln := make([]int, d) + rh := make([]int, d) + node := make([]int, n) + rp := make([]int, n) + rn := make([]int, n) + for _, a := range [][]int{lp, ln, rh, node, rp, rn} { + for i := range a { + a[i] = -1 + } + } + cached := make([]bool, d) + head, tail := -1, -1 + var used uint64 + remove := func(x int) { + if lp[x] >= 0 { + ln[lp[x]] = ln[x] + } else { + head = ln[x] + } + if ln[x] >= 0 { + lp[ln[x]] = lp[x] + } else { + tail = lp[x] + } + lp[x], ln[x] = -1, -1 + } + touch := func(x int) { + if cached[x] { + remove(x) + } + cached[x] = true + lp[x] = tail + if tail >= 0 { + ln[tail] = x + } else { + head = x + } + tail = x + } + detach := func(u int) { + x := node[u] + if x < 0 { + return + } + if rp[u] >= 0 { + rn[rp[u]] = rn[u] + } else { + rh[x] = rn[u] + } + if rn[u] >= 0 { + rp[rn[u]] = rp[u] + } + node[u], rp[u], rn[u] = -1, -1, -1 + } + attach := func(u, x int) { + node[u] = x + rn[u] = rh[x] + if rh[x] >= 0 { + rp[rh[x]] = u + } + rh[x] = u + rp[u] = -1 + } + for ; q > 0; q-- { + var op string + var u int + fmt.Fscan(in, &op, &u) + u-- + if op == "G" { + if node[u] < 0 { + fmt.Fprintln(out, "MISS") + } else { + x := node[u] + touch(x) + fmt.Fprintln(out, "HIT", x+1) + } + continue + } + var x int + fmt.Fscan(in, &x) + x-- + detach(u) + if sz[x] > cap { + continue + } + if !cached[x] { + used += sz[x] + } + touch(x) + attach(u, x) + for used > cap { + dead := head + remove(dead) + cached[dead] = false + used -= sz[dead] + for v := rh[dead]; v >= 0; { + z := rn[v] + node[v], rp[v], rn[v] = -1, -1, -1 + v = z + } + rh[dead] = -1 + } + } +} diff --git a/problems/017-graph-blob-lru/solutions/javascript/main.js b/problems/017-graph-blob-lru/solutions/javascript/main.js new file mode 100644 index 0000000..99b3b8d --- /dev/null +++ b/problems/017-graph-blob-lru/solutions/javascript/main.js @@ -0,0 +1,86 @@ +import * as std from "std"; +const a = std.in.readAsString().trim().split(/\s+/); +let p = 0, + n = Number(a[p++]), + d = Number(a[p++]), + q = Number(a[p++]), + cap = BigInt(a[p++]); +/** @type {bigint[]} */ +const sz = Array.from({ length: d }, () => BigInt(a[p++])); +const lp = new Int32Array(d), + ln = new Int32Array(d), + rh = new Int32Array(d), + node = new Int32Array(n), + rp = new Int32Array(n), + rn = new Int32Array(n), + cached = new Uint8Array(d); +for (const x of [lp, ln, rh, node, rp, rn]) x.fill(-1); +let head = -1, tail = -1, used = 0n; +/** @type {string[]} */ +const out = []; +/** @param {number} x @returns {void} */ +const remove = (x) => { + if (lp[x] >= 0) ln[lp[x]] = ln[x]; + else head = ln[x]; + if (ln[x] >= 0) lp[ln[x]] = lp[x]; + else tail = lp[x]; + lp[x] = ln[x] = -1; + }; +/** @param {number} x @returns {void} */ +const touch = (x) => { + if (cached[x]) remove(x); + cached[x] = 1; + lp[x] = tail; + if (tail >= 0) ln[tail] = x; + else head = x; + tail = x; + }; +/** @param {number} u @returns {void} */ +const detach = (u) => { + const x = node[u]; + if (x < 0) return; + if (rp[u] >= 0) rn[rp[u]] = rn[u]; + else rh[x] = rn[u]; + if (rn[u] >= 0) rp[rn[u]] = rp[u]; + node[u] = rp[u] = rn[u] = -1; + }; +/** @param {number} u @param {number} x @returns {void} */ +const attach = (u, x) => { + node[u] = x; + rn[u] = rh[x]; + if (rh[x] >= 0) rp[rh[x]] = u; + rh[x] = u; + rp[u] = -1; + }; +while (q--) { + const op = a[p++], u = Number(a[p++]) - 1; + if (op === "G") { + if (node[u] < 0) out.push("MISS"); + else { + const x = node[u]; + touch(x); + out.push(`HIT ${x + 1}`); + } + continue; + } + const x = Number(a[p++]) - 1; + detach(u); + if (sz[x] > cap) continue; + if (!cached[x]) used += sz[x]; + touch(x); + attach(u, x); + while (used > cap) { + const dead = head; + remove(dead); + cached[dead] = 0; + used -= sz[dead]; + let v = rh[dead]; + while (v >= 0) { + const z = rn[v]; + node[v] = rp[v] = rn[v] = -1; + v = z; + } + rh[dead] = -1; + } +} +std.out.puts(out.join("\n") + "\n"); diff --git a/problems/017-graph-blob-lru/solutions/python/main.py b/problems/017-graph-blob-lru/solutions/python/main.py new file mode 100644 index 0000000..e7a5e68 --- /dev/null +++ b/problems/017-graph-blob-lru/solutions/python/main.py @@ -0,0 +1,97 @@ +import sys + +it = iter(sys.stdin.read().split()) +n, d, q = int(next(it)), int(next(it)), int(next(it)) +cap = int(next(it)) +size = [int(next(it)) for _ in range(d)] +cached = [False] * d +lp = [-1] * d +ln = [-1] * d +rh = [-1] * d +node = [-1] * n +rp = [-1] * n +rn = [-1] * n +head = tail = -1 +used = 0 +out = [] + + +def lremove(x): + global head, tail + if lp[x] >= 0: + ln[lp[x]] = ln[x] + else: + head = ln[x] + if ln[x] >= 0: + lp[ln[x]] = lp[x] + else: + tail = lp[x] + lp[x] = ln[x] = -1 + + +def touch(x): + global head, tail + if cached[x]: + lremove(x) + cached[x] = True + lp[x] = tail + if tail >= 0: + ln[tail] = x + else: + head = x + tail = x + + +def detach(u): + x = node[u] + if x < 0: + return + if rp[u] >= 0: + rn[rp[u]] = rn[u] + else: + rh[x] = rn[u] + if rn[u] >= 0: + rp[rn[u]] = rp[u] + node[u] = rp[u] = rn[u] = -1 + + +def attach(u, x): + node[u] = x + rn[u] = rh[x] + if rh[x] >= 0: + rp[rh[x]] = u + rh[x] = u + rp[u] = -1 + + +for _ in range(q): + op = next(it) + u = int(next(it)) - 1 + if op == "G": + x = node[u] + if x < 0: + out.append("MISS") + else: + touch(x) + out.append(f"HIT {x+1}") + continue + x = int(next(it)) - 1 + detach(u) + if size[x] > cap: + continue + if not cached[x]: + used += size[x] + touch(x) + attach(u, x) + while used > cap: + dead = head + lremove(dead) + cached[dead] = False + used -= size[dead] + v = rh[dead] + while v >= 0: + z = rn[v] + node[v] = rp[v] = rn[v] = -1 + v = z + rh[dead] = -1 +print("\n".join(out)) diff --git a/problems/017-graph-blob-lru/solutions/rust/main.rs b/problems/017-graph-blob-lru/solutions/rust/main.rs new file mode 100644 index 0000000..6d29f44 --- /dev/null +++ b/problems/017-graph-blob-lru/solutions/rust/main.rs @@ -0,0 +1,140 @@ +use std::io::{self, Read}; +struct Cache { + cap: u64, + size: Vec, + used: u64, + cached: Vec, + lp: Vec, + ln: Vec, + rh: Vec, + node: Vec, + rp: Vec, + rn: Vec, + head: isize, + tail: isize, +} +impl Cache { + fn lr(&mut self, x: usize) { + let (a, b) = (self.lp[x], self.ln[x]); + if a >= 0 { + self.ln[a as usize] = b + } else { + self.head = b + } + if b >= 0 { + self.lp[b as usize] = a + } else { + self.tail = a + } + self.lp[x] = -1; + self.ln[x] = -1; + } + fn touch(&mut self, x: usize) { + if self.cached[x] { + self.lr(x) + } + self.cached[x] = true; + self.lp[x] = self.tail; + if self.tail >= 0 { + self.ln[self.tail as usize] = x as isize + } else { + self.head = x as isize + } + self.tail = x as isize; + } + fn detach(&mut self, u: usize) { + let x = self.node[u]; + if x < 0 { + return; + } + let (a, b) = (self.rp[u], self.rn[u]); + if a >= 0 { + self.rn[a as usize] = b + } else { + self.rh[x as usize] = b + } + if b >= 0 { + self.rp[b as usize] = a + } + self.node[u] = -1; + self.rp[u] = -1; + self.rn[u] = -1; + } + fn attach(&mut self, u: usize, x: usize) { + self.node[u] = x as isize; + self.rn[u] = self.rh[x]; + if self.rh[x] >= 0 { + self.rp[self.rh[x] as usize] = u as isize + } + self.rh[x] = u as isize; + self.rp[u] = -1; + } + fn put(&mut self, u: usize, x: usize) { + self.detach(u); + if self.size[x] > self.cap { + return; + } + if !self.cached[x] { + self.used += self.size[x] + } + self.touch(x); + self.attach(u, x); + while self.used > self.cap { + let dead = self.head as usize; + self.lr(dead); + self.cached[dead] = false; + self.used -= self.size[dead]; + let mut v = self.rh[dead]; + while v >= 0 { + let z = self.rn[v as usize]; + self.node[v as usize] = -1; + self.rp[v as usize] = -1; + self.rn[v as usize] = -1; + v = z + } + self.rh[dead] = -1; + } + } +} +fn main() { + let mut s = String::new(); + io::stdin().read_to_string(&mut s).unwrap(); + let mut it = s.split_whitespace(); + let n: usize = it.next().unwrap().parse().unwrap(); + let d: usize = it.next().unwrap().parse().unwrap(); + let q: usize = it.next().unwrap().parse().unwrap(); + let cap: u64 = it.next().unwrap().parse().unwrap(); + let size = (0..d) + .map(|_| it.next().unwrap().parse().unwrap()) + .collect(); + let mut c = Cache { + cap, + size, + used: 0, + cached: vec![false; d], + lp: vec![-1; d], + ln: vec![-1; d], + rh: vec![-1; d], + node: vec![-1; n], + rp: vec![-1; n], + rn: vec![-1; n], + head: -1, + tail: -1, + }; + let mut out = String::new(); + for _ in 0..q { + let op = it.next().unwrap(); + let u = it.next().unwrap().parse::().unwrap() - 1; + if op == "P" { + let x = it.next().unwrap().parse::().unwrap() - 1; + c.put(u, x) + } else if c.node[u] < 0 { + out.push_str("MISS\n") + } else { + let x = c.node[u] as usize; + c.touch(x); + out.push_str(&format!("HIT {}\n", x + 1)); + } + } + print!("{out}"); +} diff --git a/problems/017-graph-blob-lru/solutions/typescript/main.ts b/problems/017-graph-blob-lru/solutions/typescript/main.ts new file mode 100644 index 0000000..9e88c95 --- /dev/null +++ b/problems/017-graph-blob-lru/solutions/typescript/main.ts @@ -0,0 +1,80 @@ +import * as std from "std"; +const a: string[] = std.in.readAsString().trim().split(/\s+/); +let p = 0, + n = Number(a[p++]), + d = Number(a[p++]), + q = Number(a[p++]), + cap = BigInt(a[p++]); +const sz: bigint[] = Array.from({ length: d }, () => BigInt(a[p++])), + lp = new Int32Array(d), + ln = new Int32Array(d), + rh = new Int32Array(d), + node = new Int32Array(n), + rp = new Int32Array(n), + rn = new Int32Array(n), + cached = new Uint8Array(d); +for (const x of [lp, ln, rh, node, rp, rn]) x.fill(-1); +let head = -1, tail = -1, used = 0n; +const out: string[] = []; +const remove = (x: number): void => { + if (lp[x] >= 0) ln[lp[x]] = ln[x]; + else head = ln[x]; + if (ln[x] >= 0) lp[ln[x]] = lp[x]; + else tail = lp[x]; + lp[x] = ln[x] = -1; + }, + touch = (x: number): void => { + if (cached[x]) remove(x); + cached[x] = 1; + lp[x] = tail; + if (tail >= 0) ln[tail] = x; + else head = x; + tail = x; + }, + detach = (u: number): void => { + const x = node[u]; + if (x < 0) return; + if (rp[u] >= 0) rn[rp[u]] = rn[u]; + else rh[x] = rn[u]; + if (rn[u] >= 0) rp[rn[u]] = rp[u]; + node[u] = rp[u] = rn[u] = -1; + }, + attach = (u: number, x: number): void => { + node[u] = x; + rn[u] = rh[x]; + if (rh[x] >= 0) rp[rh[x]] = u; + rh[x] = u; + rp[u] = -1; + }; +while (q--) { + const op = a[p++], u = Number(a[p++]) - 1; + if (op === "G") { + if (node[u] < 0) out.push("MISS"); + else { + const x = node[u]; + touch(x); + out.push(`HIT ${x + 1}`); + } + continue; + } + const x = Number(a[p++]) - 1; + detach(u); + if (sz[x] > cap) continue; + if (!cached[x]) used += sz[x]; + touch(x); + attach(u, x); + while (used > cap) { + const dead = head; + remove(dead); + cached[dead] = 0; + used -= sz[dead]; + let v = rh[dead]; + while (v >= 0) { + const z = rn[v]; + node[v] = rp[v] = rn[v] = -1; + v = z; + } + rh[dead] = -1; + } +} +std.out.puts(out.join("\n") + "\n"); diff --git a/problems/017-graph-blob-lru/statement.en.md b/problems/017-graph-blob-lru/statement.en.md new file mode 100644 index 0000000..82b6a3e --- /dev/null +++ b/problems/017-graph-blob-lru/statement.en.md @@ -0,0 +1,104 @@ +# Graph Blob LRU + +Different nodes in a build graph may produce identical output, creating duplicate data that a WASM OJ build cache must handle. Storing a separate copy for every node would quickly waste storage on the same content, so the cache identifies blobs by digest. Several nodes may share one blob, whose size is charged only once. + +Sharing introduces another requirement: when a blob is evicted, every node that references that digest must become invalid immediately. When capacity is insufficient, eviction therefore operates on whole blobs in LRU order rather than removing individual node references. + +There are `N` nodes and `D` digests. Process these operations: + +- `P u d`: node `u` publishes digest `d`. First remove `u`'s old reference. If `size[d] > C`, no new reference is created and the LRU order is unchanged. Otherwise load the blob (without charging it again if it is already cached), attach `u` to it, and move it to MRU. While over capacity, repeatedly evict the LRU blob. +- `G u`: if `u`'s reference is still valid, output `HIT d` and move that blob to MRU; otherwise output `MISS`. + +A cached blob with no node references remains in the cache and participates in LRU until evicted. Repeating `P` with the same `(u,d)` still applies the complete rule: detach first, then attach and touch. + +## Input + +The first line contains `N D Q C`. The second line contains the `D` blob sizes. Each of the next `Q` lines is `P u d` or `G u`. All IDs are 1-based. Initially, no blob is cached and no node has a reference. + +## Output + +For each `G`, output one line containing `HIT d` or `MISS`. Output nothing for `P` operations. + +## Constraints + +- `1 ≤ N,D,Q ≤ 200000` +- There is at least one `G` operation. +- `0 ≤ C,size[d] ≤ 9×10^18` +- The sum of all blob sizes is at most `9×10^18`. +- Cache occupancy always fits in an unsigned 64-bit integer. +- If one eviction invalidates many nodes, all those references came from earlier `P` operations; full-credit solutions must exploit this amortized property. + +## Examples + + + +### Example One + +Input: + +```text +3 3 7 5 +3 2 4 +P 1 1 +P 2 2 +G 1 +P 3 3 +G 2 +G 3 +G 1 +``` + +Output: + +```text +HIT 1 +MISS +HIT 3 +MISS +``` + +### Example Two + +Input: + +```text +3 1 5 2 +2 +P 1 1 +P 2 1 +G 1 +P 1 1 +G 2 +``` + +Output: + +```text +HIT 1 +HIT 1 +``` + +### Example Three + +Input: + +```text +1 2 6 3 +4 3 +P 1 1 +G 1 +P 1 2 +G 1 +P 1 1 +G 1 +``` + +Output: + +```text +MISS +HIT 2 +MISS +``` + + diff --git a/problems/017-graph-blob-lru/statement.zh-TW.md b/problems/017-graph-blob-lru/statement.zh-TW.md new file mode 100644 index 0000000..d2fea4d --- /dev/null +++ b/problems/017-graph-blob-lru/statement.zh-TW.md @@ -0,0 +1,102 @@ +# Graph Blob LRU + +Build graph 中不同節點可能產生完全相同的 output,這是我們替 WASM OJ 設計 build cache 時必須處理的重複資料。若每個節點都各存一份,儲存空間會被相同內容快速耗盡;因此 cache 以 digest 識別 blob,多個節點可以共享同一份資料,容量也只計算一次。 + +共享帶來另一個問題:當一個 blob 被淘汰時,所有引用該 digest 的節點都必須立刻失效。cache 容量不足時,以 blob 為單位按照 LRU 順序淘汰,而不是個別移除節點引用。 + +有 `N` 個節點、`D` 個 digest。操作: + +- `P u d`:節點 `u` 發布 digest `d`。先移除 `u` 的舊引用。若 `size[d] > C`,新引用不成立且 LRU 不變;否則把 blob 載入(若已存在則不重複計空間)、讓 `u` 引用它並把它移到 MRU。若超容量,反覆淘汰 LRU blob。 +- `G u`:若 `u` 的引用仍有效,輸出 `HIT d` 並把 blob 移到 MRU;否則輸出 `MISS`。 + +沒有節點引用的 cached blob 仍留在 cache 並參與 LRU,直到被淘汰。對同一 `(u,d)` 再做 `P` 也依完整規則先 detach、再 attach/touch。 + +## 輸入 + +第一行 `N D Q C`。第二行有 `D` 個 blob size。接著 `Q` 行為 `P u d` 或 `G u`。所有 ID 為 1-based;初始沒有 blob 或引用。 + +## 輸出 + +依序為每個 `G` 輸出一行 `HIT d` 或 `MISS`,不輸出 `P` 的結果。 + +## 限制 + +- `1 <= N,D,Q <= 200000`,至少有一個 `G`。 +- `0 <= C,size[d] <= 9*10^18`,所有 size 總和不超過 `9*10^18`。 +- 任一時刻的 cache occupancy 以 unsigned 64-bit 表示。 +- 若一次淘汰使很多節點失效,這些引用都源自先前的 `P`;完整測資要求利用此 amortized 性質。 + +## 範例 + + + +### 範例一 + +輸入: + +```text +3 3 7 5 +3 2 4 +P 1 1 +P 2 2 +G 1 +P 3 3 +G 2 +G 3 +G 1 +``` + +輸出: + +```text +HIT 1 +MISS +HIT 3 +MISS +``` + +### 範例二 + +輸入: + +```text +3 1 5 2 +2 +P 1 1 +P 2 1 +G 1 +P 1 1 +G 2 +``` + +輸出: + +```text +HIT 1 +HIT 1 +``` + +### 範例三 + +輸入: + +```text +1 2 6 3 +4 3 +P 1 1 +G 1 +P 1 2 +G 1 +P 1 1 +G 1 +``` + +輸出: + +```text +MISS +HIT 2 +MISS +``` + + diff --git a/problems/017-graph-blob-lru/tests/adversarial-zero-dedup-eviction.in b/problems/017-graph-blob-lru/tests/adversarial-zero-dedup-eviction.in new file mode 100644 index 0000000..a4bb26a --- /dev/null +++ b/problems/017-graph-blob-lru/tests/adversarial-zero-dedup-eviction.in @@ -0,0 +1,18 @@ +4 5 16 5 +0 2 3 6 5 +P 1 1 +P 2 2 +P 3 2 +G 1 +P 1 4 +P 4 3 +G 2 +P 1 5 +G 2 +G 3 +G 4 +G 1 +P 1 5 +G 1 +P 1 4 +G 1 diff --git a/problems/017-graph-blob-lru/tests/adversarial-zero-dedup-eviction.out b/problems/017-graph-blob-lru/tests/adversarial-zero-dedup-eviction.out new file mode 100644 index 0000000..d8dc14b --- /dev/null +++ b/problems/017-graph-blob-lru/tests/adversarial-zero-dedup-eviction.out @@ -0,0 +1,8 @@ +HIT 1 +HIT 2 +MISS +MISS +MISS +HIT 5 +HIT 5 +MISS diff --git a/problems/017-graph-blob-lru/tests/sample-01.in b/problems/017-graph-blob-lru/tests/sample-01.in new file mode 100644 index 0000000..86db7cd --- /dev/null +++ b/problems/017-graph-blob-lru/tests/sample-01.in @@ -0,0 +1,9 @@ +3 3 7 5 +3 2 4 +P 1 1 +P 2 2 +G 1 +P 3 3 +G 2 +G 3 +G 1 diff --git a/problems/017-graph-blob-lru/tests/sample-01.out b/problems/017-graph-blob-lru/tests/sample-01.out new file mode 100644 index 0000000..2d7b1b3 --- /dev/null +++ b/problems/017-graph-blob-lru/tests/sample-01.out @@ -0,0 +1,4 @@ +HIT 1 +MISS +HIT 3 +MISS diff --git a/problems/017-graph-blob-lru/tests/sample-02.in b/problems/017-graph-blob-lru/tests/sample-02.in new file mode 100644 index 0000000..a26967f --- /dev/null +++ b/problems/017-graph-blob-lru/tests/sample-02.in @@ -0,0 +1,7 @@ +3 1 5 2 +2 +P 1 1 +P 2 1 +G 1 +P 1 1 +G 2 diff --git a/problems/017-graph-blob-lru/tests/sample-02.out b/problems/017-graph-blob-lru/tests/sample-02.out new file mode 100644 index 0000000..344c5b5 --- /dev/null +++ b/problems/017-graph-blob-lru/tests/sample-02.out @@ -0,0 +1,2 @@ +HIT 1 +HIT 1 diff --git a/problems/017-graph-blob-lru/tests/sample-03.in b/problems/017-graph-blob-lru/tests/sample-03.in new file mode 100644 index 0000000..d72126a --- /dev/null +++ b/problems/017-graph-blob-lru/tests/sample-03.in @@ -0,0 +1,8 @@ +1 2 6 3 +4 3 +P 1 1 +G 1 +P 1 2 +G 1 +P 1 1 +G 1 diff --git a/problems/017-graph-blob-lru/tests/sample-03.out b/problems/017-graph-blob-lru/tests/sample-03.out new file mode 100644 index 0000000..9420d9b --- /dev/null +++ b/problems/017-graph-blob-lru/tests/sample-03.out @@ -0,0 +1,3 @@ +MISS +HIT 2 +MISS diff --git a/problems/017-graph-blob-lru/validator.py b/problems/017-graph-blob-lru/validator.py new file mode 100644 index 0000000..57d364c --- /dev/null +++ b/problems/017-graph-blob-lru/validator.py @@ -0,0 +1,36 @@ +import sys + +U = 9_000_000_000_000_000_000 + + +def main(): + ls = sys.stdin.read().splitlines() + assert len(ls) >= 3 + h = ls[0].split() + assert len(h) == 4 + n, d, q, c = map(int, h) + assert ( + 1 <= n <= 200000 + and 1 <= d <= 200000 + and 1 <= q <= 200000 + and 0 <= c <= U + and len(ls) == q + 2 + ) + z = list(map(int, ls[1].split())) + assert len(z) == d and all(0 <= x <= U for x in z) and sum(z) <= U + gets = 0 + for line in ls[2:]: + x = line.split() + assert x and x[0] in ("P", "G") + if x[0] == "P": + assert len(x) == 3 and 1 <= int(x[1]) <= n and 1 <= int(x[2]) <= d + else: + assert len(x) == 2 and 1 <= int(x[1]) <= n + gets += 1 + assert gets > 0 + + +try: + main() +except (AssertionError, ValueError): + sys.exit(1) diff --git a/problems/018-worker-generations/editorial.en.md b/problems/018-worker-generations/editorial.en.md new file mode 100644 index 0000000..a55b20f --- /dev/null +++ b/problems/018-worker-generations/editorial.en.md @@ -0,0 +1,26 @@ +# Editorial + +## Intuitive Approach + +Store every assignment and replay the history before build `i` to recover the active generation, family, and used stages. This is correct but takes `O(N^2)` total time. + +## Optimal Approach: Keep Only the Current Generation + +Only four state values are needed: the current generation ID, its family, its used budget, and the rejection count. Handle `stages=0` first, followed by the two rejection conditions; neither branch may alter worker state. For a valid cache miss, if the current worker cannot serve it, increment the generation ID, replace the family, and reset used budget to zero. Then add `stages`. + +This is also the forced greedy choice: when the active worker is compatible, reusing it does not create a worker; when it is not compatible, creating a new generation is the only legal action. + +## Correctness Proof + +Induct over the build prefix. Initially no worker exists, so the state is correct. Cache and rejection branches output exactly as defined and preserve state. For a valid miss, if the active worker has the same family and enough capacity, it can and must serve the build; the algorithm does so and increases used budget correctly. Otherwise no legal active worker exists, and the only permitted action is to create the next generation; the algorithm assigns the next consecutive ID and places the build there. Every output and successor state is therefore uniquely correct, as are the final counts. + +## Complexity + +Each build takes constant work, so time is `O(N)`. Excluding output buffering, additional space is `O(1)`; the current family string has length at most 20. + +## Common Mistakes + +- Switching the active family on a cache hit. +- Consuming budget or creating a generation for a rejected build. +- Reusing an older worker when the family later changes back. +- Checking `stages>B` in a way that lets `stages=0` modify state in a corner case. diff --git a/problems/018-worker-generations/editorial.zh-TW.md b/problems/018-worker-generations/editorial.zh-TW.md new file mode 100644 index 0000000..b0067da --- /dev/null +++ b/problems/018-worker-generations/editorial.zh-TW.md @@ -0,0 +1,26 @@ +# 解題說明 + +## 直覺解 + +保存全部 assignment,處理第 `i` 筆前從頭重播,推回 active generation、family 與 used stages。這正確但總時間 `O(N^2)`。 + +## 最佳解 + +只需四個狀態:目前 generation ID、目前 family、目前 used、reject count。先處理 `stages=0`,再處理兩個 reject 條件;兩者都不得改狀態。有效 miss 若不符合目前 Worker,就遞增 ID、替換 family 並把 used 歸零,最後累加 stages。 + +這同時是 greedy:規格要求只能用 active generation;符合時沿用不會增加 Worker 數,不符合時建立新 generation 是唯一可行動作。 + +## 正確性證明 + +以 build 前綴歸納。初始沒有 Worker,狀態正確。cache/reject 分支依定義輸出且不改狀態。對有效 miss,若 active Worker 同 family 且容量足,規格要求可且應使用它;演算法如此做並正確增加 used。否則沒有合法 active Worker,唯一合法選擇是新 generation;演算法建立下一個連續 ID 並配置該 build。故每一步輸出與後繼狀態皆唯一正確,最終兩個計數也正確。 + +## 複雜度 + +每筆常數工作,時間 `O(N)`;除輸出緩衝外額外空間 `O(1)`(目前 family 字串長度至多 20)。 + +## 常見錯誤 + +- cache hit 切換了 active family。 +- rejected build 消耗容量或建立 generation。 +- family 切回舊值時回用了舊 Worker。 +- 先判 `stages>B`,卻讓 `stages=0` 在某些特例改變狀態。 diff --git a/problems/018-worker-generations/generator.py b/problems/018-worker-generations/generator.py new file mode 100644 index 0000000..4b0c087 --- /dev/null +++ b/problems/018-worker-generations/generator.py @@ -0,0 +1,9 @@ +import random, sys + +seed, index = map(int, sys.argv[1:]) +r = random.Random(seed + index * 1009) +n = 10 + index % 15 +b = r.randrange(1, 10) +print(n, b) +for _ in range(n): + print("f" + str(r.randrange(4)), r.randrange(13)) diff --git a/problems/018-worker-generations/oracle.py b/problems/018-worker-generations/oracle.py new file mode 100644 index 0000000..78a3e01 --- /dev/null +++ b/problems/018-worker-generations/oracle.py @@ -0,0 +1,39 @@ +import sys + +it = iter(sys.stdin.read().split()) +n = int(next(it)) +b = int(next(it)) +history = [] +reject = 0 +out = [] +for _ in range(n): + f = next(it) + s = int(next(it)) + if s == 0: + out.append("CACHE") + continue + if s > 8 or s > b: + reject += 1 + out.append("REJECT") + continue + generation = 0 + family = None + used = 0 + for pf, ps, accepted in history: + if not accepted or ps == 0: + continue + if family != pf or used + ps > b: + generation += 1 + family = pf + used = 0 + used += ps + if family != f or used + s > b: + generation += 1 + out.append(f"WORKER {generation}") + history.append((f, s, True)) +print("\n".join(out)) +print( + "SUMMARY", + max([0] + [int(x.split()[1]) for x in out if x.startswith("WORKER")]), + reject, +) diff --git a/problems/018-worker-generations/problem.json b/problems/018-worker-generations/problem.json new file mode 100644 index 0000000..4692d33 --- /dev/null +++ b/problems/018-worker-generations/problem.json @@ -0,0 +1,147 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 18, + "slug": "worker-generations", + "title": { + "zh-TW": "八階段編譯器", + "en": "Eight-Stage Compiler" + }, + "difficulty": "medium", + "tags": [ + "greedy", + "simulation", + "state-machine", + "resource-accounting" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-state-preservation", + "kind": "adversarial", + "input": "tests/adversarial-state-preservation.in", + "output": "tests/adversarial-state-preservation.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 7000000, + "memoryLimitBytes": 268435456 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 1500000, + "memoryLimitBytes": 201326592 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 550000, + "memoryLimitBytes": 134217728 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "每次重播歷史恢復 Worker 狀態", + "en": "Replay History to Recover Worker State" + }, + "time": "O(N^2)", + "space": "O(N)", + "accepted": false + }, + { + "name": { + "zh-TW": "單一目前 generation 狀態", + "en": "Single Current-Generation State" + }, + "time": "O(N)", + "space": "O(1) excluding output", + "accepted": true + } + ] +} diff --git a/problems/018-worker-generations/solutions/c/main.c b/problems/018-worker-generations/solutions/c/main.c new file mode 100644 index 0000000..aaa612d --- /dev/null +++ b/problems/018-worker-generations/solutions/c/main.c @@ -0,0 +1,35 @@ +#include +#include +typedef unsigned long long U; +int main(void) { + int n; + if (scanf("%d", &n) != 1) + return 0; + U b, used = 0; + scanf("%llu", &b); + char cur[21] = ""; + int gen = 0, reject = 0; + while (n--) { + char f[21]; + U s; + scanf("%20s%llu", f, &s); + if (!s) { + puts("CACHE"); + continue; + } + if (s > 8 || s > b) { + puts("REJECT"); + reject++; + continue; + } + if (strcmp(cur, f) || used + s > b) { + strcpy(cur, f); + used = 0; + gen++; + } + used += s; + printf("WORKER %d\n", gen); + } + printf("SUMMARY %d %d\n", gen, reject); + return 0; +} diff --git a/problems/018-worker-generations/solutions/cpp/main.cpp b/problems/018-worker-generations/solutions/cpp/main.cpp new file mode 100644 index 0000000..ed642f2 --- /dev/null +++ b/problems/018-worker-generations/solutions/cpp/main.cpp @@ -0,0 +1,37 @@ +#include +#include +#include +using namespace std; +int main() { + ios::sync_with_stdio(false); + cin.tie(nullptr); + int n; + if (!(cin >> n)) + return 0; + uint64_t b, used = 0; + cin >> b; + string cur; + int gen = 0, reject = 0; + while (n--) { + string f; + uint64_t s; + cin >> f >> s; + if (s == 0) { + cout << "CACHE\n"; + continue; + } + if (s > 8 || s > b) { + cout << "REJECT\n"; + ++reject; + continue; + } + if (cur != f || used + s > b) { + cur = f; + used = 0; + ++gen; + } + used += s; + cout << "WORKER " << gen << '\n'; + } + cout << "SUMMARY " << gen << ' ' << reject << '\n'; +} diff --git a/problems/018-worker-generations/solutions/go/main.go b/problems/018-worker-generations/solutions/go/main.go new file mode 100644 index 0000000..c2177c8 --- /dev/null +++ b/problems/018-worker-generations/solutions/go/main.go @@ -0,0 +1,40 @@ +package main + +import ( + "bufio" + "fmt" + "os" +) + +func main() { + in := bufio.NewReader(os.Stdin) + out := bufio.NewWriter(os.Stdout) + defer out.Flush() + var n int + var b, used uint64 + fmt.Fscan(in, &n, &b) + cur := "" + gen, reject := 0, 0 + for ; n > 0; n-- { + var f string + var s uint64 + fmt.Fscan(in, &f, &s) + if s == 0 { + fmt.Fprintln(out, "CACHE") + continue + } + if s > 8 || s > b { + fmt.Fprintln(out, "REJECT") + reject++ + continue + } + if cur != f || used+s > b { + cur = f + used = 0 + gen++ + } + used += s + fmt.Fprintln(out, "WORKER", gen) + } + fmt.Fprintln(out, "SUMMARY", gen, reject) +} diff --git a/problems/018-worker-generations/solutions/javascript/main.js b/problems/018-worker-generations/solutions/javascript/main.js new file mode 100644 index 0000000..abefbe2 --- /dev/null +++ b/problems/018-worker-generations/solutions/javascript/main.js @@ -0,0 +1,31 @@ +import * as std from "std"; +const a = std.in.readAsString().trim().split(/\s+/); +let p = 0, + n = Number(a[p++]), + b = BigInt(a[p++]), + used = 0n, + gen = 0, + reject = 0, + cur = null, + out = []; +while (n--) { + const f = a[p++], s = BigInt(a[p++]); + if (s === 0n) { + out.push("CACHE"); + continue; + } + if (s > 8n || s > b) { + out.push("REJECT"); + reject++; + continue; + } + if (cur !== f || used + s > b) { + cur = f; + used = 0n; + gen++; + } + used += s; + out.push(`WORKER ${gen}`); +} +out.push(`SUMMARY ${gen} ${reject}`); +std.out.puts(out.join("\n") + "\n"); diff --git a/problems/018-worker-generations/solutions/python/main.py b/problems/018-worker-generations/solutions/python/main.py new file mode 100644 index 0000000..6af0080 --- /dev/null +++ b/problems/018-worker-generations/solutions/python/main.py @@ -0,0 +1,25 @@ +import sys + +it = iter(sys.stdin.read().split()) +n = int(next(it)) +b = int(next(it)) +gen = used = reject = 0 +family = None +out = [] +for _ in range(n): + f = next(it) + s = int(next(it)) + if s == 0: + out.append("CACHE") + elif s > 8 or s > b: + reject += 1 + out.append("REJECT") + else: + if family != f or used + s > b: + gen += 1 + family = f + used = 0 + used += s + out.append(f"WORKER {gen}") +out.append(f"SUMMARY {gen} {reject}") +print("\n".join(out)) diff --git a/problems/018-worker-generations/solutions/rust/main.rs b/problems/018-worker-generations/solutions/rust/main.rs new file mode 100644 index 0000000..3f76b85 --- /dev/null +++ b/problems/018-worker-generations/solutions/rust/main.rs @@ -0,0 +1,31 @@ +use std::io::{self, Read}; +fn main() { + let mut x = String::new(); + io::stdin().read_to_string(&mut x).unwrap(); + let mut it = x.split_whitespace(); + let n: usize = it.next().unwrap().parse().unwrap(); + let b: u64 = it.next().unwrap().parse().unwrap(); + let (mut generation, mut used, mut reject) = (0, 0u64, 0); + let mut family = ""; + let mut out = String::new(); + for _ in 0..n { + let f = it.next().unwrap(); + let s: u64 = it.next().unwrap().parse().unwrap(); + if s == 0 { + out.push_str("CACHE\n") + } else if s > 8 || s > b { + reject += 1; + out.push_str("REJECT\n") + } else { + if family != f || used + s > b { + generation += 1; + family = f; + used = 0 + } + used += s; + out.push_str(&format!("WORKER {generation}\n")); + } + } + out.push_str(&format!("SUMMARY {generation} {reject}\n")); + print!("{out}"); +} diff --git a/problems/018-worker-generations/solutions/typescript/main.ts b/problems/018-worker-generations/solutions/typescript/main.ts new file mode 100644 index 0000000..6fa858e --- /dev/null +++ b/problems/018-worker-generations/solutions/typescript/main.ts @@ -0,0 +1,31 @@ +import * as std from "std"; +const a: string[] = std.in.readAsString().trim().split(/\s+/); +let p = 0, + n = Number(a[p++]), + b = BigInt(a[p++]), + used = 0n, + gen = 0, + reject = 0, + cur: string | null = null; +const out: string[] = []; +while (n--) { + const f = a[p++], s = BigInt(a[p++]); + if (s === 0n) { + out.push("CACHE"); + continue; + } + if (s > 8n || s > b) { + out.push("REJECT"); + reject++; + continue; + } + if (cur !== f || used + s > b) { + cur = f; + used = 0n; + gen++; + } + used += s; + out.push(`WORKER ${gen}`); +} +out.push(`SUMMARY ${gen} ${reject}`); +std.out.puts(out.join("\n") + "\n"); diff --git a/problems/018-worker-generations/statement.en.md b/problems/018-worker-generations/statement.en.md new file mode 100644 index 0000000..0ee0742 --- /dev/null +++ b/problems/018-worker-generations/statement.en.md @@ -0,0 +1,113 @@ +# Eight-Stage Compiler + +Starting a toolchain for every in-browser build would impose unnecessary cost on a WASM OJ, so we want to reuse workers. A worker cannot accept jobs forever, however, because accumulated state and resource usage would become difficult to control. The coordinator therefore manages workers in generations and gives each generation a lifetime budget. + +A supported build contains at most eight output-ready stages. Every stage completed successfully consumes one unit of budget. A generation may consume at most `B` units and may serve only one toolchain family. Assign builds in arrival order according to these rules: + +- `stages=0` is a complete cache hit. Output `CACHE`; do not create, switch, or consume the current worker. +- If `stages>8` or `stages>B`, output `REJECT`. A rejection does not change the current worker. +- Every other build must use the **current** generation. If none exists, the family differs, or remaining budget is insufficient, create the next generation and assign the build to it. + +Generation IDs start at 1 and increase consecutively. The coordinator keeps only one active worker, so once it leaves an old generation, that generation is never reused even if it still has budget remaining. + +## Input + +The first line contains `N B`. Each of the next `N` lines contains `family stages`. + +## Output + +For every build, output one line containing `CACHE`, `REJECT`, or `WORKER g`. Finally output: + +```text +SUMMARY workerCount rejectedCount +``` + +A cache hit counts as neither a worker nor a rejection. + +## Constraints + +- `1 ≤ N ≤ 300000` +- `1 ≤ B ≤ 9×10^18` +- `0 ≤ stages ≤ 12` +- A family has length `1..20` and contains only lowercase letters, digits, and `-`. +- All counters fit in unsigned 64-bit integers; JavaScript and TypeScript must handle `B` above the safe-integer range correctly. + +The full constraints rule out replaying all previous assignments before every build to reconstruct the current generation. + +## Examples + + + +### Example One + +Input: + +```text +6 5 +a 3 +a 2 +a 1 +b 0 +b 4 +b 2 +``` + +Output: + +```text +WORKER 1 +WORKER 1 +WORKER 2 +CACHE +WORKER 3 +WORKER 4 +SUMMARY 4 0 +``` + +### Example Two + +Input: + +```text +4 4 +x 5 +y 9 +x 0 +x 4 +``` + +Output: + +```text +REJECT +REJECT +CACHE +WORKER 1 +SUMMARY 1 2 +``` + +### Example Three + +Input: + +```text +5 8 +a 4 +b 0 +a 4 +b 1 +a 1 +``` + +Output: + +```text +WORKER 1 +CACHE +WORKER 1 +WORKER 2 +WORKER 3 +SUMMARY 3 0 +``` + + diff --git a/problems/018-worker-generations/statement.zh-TW.md b/problems/018-worker-generations/statement.zh-TW.md new file mode 100644 index 0000000..d4ae4a1 --- /dev/null +++ b/problems/018-worker-generations/statement.zh-TW.md @@ -0,0 +1,110 @@ +# 八階段編譯器 + +瀏覽器內編譯若每次 build 都重新啟動 toolchain,會為 WASM OJ 帶來不必要的成本,因此我們希望重複使用 Worker;但 Worker 也不能無限期承接工作,否則累積的狀態與資源用量會變得難以控制。為此,coordinator 以 generation 管理 Worker,並為每一代設定 lifetime budget。 + +系統支援的 build 最多包含八個 output-ready stage。每個成功完成的 stage 消耗一單位 budget;同一 generation 最多可消耗 `B` 單位,而且只能服務一個 toolchain family。build 必須依到達順序按以下規則分派: + +- `stages=0` 表示完整 cache hit,輸出 `CACHE`,不建立、切換或消耗目前 Worker。 +- `stages>8`,或 `stages>B`,輸出 `REJECT`;拒絕不改變目前 Worker。 +- 其他 build 必須交給**目前** generation。若目前不存在、family 不同、或剩餘 budget 不足,就建立下一個 generation,再把 build 指派給它。 + +Generation ID 從 1 連續遞增。coordinator 同一時間只保留一個 active Worker,因此一旦切離舊 generation,就不再回用,即使它仍有剩餘 budget。 + +## 輸入 + +第一行 `N B`。接著 `N` 行 `family stages`。 + +## 輸出 + +對每個 build 輸出一行 `CACHE`、`REJECT` 或 `WORKER g`。最後輸出: + +```text +SUMMARY workerCount rejectedCount +``` + +Cache hit 不計 worker,也不計 rejected。 + +## 限制 + +- `1 <= N <= 300000`,`1 <= B <= 9*10^18`。 +- `0 <= stages <= 12`;family 長 1 到 20,只含小寫字母、數字、`-`。 +- 所有計數可放入 unsigned 64-bit;JS/TS 必須正確處理大於 safe integer 的 `B`。 +- 完整限制排除每筆重播全部歷史來恢復 current generation 的方法。 + +## 範例 + + + +### 範例一 + +輸入: + +```text +6 5 +a 3 +a 2 +a 1 +b 0 +b 4 +b 2 +``` + +輸出: + +```text +WORKER 1 +WORKER 1 +WORKER 2 +CACHE +WORKER 3 +WORKER 4 +SUMMARY 4 0 +``` + +### 範例二 + +輸入: + +```text +4 4 +x 5 +y 9 +x 0 +x 4 +``` + +輸出: + +```text +REJECT +REJECT +CACHE +WORKER 1 +SUMMARY 1 2 +``` + +### 範例三 + +輸入: + +```text +5 8 +a 4 +b 0 +a 4 +b 1 +a 1 +``` + +輸出: + +```text +WORKER 1 +CACHE +WORKER 1 +WORKER 2 +WORKER 3 +SUMMARY 3 0 +``` + + diff --git a/problems/018-worker-generations/tests/adversarial-state-preservation.in b/problems/018-worker-generations/tests/adversarial-state-preservation.in new file mode 100644 index 0000000..014cf67 --- /dev/null +++ b/problems/018-worker-generations/tests/adversarial-state-preservation.in @@ -0,0 +1,13 @@ +12 7 +a 0 +a 8 +a 7 +b 9 +b 0 +a 1 +a 6 +b 3 +a 3 +a 4 +a 12 +a 1 diff --git a/problems/018-worker-generations/tests/adversarial-state-preservation.out b/problems/018-worker-generations/tests/adversarial-state-preservation.out new file mode 100644 index 0000000..ce68216 --- /dev/null +++ b/problems/018-worker-generations/tests/adversarial-state-preservation.out @@ -0,0 +1,13 @@ +CACHE +REJECT +WORKER 1 +REJECT +CACHE +WORKER 2 +WORKER 2 +WORKER 3 +WORKER 4 +WORKER 4 +REJECT +WORKER 5 +SUMMARY 5 3 diff --git a/problems/018-worker-generations/tests/sample-01.in b/problems/018-worker-generations/tests/sample-01.in new file mode 100644 index 0000000..4e1aef2 --- /dev/null +++ b/problems/018-worker-generations/tests/sample-01.in @@ -0,0 +1,7 @@ +6 5 +a 3 +a 2 +a 1 +b 0 +b 4 +b 2 diff --git a/problems/018-worker-generations/tests/sample-01.out b/problems/018-worker-generations/tests/sample-01.out new file mode 100644 index 0000000..b21e199 --- /dev/null +++ b/problems/018-worker-generations/tests/sample-01.out @@ -0,0 +1,7 @@ +WORKER 1 +WORKER 1 +WORKER 2 +CACHE +WORKER 3 +WORKER 4 +SUMMARY 4 0 diff --git a/problems/018-worker-generations/tests/sample-02.in b/problems/018-worker-generations/tests/sample-02.in new file mode 100644 index 0000000..c07b7a6 --- /dev/null +++ b/problems/018-worker-generations/tests/sample-02.in @@ -0,0 +1,5 @@ +4 4 +x 5 +y 9 +x 0 +x 4 diff --git a/problems/018-worker-generations/tests/sample-02.out b/problems/018-worker-generations/tests/sample-02.out new file mode 100644 index 0000000..8069e39 --- /dev/null +++ b/problems/018-worker-generations/tests/sample-02.out @@ -0,0 +1,5 @@ +REJECT +REJECT +CACHE +WORKER 1 +SUMMARY 1 2 diff --git a/problems/018-worker-generations/tests/sample-03.in b/problems/018-worker-generations/tests/sample-03.in new file mode 100644 index 0000000..eb840e8 --- /dev/null +++ b/problems/018-worker-generations/tests/sample-03.in @@ -0,0 +1,6 @@ +5 8 +a 4 +b 0 +a 4 +b 1 +a 1 diff --git a/problems/018-worker-generations/tests/sample-03.out b/problems/018-worker-generations/tests/sample-03.out new file mode 100644 index 0000000..bcad733 --- /dev/null +++ b/problems/018-worker-generations/tests/sample-03.out @@ -0,0 +1,6 @@ +WORKER 1 +CACHE +WORKER 1 +WORKER 2 +WORKER 3 +SUMMARY 3 0 diff --git a/problems/018-worker-generations/validator.py b/problems/018-worker-generations/validator.py new file mode 100644 index 0000000..a90cb05 --- /dev/null +++ b/problems/018-worker-generations/validator.py @@ -0,0 +1,24 @@ +import re, sys + +U = 9_000_000_000_000_000_000 + + +def main(): + ls = sys.stdin.read().splitlines() + assert ls + h = ls[0].split() + assert len(h) == 2 + n = int(h[0]) + b = int(h[1]) + assert 1 <= n <= 300000 and 1 <= b <= U and len(ls) == n + 1 + for x in ls[1:]: + p = x.split() + assert len(p) == 2 and re.fullmatch(r"[a-z0-9-]{1,20}", p[0]) + s = int(p[1]) + assert str(s) == p[1] and 0 <= s <= 12 + + +try: + main() +except (AssertionError, ValueError): + sys.exit(1) diff --git a/problems/019-reproducible-build-order/editorial.en.md b/problems/019-reproducible-build-order/editorial.en.md new file mode 100644 index 0000000..0588991 --- /dev/null +++ b/problems/019-reproducible-build-order/editorial.en.md @@ -0,0 +1,26 @@ +# Editorial + +## Intuitive Approach + +Repeatedly scan all unbuilt packages for the lexicographically smallest one with indegree zero. Even if every edge is updated only once, finding the minimum takes `O(N^2)` time. + +## Optimal Approach: Kahn's Algorithm with a Name Min-Heap + +Sort `(name,ID)` by name. While reading an edge, find both IDs by binary search and remember the first edge with an unknown endpoint. If any dangling edge exists, report it immediately as required. For a legal relation `a depends b`, create edge `b -> a` and increment `indegree[a]`. This comparison-based lookup gives deterministic worst-case bounds in every reference language without relying on expected hash-table behavior. + +Insert all indegree-zero IDs into a min-heap ordered by package name. Repeatedly pop and output the minimum, decrement every downstream indegree, and push a downstream package when its indegree becomes zero. If fewer than `N` packages are output, report a cycle. + +## Correctness Proof + +If a dangling edge is reported, the stored edge has the smallest input index among all unknown endpoints, so it satisfies the highest-priority error. Now assume no dangling edge. Maintain the Kahn invariant that the heap contains exactly all unbuilt nodes of indegree zero. It holds initially. Popping a node removes exactly its outgoing edges, adding a downstream node precisely when its last unbuilt dependency disappears, so the invariant is preserved. At each step, the heap minimum is exactly the lexicographically smallest ready package, making a successful order uniquely correct. If processing stops early, Kahn's theorem guarantees a directed cycle among or blocking the remaining nodes; conversely, a DAG always has another indegree-zero node. Thus cycle detection is also correct. + +## Complexity + +Sorting names takes `O(N log N)`. Every edge performs two `O(log N)` binary searches, and each node enters and leaves the heap at most once. Total time is `O((N+M) log N)` and space is `O(N+M)`. + +## Common Mistakes + +- Building `a -> b` for `a depends b` instead of `b -> a`. +- Using a FIFO queue and producing a valid but noncanonical topological order. +- Reporting a cycle before a higher-priority dangling edge. +- Ordering heap entries by ID rather than package name. diff --git a/problems/019-reproducible-build-order/editorial.zh-TW.md b/problems/019-reproducible-build-order/editorial.zh-TW.md new file mode 100644 index 0000000..4d0900f --- /dev/null +++ b/problems/019-reproducible-build-order/editorial.zh-TW.md @@ -0,0 +1,26 @@ +# 解題說明 + +## 直覺解 + +重複掃描所有未輸出 package,找 indegree=0 且名稱最小者;每次輸出後更新下游。即使更新邊只做一次,找最小者仍為 `O(N^2)`。 + +## 最佳解 + +先把 `(name, ID)` 依 name 排序;讀 edge 時以 binary search 找 ID,並記錄第一條未知端點。若有 dangling 立即依規格輸出。對合法 edge `a depends b` 建立方向 `b -> a`,並增加 `indegree[a]`。這條 comparison-based lookup 路徑在所有 reference language 都具有 deterministic worst-case bound,不依賴 hash table 的 expected-time 假設。 + +把所有 indegree 0 的 ID 放進按 package name 排序的 min-heap。反覆 pop、輸出,並遞減其下游 indegree;變成 0 時 push。若最後輸出少於 `N`,剩下節點必位於 cycle 或受 cycle 阻擋,輸出 cycle error。 + +## 正確性證明 + +若回報 dangling,所選 edge 是讀取時最小索引,符合第一優先錯誤。以下假設無 dangling。Kahn invariant:heap 恰含所有尚未輸出且 indegree=0 的節點;初始化成立,pop 後只移除該節點的 outgoing edges,恰在下游最後一個未完成依賴消失時將它加入,故維持。每一步 heap minimum 正是規格要求的字典序最小 ready package,因此成功時整個 ORDER 唯一正確。若無法輸出全部節點,Kahn 定理保證剩餘有 directed cycle;反之 DAG 必能持續找到 indegree 0,故 cycle 判定亦正確。 + +## 複雜度 + +排序 name table 為 `O(N log N)`;每個 edge 做兩次 `O(log N)` binary search,每個節點至多一次 heap push/pop,因此總時間 `O((N+M) log N)`,空間 `O(N+M)`。 + +## 常見錯誤 + +- 把 `a depends b` 建成 `a -> b`。 +- 用 FIFO queue,結果雖是拓撲序卻不符合 deterministic tie-break。 +- 有 dangling 時仍先回報 cycle。 +- 依 ID 而不是 package name 比較 heap 元素。 diff --git a/problems/019-reproducible-build-order/generator.py b/problems/019-reproducible-build-order/generator.py new file mode 100644 index 0000000..b8b2fa3 --- /dev/null +++ b/problems/019-reproducible-build-order/generator.py @@ -0,0 +1,20 @@ +import random, sys + +seed, index = map(int, sys.argv[1:]) +r = random.Random(seed * 17 + index) +n = 8 + index % 10 +names = [f"p{i:02d}" for i in range(n)] +edges = [] +for a in range(n): + for b in range(a): + if r.random() < 0.12: + edges.append((names[a], names[b])) +if index % 5 == 1: + edges.append((names[0], "ghost")) +elif index % 5 == 2: + edges.extend(((names[0], names[1]), (names[1], names[0]))) +edges = list(dict.fromkeys(edges)) +print(n, len(edges)) +print(*names, sep="\n") +for e in edges: + print(*e) diff --git a/problems/019-reproducible-build-order/oracle.py b/problems/019-reproducible-build-order/oracle.py new file mode 100644 index 0000000..80bbe73 --- /dev/null +++ b/problems/019-reproducible-build-order/oracle.py @@ -0,0 +1,28 @@ +import sys + +it = iter(sys.stdin.read().split()) +n = int(next(it)) +m = int(next(it)) +names = [next(it) for _ in range(n)] +known = set(names) +edges = [] +bad = None +for i in range(1, m + 1): + a, b = next(it), next(it) + if bad is None and (a not in known or b not in known): + bad = i + edges.append((a, b)) +if bad is not None: + print("INVALID DANGLING", bad) + raise SystemExit +left = set(names) +order = [] +while left: + ready = [x for x in left if all(a != x or b not in left for a, b in edges)] + if not ready: + print("INVALID CYCLE") + raise SystemExit + x = min(ready) + left.remove(x) + order.append(x) +print("ORDER", *order) diff --git a/problems/019-reproducible-build-order/problem.json b/problems/019-reproducible-build-order/problem.json new file mode 100644 index 0000000..ad0be3d --- /dev/null +++ b/problems/019-reproducible-build-order/problem.json @@ -0,0 +1,147 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 19, + "slug": "reproducible-build-order", + "title": { + "zh-TW": "可重現的套件建置順序", + "en": "Reproducible Package Build Order" + }, + "difficulty": "medium", + "tags": [ + "graph", + "topological-sort", + "heap", + "determinism" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-dangling-before-cycle", + "kind": "adversarial", + "input": "tests/adversarial-dangling-before-cycle.in", + "output": "tests/adversarial-dangling-before-cycle.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 200000000, + "memoryLimitBytes": 536870912 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 1000000, + "memoryLimitBytes": 402653184 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 350000, + "memoryLimitBytes": 268435456 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "每輪掃描所有未建置套件", + "en": "Scan All Unbuilt Packages per Step" + }, + "time": "O(N^2 + M)", + "space": "O(N+M)", + "accepted": false + }, + { + "name": { + "zh-TW": "Kahn 與名稱最小堆", + "en": "Kahn's Algorithm with a Name Min-Heap" + }, + "time": "O((N+M) log N)", + "space": "O(N+M)", + "accepted": true + } + ] +} diff --git a/problems/019-reproducible-build-order/solutions/c/main.c b/problems/019-reproducible-build-order/solutions/c/main.c new file mode 100644 index 0000000..8e3b756 --- /dev/null +++ b/problems/019-reproducible-build-order/solutions/c/main.c @@ -0,0 +1,113 @@ +#include +#include +#include +typedef struct { + char *s; + int id; +} E; +static E *mapv; +static char (*namev)[31]; +int ec(const void *a, const void *b) { + return strcmp(((const E *)a)->s, ((const E *)b)->s); +} +int findid(const char *s, int n) { + int l = 0, r = n; + while (l < r) { + int m = (l + r) / 2, c = strcmp(mapv[m].s, s); + if (c < 0) + l = m + 1; + else + r = m; + } + return l < n && !strcmp(mapv[l].s, s) ? mapv[l].id : -1; +} +int less(int a, int b) { return strcmp(namev[a], namev[b]) < 0; } +void push(int *h, int *z, int x) { + int i = (*z)++; + h[i] = x; + while (i) { + int p = (i - 1) / 2; + if (!less(h[i], h[p])) + break; + int t = h[i]; + h[i] = h[p]; + h[p] = t; + i = p; + } +} +int pop(int *h, int *z) { + int ans = h[0], x = h[--*z], i = 0; + if (*z) + h[0] = x; + for (;;) { + int l = i * 2 + 1, r = l + 1, b = i; + if (l < *z && less(h[l], h[b])) + b = l; + if (r < *z && less(h[r], h[b])) + b = r; + if (b == i) + break; + int t = h[i]; + h[i] = h[b]; + h[b] = t; + i = b; + } + return ans; +} +int main(void) { + int n, m; + if (scanf("%d%d", &n, &m) != 2) + return 0; + namev = malloc(sizeof(*namev) * (size_t)n); + mapv = malloc(sizeof(E) * (size_t)n); + for (int i = 0; i < n; i++) { + scanf("%30s", namev[i]); + mapv[i] = (E){namev[i], i}; + } + qsort(mapv, (size_t)n, sizeof(E), ec); + int *head = malloc(sizeof(int) * (size_t)n), + *to = malloc(sizeof(int) * (size_t)(m ? m : 1)), + *next = malloc(sizeof(int) * (size_t)(m ? m : 1)), + *deg = calloc((size_t)n, sizeof(int)); + for (int i = 0; i < n; i++) + head[i] = -1; + int bad = 0; + for (int i = 0; i < m; i++) { + char a[31], b[31]; + scanf("%30s%30s", a, b); + int x = findid(a, n), y = findid(b, n); + if ((x < 0 || y < 0) && !bad) + bad = i + 1; + if (x >= 0 && y >= 0) { + to[i] = x; + next[i] = head[y]; + head[y] = i; + deg[x]++; + } + } + if (bad) { + printf("INVALID DANGLING %d\n", bad); + return 0; + } + int *h = malloc(sizeof(int) * (size_t)n), z = 0, + *out = malloc(sizeof(int) * (size_t)n), k = 0; + for (int i = 0; i < n; i++) + if (!deg[i]) + push(h, &z, i); + while (z) { + int u = pop(h, &z); + out[k++] = u; + for (int e = head[u]; e >= 0; e = next[e]) + if (!--deg[to[e]]) + push(h, &z, to[e]); + } + if (k < n) + puts("INVALID CYCLE"); + else { + printf("ORDER"); + for (int i = 0; i < n; i++) + printf(" %s", namev[out[i]]); + putchar('\n'); + } + return 0; +} diff --git a/problems/019-reproducible-build-order/solutions/cpp/main.cpp b/problems/019-reproducible-build-order/solutions/cpp/main.cpp new file mode 100644 index 0000000..a59411e --- /dev/null +++ b/problems/019-reproducible-build-order/solutions/cpp/main.cpp @@ -0,0 +1,68 @@ +#include +#include +#include +#include +#include +#include +using namespace std; +int main() { + ios::sync_with_stdio(false); + cin.tie(nullptr); + int n, m; + if (!(cin >> n >> m)) + return 0; + vector names(n); + for (int i = 0; i < n; i++) + cin >> names[i]; + vector name_order(n); + iota(name_order.begin(), name_order.end(), 0); + sort(name_order.begin(), name_order.end(), + [&](int x, int y) { return names[x] < names[y]; }); + auto find_id = [&](const string &name) { + auto it = + lower_bound(name_order.begin(), name_order.end(), name, + [&](int id, const string &key) { return names[id] < key; }); + return it != name_order.end() && names[*it] == name ? *it : -1; + }; + vector> g(n); + vector deg(n); + int bad = 0; + for (int i = 1; i <= m; i++) { + string a, b; + cin >> a >> b; + int x = find_id(a), y = find_id(b); + if (x < 0 || y < 0) { + if (!bad) + bad = i; + } else { + g[y].push_back(x); + deg[x]++; + } + } + if (bad) { + cout << "INVALID DANGLING " << bad << '\n'; + return 0; + } + auto name_greater = [&](int x, int y) { return names[x] > names[y]; }; + priority_queue, decltype(name_greater)> q(name_greater); + for (int i = 0; i < n; i++) + if (!deg[i]) + q.push(i); + vector out; + while (!q.empty()) { + int u = q.top(); + q.pop(); + out.push_back(u); + for (int v : g[u]) + if (!--deg[v]) + q.push(v); + } + if ((int)out.size() < n) + cout << "INVALID CYCLE\n"; + else { + cout << "ORDER"; + for (int id : out) + cout << ' ' << names[id]; + cout << '\n'; + } +} diff --git a/problems/019-reproducible-build-order/solutions/go/main.go b/problems/019-reproducible-build-order/solutions/go/main.go new file mode 100644 index 0000000..89e5d03 --- /dev/null +++ b/problems/019-reproducible-build-order/solutions/go/main.go @@ -0,0 +1,90 @@ +package main + +import ( + "bufio" + "container/heap" + "fmt" + "os" + "sort" +) + +type H struct { + a []int + n []string +} + +func (h H) Len() int { return len(h.a) } +func (h H) Less(i, j int) bool { return h.n[h.a[i]] < h.n[h.a[j]] } +func (h H) Swap(i, j int) { h.a[i], h.a[j] = h.a[j], h.a[i] } +func (h *H) Push(x any) { h.a = append(h.a, x.(int)) } +func (h *H) Pop() any { x := h.a[len(h.a)-1]; h.a = h.a[:len(h.a)-1]; return x } +func main() { + in := bufio.NewReader(os.Stdin) + var n, m int + fmt.Fscan(in, &n, &m) + names := make([]string, n) + for i := range names { + fmt.Fscan(in, &names[i]) + } + nameOrder := make([]int, n) + for i := range nameOrder { + nameOrder[i] = i + } + sort.Slice(nameOrder, func(i, j int) bool { return names[nameOrder[i]] < names[nameOrder[j]] }) + findID := func(name string) int { + i := sort.Search(n, func(i int) bool { return names[nameOrder[i]] >= name }) + if i < n && names[nameOrder[i]] == name { + return nameOrder[i] + } + return -1 + } + g := make([][]int, n) + deg := make([]int, n) + bad := 0 + for i := 1; i <= m; i++ { + var a, b string + fmt.Fscan(in, &a, &b) + x, y := findID(a), findID(b) + if x < 0 || y < 0 { + if bad == 0 { + bad = i + } + } else { + g[y] = append(g[y], x) + deg[x]++ + } + } + if bad > 0 { + fmt.Println("INVALID DANGLING", bad) + return + } + h := &H{n: names} + heap.Init(h) + for i := range names { + if deg[i] == 0 { + heap.Push(h, i) + } + } + out := []string{} + for h.Len() > 0 { + u := heap.Pop(h).(int) + out = append(out, names[u]) + for _, v := range g[u] { + deg[v]-- + if deg[v] == 0 { + heap.Push(h, v) + } + } + } + w := bufio.NewWriter(os.Stdout) + defer w.Flush() + if len(out) < n { + fmt.Fprintln(w, "INVALID CYCLE") + } else { + fmt.Fprint(w, "ORDER") + for _, x := range out { + fmt.Fprint(w, " ", x) + } + fmt.Fprintln(w) + } +} diff --git a/problems/019-reproducible-build-order/solutions/javascript/main.js b/problems/019-reproducible-build-order/solutions/javascript/main.js new file mode 100644 index 0000000..30d93e0 --- /dev/null +++ b/problems/019-reproducible-build-order/solutions/javascript/main.js @@ -0,0 +1,76 @@ +import * as std from "std"; +const a = std.in.readAsString().trim().split(/\s+/); +let p = 0, + n = Number(a[p++]), + m = Number(a[p++]); +/** @type {string[]} */ +const names = Array.from({ length: n }, () => a[p++]); +/** @type {number[]} */ +const nameOrder = Array.from({ length: n }, (_, i) => i).sort((x, y) => + names[x] < names[y] ? -1 : names[x] > names[y] ? 1 : 0 +); +/** @type {number[][]} */ +const g = Array.from({ length: n }, () => []); +const deg = new Int32Array(n); +let bad = 0; +/** @param {string} name @returns {number} */ +const findId = (name) => { + let lo = 0, hi = n; + while (lo < hi) { + const mid = (lo + hi) >> 1; + if (names[nameOrder[mid]] < name) lo = mid + 1; + else hi = mid; + } + return lo < n && names[nameOrder[lo]] === name ? nameOrder[lo] : -1; +}; +for (let i = 1; i <= m; i++) { + const x = findId(a[p++]), y = findId(a[p++]); + if (x < 0 || y < 0) { if (!bad) bad = i; } + else { + g[y].push(x); + deg[x]++; + } +} +if (bad) std.out.puts(`INVALID DANGLING ${bad}\n`); +else { + /** @type {number[]} */ + const h = []; + /** @param {number} x @param {number} y @returns {boolean} */ + const less = (x, y) => names[x] < names[y]; + /** @param {number} x @returns {void} */ + const push = (x) => { + let i = h.length; + h.push(x); + while (i) { + let q = (i - 1) >> 1; + if (!less(h[i], h[q])) break; + [h[i], h[q]] = [h[q], h[i]]; + i = q; + } + }; + /** @returns {number} */ + const pop = () => { + const r = h[0], x = /** @type {number} */ (h.pop()); + if (h.length) { + h[0] = x; + for (let i = 0;;) { + let l = i * 2 + 1, b = i; + if (l < h.length && less(h[l], h[b])) b = l; + if (l + 1 < h.length && less(h[l + 1], h[b])) b = l + 1; + if (b === i) break; + [h[i], h[b]] = [h[b], h[i]]; + i = b; + } + } + return r; + }; + for (let i = 0; i < n; i++) if (!deg[i]) push(i); + /** @type {string[]} */ + const out = []; + while (h.length) { + const u = pop(); + out.push(names[u]); + for (const v of g[u]) if (--deg[v] === 0) push(v); + } + std.out.puts(out.length < n ? "INVALID CYCLE\n" : `ORDER ${out.join(" ")}\n`); +} diff --git a/problems/019-reproducible-build-order/solutions/python/main.py b/problems/019-reproducible-build-order/solutions/python/main.py new file mode 100644 index 0000000..0987d91 --- /dev/null +++ b/problems/019-reproducible-build-order/solutions/python/main.py @@ -0,0 +1,44 @@ +import bisect, heapq, sys + +it = iter(sys.stdin.read().split()) +n = int(next(it)) +m = int(next(it)) +names = [next(it) for _ in range(n)] +name_order = sorted((name, i) for i, name in enumerate(names)) + + +def find_id(name): + position = bisect.bisect_left(name_order, (name, -1)) + return ( + name_order[position][1] + if position < n and name_order[position][0] == name + else None + ) + + +g = [[] for _ in range(n)] +deg = [0] * n +bad = None +for i in range(1, m + 1): + a, b = next(it), next(it) + x, y = find_id(a), find_id(b) + if x is None or y is None: + if bad is None: + bad = i + else: + g[y].append(x) + deg[x] += 1 +if bad is not None: + print("INVALID DANGLING", bad) + raise SystemExit +h = [(names[i], i) for i in range(n) if deg[i] == 0] +heapq.heapify(h) +out = [] +while h: + name, u = heapq.heappop(h) + out.append(name) + for v in g[u]: + deg[v] -= 1 + if deg[v] == 0: + heapq.heappush(h, (names[v], v)) +print("INVALID CYCLE" if len(out) < n else "ORDER " + " ".join(out)) diff --git a/problems/019-reproducible-build-order/solutions/rust/main.rs b/problems/019-reproducible-build-order/solutions/rust/main.rs new file mode 100644 index 0000000..4de7391 --- /dev/null +++ b/problems/019-reproducible-build-order/solutions/rust/main.rs @@ -0,0 +1,60 @@ +use std::cmp::Reverse; +use std::collections::BinaryHeap; +use std::io::{self, Read}; +fn find_id(names: &[String], order: &[usize], key: &str) -> Option { + order + .binary_search_by(|&index| names[index].as_str().cmp(key)) + .ok() + .map(|position| order[position]) +} +fn main() { + let mut s = String::new(); + io::stdin().read_to_string(&mut s).unwrap(); + let mut it = s.split_whitespace(); + let n: usize = it.next().unwrap().parse().unwrap(); + let m: usize = it.next().unwrap().parse().unwrap(); + let names: Vec = (0..n).map(|_| it.next().unwrap().to_string()).collect(); + let mut name_order: Vec = (0..n).collect(); + name_order.sort_by(|&x, &y| names[x].cmp(&names[y])); + let mut g = vec![vec![]; n]; + let mut deg = vec![0; n]; + let mut bad = 0; + for i in 1..=m { + let a = it.next().unwrap(); + let b = it.next().unwrap(); + if let (Some(x), Some(y)) = ( + find_id(&names, &name_order, a), + find_id(&names, &name_order, b), + ) { + g[y].push(x); + deg[x] += 1 + } else if bad == 0 { + bad = i + } + } + if bad > 0 { + println!("INVALID DANGLING {bad}"); + return; + } + let mut h = BinaryHeap::new(); + for i in 0..n { + if deg[i] == 0 { + h.push(Reverse((names[i].clone(), i))) + } + } + let mut out = vec![]; + while let Some(Reverse((name, u))) = h.pop() { + out.push(name); + for &v in &g[u] { + deg[v] -= 1; + if deg[v] == 0 { + h.push(Reverse((names[v].clone(), v))) + } + } + } + if out.len() < n { + println!("INVALID CYCLE") + } else { + println!("ORDER {}", out.join(" ")) + } +} diff --git a/problems/019-reproducible-build-order/solutions/typescript/main.ts b/problems/019-reproducible-build-order/solutions/typescript/main.ts new file mode 100644 index 0000000..4b21471 --- /dev/null +++ b/problems/019-reproducible-build-order/solutions/typescript/main.ts @@ -0,0 +1,65 @@ +import * as std from "std"; +const a: string[] = std.in.readAsString().trim().split(/\s+/); +let p = 0, n = Number(a[p++]), m = Number(a[p++]); +const names: string[] = Array.from({ length: n }, () => a[p++]), + nameOrder: number[] = Array.from({ length: n }, (_, i) => i).sort((x, y) => + names[x] < names[y] ? -1 : names[x] > names[y] ? 1 : 0 + ), + g: number[][] = Array.from({ length: n }, () => []), + deg = new Int32Array(n); +const findId = (name: string): number => { + let lo = 0, hi = n; + while (lo < hi) { + const mid = (lo + hi) >> 1; + if (names[nameOrder[mid]] < name) lo = mid + 1; + else hi = mid; + } + return lo < n && names[nameOrder[lo]] === name ? nameOrder[lo] : -1; +}; +let bad = 0; +for (let i = 1; i <= m; i++) { + const x = findId(a[p++]), y = findId(a[p++]); + if (x < 0 || y < 0) { if (!bad) bad = i; } + else { + g[y].push(x); + deg[x]++; + } +} +if (bad) std.out.puts(`INVALID DANGLING ${bad}\n`); +else { + const h: number[] = [], + less = (x: number, y: number): boolean => names[x] < names[y], + push = (x: number): void => { + let i = h.length; + h.push(x); + while (i) { + let q = (i - 1) >> 1; + if (!less(h[i], h[q])) break; + [h[i], h[q]] = [h[q], h[i]]; + i = q; + } + }, + pop = (): number => { + const r = h[0], x = h.pop()!; + if (h.length) { + h[0] = x; + for (let i = 0;;) { + let l = i * 2 + 1, b = i; + if (l < h.length && less(h[l], h[b])) b = l; + if (l + 1 < h.length && less(h[l + 1], h[b])) b = l + 1; + if (b === i) break; + [h[i], h[b]] = [h[b], h[i]]; + i = b; + } + } + return r; + }; + for (let i = 0; i < n; i++) if (!deg[i]) push(i); + const out: string[] = []; + while (h.length) { + const u = pop(); + out.push(names[u]); + for (const v of g[u]) if (--deg[v] === 0) push(v); + } + std.out.puts(out.length < n ? "INVALID CYCLE\n" : `ORDER ${out.join(" ")}\n`); +} diff --git a/problems/019-reproducible-build-order/statement.en.md b/problems/019-reproducible-build-order/statement.en.md new file mode 100644 index 0000000..0811845 --- /dev/null +++ b/problems/019-reproducible-build-order/statement.en.md @@ -0,0 +1,89 @@ +# Reproducible Package Build Order + +An offline WASM OJ toolchain must build its packages according to a dependency graph. The same graph often permits several valid orders. If each host chooses an arbitrary package whenever there is a choice, the resulting artifacts and build logs may no longer be reproducible byte for byte. + +We therefore use a deterministic rule: whenever several packages have all their dependencies completed, choose the package with the ASCII-lexicographically smallest name. If package `a` depends on package `b`, then `b` must be built before `a`. + +The lockfile itself may also be corrupt. A dependency edge is dangling if either endpoint is absent from the known package list. If every endpoint is valid but not all packages can be completed, the graph contains a cycle. Validate the data using the specified error priority, or produce the unique build order. + +## Input + +The first line contains `N M`. The next `N` lines contain distinct known package names. Each of the following `M` lines contains `a b`, meaning package `a` **depends on** package `b`, so `b` must be built first. An edge may contain a name not present in the known list, representing a corrupt lockfile. + +## Output + +Errors take priority over building: + +1. If a dangling edge exists, output `INVALID DANGLING i`, where `i` is the 1-based index of the first input edge with either endpoint unknown. Do not check for cycles afterward. +2. If no edge is dangling but the graph contains a cycle, output `INVALID CYCLE`. +3. Otherwise output `ORDER p_1 ... p_N`, the unique order produced by the selection rule. + +## Constraints + +- `1 ≤ N ≤ 200000` +- `0 ≤ M ≤ 400000` +- A package name has length `1..30` and contains only lowercase letters, digits, and `-`. +- Known names are distinct; edge pairs are distinct and contain no self-loop. +- Lexicographic comparisons use ASCII bytes, not locale rules. + +The full constraints rule out scanning every remaining package linearly at each step. + +## Examples + + + +### Example One + +Input: + +```text +3 2 +app +core +util +app core +app util +``` + +Output: + +```text +ORDER core util app +``` + +### Example Two + +Input: + +```text +2 1 +app +core +app ghost +``` + +Output: + +```text +INVALID DANGLING 1 +``` + +### Example Three + +Input: + +```text +2 2 +a +b +a b +b a +``` + +Output: + +```text +INVALID CYCLE +``` + + diff --git a/problems/019-reproducible-build-order/statement.zh-TW.md b/problems/019-reproducible-build-order/statement.zh-TW.md new file mode 100644 index 0000000..b806109 --- /dev/null +++ b/problems/019-reproducible-build-order/statement.zh-TW.md @@ -0,0 +1,86 @@ +# 可重現的套件建置順序 + +一套可離線使用的 WASM OJ toolchain,必須先按照 dependency graph 建置其中的套件。同一張 graph 往往有多個合法順序;如果每台 host 任意選擇下一個可建置套件,產生的 artifact 與建置紀錄就可能無法逐位元重現。 + +因此我們制定一條 deterministic 規則:任何時刻若有多個套件的 dependencies 都已完成,必須選 package name 依 ASCII 字典序最小者。套件 `a` 依賴 `b` 時,`b` 必須先於 `a` 建置。 + +lockfile 本身也可能損壞。若 dependency edge 的任一端不在已知 package 清單中,該 edge 是 dangling;如果所有端點都有效,但相依關係無法完成全部套件,則 graph 含有 cycle。請依題目指定的錯誤優先順序驗證資料,或產生唯一的建置順序。 + +## 輸入 + +第一行 `N M`。接著 `N` 行是互異的已知 package name。再接著 `M` 行 `a b`,表示 package `a` **依賴** package `b`,所以 `b` 必須先建置。Edge 中可以出現不在已知清單的名稱,用來表示損壞的 lockfile。 + +## 輸出 + +錯誤優先於建置: + +1. 若存在 dangling edge,輸出 `INVALID DANGLING i`,其中 `i` 是輸入順序第一條任一端未知的 edge(1-based)。此時不再檢查 cycle。 +2. 沒有 dangling、但 graph 有 cycle 時,輸出 `INVALID CYCLE`。 +3. 否則輸出 `ORDER p_1 ... p_N`,依規則得到唯一順序。 + +## 限制 + +- `1 <= N <= 200000`,`0 <= M <= 400000`。 +- package name 長 1 到 30,只含小寫字母、數字、`-`;已知名稱互異,edge pair 互異且無 self-loop。 +- 字典序比較 ASCII bytes,不使用 locale。 +- 完整測資排除每次線性掃描全部 remaining packages 的作法。 + +## 範例 + + + +### 範例一 + +輸入: + +```text +3 2 +app +core +util +app core +app util +``` + +輸出: + +```text +ORDER core util app +``` + +### 範例二 + +輸入: + +```text +2 1 +app +core +app ghost +``` + +輸出: + +```text +INVALID DANGLING 1 +``` + +### 範例三 + +輸入: + +```text +2 2 +a +b +a b +b a +``` + +輸出: + +```text +INVALID CYCLE +``` + + diff --git a/problems/019-reproducible-build-order/tests/adversarial-dangling-before-cycle.in b/problems/019-reproducible-build-order/tests/adversarial-dangling-before-cycle.in new file mode 100644 index 0000000..9b76911 --- /dev/null +++ b/problems/019-reproducible-build-order/tests/adversarial-dangling-before-cycle.in @@ -0,0 +1,9 @@ +4 4 +a +b +c +d +a b +c ghost +b a +unknown d diff --git a/problems/019-reproducible-build-order/tests/adversarial-dangling-before-cycle.out b/problems/019-reproducible-build-order/tests/adversarial-dangling-before-cycle.out new file mode 100644 index 0000000..9b334a4 --- /dev/null +++ b/problems/019-reproducible-build-order/tests/adversarial-dangling-before-cycle.out @@ -0,0 +1 @@ +INVALID DANGLING 2 diff --git a/problems/019-reproducible-build-order/tests/sample-01.in b/problems/019-reproducible-build-order/tests/sample-01.in new file mode 100644 index 0000000..81b7560 --- /dev/null +++ b/problems/019-reproducible-build-order/tests/sample-01.in @@ -0,0 +1,6 @@ +3 2 +app +core +util +app core +app util diff --git a/problems/019-reproducible-build-order/tests/sample-01.out b/problems/019-reproducible-build-order/tests/sample-01.out new file mode 100644 index 0000000..ef5abfc --- /dev/null +++ b/problems/019-reproducible-build-order/tests/sample-01.out @@ -0,0 +1 @@ +ORDER core util app diff --git a/problems/019-reproducible-build-order/tests/sample-02.in b/problems/019-reproducible-build-order/tests/sample-02.in new file mode 100644 index 0000000..84653f3 --- /dev/null +++ b/problems/019-reproducible-build-order/tests/sample-02.in @@ -0,0 +1,4 @@ +2 1 +app +core +app ghost diff --git a/problems/019-reproducible-build-order/tests/sample-02.out b/problems/019-reproducible-build-order/tests/sample-02.out new file mode 100644 index 0000000..253c5b9 --- /dev/null +++ b/problems/019-reproducible-build-order/tests/sample-02.out @@ -0,0 +1 @@ +INVALID DANGLING 1 diff --git a/problems/019-reproducible-build-order/tests/sample-03.in b/problems/019-reproducible-build-order/tests/sample-03.in new file mode 100644 index 0000000..25b27f7 --- /dev/null +++ b/problems/019-reproducible-build-order/tests/sample-03.in @@ -0,0 +1,5 @@ +2 2 +a +b +a b +b a diff --git a/problems/019-reproducible-build-order/tests/sample-03.out b/problems/019-reproducible-build-order/tests/sample-03.out new file mode 100644 index 0000000..eb619fc --- /dev/null +++ b/problems/019-reproducible-build-order/tests/sample-03.out @@ -0,0 +1 @@ +INVALID CYCLE diff --git a/problems/019-reproducible-build-order/validator.py b/problems/019-reproducible-build-order/validator.py new file mode 100644 index 0000000..c93545b --- /dev/null +++ b/problems/019-reproducible-build-order/validator.py @@ -0,0 +1,30 @@ +import re, sys + +R = re.compile(r"[a-z0-9-]{1,30}$") + + +def main(): + ls = sys.stdin.read().splitlines() + assert ls + h = ls[0].split() + assert len(h) == 2 + n, m = map(int, h) + assert 1 <= n <= 200000 and 0 <= m <= 400000 and len(ls) == 1 + n + m + names = [x.strip() for x in ls[1 : n + 1]] + assert all(R.fullmatch(x) for x in names) and len(names) == len(set(names)) + seen = set() + for line in ls[n + 1 :]: + x = line.split() + assert ( + len(x) == 2 + and all(R.fullmatch(v) for v in x) + and x[0] != x[1] + and tuple(x) not in seen + ) + seen.add(tuple(x)) + + +try: + main() +except (AssertionError, ValueError): + sys.exit(1) diff --git a/problems/020-offline-dependency-bundle/editorial.en.md b/problems/020-offline-dependency-bundle/editorial.en.md new file mode 100644 index 0000000..a46616a --- /dev/null +++ b/problems/020-offline-dependency-bundle/editorial.en.md @@ -0,0 +1,26 @@ +# Editorial + +## Intuitive Approach + +For every package, search all payloads linearly, then scan required records for every payload. This takes `O(NM)` time and makes duplicates and category priority easy to mishandle. + +## Optimal Approach: Sort and Compare Digest Groups + +Sort lock records and payload records separately by digest. Equal digests become contiguous: a lock group can be checked for inconsistent sizes and compressed into one required record, while a payload group can be checked for duplicates. + +Finish checking an entire error category before proceeding to the next. First find the smallest lock conflict, then the smallest payload duplicate. Afterward, binary search or two pointers can find the smallest missing digest, extra digest, and size mismatch in order. If no error exists, the package-size total and unique-required total accumulated during processing yield the requested statistics. + +## Correctness Proof + +Sorting makes all records of one digest adjacent, so a group comparison detects exactly whether that digest has a lock conflict or duplicate payload. The first such group is the lexicographically smallest digest in its category. After compression, required and payload records are sorted sets. Membership comparison detects missing and extra digests exactly; once the sets match, comparing sizes at equal keys detects exactly `SIZE`. The algorithm examines a later category only after proving the earlier category empty, so error priority is correct. With no error, every required digest has exactly one equal-sized payload, and the difference between package total and unique-digest total is precisely the bytes saved by deduplication. + +## Complexity + +Sorting takes `O((N+M) log(N+M))`; subsequent scans or searches stay within that bound. Space is `O(N+M)`. In the comparison model, canonical ordering of arbitrary digest tokens requires this asymptotic scale. + +## Common Mistakes + +- Reporting a missing digest immediately and overlooking a higher-priority duplicate payload. +- Counting the same digest repeatedly in `deduplicatedBytes`. +- Comparing sets by package name rather than digest. +- Accumulating into a 32-bit temporary before converting to 64 bits. diff --git a/problems/020-offline-dependency-bundle/editorial.zh-TW.md b/problems/020-offline-dependency-bundle/editorial.zh-TW.md new file mode 100644 index 0000000..95b9f11 --- /dev/null +++ b/problems/020-offline-dependency-bundle/editorial.zh-TW.md @@ -0,0 +1,26 @@ +# 解題說明 + +## 直覺解 + +對每個 package 線性搜尋所有 payload,並對 payload 再掃描 required,最壞 `O(NM)`;同 digest 的重複與優先序也容易漏判。 + +## 最佳解 + +把 lock records 與 payload records 分別依 digest 排序。相同 digest 連續:lock group 可檢查 size 是否一致並壓成唯一 required record;payload group 可檢查 duplicate。 + +必須按規格優先序完成整個類別後才進下一類:先找所有 lock conflict 的第一個,再找 payload duplicate;之後可用 binary search 或 two pointers 依序找第一個 missing、extra、size mismatch。若皆無,排序過程同時累加 package total 與 unique required total,即可輸出統計。 + +## 正確性證明 + +排序使同 digest 的所有紀錄相鄰,因此每組比較能且只能偵測該 digest 的 lock conflict/duplicate,從左至右第一個即同類字典序最小者。壓縮後 required 與 payload 各是一個按 digest 排序的集合;membership 比較精確判定 missing 與 extra,兩集合相同後同 key 的 size 比較精確判定 SIZE。演算法僅在前一類完全不存在時檢查下一類,故錯誤優先序正確。無錯誤時每個 required digest 恰一 payload 且 size 相同;unique sum 與 package sum 的差正是內容去重節省,VALID 統計正確。 + +## 複雜度 + +排序時間 `O((N+M)log(N+M))`,後續掃描(或 binary search)不超過同一界;空間 `O(N+M)`。在比較模型下任意 digest 的 canonical 排序需要此量級。 + +## 常見錯誤 + +- 看到 missing 就立刻輸出,卻漏掉優先級更高的 duplicate payload。 +- 相同 digest 重複計入 deduplicatedBytes。 +- 用 package name 而非 digest 做集合比較。 +- 64-bit 加總前先用 32-bit 暫存。 diff --git a/problems/020-offline-dependency-bundle/generator.py b/problems/020-offline-dependency-bundle/generator.py new file mode 100644 index 0000000..60d3ae6 --- /dev/null +++ b/problems/020-offline-dependency-bundle/generator.py @@ -0,0 +1,27 @@ +import random, sys + +seed, index = map(int, sys.argv[1:]) +r = random.Random(seed * 101 + index) +n = 8 + index % 8 +pool = [f"{i:08x}" for i in range(1, 6)] +sizes = {d: r.randrange(20) for d in pool} +lock = [(f"p{i}", r.choice(pool), 0) for i in range(n)] +lock = [(a, d, sizes[d]) for a, d, _ in lock] +need = sorted({d for _, d, _ in lock}) +pay = [(d, sizes[d]) for d in need] +mode = index % 6 +if mode == 1 and n > 1: + lock[1] = (lock[1][0], lock[0][1], lock[0][2] + 1) +elif mode == 2: + pay.append(pay[0]) +elif mode == 3: + pay = pay[1:] +elif mode == 4: + pay.append(("ffffffff", 3)) +elif mode == 5: + pay[0] = (pay[0][0], pay[0][1] + 1) +print(n, len(pay)) +for x in lock: + print(*x) +for x in pay: + print(*x) diff --git a/problems/020-offline-dependency-bundle/oracle.py b/problems/020-offline-dependency-bundle/oracle.py new file mode 100644 index 0000000..6370768 --- /dev/null +++ b/problems/020-offline-dependency-bundle/oracle.py @@ -0,0 +1,36 @@ +import sys + +it = iter(sys.stdin.read().split()) +n = int(next(it)) +m = int(next(it)) +lock = [] +for _ in range(n): + lock.append((next(it), next(it), int(next(it)))) +pay = [(next(it), int(next(it))) for _ in range(m)] +dig = sorted({x[1] for x in lock}) +for d in dig: + z = {x[2] for x in lock if x[1] == d} + if len(z) > 1: + print("LOCK_CONFLICT", d) + raise SystemExit +for d in sorted({x[0] for x in pay}): + if sum(x[0] == d for x in pay) > 1: + print("DUPLICATE_PAYLOAD", d) + raise SystemExit +pd = {x[0]: x[1] for x in pay} +req = {d: next(x[2] for x in lock if x[1] == d) for d in dig} +for d in dig: + if d not in pd: + print("MISSING", d) + raise SystemExit +for d in sorted(pd): + if d not in req: + print("EXTRA", d) + raise SystemExit +for d in dig: + if req[d] != pd[d]: + print("SIZE", d) + raise SystemExit +allbytes = sum(x[2] for x in lock) +unique = sum(req.values()) +print("VALID", len(req), unique, allbytes - unique) diff --git a/problems/020-offline-dependency-bundle/problem.json b/problems/020-offline-dependency-bundle/problem.json new file mode 100644 index 0000000..648a888 --- /dev/null +++ b/problems/020-offline-dependency-bundle/problem.json @@ -0,0 +1,153 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 20, + "slug": "offline-dependency-bundle", + "title": { + "zh-TW": "離線依賴行李箱", + "en": "Offline Dependency Suitcase" + }, + "difficulty": "medium", + "tags": [ + "sorting", + "sets", + "deduplication", + "validation" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-bigint-dedup", + "kind": "adversarial", + "input": "tests/adversarial-bigint-dedup.in", + "output": "tests/adversarial-bigint-dedup.out" + }, + { + "id": "adversarial-error-priority", + "kind": "adversarial", + "input": "tests/adversarial-error-priority.in", + "output": "tests/adversarial-error-priority.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 10000000, + "memoryLimitBytes": 536870912 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 1500000, + "memoryLimitBytes": 402653184 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 550000, + "memoryLimitBytes": 268435456 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "每個 lock item 線性搜尋 payload", + "en": "Linear Payload Search per Lock Item" + }, + "time": "O(NM)", + "space": "O(N+M)", + "accepted": false + }, + { + "name": { + "zh-TW": "依 digest 排序與集合比較", + "en": "Digest Sorting and Set Comparison" + }, + "time": "O((N+M) log(N+M))", + "space": "O(N+M)", + "accepted": true + } + ] +} diff --git a/problems/020-offline-dependency-bundle/solutions/c/main.c b/problems/020-offline-dependency-bundle/solutions/c/main.c new file mode 100644 index 0000000..5b412d7 --- /dev/null +++ b/problems/020-offline-dependency-bundle/solutions/c/main.c @@ -0,0 +1,79 @@ +#include +#include +#include +typedef unsigned long long U; +typedef struct { + char d[65]; + U z; +} R; +int cmp(const void *a, const void *b) { + return strcmp(((const R *)a)->d, ((const R *)b)->d); +} +int find(R *a, int n, const char *d) { + int l = 0, r = n; + while (l < r) { + int m = (l + r) / 2; + if (strcmp(a[m].d, d) < 0) + l = m + 1; + else + r = m; + } + return l < n && !strcmp(a[l].d, d) ? l : -1; +} +int main(void) { + int n, m; + if (scanf("%d%d", &n, &m) != 2) + return 0; + R *l = malloc(sizeof(R) * (size_t)n), *p = malloc(sizeof(R) * (size_t)m), + *req = malloc(sizeof(R) * (size_t)n); + U total = 0; + for (int i = 0; i < n; i++) { + char name[31]; + scanf("%30s%64s%llu", name, l[i].d, &l[i].z); + total += l[i].z; + } + for (int i = 0; i < m; i++) + scanf("%64s%llu", p[i].d, &p[i].z); + qsort(l, (size_t)n, sizeof(R), cmp); + qsort(p, (size_t)m, sizeof(R), cmp); + int u = 0; + for (int i = 0; i < n;) { + int j = i + 1; + while (j < n && !strcmp(l[j].d, l[i].d)) { + if (l[j].z != l[i].z) { + printf("LOCK_CONFLICT %s\n", l[i].d); + return 0; + } + j++; + } + req[u++] = l[i]; + i = j; + } + for (int i = 1; i < m; i++) + if (!strcmp(p[i].d, p[i - 1].d)) { + printf("DUPLICATE_PAYLOAD %s\n", p[i].d); + return 0; + } + for (int i = 0; i < u; i++) + if (find(p, m, req[i].d) < 0) { + printf("MISSING %s\n", req[i].d); + return 0; + } + for (int i = 0; i < m; i++) + if (find(req, u, p[i].d) < 0) { + printf("EXTRA %s\n", p[i].d); + return 0; + } + for (int i = 0; i < u; i++) { + int j = find(p, m, req[i].d); + if (p[j].z != req[i].z) { + printf("SIZE %s\n", req[i].d); + return 0; + } + } + U unique = 0; + for (int i = 0; i < u; i++) + unique += req[i].z; + printf("VALID %d %llu %llu\n", u, unique, total - unique); + return 0; +} diff --git a/problems/020-offline-dependency-bundle/solutions/cpp/main.cpp b/problems/020-offline-dependency-bundle/solutions/cpp/main.cpp new file mode 100644 index 0000000..b3e769c --- /dev/null +++ b/problems/020-offline-dependency-bundle/solutions/cpp/main.cpp @@ -0,0 +1,71 @@ +#include +#include +#include +#include +#include +using namespace std; +struct R { + string d; + uint64_t z; +}; +int main() { + ios::sync_with_stdio(false); + cin.tie(nullptr); + int n, m; + if (!(cin >> n >> m)) + return 0; + vector l(n), p(m), req; + uint64_t total = 0; + for (auto &x : l) { + string name; + cin >> name >> x.d >> x.z; + total += x.z; + } + for (auto &x : p) + cin >> x.d >> x.z; + auto less = [](const R &a, const R &b) { return a.d < b.d; }; + sort(l.begin(), l.end(), less); + sort(p.begin(), p.end(), less); + for (int i = 0; i < n;) { + int j = i + 1; + while (j < n && l[j].d == l[i].d) { + if (l[j].z != l[i].z) { + cout << "LOCK_CONFLICT " << l[i].d << '\n'; + return 0; + } + j++; + } + req.push_back(l[i]); + i = j; + } + for (int i = 1; i < m; i++) + if (p[i].d == p[i - 1].d) { + cout << "DUPLICATE_PAYLOAD " << p[i].d << '\n'; + return 0; + } + auto has = [](const vector &a, const string &d) { + return lower_bound(a.begin(), a.end(), R{d, 0}, + [](auto &x, auto &y) { return x.d < y.d; }); + }; + for (auto &x : req) + if (has(p, x.d) == p.end() || has(p, x.d)->d != x.d) { + cout << "MISSING " << x.d << '\n'; + return 0; + } + for (auto &x : p) + if (has(req, x.d) == req.end() || has(req, x.d)->d != x.d) { + cout << "EXTRA " << x.d << '\n'; + return 0; + } + uint64_t unique = 0; + for (auto &x : req) { + auto y = has(p, x.d); + if (y->z != x.z) { + cout << "SIZE " << x.d << '\n'; + return 0; + } + unique += x.z; + } + cout << "VALID " << req.size() << ' ' << unique << ' ' << total - unique + << '\n'; +} diff --git a/problems/020-offline-dependency-bundle/solutions/go/main.go b/problems/020-offline-dependency-bundle/solutions/go/main.go new file mode 100644 index 0000000..ae54159 --- /dev/null +++ b/problems/020-offline-dependency-bundle/solutions/go/main.go @@ -0,0 +1,79 @@ +package main + +import ( + "bufio" + "fmt" + "os" + "sort" +) + +type R struct { + d string + z uint64 +} + +func find(a []R, d string) int { + i := sort.Search(len(a), func(i int) bool { return a[i].d >= d }) + if i < len(a) && a[i].d == d { + return i + } + return -1 +} +func main() { + in := bufio.NewReader(os.Stdin) + var n, m int + fmt.Fscan(in, &n, &m) + l := make([]R, n) + p := make([]R, m) + var total uint64 + for i := range l { + var name string + fmt.Fscan(in, &name, &l[i].d, &l[i].z) + total += l[i].z + } + for i := range p { + fmt.Fscan(in, &p[i].d, &p[i].z) + } + sort.Slice(l, func(i, j int) bool { return l[i].d < l[j].d }) + sort.Slice(p, func(i, j int) bool { return p[i].d < p[j].d }) + req := []R{} + for i := 0; i < n; { + j := i + 1 + for j < n && l[j].d == l[i].d { + if l[j].z != l[i].z { + fmt.Println("LOCK_CONFLICT", l[i].d) + return + } + j++ + } + req = append(req, l[i]) + i = j + } + for i := 1; i < m; i++ { + if p[i].d == p[i-1].d { + fmt.Println("DUPLICATE_PAYLOAD", p[i].d) + return + } + } + for _, x := range req { + if find(p, x.d) < 0 { + fmt.Println("MISSING", x.d) + return + } + } + for _, x := range p { + if find(req, x.d) < 0 { + fmt.Println("EXTRA", x.d) + return + } + } + var unique uint64 + for _, x := range req { + if p[find(p, x.d)].z != x.z { + fmt.Println("SIZE", x.d) + return + } + unique += x.z + } + fmt.Println("VALID", len(req), unique, total-unique) +} diff --git a/problems/020-offline-dependency-bundle/solutions/javascript/main.js b/problems/020-offline-dependency-bundle/solutions/javascript/main.js new file mode 100644 index 0000000..8b51854 --- /dev/null +++ b/problems/020-offline-dependency-bundle/solutions/javascript/main.js @@ -0,0 +1,71 @@ +import * as std from "std"; +/** @typedef {[string, bigint]} R */ +const a = std.in.readAsString().trim().split(/\s+/); +let p = 0, + n = Number(a[p++]), + m = Number(a[p++]); +/** @type {R[]} */ +const lock = []; +/** @type {R[]} */ +const pay = []; +let total = 0n; +for (let i = 0; i < n; i++) { + p++; + const d = a[p++], z = BigInt(a[p++]); + lock.push([d, z]); + total += z; +} +for (let i = 0; i < m; i++) pay.push([a[p++], BigInt(a[p++])]); +lock.sort((x, y) => x[0] < y[0] ? -1 : x[0] > y[0] ? 1 : 0); +pay.sort((x, y) => x[0] < y[0] ? -1 : x[0] > y[0] ? 1 : 0); +/** @type {R[]} */ +const req = []; +/** @type {string | null} */ +let out = null; +for (let i = 0; i < n;) { + let j = i + 1; + while (j < n && lock[j][0] === lock[i][0]) { + if (lock[j][1] !== lock[i][1]) out = `LOCK_CONFLICT ${lock[i][0]}`; + j++; + } + req.push(lock[i]); + if (out) break; + i = j; +} +if (!out) { + for (let i = 1; i < m; i++) { + if (pay[i][0] === pay[i - 1][0]) { + out = `DUPLICATE_PAYLOAD ${pay[i][0]}`; + break; + } + } +} +let unique = 0n; +if (!out) { + let i = 0, j = 0; + /** @type {string | null} */ + let missing = null; + /** @type {string | null} */ + let extra = null; + /** @type {string | null} */ + let sizeError = null; + while (i < req.length || j < pay.length) { + if (j === pay.length || i < req.length && req[i][0] < pay[j][0]) { + if (missing === null) missing = req[i][0]; + i++; + } else if (i === req.length || pay[j][0] < req[i][0]) { + if (extra === null) extra = pay[j][0]; + j++; + } else { + if (req[i][1] !== pay[j][1] && sizeError === null) sizeError = req[i][0]; + i++; + j++; + } + } + if (missing !== null) out = `MISSING ${missing}`; + else if (extra !== null) out = `EXTRA ${extra}`; + else if (sizeError !== null) out = `SIZE ${sizeError}`; + else for (const [, z] of req) unique += z; +} +if (!out) out = `VALID ${req.length} ${unique} ${total - unique}`; +std.out.puts(out + "\n"); diff --git a/problems/020-offline-dependency-bundle/solutions/python/main.py b/problems/020-offline-dependency-bundle/solutions/python/main.py new file mode 100644 index 0000000..145a63c --- /dev/null +++ b/problems/020-offline-dependency-bundle/solutions/python/main.py @@ -0,0 +1,58 @@ +import sys + +it = iter(sys.stdin.read().split()) +n = int(next(it)) +m = int(next(it)) +lock = [] +total = 0 +for _ in range(n): + next(it) + d = next(it) + z = int(next(it)) + lock.append((d, z)) + total += z +pay = [(next(it), int(next(it))) for _ in range(m)] +lock.sort() +pay.sort() +req = [] +i = 0 +while i < n: + j = i + 1 + while j < n and lock[j][0] == lock[i][0]: + j += 1 + if any(lock[k][1] != lock[i][1] for k in range(i + 1, j)): + print("LOCK_CONFLICT", lock[i][0]) + raise SystemExit + req.append(lock[i]) + i = j +for i in range(1, m): + if pay[i][0] == pay[i - 1][0]: + print("DUPLICATE_PAYLOAD", pay[i][0]) + raise SystemExit +missing = extra = size_error = None +i = j = 0 +while i < len(req) or j < len(pay): + if j == len(pay) or (i < len(req) and req[i][0] < pay[j][0]): + if missing is None: + missing = req[i][0] + i += 1 + elif i == len(req) or pay[j][0] < req[i][0]: + if extra is None: + extra = pay[j][0] + j += 1 + else: + if req[i][1] != pay[j][1] and size_error is None: + size_error = req[i][0] + i += 1 + j += 1 +if missing is not None: + print("MISSING", missing) + raise SystemExit +if extra is not None: + print("EXTRA", extra) + raise SystemExit +if size_error is not None: + print("SIZE", size_error) + raise SystemExit +unique = sum(z for _, z in req) +print("VALID", len(req), unique, total - unique) diff --git a/problems/020-offline-dependency-bundle/solutions/rust/main.rs b/problems/020-offline-dependency-bundle/solutions/rust/main.rs new file mode 100644 index 0000000..3daad18 --- /dev/null +++ b/problems/020-offline-dependency-bundle/solutions/rust/main.rs @@ -0,0 +1,72 @@ +use std::io::{self, Read}; +fn pos(a: &[(String, u64)], d: &str) -> Result { + a.binary_search_by(|x| x.0.as_str().cmp(d)) +} +fn main() { + let mut s = String::new(); + io::stdin().read_to_string(&mut s).unwrap(); + let mut it = s.split_whitespace(); + let n: usize = it.next().unwrap().parse().unwrap(); + let m: usize = it.next().unwrap().parse().unwrap(); + let mut l = vec![]; + let mut total = 0u64; + for _ in 0..n { + it.next(); + let d = it.next().unwrap().to_string(); + let z = it.next().unwrap().parse().unwrap(); + total += z; + l.push((d, z)); + } + let mut p: Vec<(String, u64)> = (0..m) + .map(|_| { + ( + it.next().unwrap().to_string(), + it.next().unwrap().parse().unwrap(), + ) + }) + .collect(); + l.sort(); + p.sort(); + let mut req = vec![]; + let mut i = 0; + while i < n { + let mut j = i + 1; + while j < n && l[j].0 == l[i].0 { + if l[j].1 != l[i].1 { + println!("LOCK_CONFLICT {}", l[i].0); + return; + } + j += 1 + } + req.push(l[i].clone()); + i = j + } + for i in 1..m { + if p[i].0 == p[i - 1].0 { + println!("DUPLICATE_PAYLOAD {}", p[i].0); + return; + } + } + for x in &req { + if pos(&p, &x.0).is_err() { + println!("MISSING {}", x.0); + return; + } + } + for x in &p { + if pos(&req, &x.0).is_err() { + println!("EXTRA {}", x.0); + return; + } + } + let mut unique = 0; + for x in &req { + let y = &p[pos(&p, &x.0).unwrap()]; + if x.1 != y.1 { + println!("SIZE {}", x.0); + return; + } + unique += x.1 + } + println!("VALID {} {} {}", req.len(), unique, total - unique); +} diff --git a/problems/020-offline-dependency-bundle/solutions/typescript/main.ts b/problems/020-offline-dependency-bundle/solutions/typescript/main.ts new file mode 100644 index 0000000..2ef33ad --- /dev/null +++ b/problems/020-offline-dependency-bundle/solutions/typescript/main.ts @@ -0,0 +1,61 @@ +import * as std from "std"; +type R = [string, bigint]; +const a: string[] = std.in.readAsString().trim().split(/\s+/); +let p = 0, n = Number(a[p++]), m = Number(a[p++]); +const lock: R[] = [], pay: R[] = []; +let total = 0n; +for (let i = 0; i < n; i++) { + p++; + const d = a[p++], z = BigInt(a[p++]); + lock.push([d, z]); + total += z; +} +for (let i = 0; i < m; i++) pay.push([a[p++], BigInt(a[p++])]); +lock.sort((x, y) => x[0] < y[0] ? -1 : x[0] > y[0] ? 1 : 0); +pay.sort((x, y) => x[0] < y[0] ? -1 : x[0] > y[0] ? 1 : 0); +const req: R[] = []; +let out: string | null = null; +for (let i = 0; i < n;) { + let j = i + 1; + while (j < n && lock[j][0] === lock[i][0]) { + if (lock[j][1] !== lock[i][1]) out = `LOCK_CONFLICT ${lock[i][0]}`; + j++; + } + req.push(lock[i]); + if (out) break; + i = j; +} +if (!out) { + for (let i = 1; i < m; i++) { + if (pay[i][0] === pay[i - 1][0]) { + out = `DUPLICATE_PAYLOAD ${pay[i][0]}`; + break; + } + } +} +let unique = 0n; +if (!out) { + let i = 0, j = 0; + let missing: string | null = null, + extra: string | null = null, + sizeError: string | null = null; + while (i < req.length || j < pay.length) { + if (j === pay.length || i < req.length && req[i][0] < pay[j][0]) { + if (missing === null) missing = req[i][0]; + i++; + } else if (i === req.length || pay[j][0] < req[i][0]) { + if (extra === null) extra = pay[j][0]; + j++; + } else { + if (req[i][1] !== pay[j][1] && sizeError === null) sizeError = req[i][0]; + i++; + j++; + } + } + if (missing !== null) out = `MISSING ${missing}`; + else if (extra !== null) out = `EXTRA ${extra}`; + else if (sizeError !== null) out = `SIZE ${sizeError}`; + else for (const [, z] of req) unique += z; +} +if (!out) out = `VALID ${req.length} ${unique} ${total - unique}`; +std.out.puts(out + "\n"); diff --git a/problems/020-offline-dependency-bundle/statement.en.md b/problems/020-offline-dependency-bundle/statement.en.md new file mode 100644 index 0000000..b5f7026 --- /dev/null +++ b/problems/020-offline-dependency-bundle/statement.en.md @@ -0,0 +1,110 @@ +# Offline Dependency Suitcase + +To let an offline WASM OJ toolchain load directly in the browser, we need to package the dependencies required by its lockfile together with their payloads instead of downloading them at execution time. Copying one file per package would waste space because different packages may refer to the same content digest. + +The bundle therefore deduplicates content by digest. It must provide exactly one payload for every **unique required digest** in the lockfile: none may be missing, none may be extra, and every payload size must match its declaration. A zero-size payload still represents a digest that must be validated. + +Two internal contradictions must also be handled. If several packages declare different sizes for one digest, the lockfile conflicts with itself. If the bundle lists one digest more than once, its payload is no longer unique. When several error kinds apply, use the category priority specified below; within one category, choose the ASCII-lexicographically smallest digest. + +## Input + +The first line contains `N M`. The next `N` lines contain: + +```text +packageName digest declaredSize +``` + +The following `M` lines contain: + +```text +digest payloadSize +``` + +Package names are unique. Digests are precomputed lowercase hexadecimal tokens and are treated as collision-free. + +## Output + +Output only the first applicable category below. When several digests belong to that category, choose the ASCII-lexicographically smallest one: + +1. `LOCK_CONFLICT digest`: the same required digest has different declared sizes. +2. `DUPLICATE_PAYLOAD digest`: the bundle contains the same digest more than once. +3. `MISSING digest`: a required digest has no payload. +4. `EXTRA digest`: a payload digest is not required. +5. `SIZE digest`: required size and payload size differ. + +If every check passes, output: + +```text +VALID uniqueDigestCount deduplicatedBytes savedBytes +``` + +`deduplicatedBytes` is the sum of sizes over unique digests. `savedBytes` is the sum of every package's declared size minus `deduplicatedBytes`. A zero-size digest still counts as one digest. + +## Constraints + +- `1 ≤ N,M ≤ 200000` +- `packageName` matches `[a-z0-9-]{1,30}` and package names are distinct. +- A digest matches `[0-9a-f]{8,64}`. +- Each size lies from 0 through `9×10^18`. +- The sum of all package declared sizes is at most `9×10^18`. + +The full constraints rule out pairwise linear searches between required and payload records. + +## Examples + + + +### Example One + +Input: + +```text +3 2 +a aaaaaaaa 5 +b bbbbbbbb 7 +c aaaaaaaa 5 +aaaaaaaa 5 +bbbbbbbb 7 +``` + +Output: + +```text +VALID 2 12 5 +``` + +### Example Two + +Input: + +```text +2 1 +a aaaaaaaa 5 +b aaaaaaaa 6 +aaaaaaaa 5 +``` + +Output: + +```text +LOCK_CONFLICT aaaaaaaa +``` + +### Example Three + +Input: + +```text +1 2 +a aaaaaaaa 5 +aaaaaaaa 5 +aaaaaaaa 5 +``` + +Output: + +```text +DUPLICATE_PAYLOAD aaaaaaaa +``` + + diff --git a/problems/020-offline-dependency-bundle/statement.zh-TW.md b/problems/020-offline-dependency-bundle/statement.zh-TW.md new file mode 100644 index 0000000..745da66 --- /dev/null +++ b/problems/020-offline-dependency-bundle/statement.zh-TW.md @@ -0,0 +1,108 @@ +# 離線依賴行李箱 + +為了讓 WASM OJ 的離線 toolchain 能在瀏覽器中直接載入,我們需要把 lockfile 要求的依賴與實際 payload 一起封裝,不必等到執行時才連線下載。直接按照 package 數量複製檔案會浪費空間,因為不同 package 可能指向相同的內容 digest。 + +bundle 因此以 digest 去除重複內容。對 lockfile 中每個**唯一 required digest**,bundle 必須恰好提供一份 payload:不能缺少、不能多帶,payload size 也必須與宣告相符。即使 payload size 為零,它仍是一個需要驗證的 digest。 + +驗證前還要處理兩種內部矛盾:多個 package 若為同一 digest 宣告不同 size,表示 lockfile 衝突;bundle 若重複列出同一 digest,則 payload 不再是唯一。當錯誤不只一種時,必須使用題目指定的類別優先順序;同類別內則選 ASCII 字典序最小的 digest。 + +## 輸入 + +第一行 `N M`。接著 `N` 行: + +```text +packageName digest declaredSize +``` + +再接 `M` 行: + +```text +digest payloadSize +``` + +package name 唯一;digest 是已計算完成且視為不碰撞的 lowercase hexadecimal token。 + +## 輸出 + +只輸出下列第一個適用類別;同類別有多個 digest 時選 ASCII 字典序最小者: + +1. `LOCK_CONFLICT digest`:required 同 digest 有不同 declaredSize。 +2. `DUPLICATE_PAYLOAD digest`:bundle 同 digest 出現超過一次。 +3. `MISSING digest`:required digest 沒有 payload。 +4. `EXTRA digest`:payload digest 不在 required set。 +5. `SIZE digest`:required 與 payload size 不同。 + +全部通過則輸出: + +```text +VALID uniqueDigestCount deduplicatedBytes savedBytes +``` + +`deduplicatedBytes` 是每個唯一 digest 的 size 加總;`savedBytes` 是所有 package declaredSize 加總減去 deduplicatedBytes。即使 size 為 0 也照常是一個 digest。 + +## 限制 + +- `1 <= N,M <= 200000`。 +- packageName 符合 `[a-z0-9-]{1,30}` 且互異。 +- digest 符合 `[0-9a-f]{8,64}`。 +- size 介於 0 與 `9*10^18`;所有 package declaredSize 加總不超過 `9*10^18`。 +- 完整測資排除 required 與 payload 逐對線性搜尋。 + +## 範例 + + + +### 範例一 + +輸入: + +```text +3 2 +a aaaaaaaa 5 +b bbbbbbbb 7 +c aaaaaaaa 5 +aaaaaaaa 5 +bbbbbbbb 7 +``` + +輸出: + +```text +VALID 2 12 5 +``` + +### 範例二 + +輸入: + +```text +2 1 +a aaaaaaaa 5 +b aaaaaaaa 6 +aaaaaaaa 5 +``` + +輸出: + +```text +LOCK_CONFLICT aaaaaaaa +``` + +### 範例三 + +輸入: + +```text +1 2 +a aaaaaaaa 5 +aaaaaaaa 5 +aaaaaaaa 5 +``` + +輸出: + +```text +DUPLICATE_PAYLOAD aaaaaaaa +``` + + diff --git a/problems/020-offline-dependency-bundle/tests/adversarial-bigint-dedup.in b/problems/020-offline-dependency-bundle/tests/adversarial-bigint-dedup.in new file mode 100644 index 0000000..c04ebaa --- /dev/null +++ b/problems/020-offline-dependency-bundle/tests/adversarial-bigint-dedup.in @@ -0,0 +1,6 @@ +3 2 +p1 aaaaaaaa 4500000000000000000 +p2 aaaaaaaa 4500000000000000000 +p3 bbbbbbbb 0 +aaaaaaaa 4500000000000000000 +bbbbbbbb 0 diff --git a/problems/020-offline-dependency-bundle/tests/adversarial-bigint-dedup.out b/problems/020-offline-dependency-bundle/tests/adversarial-bigint-dedup.out new file mode 100644 index 0000000..f4d9bb3 --- /dev/null +++ b/problems/020-offline-dependency-bundle/tests/adversarial-bigint-dedup.out @@ -0,0 +1 @@ +VALID 2 4500000000000000000 4500000000000000000 diff --git a/problems/020-offline-dependency-bundle/tests/adversarial-error-priority.in b/problems/020-offline-dependency-bundle/tests/adversarial-error-priority.in new file mode 100644 index 0000000..a449382 --- /dev/null +++ b/problems/020-offline-dependency-bundle/tests/adversarial-error-priority.in @@ -0,0 +1,8 @@ +3 4 +p1 11111111 5 +p2 22222222 7 +p3 11111111 5 +33333333 1 +22222222 8 +33333333 2 +44444444 1 diff --git a/problems/020-offline-dependency-bundle/tests/adversarial-error-priority.out b/problems/020-offline-dependency-bundle/tests/adversarial-error-priority.out new file mode 100644 index 0000000..d449492 --- /dev/null +++ b/problems/020-offline-dependency-bundle/tests/adversarial-error-priority.out @@ -0,0 +1 @@ +DUPLICATE_PAYLOAD 33333333 diff --git a/problems/020-offline-dependency-bundle/tests/sample-01.in b/problems/020-offline-dependency-bundle/tests/sample-01.in new file mode 100644 index 0000000..e17e215 --- /dev/null +++ b/problems/020-offline-dependency-bundle/tests/sample-01.in @@ -0,0 +1,6 @@ +3 2 +a aaaaaaaa 5 +b bbbbbbbb 7 +c aaaaaaaa 5 +aaaaaaaa 5 +bbbbbbbb 7 diff --git a/problems/020-offline-dependency-bundle/tests/sample-01.out b/problems/020-offline-dependency-bundle/tests/sample-01.out new file mode 100644 index 0000000..939f9a2 --- /dev/null +++ b/problems/020-offline-dependency-bundle/tests/sample-01.out @@ -0,0 +1 @@ +VALID 2 12 5 diff --git a/problems/020-offline-dependency-bundle/tests/sample-02.in b/problems/020-offline-dependency-bundle/tests/sample-02.in new file mode 100644 index 0000000..abe20ef --- /dev/null +++ b/problems/020-offline-dependency-bundle/tests/sample-02.in @@ -0,0 +1,4 @@ +2 1 +a aaaaaaaa 5 +b aaaaaaaa 6 +aaaaaaaa 5 diff --git a/problems/020-offline-dependency-bundle/tests/sample-02.out b/problems/020-offline-dependency-bundle/tests/sample-02.out new file mode 100644 index 0000000..2a1ef1f --- /dev/null +++ b/problems/020-offline-dependency-bundle/tests/sample-02.out @@ -0,0 +1 @@ +LOCK_CONFLICT aaaaaaaa diff --git a/problems/020-offline-dependency-bundle/tests/sample-03.in b/problems/020-offline-dependency-bundle/tests/sample-03.in new file mode 100644 index 0000000..b5623af --- /dev/null +++ b/problems/020-offline-dependency-bundle/tests/sample-03.in @@ -0,0 +1,4 @@ +1 2 +a aaaaaaaa 5 +aaaaaaaa 5 +aaaaaaaa 5 diff --git a/problems/020-offline-dependency-bundle/tests/sample-03.out b/problems/020-offline-dependency-bundle/tests/sample-03.out new file mode 100644 index 0000000..087740a --- /dev/null +++ b/problems/020-offline-dependency-bundle/tests/sample-03.out @@ -0,0 +1 @@ +DUPLICATE_PAYLOAD aaaaaaaa diff --git a/problems/020-offline-dependency-bundle/validator.py b/problems/020-offline-dependency-bundle/validator.py new file mode 100644 index 0000000..c66ba5a --- /dev/null +++ b/problems/020-offline-dependency-bundle/validator.py @@ -0,0 +1,40 @@ +import re, sys + +N = re.compile(r"[a-z0-9-]{1,30}$") +D = re.compile(r"[0-9a-f]{8,64}$") +U = 9_000_000_000_000_000_000 + + +def main(): + ls = sys.stdin.read().splitlines() + assert ls + h = ls[0].split() + assert len(h) == 2 + n, m = map(int, h) + assert 1 <= n <= 200000 and 1 <= m <= 200000 and len(ls) == 1 + n + m + names = set() + total = 0 + for line in ls[1 : n + 1]: + x = line.split() + assert ( + len(x) == 3 + and N.fullmatch(x[0]) + and D.fullmatch(x[1]) + and x[0] not in names + ) + names.add(x[0]) + z = int(x[2]) + assert str(z) == x[2] and 0 <= z <= U + total += z + assert total <= U + for line in ls[n + 1 :]: + x = line.split() + assert len(x) == 2 and D.fullmatch(x[0]) + z = int(x[1]) + assert str(z) == x[1] and 0 <= z <= U + + +try: + main() +except (AssertionError, ValueError): + sys.exit(1) diff --git a/problems/021-compiler-race/editorial.en.md b/problems/021-compiler-race/editorial.en.md new file mode 100644 index 0000000..e75d1f1 --- /dev/null +++ b/problems/021-compiler-race/editorial.en.md @@ -0,0 +1,26 @@ +# Editorial + +## Intuitive Approach + +Store every job in an array. On `S`, scan all jobs and cancel live background ones; requests may also scan for a matching key. This can perform quadratically many checks and is infeasible for `N=200000`. + +## Optimal Approach: Generation Stamps + +Use a hash map from each key to its most recently associated job ID. Store every job's key, kind, creation generation, and explicit `alive` flag in arrays. Also maintain current generation `epoch` and the number `liveBg` of live background jobs in it. + +A background job is alive exactly when its flag is true and `job.epoch==epoch`; a foreground job only checks the flag. `S` outputs `liveBg`, resets it to zero, and increments `epoch`, cancelling arbitrarily many jobs in `O(1)`. Stale background entries remain in the map lazily; when a later request finds one, the generation check rejects it and the map entry is overwritten. + +## Correctness Proof + +Induct over events. Initially no jobs exist. A request uses the map to find the only possible most-recent live job for its key; the alive predicate exactly matches the specification, so the algorithm outputs the correct `JOIN` or `NEW`. A `D` uses the same predicate and clears `alive` and the count on success, so a job completes at most once. Before `S`, `liveBg` equals the number of live background jobs in the current generation. Incrementing `epoch` makes all their generation stamps differ simultaneously, while foreground liveness does not depend on the epoch. This is exactly supersede behavior, so every output is correct. + +## Complexity + +Hash-map operations are expected `O(1)`, so every event is expected `O(1)`, total expected time is `O(N)`, and space is `O(N)`. + +## Common Mistakes + +- Cancelling foreground jobs on `S`. +- Returning `DONE` for a superseded job. +- Upgrading a background job to foreground on `JOIN`; no such rule exists. +- Clearing a key-map entry without checking that it still points to the completed ID. diff --git a/problems/021-compiler-race/editorial.zh-TW.md b/problems/021-compiler-race/editorial.zh-TW.md new file mode 100644 index 0000000..4b6e2e9 --- /dev/null +++ b/problems/021-compiler-race/editorial.zh-TW.md @@ -0,0 +1,26 @@ +# 解題說明 + +## 直覺解 + +以陣列保存所有工作。`S` 時逐一掃描並取消仍存活的背景工作;請求也可掃描所有工作尋找相同 key。最壞會做平方次檢查,`N=200000` 時不可行。 + +## 最佳解:世代戳記 + +用 hash map 保存每個 key 最後指向的工作編號,並以陣列保存工作的 key、種類、建立世代與顯式 alive 標記。另維護目前世代 `epoch` 和其中的存活背景工作數 `liveBg`。 + +背景工作在且僅在 `alive` 且 `job.epoch == epoch` 時存活;前景工作只檢查 `alive`。`S` 只要輸出 `liveBg`、令它歸零並增加 `epoch`,因此大量取消是 O(1)。map 中的舊背景工作採懶清除:下次查到時檢查世代,若已失效便覆寫。 + +## 正確性證明 + +歸納每個事件。初始沒有工作,表示正確。請求事件透過 map 找到該 key 唯一可能存活的最後工作;存活判定恰與題意一致,因此正確 JOIN 或 NEW。`D` 使用同一判定,成功時清除 alive 並同步計數,故恰好只能完成一次。`S` 前 `liveBg` 等於目前世代所有存活背景工作數;增加世代後,這些工作的世代全不相等而同時失效,前景工作不看世代,完全符合取消規則。故所有輸出正確。 + +## 複雜度 + +hash map 預期 O(1),每事件預期 O(1),總時間 O(N),空間 O(N)。 + +## 常見錯誤 + +- `S` 時把前景工作也取消。 +- 已被 supersede 的工作在 `D` 時仍輸出 DONE。 +- JOIN 背景工作時誤把它升級成前景工作;題目沒有升級規則。 +- 清除 key map 時沒有確認它仍指向被完成的 id。 diff --git a/problems/021-compiler-race/generator.py b/problems/021-compiler-race/generator.py new file mode 100644 index 0000000..ced37a8 --- /dev/null +++ b/problems/021-compiler-race/generator.py @@ -0,0 +1,18 @@ +#!/usr/bin/env python3 +import random, sys + +seed, index = map(int, sys.argv[1:]) +r = random.Random((seed << 32) ^ index) +n = 20 + index % 31 +out = [str(n)] +made = 0 +for _ in range(n): + t = r.randrange(10) + if t < 6: + out.append(f"{'B' if t < 4 else 'F'} {chr(97 + r.randrange(8))}") + made += 1 + elif t < 8: + out.append("S") + else: + out.append(f"D {r.randint(1, max(1, made + 2))}") +print("\n".join(out)) diff --git a/problems/021-compiler-race/oracle.py b/problems/021-compiler-race/oracle.py new file mode 100644 index 0000000..34de8b4 --- /dev/null +++ b/problems/021-compiler-race/oracle.py @@ -0,0 +1,35 @@ +#!/usr/bin/env python3 +import sys + +it = iter(sys.stdin.read().splitlines()) +n = int(next(it)) +jobs = [] +out = [] +for line in it: + p = line.split() + t = p[0] + if t in ("B", "F"): + found = None + for i, j in enumerate(jobs): + if j[0] == p[1] and j[2]: + found = i + 1 + if found is None: + jobs.append([p[1], t, True]) + out.append(f"NEW {len(jobs)}") + else: + out.append(f"JOIN {found}") + elif t == "S": + k = 0 + for j in jobs: + if j[1] == "B" and j[2]: + j[2] = False + k += 1 + out.append(f"CANCEL {k}") + else: + x = int(p[1]) - 1 + if 0 <= x < len(jobs) and jobs[x][2]: + jobs[x][2] = False + out.append("DONE") + else: + out.append("STALE") +print("\n".join(out)) diff --git a/problems/021-compiler-race/problem.json b/problems/021-compiler-race/problem.json new file mode 100644 index 0000000..50c930b --- /dev/null +++ b/problems/021-compiler-race/problem.json @@ -0,0 +1,146 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 21, + "slug": "compiler-race", + "title": { + "zh-TW": "編譯工作世代競賽", + "en": "Compiler Job Generation Race" + }, + "difficulty": "medium", + "tags": [ + "state-machine", + "lazy-invalidation", + "hash-map" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-join-kind-generation", + "kind": "adversarial", + "input": "tests/adversarial-join-kind-generation.in", + "output": "tests/adversarial-join-kind-generation.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 8500000, + "memoryLimitBytes": 536870912 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 2000000, + "memoryLimitBytes": 402653184 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 650000, + "memoryLimitBytes": 268435456 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "每次 supersede 掃描所有工作", + "en": "Scan All Jobs on Every Supersede" + }, + "time": "O(N^2)", + "space": "O(N)", + "accepted": false + }, + { + "name": { + "zh-TW": "世代戳記與索引", + "en": "Generation Stamps and Indexing" + }, + "time": "O(N) expected", + "space": "O(N)", + "accepted": true + } + ] +} diff --git a/problems/021-compiler-race/solutions/c/main.c b/problems/021-compiler-race/solutions/c/main.c new file mode 100644 index 0000000..4c80048 --- /dev/null +++ b/problems/021-compiler-race/solutions/c/main.c @@ -0,0 +1,88 @@ +#include +#include +#include +#include + +typedef struct { + char *key; + int job; +} Slot; +typedef struct { + char *key; + int epoch; + unsigned char kind, alive; +} Job; +static uint64_t hash_key(const char *s) { + uint64_t h = 1469598103934665603ULL; + while (*s) { + h ^= (unsigned char)*s++; + h *= 1099511628211ULL; + } + return h; +} +int main(void) { + int n; + if (scanf("%d", &n) != 1) + return 0; + size_t cap = 1; + while (cap < (size_t)n * 3) + cap <<= 1; + Slot *tab = calloc(cap, sizeof(*tab)); + Job *jobs = calloc((size_t)n + 1, sizeof(*jobs)); + int made = 0, epoch = 0, live_bg = 0; + char op[2], key[21]; + for (int z = 0; z < n; z++) { + scanf("%1s", op); + if (op[0] == 'B' || op[0] == 'F') { + scanf("%20s", key); + size_t i = (size_t)hash_key(key) & (cap - 1); + while (tab[i].key && strcmp(tab[i].key, key)) + i = (i + 1) & (cap - 1); + if (!tab[i].key) { + size_t len = strlen(key) + 1; + tab[i].key = malloc(len); + memcpy(tab[i].key, key, len); + } + int id = tab[i].job, + ok = id && jobs[id].alive && + (jobs[id].kind == 'F' || jobs[id].epoch == epoch); + if (ok) + printf("JOIN %d\n", id); + else { + id = ++made; + jobs[id] = (Job){tab[i].key, epoch, (unsigned char)op[0], 1}; + tab[i].job = id; + if (op[0] == 'B') + live_bg++; + printf("NEW %d\n", id); + } + } else if (op[0] == 'S') { + printf("CANCEL %d\n", live_bg); + live_bg = 0; + epoch++; + } else { + int id; + scanf("%d", &id); + int ok = id <= made && jobs[id].alive && + (jobs[id].kind == 'F' || jobs[id].epoch == epoch); + if (!ok) { + puts("STALE"); + continue; + } + jobs[id].alive = 0; + if (jobs[id].kind == 'B') + live_bg--; + size_t i = (size_t)hash_key(jobs[id].key) & (cap - 1); + while (strcmp(tab[i].key, jobs[id].key)) + i = (i + 1) & (cap - 1); + if (tab[i].job == id) + tab[i].job = 0; + puts("DONE"); + } + } + for (size_t i = 0; i < cap; i++) + free(tab[i].key); + free(tab); + free(jobs); + return 0; +} diff --git a/problems/021-compiler-race/solutions/cpp/main.cpp b/problems/021-compiler-race/solutions/cpp/main.cpp new file mode 100644 index 0000000..8a82f2a --- /dev/null +++ b/problems/021-compiler-race/solutions/cpp/main.cpp @@ -0,0 +1,58 @@ +#include +#include +#include +#include +struct Job { + std::string key; + int epoch; + char kind; + bool alive; +}; +int main() { + std::ios::sync_with_stdio(false); + std::cin.tie(nullptr); + int n; + std::cin >> n; + std::unordered_map by; + std::vector a(1); + int ep = 0, bg = 0; + while (n--) { + char t; + std::cin >> t; + if (t == 'B' || t == 'F') { + std::string k; + std::cin >> k; + int id = by.count(k) ? by[k] : 0; + bool live = id && a[id].alive && (a[id].kind == 'F' || a[id].epoch == ep); + if (live) + std::cout << "JOIN " << id << '\n'; + else { + a.push_back({k, ep, t, true}); + id = (int)a.size() - 1; + by[k] = id; + if (t == 'B') + bg++; + std::cout << "NEW " << id << '\n'; + } + } else if (t == 'S') { + std::cout << "CANCEL " << bg << '\n'; + bg = 0; + ep++; + } else { + int id; + std::cin >> id; + bool live = id < (int)a.size() && a[id].alive && + (a[id].kind == 'F' || a[id].epoch == ep); + if (!live) + std::cout << "STALE\n"; + else { + a[id].alive = false; + if (a[id].kind == 'B') + bg--; + if (by[a[id].key] == id) + by.erase(a[id].key); + std::cout << "DONE\n"; + } + } + } +} diff --git a/problems/021-compiler-race/solutions/go/main.go b/problems/021-compiler-race/solutions/go/main.go new file mode 100644 index 0000000..05a131e --- /dev/null +++ b/problems/021-compiler-race/solutions/go/main.go @@ -0,0 +1,67 @@ +package main + +import ( + "bufio" + "fmt" + "os" +) + +type Job struct { + key string + epoch int + kind byte + alive bool +} + +func main() { + in := bufio.NewReader(os.Stdin) + out := bufio.NewWriter(os.Stdout) + defer out.Flush() + var n int + fmt.Fscan(in, &n) + by := map[string]int{} + a := make([]Job, 1, n+1) + ep, bg := 0, 0 + for ; n > 0; n-- { + var ts string + fmt.Fscan(in, &ts) + t := ts[0] + if t == 'B' || t == 'F' { + var k string + fmt.Fscan(in, &k) + id := by[k] + live := id > 0 && a[id].alive && (a[id].kind == 'F' || a[id].epoch == ep) + if live { + fmt.Fprintln(out, "JOIN", id) + } else { + a = append(a, Job{k, ep, t, true}) + id = len(a) - 1 + by[k] = id + if t == 'B' { + bg++ + } + fmt.Fprintln(out, "NEW", id) + } + } else if t == 'S' { + fmt.Fprintln(out, "CANCEL", bg) + bg = 0 + ep++ + } else { + var id int + fmt.Fscan(in, &id) + live := id < len(a) && a[id].alive && (a[id].kind == 'F' || a[id].epoch == ep) + if !live { + fmt.Fprintln(out, "STALE") + } else { + a[id].alive = false + if a[id].kind == 'B' { + bg-- + } + if by[a[id].key] == id { + delete(by, a[id].key) + } + fmt.Fprintln(out, "DONE") + } + } + } +} diff --git a/problems/021-compiler-race/solutions/javascript/main.js b/problems/021-compiler-race/solutions/javascript/main.js new file mode 100644 index 0000000..3e2b44c --- /dev/null +++ b/problems/021-compiler-race/solutions/javascript/main.js @@ -0,0 +1,44 @@ +import * as std from "std"; +/** @typedef {{ key: string, epoch: number, kind: string, alive: boolean }} Job */ +const x = std.in.readAsString().trim().split(/\s+/); +let p = 0, n = Number(x[p++]), epoch = 0, bg = 0; +/** @type {Map} */ +const by = new Map(); +/** @type {(Job | null)[]} */ +const jobs = [null]; +/** @type {string[]} */ +const out = []; +while (n--) { + const t = x[p++]; + if (t === "B" || t === "F") { + const k = x[p++], + i = by.get(k) || 0, + j = jobs[i], + live = !!j && j.alive && (j.kind === "F" || j.epoch === epoch); + if (live) out.push(`JOIN ${i}`); + else { + const id = jobs.length; + jobs.push({ key: k, epoch, kind: t, alive: true }); + by.set(k, id); + if (t === "B") bg++; + out.push(`NEW ${id}`); + } + } else if (t === "S") { + out.push(`CANCEL ${bg}`); + bg = 0; + epoch++; + } else { + const i = Number(x[p++]), + j = jobs[i], + live = j && j.alive && (j.kind === "F" || j.epoch === epoch); + if (!live) out.push("STALE"); + else { + const activeJob = /** @type {Job} */ (j); + activeJob.alive = false; + if (activeJob.kind === "B") bg--; + if (by.get(activeJob.key) === i) by.delete(activeJob.key); + out.push("DONE"); + } + } +} +std.out.puts(out.join("\n") + "\n"); diff --git a/problems/021-compiler-race/solutions/python/main.py b/problems/021-compiler-race/solutions/python/main.py new file mode 100644 index 0000000..2e64a75 --- /dev/null +++ b/problems/021-compiler-race/solutions/python/main.py @@ -0,0 +1,40 @@ +import sys + +it = iter(sys.stdin.buffer.read().split()) +n = int(next(it)) +by = {} +jobs = [None] +epoch = bg = 0 +out = [] +for _ in range(n): + t = next(it).decode() + if t in ("B", "F"): + k = next(it) + i = by.get(k, 0) + live = i and jobs[i][3] and (jobs[i][2] == "F" or jobs[i][1] == epoch) + if live: + out.append(f"JOIN {i}") + else: + i = len(jobs) + jobs.append([k, epoch, t, True]) + by[k] = i + bg += t == "B" + out.append(f"NEW {i}") + elif t == "S": + out.append(f"CANCEL {bg}") + bg = 0 + epoch += 1 + else: + i = int(next(it)) + live = ( + i < len(jobs) and jobs[i][3] and (jobs[i][2] == "F" or jobs[i][1] == epoch) + ) + if not live: + out.append("STALE") + else: + jobs[i][3] = False + bg -= jobs[i][2] == "B" + if by.get(jobs[i][0]) == i: + del by[jobs[i][0]] + out.append("DONE") +print("\n".join(out)) diff --git a/problems/021-compiler-race/solutions/rust/main.rs b/problems/021-compiler-race/solutions/rust/main.rs new file mode 100644 index 0000000..f4c586d --- /dev/null +++ b/problems/021-compiler-race/solutions/rust/main.rs @@ -0,0 +1,67 @@ +use std::collections::HashMap; +use std::io::{self, Read}; +struct Job { + key: String, + epoch: i32, + kind: u8, + alive: bool, +} +fn main() { + let mut s = String::new(); + io::stdin().read_to_string(&mut s).unwrap(); + let mut it = s.split_whitespace(); + let n: usize = it.next().unwrap().parse().unwrap(); + let mut by: HashMap = HashMap::new(); + let mut a = vec![Job { + key: String::new(), + epoch: 0, + kind: 0, + alive: false, + }]; + let (mut ep, mut bg) = (0, 0); + let mut out = String::new(); + for _ in 0..n { + let t = it.next().unwrap().as_bytes()[0]; + if t == b'B' || t == b'F' { + let k = it.next().unwrap(); + let id = *by.get(k).unwrap_or(&0); + let live = id > 0 && a[id].alive && (a[id].kind == b'F' || a[id].epoch == ep); + if live { + out += &format!("JOIN {id}\n") + } else { + let id = a.len(); + a.push(Job { + key: k.to_string(), + epoch: ep, + kind: t, + alive: true, + }); + by.insert(k.to_string(), id); + if t == b'B' { + bg += 1 + } + out += &format!("NEW {id}\n") + } + } else if t == b'S' { + out += &format!("CANCEL {bg}\n"); + bg = 0; + ep += 1 + } else { + let id: usize = it.next().unwrap().parse().unwrap(); + let live = id < a.len() && a[id].alive && (a[id].kind == b'F' || a[id].epoch == ep); + if !live { + out += "STALE\n" + } else { + a[id].alive = false; + if a[id].kind == b'B' { + bg -= 1 + } + if by.get(&a[id].key) == Some(&id) { + by.remove(&a[id].key); + } + out += "DONE\n" + } + } + } + print!("{out}") +} diff --git a/problems/021-compiler-race/solutions/typescript/main.ts b/problems/021-compiler-race/solutions/typescript/main.ts new file mode 100644 index 0000000..c567ca4 --- /dev/null +++ b/problems/021-compiler-race/solutions/typescript/main.ts @@ -0,0 +1,40 @@ +import * as std from "std"; +type Job = { key: string; epoch: number; kind: string; alive: boolean }; +const x = std.in.readAsString().trim().split(/\s+/); +let p = 0, n = Number(x[p++]), epoch = 0, bg = 0; +const by = new Map(), + jobs: (Job | null)[] = [null], + out: string[] = []; +while (n--) { + const t = x[p++]; + if (t === "B" || t === "F") { + const k = x[p++], + i = by.get(k) || 0, + j = jobs[i], + live = !!j && j.alive && (j.kind === "F" || j.epoch === epoch); + if (live) out.push(`JOIN ${i}`); + else { + const id = jobs.length; + jobs.push({ key: k, epoch, kind: t, alive: true }); + by.set(k, id); + if (t === "B") bg++; + out.push(`NEW ${id}`); + } + } else if (t === "S") { + out.push(`CANCEL ${bg}`); + bg = 0; + epoch++; + } else { + const i = Number(x[p++]), + j = jobs[i], + live = !!j && j.alive && (j.kind === "F" || j.epoch === epoch); + if (!live) out.push("STALE"); + else { + j!.alive = false; + if (j!.kind === "B") bg--; + if (by.get(j!.key) === i) by.delete(j!.key); + out.push("DONE"); + } + } +} +std.out.puts(out.join("\n") + "\n"); diff --git a/problems/021-compiler-race/statement.en.md b/problems/021-compiler-race/statement.en.md new file mode 100644 index 0000000..5106945 --- /dev/null +++ b/problems/021-compiler-race/statement.en.md @@ -0,0 +1,123 @@ +# Compiler Job Generation Race + +Automatic checks, manual runs, and interface updates may trigger several in-browser compilation jobs for the same WASM OJ source in quick succession. Creating another compilation when identical input is already being processed wastes instruction cost and can allow an older result to overwrite newer state. + +The coordinator therefore coalesces live jobs with the same key and uses generations to distinguish background requests for different versions. When new state supersedes old state, an `S` event cancels every background job still alive in the current generation. Foreground jobs remain alive until they complete successfully. Events are already ordered by when they actually occurred, so there are no undefined thread interleavings. + +Job IDs start at 1 and increase only when a job is created. The current generation starts at 0. Process these events: + +- `B key`: request a background job. +- `F key`: request a foreground job. +- `S`: cancel every background job that is still alive in the current generation, then increment the generation. Foreground jobs are unaffected. +- `D id`: attempt to complete job `id`. + +On `B` or `F`, if that key already has a live job, coalesce the request into that existing job regardless of the new request's kind. Otherwise create a background or foreground job according to the event. A background job is alive only in its creation generation; a foreground job remains alive until it completes successfully. Jobs cancelled by `S` never revive. A key is a nonempty lowercase English string. + +## Input + +The first line contains event count `N`. Each of the next `N` lines contains one event. + +## Output + +Output one line for each event: + +- New job: `NEW id` +- Coalesced job: `JOIN id` +- `S`: `CANCEL k`, where `k` is the number of jobs actually cancelled by this event +- Successful completion: `DONE` +- Completion of a nonexistent, completed, or cancelled job: `STALE` + +## Constraints + +- `1 ≤ N ≤ 200000` +- `1 ≤ |key| ≤ 20` +- The total length of all keys is at most `2000000`. +- `1 ≤ id ≤ N+1` +- `D` may name a nonexistent, already completed, or cancelled job. + +The full constraints apply to every official test. + +## Examples + + + +### Example One + +Input: + +```text +8 +B a +B a +F x +S +D 1 +B a +D 2 +D 3 +``` + +Output: + +```text +NEW 1 +JOIN 1 +NEW 2 +CANCEL 1 +STALE +NEW 3 +DONE +DONE +``` + +### Example Two + +Input: + +```text +5 +S +F a +S +F a +D 1 +``` + +Output: + +```text +CANCEL 0 +NEW 1 +CANCEL 0 +JOIN 1 +DONE +``` + +### Example Three + +Input: + +```text +7 +B a +B b +D 1 +S +D 2 +B b +D 3 +``` + +Output: + +```text +NEW 1 +NEW 2 +DONE +CANCEL 1 +STALE +NEW 3 +DONE +``` + + diff --git a/problems/021-compiler-race/statement.zh-TW.md b/problems/021-compiler-race/statement.zh-TW.md new file mode 100644 index 0000000..1d7d1e0 --- /dev/null +++ b/problems/021-compiler-race/statement.zh-TW.md @@ -0,0 +1,121 @@ +# 編譯工作世代競賽 + +自動檢查、手動執行與介面更新,可能讓 WASM OJ 的瀏覽器內編譯器在短時間內為同一份來源觸發多次工作。如果相同輸入已經有工作正在進行,重複建立編譯不但浪費 instruction cost,也可能讓較舊的結果覆蓋較新的畫面。 + +因此 coordinator 會依 key 合併仍存活的相同工作,並以 generation 區分不同版本的背景請求。當新的狀態 supersede 舊狀態時,事件 `S` 會一次取消目前 generation 中仍存活的所有背景工作;前景工作則保留,直到成功完成。輸入已依實際發生順序排列,不存在未定義的執行緒交錯。 + +工作編號從 1 開始,只在建立工作時遞增。維護目前世代,初始為 0,並處理以下事件: + +- `B key`:請求背景工作; +- `F key`:請求前景工作; +- `S`:取消目前仍存活的所有背景工作,然後令世代加一;前景工作不受影響; +- `D id`:嘗試完成編號 `id` 的工作。 + +收到 `B` 或 `F` 時,若該 key 已有存活工作,不論新請求種類為何都合併至原工作;否則依事件種類建立背景或前景工作。背景工作只在建立世代中存活;前景工作持續存活直到成功完成。`S` 取消的工作之後永遠不會復活。key 為非空小寫英文字串。 + +## 輸入 + +第一行為事件數 `N`。接著 `N` 行各為一個事件。 + +- `1 ≤ N ≤ 200000` +- `1 ≤ |key| ≤ 20`,所有 key 總長度不超過 `2000000` +- `1 ≤ id ≤ N+1`;`D` 可指向不存在、已完成或已取消的工作 + +## 輸出 + +每個事件輸出一行: + +- 新建工作:`NEW id` +- 合併工作:`JOIN id` +- `S`:`CANCEL k`,其中 `k` 是這次實際取消的工作數 +- 成功完成:`DONE` +- 完成不存在、已完成或已取消工作:`STALE` + +## 範例 + + + +### 範例一 + +輸入: + +```text +8 +B a +B a +F x +S +D 1 +B a +D 2 +D 3 +``` + +輸出: + +```text +NEW 1 +JOIN 1 +NEW 2 +CANCEL 1 +STALE +NEW 3 +DONE +DONE +``` + +### 範例二 + +輸入: + +```text +5 +S +F a +S +F a +D 1 +``` + +輸出: + +```text +CANCEL 0 +NEW 1 +CANCEL 0 +JOIN 1 +DONE +``` + +### 範例三 + +輸入: + +```text +7 +B a +B b +D 1 +S +D 2 +B b +D 3 +``` + +輸出: + +```text +NEW 1 +NEW 2 +DONE +CANCEL 1 +STALE +NEW 3 +DONE +``` + + + +## 限制 + +所有數量、字串格式與整數範圍均列於「輸入」段落;完整限制適用於每一筆正式測資。 diff --git a/problems/021-compiler-race/tests/adversarial-join-kind-generation.in b/problems/021-compiler-race/tests/adversarial-join-kind-generation.in new file mode 100644 index 0000000..9a9e240 --- /dev/null +++ b/problems/021-compiler-race/tests/adversarial-join-kind-generation.in @@ -0,0 +1,18 @@ +17 +B a +F a +S +D 1 +F a +B a +S +D 2 +D 2 +D 18 +B b +B c +D 3 +S +D 4 +F c +S diff --git a/problems/021-compiler-race/tests/adversarial-join-kind-generation.out b/problems/021-compiler-race/tests/adversarial-join-kind-generation.out new file mode 100644 index 0000000..2359383 --- /dev/null +++ b/problems/021-compiler-race/tests/adversarial-join-kind-generation.out @@ -0,0 +1,17 @@ +NEW 1 +JOIN 1 +CANCEL 1 +STALE +NEW 2 +JOIN 2 +CANCEL 0 +DONE +STALE +STALE +NEW 3 +NEW 4 +DONE +CANCEL 1 +STALE +NEW 5 +CANCEL 0 diff --git a/problems/021-compiler-race/tests/sample-01.in b/problems/021-compiler-race/tests/sample-01.in new file mode 100644 index 0000000..547f097 --- /dev/null +++ b/problems/021-compiler-race/tests/sample-01.in @@ -0,0 +1,9 @@ +8 +B a +B a +F x +S +D 1 +B a +D 2 +D 3 diff --git a/problems/021-compiler-race/tests/sample-01.out b/problems/021-compiler-race/tests/sample-01.out new file mode 100644 index 0000000..08f6d7d --- /dev/null +++ b/problems/021-compiler-race/tests/sample-01.out @@ -0,0 +1,8 @@ +NEW 1 +JOIN 1 +NEW 2 +CANCEL 1 +STALE +NEW 3 +DONE +DONE diff --git a/problems/021-compiler-race/tests/sample-02.in b/problems/021-compiler-race/tests/sample-02.in new file mode 100644 index 0000000..a41b754 --- /dev/null +++ b/problems/021-compiler-race/tests/sample-02.in @@ -0,0 +1,6 @@ +5 +S +F a +S +F a +D 1 diff --git a/problems/021-compiler-race/tests/sample-02.out b/problems/021-compiler-race/tests/sample-02.out new file mode 100644 index 0000000..ead3ecc --- /dev/null +++ b/problems/021-compiler-race/tests/sample-02.out @@ -0,0 +1,5 @@ +CANCEL 0 +NEW 1 +CANCEL 0 +JOIN 1 +DONE diff --git a/problems/021-compiler-race/tests/sample-03.in b/problems/021-compiler-race/tests/sample-03.in new file mode 100644 index 0000000..3d7dd76 --- /dev/null +++ b/problems/021-compiler-race/tests/sample-03.in @@ -0,0 +1,8 @@ +7 +B a +B b +D 1 +S +D 2 +B b +D 3 diff --git a/problems/021-compiler-race/tests/sample-03.out b/problems/021-compiler-race/tests/sample-03.out new file mode 100644 index 0000000..914c459 --- /dev/null +++ b/problems/021-compiler-race/tests/sample-03.out @@ -0,0 +1,7 @@ +NEW 1 +NEW 2 +DONE +CANCEL 1 +STALE +NEW 3 +DONE diff --git a/problems/021-compiler-race/validator.py b/problems/021-compiler-race/validator.py new file mode 100644 index 0000000..bcff556 --- /dev/null +++ b/problems/021-compiler-race/validator.py @@ -0,0 +1,38 @@ +#!/usr/bin/env python3 +import re, sys + + +def fail(): + raise ValueError + + +try: + lines = sys.stdin.read().splitlines() + if not lines or not re.fullmatch(r"[1-9][0-9]*", lines[0]): + fail() + n = int(lines[0]) + if not 1 <= n <= 200000 or len(lines) != n + 1: + fail() + total = 0 + for s in lines[1:]: + p = s.split(" ") + if p[0] in ("B", "F"): + if len(p) != 2 or not re.fullmatch(r"[a-z]{1,20}", p[1]): + fail() + total += len(p[1]) + elif p[0] == "S": + if p != ["S"]: + fail() + elif p[0] == "D": + if ( + len(p) != 2 + or not re.fullmatch(r"[1-9][0-9]*", p[1]) + or int(p[1]) > n + 1 + ): + fail() + else: + fail() + if total > 2000000: + fail() +except Exception: + sys.exit(1) diff --git a/problems/022-submission-conveyor/editorial.en.md b/problems/022-submission-conveyor/editorial.en.md new file mode 100644 index 0000000..96334f5 --- /dev/null +++ b/problems/022-submission-conveyor/editorial.en.md @@ -0,0 +1,26 @@ +# Editorial + +## Intuitive Approach + +Represent the true waiting queue with an array. Cancelling searches and removes an element, while starting the next submission shifts all remaining elements from the front. Interleaved additions and cancellations can cost `O(N^2)`. + +## Optimal Approach: Queue with Lazy Deletion + +Each ID has one of four states: nonexistent, `queued`, `active`, or `terminal`. Append every added waiting ID to a deque. To cancel a waiting submission, only change its state to terminal in the hash map; do not remove it from the middle. When a submission must start, repeatedly discard non-queued IDs from the front, then change the first queued ID to active. Every ID is enqueued and dequeued at most once. + +Maintain a separate `waiting` counter: increment it when adding to a system with an active submission, decrement it when cancelling a queued submission, and also decrement it when a queued submission becomes active. + +## Correctness Proof + +The deque preserves insertion order for every ID not yet examined at the front. Elements whose state is `queued` are exactly the valid waiters; terminal elements are tombstones that may be skipped safely. Thus after skipping tombstones, the first queued element is exactly the earliest valid waiting submission required by the specification. Each event performs only its specified state transition and invokes the start routine whenever the active submission disappears. By induction, both reported active ID and waiting count are correct after every event. + +## Complexity + +Hash operations are expected `O(1)`. Across all events, deque removals total `O(N)`, so total expected time is `O(N)` and space is `O(N)`. + +## Common Mistakes + +- Including the active submission in `waiting`. +- Forgetting to decrement the counter when cancelling a queued submission. +- Removing cancelled IDs from the middle of the deque and causing quadratic time. +- Starting a job or reporting an error when `E` occurs on an empty system. diff --git a/problems/022-submission-conveyor/editorial.zh-TW.md b/problems/022-submission-conveyor/editorial.zh-TW.md new file mode 100644 index 0000000..e9f5675 --- /dev/null +++ b/problems/022-submission-conveyor/editorial.zh-TW.md @@ -0,0 +1,26 @@ +# 解題說明 + +## 直覺解 + +用陣列表示真正的等待佇列。取消時搜尋並刪除元素,啟動下一份時從陣首搬移所有元素。交錯加入與取消可造成 O(N²)。 + +## 最佳解 + +每個 id 只有 `queued`、`active`、`terminal`(或不存在)四種狀態。把每次加入的 id 追加到 deque;取消等待者時只把 hash map 中狀態改為 terminal,不從 deque 中間移除。需要啟動工作時,持續從隊首丟掉非 queued id,第一個 queued id 改為 active。每個 id 最多入隊、出隊各一次。 + +另維護 `waiting` 計數器:加入到已有 active 的系統時加一;取消 queued 時減一;queued 轉 active 時也減一。 + +## 正確性證明 + +deque 始終依加入時間保存所有尚未從隊首檢查過的 id。狀態為 queued 的元素恰為有效等待者;terminal 元素是可安全略過的墓碑。因此啟動函式略過墓碑後取到的第一個 queued 元素,正是題意要求的最早有效等待者。每種事件只做指定狀態轉移並於 active 消失時呼叫啟動函式,歸納可得輸出的 active 與 waiting 永遠正確。 + +## 複雜度 + +hash 操作預期 O(1);所有 dequeue 總共 O(N),故總時間 O(N)、空間 O(N)。 + +## 常見錯誤 + +- 將 active 也算進 waiting。 +- 取消 queued 後忘記減計數。 +- 把已取消 id 從 deque 中間刪除,導致平方時間。 +- `E` 在空系統上誤啟動或產生錯誤。 diff --git a/problems/022-submission-conveyor/generator.py b/problems/022-submission-conveyor/generator.py new file mode 100644 index 0000000..25e0a4c --- /dev/null +++ b/problems/022-submission-conveyor/generator.py @@ -0,0 +1,23 @@ +#!/usr/bin/env python3 +import random, sys + +seed, index = map(int, sys.argv[1:]) +r = random.Random(seed * 1000003 + index) +n = 25 + index % 25 +next_id = 1 +known = [] +out = [str(n)] +for _ in range(n): + t = r.randrange(10) + if t < 5: + x = next_id + next_id += 1 + known.append(x) + out.append(f"A {x}") + elif t < 8: + out.append( + f"C {r.choice(known) if known and r.randrange(4) else next_id+r.randrange(5)}" + ) + else: + out.append("E") +print("\n".join(out)) diff --git a/problems/022-submission-conveyor/oracle.py b/problems/022-submission-conveyor/oracle.py new file mode 100644 index 0000000..9695c0d --- /dev/null +++ b/problems/022-submission-conveyor/oracle.py @@ -0,0 +1,35 @@ +#!/usr/bin/env python3 +import sys + +lines = sys.stdin.read().splitlines()[1:] +active = 0 +q = [] +terminal = set() +out = [] +for s in lines: + p = s.split() + t = p[0] + if t == "A": + x = int(p[1]) + if active == 0: + active = x + else: + q.append(x) + elif t == "C": + x = int(p[1]) + terminal.add(x) + if active == x: + active = 0 + else: + try: + q.remove(x) + except ValueError: + pass + else: + if active: + terminal.add(active) + active = 0 + if active == 0 and q: + active = q.pop(0) + out.append(f"{active} {len(q)}") +print("\n".join(out)) diff --git a/problems/022-submission-conveyor/problem.json b/problems/022-submission-conveyor/problem.json new file mode 100644 index 0000000..394c2b2 --- /dev/null +++ b/problems/022-submission-conveyor/problem.json @@ -0,0 +1,146 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 22, + "slug": "submission-conveyor", + "title": { + "zh-TW": "Submission 輸送帶", + "en": "Submission Conveyor" + }, + "difficulty": "medium", + "tags": [ + "queue", + "lazy-deletion", + "state-machine" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-future-cancel-lazy-queue", + "kind": "adversarial", + "input": "tests/adversarial-future-cancel-lazy-queue.in", + "output": "tests/adversarial-future-cancel-lazy-queue.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 7500000, + "memoryLimitBytes": 536870912 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 1500000, + "memoryLimitBytes": 402653184 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 550000, + "memoryLimitBytes": 268435456 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "陣列搬移佇列", + "en": "Array-Shifting Queue" + }, + "time": "O(N^2)", + "space": "O(N)", + "accepted": false + }, + { + "name": { + "zh-TW": "deque 與懶刪除", + "en": "Deque with Lazy Deletion" + }, + "time": "O(N) expected", + "space": "O(N)", + "accepted": true + } + ] +} diff --git a/problems/022-submission-conveyor/solutions/c/main.c b/problems/022-submission-conveyor/solutions/c/main.c new file mode 100644 index 0000000..74d498b --- /dev/null +++ b/problems/022-submission-conveyor/solutions/c/main.c @@ -0,0 +1,71 @@ +#include +#include +#include +typedef struct { + int key; + unsigned char state; +} Slot; +static size_t locate(Slot *t, size_t m, int x) { + size_t i = ((uint32_t)x * 2654435761u) & (m - 1); + while (t[i].key && t[i].key != x) + i = (i + 1) & (m - 1); + return i; +} +int main(void) { + int n; + if (scanf("%d", &n) != 1) + return 0; + size_t m = 1; + while (m < (size_t)n * 3) + m <<= 1; + Slot *t = calloc(m, sizeof(*t)); + int *q = malloc((size_t)n * sizeof(*q)); + int h = 0, z = 0, active = 0, waiting = 0; + for (int e = 0; e < n; e++) { + char op; + scanf(" %c", &op); + if (op == 'A') { + int x; + scanf("%d", &x); + size_t i = locate(t, m, x); + t[i].key = x; + if (!active) { + active = x; + t[i].state = 2; + } else { + t[i].state = 1; + q[z++] = x; + waiting++; + } + } else if (op == 'C') { + int x; + scanf("%d", &x); + size_t i = locate(t, m, x); + if (t[i].key && t[i].state == 1) { + t[i].state = 3; + waiting--; + } else if (t[i].key && t[i].state == 2) { + t[i].state = 3; + active = 0; + } + } else if (active) { + size_t i = locate(t, m, active); + t[i].state = 3; + active = 0; + } + if (!active) + while (h < z) { + int x = q[h++]; + size_t i = locate(t, m, x); + if (t[i].state == 1) { + t[i].state = 2; + active = x; + waiting--; + break; + } + } + printf("%d %d\n", active, waiting); + } + free(t); + free(q); +} diff --git a/problems/022-submission-conveyor/solutions/cpp/main.cpp b/problems/022-submission-conveyor/solutions/cpp/main.cpp new file mode 100644 index 0000000..365b1ce --- /dev/null +++ b/problems/022-submission-conveyor/solutions/cpp/main.cpp @@ -0,0 +1,53 @@ +#include +#include +#include +int main() { + std::ios::sync_with_stdio(false); + std::cin.tie(nullptr); + int n, active = 0, waiting = 0; + std::cin >> n; + std::deque q; + std::unordered_map s; + auto advance = [&] { + while (!active && !q.empty()) { + int x = q.front(); + q.pop_front(); + if (s[x] == 1) { + s[x] = 2; + active = x; + waiting--; + } + } + }; + while (n--) { + char t; + std::cin >> t; + if (t == 'A') { + int x; + std::cin >> x; + if (!active) { + active = x; + s[x] = 2; + } else { + s[x] = 1; + q.push_back(x); + waiting++; + } + } else if (t == 'C') { + int x; + std::cin >> x; + if (s[x] == 1) { + s[x] = 3; + waiting--; + } else if (s[x] == 2) { + s[x] = 3; + active = 0; + } + } else if (active) { + s[active] = 3; + active = 0; + } + advance(); + std::cout << active << ' ' << waiting << '\n'; + } +} diff --git a/problems/022-submission-conveyor/solutions/go/main.go b/problems/022-submission-conveyor/solutions/go/main.go new file mode 100644 index 0000000..cde9532 --- /dev/null +++ b/problems/022-submission-conveyor/solutions/go/main.go @@ -0,0 +1,58 @@ +package main + +import ( + "bufio" + "fmt" + "os" +) + +func main() { + in := bufio.NewReader(os.Stdin) + out := bufio.NewWriter(os.Stdout) + defer out.Flush() + var n int + fmt.Fscan(in, &n) + s := map[int]byte{} + q := make([]int, 0, n) + head, active, waiting := 0, 0, 0 + for ; n > 0; n-- { + var t string + fmt.Fscan(in, &t) + if t == "A" { + var x int + fmt.Fscan(in, &x) + if active == 0 { + active = x + s[x] = 2 + } else { + s[x] = 1 + q = append(q, x) + waiting++ + } + } else if t == "C" { + var x int + fmt.Fscan(in, &x) + if s[x] == 1 { + s[x] = 3 + waiting-- + } else if s[x] == 2 { + s[x] = 3 + active = 0 + } + } else if active != 0 { + s[active] = 3 + active = 0 + } + for active == 0 && head < len(q) { + x := q[head] + head++ + if s[x] == 1 { + s[x] = 2 + active = x + waiting-- + break + } + } + fmt.Fprintln(out, active, waiting) + } +} diff --git a/problems/022-submission-conveyor/solutions/javascript/main.js b/problems/022-submission-conveyor/solutions/javascript/main.js new file mode 100644 index 0000000..5cb9e0a --- /dev/null +++ b/problems/022-submission-conveyor/solutions/javascript/main.js @@ -0,0 +1,41 @@ +import * as std from "std"; +const a = std.in.readAsString().trim().split(/\s+/); +let p = 0, n = +a[p++], active = 0, waiting = 0, head = 0; +const state = new Map(), q = [], out = []; +while (n--) { + const t = a[p++]; + if (t === "A") { + const x = +a[p++]; + if (!active) { + active = x; + state.set(x, 2); + } else { + state.set(x, 1); + q.push(x); + waiting++; + } + } else if (t === "C") { + const x = +a[p++]; + if (state.get(x) === 1) { + state.set(x, 3); + waiting--; + } else if (state.get(x) === 2) { + state.set(x, 3); + active = 0; + } + } else if (active) { + state.set(active, 3); + active = 0; + } + while (!active && head < q.length) { + const x = q[head++]; + if (state.get(x) === 1) { + state.set(x, 2); + active = x; + waiting--; + break; + } + } + out.push(`${active} ${waiting}`); +} +std.out.puts(out.join("\n") + "\n"); diff --git a/problems/022-submission-conveyor/solutions/python/main.py b/problems/022-submission-conveyor/solutions/python/main.py new file mode 100644 index 0000000..771fe6b --- /dev/null +++ b/problems/022-submission-conveyor/solutions/python/main.py @@ -0,0 +1,39 @@ +import sys + +it = iter(sys.stdin.buffer.read().split()) +n = int(next(it)) +state = {} +q = [] +head = active = waiting = 0 +out = [] +for _ in range(n): + t = next(it) + if t == b"A": + x = int(next(it)) + if not active: + active = x + state[x] = 2 + else: + state[x] = 1 + q.append(x) + waiting += 1 + elif t == b"C": + x = int(next(it)) + if state.get(x) == 1: + state[x] = 3 + waiting -= 1 + elif state.get(x) == 2: + state[x] = 3 + active = 0 + elif active: + state[active] = 3 + active = 0 + while not active and head < len(q): + x = q[head] + head += 1 + if state[x] == 1: + state[x] = 2 + active = x + waiting -= 1 + out.append(f"{active} {waiting}") +print("\n".join(out)) diff --git a/problems/022-submission-conveyor/solutions/rust/main.rs b/problems/022-submission-conveyor/solutions/rust/main.rs new file mode 100644 index 0000000..6206905 --- /dev/null +++ b/problems/022-submission-conveyor/solutions/rust/main.rs @@ -0,0 +1,58 @@ +use std::{ + collections::{HashMap, VecDeque}, + io::{self, Read}, +}; +fn main() { + let mut z = String::new(); + io::stdin().read_to_string(&mut z).unwrap(); + let mut it = z.split_whitespace(); + let n: usize = it.next().unwrap().parse().unwrap(); + let (mut active, mut waiting) = (0i32, 0i32); + let mut q = VecDeque::new(); + let mut s: HashMap = HashMap::new(); + let mut out = String::new(); + for _ in 0..n { + let t = it.next().unwrap(); + if t == "A" { + let x = it.next().unwrap().parse().unwrap(); + if active == 0 { + active = x; + s.insert(x, 2); + } else { + s.insert(x, 1); + q.push_back(x); + waiting += 1; + } + } else if t == "C" { + let x = it.next().unwrap().parse().unwrap(); + match s.get(&x).copied() { + Some(1) => { + s.insert(x, 3); + waiting -= 1 + } + Some(2) => { + s.insert(x, 3); + active = 0 + } + _ => {} + } + } else if active != 0 { + s.insert(active, 3); + active = 0 + } + while active == 0 { + if let Some(x) = q.pop_front() { + if s.get(&x) == Some(&1) { + s.insert(x, 2); + active = x; + waiting -= 1; + break; + } + } else { + break; + } + } + out += &format!("{active} {waiting}\n") + } + print!("{out}") +} diff --git a/problems/022-submission-conveyor/solutions/typescript/main.ts b/problems/022-submission-conveyor/solutions/typescript/main.ts new file mode 100644 index 0000000..bb93ed8 --- /dev/null +++ b/problems/022-submission-conveyor/solutions/typescript/main.ts @@ -0,0 +1,41 @@ +import * as std from "std"; +const a = std.in.readAsString().trim().split(/\s+/); +let p = 0, n = +a[p++], active = 0, waiting = 0, head = 0; +const state = new Map(), q: number[] = [], out: string[] = []; +while (n--) { + const t = a[p++]; + if (t === "A") { + const x = +a[p++]; + if (!active) { + active = x; + state.set(x, 2); + } else { + state.set(x, 1); + q.push(x); + waiting++; + } + } else if (t === "C") { + const x = +a[p++]; + if (state.get(x) === 1) { + state.set(x, 3); + waiting--; + } else if (state.get(x) === 2) { + state.set(x, 3); + active = 0; + } + } else if (active) { + state.set(active, 3); + active = 0; + } + while (!active && head < q.length) { + const x = q[head++]; + if (state.get(x) === 1) { + state.set(x, 2); + active = x; + waiting--; + break; + } + } + out.push(`${active} ${waiting}`); +} +std.out.puts(out.join("\n") + "\n"); diff --git a/problems/022-submission-conveyor/statement.en.md b/problems/022-submission-conveyor/statement.en.md new file mode 100644 index 0000000..904b00b --- /dev/null +++ b/problems/022-submission-conveyor/statement.en.md @@ -0,0 +1,110 @@ +# Submission Conveyor + +When a WASM OJ submission scheduler has one execution slot, at most one submission can run at a time and every other submission waits in insertion order. Besides normal completion, a user may cancel a submission that is active or still queued, so the scheduler must maintain an unambiguous active job and waiting count after every event. + +Events are given in a deterministic total order. Once a submission finishes normally or is cancelled, it becomes terminal and never runs again. Process these events: + +- `A id`: add a submission whose ID has never appeared before. If there is no active submission, it becomes active immediately; otherwise it joins the back of the queue. +- `C id`: cancel that ID. If it is waiting or active, it becomes terminal; otherwise do nothing. If the active submission is cancelled, immediately start the earliest-added submission that is still waiting. +- `E`: the active submission finishes normally and becomes terminal; do nothing if no submission is active. Then likewise start the earliest waiting submission. + +Whenever the active submission leaves the system, the scheduler immediately starts the earliest-added submission that is still waiting. Cancelling a waiting submission does not change the relative order of the others. Cancelling an ID that has not been added or is already terminal changes no state. + +## Input + +The first line contains `N`, followed by `N` event lines. + +## Output + +After every event, output `active waiting`. Output `0` when there is no active submission. `waiting` is the number of still-valid waiting submissions and does not include the active submission. + +## Constraints + +- `1 ≤ N ≤ 200000` +- `1 ≤ id ≤ 10^9` +- IDs in `A id` events are all distinct. +- `C` may name an ID that has not been added or is already terminal. +- The full constraints apply to every official test. + +## Examples + + + +### Example One + +Input: + +```text +7 +A 10 +A 20 +A 30 +C 20 +E +C 10 +E +``` + +Output: + +```text +10 0 +10 1 +10 2 +10 1 +30 0 +30 0 +0 0 +``` + +### Example Two + +Input: + +```text +6 +A 1 +C 1 +E +A 2 +A 3 +C 2 +``` + +Output: + +```text +1 0 +0 0 +0 0 +2 0 +2 1 +3 0 +``` + +### Example Three + +Input: + +```text +6 +A 5 +A 6 +C 6 +A 7 +C 5 +E +``` + +Output: + +```text +5 0 +5 1 +5 0 +5 1 +7 0 +0 0 +``` + + diff --git a/problems/022-submission-conveyor/statement.zh-TW.md b/problems/022-submission-conveyor/statement.zh-TW.md new file mode 100644 index 0000000..906fc7c --- /dev/null +++ b/problems/022-submission-conveyor/statement.zh-TW.md @@ -0,0 +1,110 @@ +# Submission 輸送帶 + +WASM OJ 的 submission 排程器若只有一個 execution slot,同一時間就最多執行一份 submission,其餘工作依加入順序等待。除了正常完成以外,使用者也可能取消正在執行或仍在排隊的 submission,因此 scheduler 必須在每個事件後維持明確的 active 狀態與等待數量。 + +所有事件已排成確定的全序。submission 一旦正常完成或被取消,就進入 terminal 狀態,不會再次執行。處理以下事件: + +- `A id`:加入從未出現過的 submission。若當下沒有 active submission,它立刻成為 active;否則排到隊尾。 +- `C id`:取消該 id。若它正在等待或執行,狀態變成 terminal;否則不做事。若 active 被取消,立即啟動仍在等待者中最早加入的一份。 +- `E`:active submission 正常結束並成為 terminal;若沒有 active 則不做事。之後同樣啟動最早等待者。 + +若 active submission 離開系統,scheduler 必須立即啟動仍在等待者中最早加入的一份。取消等待者不改變其他等待者的相對順序;對尚未加入或已 terminal 的 id 取消則不影響任何狀態。 + +## 輸入 + +第一行是 `N`,接著 `N` 行事件。 + +- `1 ≤ N ≤ 200000` +- `1 ≤ id ≤ 10^9` +- 每個 `A id` 的 id 互不相同;`C` 可以指向尚未加入或已 terminal 的 id + +## 輸出 + +每處理一個事件,輸出 `active waiting`。沒有 active 時輸出 `0`;`waiting` 是仍有效、且不含 active 的等待數量。 + +## 範例 + + + +### 範例一 + +輸入: + +```text +7 +A 10 +A 20 +A 30 +C 20 +E +C 10 +E +``` + +輸出: + +```text +10 0 +10 1 +10 2 +10 1 +30 0 +30 0 +0 0 +``` + +### 範例二 + +輸入: + +```text +6 +A 1 +C 1 +E +A 2 +A 3 +C 2 +``` + +輸出: + +```text +1 0 +0 0 +0 0 +2 0 +2 1 +3 0 +``` + +### 範例三 + +輸入: + +```text +6 +A 5 +A 6 +C 6 +A 7 +C 5 +E +``` + +輸出: + +```text +5 0 +5 1 +5 0 +5 1 +7 0 +0 0 +``` + + + +## 限制 + +所有數量、字串格式與整數範圍均列於「輸入」段落;完整限制適用於每一筆正式測資。 diff --git a/problems/022-submission-conveyor/tests/adversarial-future-cancel-lazy-queue.in b/problems/022-submission-conveyor/tests/adversarial-future-cancel-lazy-queue.in new file mode 100644 index 0000000..dbf14f5 --- /dev/null +++ b/problems/022-submission-conveyor/tests/adversarial-future-cancel-lazy-queue.in @@ -0,0 +1,12 @@ +11 +C 5 +A 5 +A 1 +A 2 +C 1 +C 5 +E +C 2 +E +A 9 +E diff --git a/problems/022-submission-conveyor/tests/adversarial-future-cancel-lazy-queue.out b/problems/022-submission-conveyor/tests/adversarial-future-cancel-lazy-queue.out new file mode 100644 index 0000000..a54ff84 --- /dev/null +++ b/problems/022-submission-conveyor/tests/adversarial-future-cancel-lazy-queue.out @@ -0,0 +1,11 @@ +0 0 +5 0 +5 1 +5 2 +5 1 +2 0 +0 0 +0 0 +0 0 +9 0 +0 0 diff --git a/problems/022-submission-conveyor/tests/sample-01.in b/problems/022-submission-conveyor/tests/sample-01.in new file mode 100644 index 0000000..df1448f --- /dev/null +++ b/problems/022-submission-conveyor/tests/sample-01.in @@ -0,0 +1,8 @@ +7 +A 10 +A 20 +A 30 +C 20 +E +C 10 +E diff --git a/problems/022-submission-conveyor/tests/sample-01.out b/problems/022-submission-conveyor/tests/sample-01.out new file mode 100644 index 0000000..964388d --- /dev/null +++ b/problems/022-submission-conveyor/tests/sample-01.out @@ -0,0 +1,7 @@ +10 0 +10 1 +10 2 +10 1 +30 0 +30 0 +0 0 diff --git a/problems/022-submission-conveyor/tests/sample-02.in b/problems/022-submission-conveyor/tests/sample-02.in new file mode 100644 index 0000000..7048bc2 --- /dev/null +++ b/problems/022-submission-conveyor/tests/sample-02.in @@ -0,0 +1,7 @@ +6 +A 1 +C 1 +E +A 2 +A 3 +C 2 diff --git a/problems/022-submission-conveyor/tests/sample-02.out b/problems/022-submission-conveyor/tests/sample-02.out new file mode 100644 index 0000000..fcadcdd --- /dev/null +++ b/problems/022-submission-conveyor/tests/sample-02.out @@ -0,0 +1,6 @@ +1 0 +0 0 +0 0 +2 0 +2 1 +3 0 diff --git a/problems/022-submission-conveyor/tests/sample-03.in b/problems/022-submission-conveyor/tests/sample-03.in new file mode 100644 index 0000000..756c4e8 --- /dev/null +++ b/problems/022-submission-conveyor/tests/sample-03.in @@ -0,0 +1,7 @@ +6 +A 5 +A 6 +C 6 +A 7 +C 5 +E diff --git a/problems/022-submission-conveyor/tests/sample-03.out b/problems/022-submission-conveyor/tests/sample-03.out new file mode 100644 index 0000000..fcc2084 --- /dev/null +++ b/problems/022-submission-conveyor/tests/sample-03.out @@ -0,0 +1,6 @@ +5 0 +5 1 +5 0 +5 1 +7 0 +0 0 diff --git a/problems/022-submission-conveyor/validator.py b/problems/022-submission-conveyor/validator.py new file mode 100644 index 0000000..0bcfcf6 --- /dev/null +++ b/problems/022-submission-conveyor/validator.py @@ -0,0 +1,24 @@ +#!/usr/bin/env python3 +import re, sys + +try: + a = sys.stdin.read().splitlines() + assert a and re.fullmatch(r"[1-9][0-9]*", a[0]) + n = int(a[0]) + assert 1 <= n <= 200000 and len(a) == n + 1 + seen = set() + for s in a[1:]: + p = s.split(" ") + if p[0] in ("A", "C"): + assert ( + len(p) == 2 + and re.fullmatch(r"[1-9][0-9]*", p[1]) + and int(p[1]) <= 10**9 + ) + if p[0] == "A": + assert p[1] not in seen + seen.add(p[1]) + else: + assert p == ["E"] +except Exception: + sys.exit(1) diff --git a/problems/023-storage-evacuation/editorial.en.md b/problems/023-storage-evacuation/editorial.en.md new file mode 100644 index 0000000..b630037 --- /dev/null +++ b/problems/023-storage-evacuation/editorial.en.md @@ -0,0 +1,24 @@ +# Editorial + +## Intuitive Approach + +Repeatedly search all remaining items for the next one in policy order, taking `O(N^2)` time. Knapsack or size-based selection is incorrect because the statement mandates one unique policy order. + +## Optimal Approach: Sort Once and Take a Prefix + +Compute `T` and `need`. If `need>T`, output `IMPOSSIBLE`. Otherwise sort by `(priority,lastUsed,participant,key)` and accumulate item sizes from the front until the total first reaches `need`. + +## Correctness Proof + +After sorting, item `i` is exactly the next item selected by policy after items `1` through `i-1` have been removed. Therefore the algorithm's sequence is identical to the policy's step-by-step sequence. Before stopping, the freed total is below `need`; after including the last item, it is at least `need`. Hence the algorithm also stops at exactly the first point required by policy. + +## Complexity + +Sorting takes `O(N log N)`, scanning takes `O(N)`, and space is `O(N)`. In a comparison model with arbitrary participant and key strings, emitting the complete policy order can encode a sort, so this is asymptotically optimal. + +## Common Mistakes + +- Using only `T-C` and omitting the browser reserve deficit. +- Evicting higher-priority items first. +- Using locale-aware string ordering instead of ASCII byte order. +- Partially deleting the last item when it exceeds the remaining need. diff --git a/problems/023-storage-evacuation/editorial.zh-TW.md b/problems/023-storage-evacuation/editorial.zh-TW.md new file mode 100644 index 0000000..ea34463 --- /dev/null +++ b/problems/023-storage-evacuation/editorial.zh-TW.md @@ -0,0 +1,24 @@ +# 解題說明 + +## 直覺解 + +每次在尚未刪除項目中線性尋找政策順序最小者,最壞 O(N²)。背包或依 size 選擇都是錯的,因為題目明定唯一政策順序。 + +## 最佳解 + +先計算 `T` 與 need。若 need>T 輸出 IMPOSSIBLE;否則依 `(priority,lastUsed,participant,key)` 排序,從頭累加 size,到第一次達到 need 為止。 + +## 正確性證明 + +排序後第 i 個元素恰是政策在刪除前 i-1 個項目後指定的下一項。故演算法產生的序列與政策逐步選擇完全相同。停止前釋放量小於 need,停止後不少於 need,因此它也恰在政策規定的第一次滿足時停止。 + +## 複雜度 + +排序 O(N log N),掃描 O(N),空間 O(N)。在只能比較任意 participant/key 的模型中,輸出完整政策次序可歸約排序,為漸近最佳。 + +## 常見錯誤 + +- 只取 `T-C` 而漏掉瀏覽器 reserve 缺口。 +- 把 priority 大者先淘汰。 +- 對字串使用 locale 排序;本題是 ASCII byte order。 +- 最後一個項目超過 need 時嘗試部分刪除。 diff --git a/problems/023-storage-evacuation/generator.py b/problems/023-storage-evacuation/generator.py new file mode 100644 index 0000000..0d0abea --- /dev/null +++ b/problems/023-storage-evacuation/generator.py @@ -0,0 +1,18 @@ +#!/usr/bin/env python3 +import random, sys + +seed, index = map(int, sys.argv[1:]) +r = random.Random(seed ^ index * 0x9E3779B1) +n = 8 + index % 13 +items = [] +for i in range(n): + items.append( + (r.randint(1, 30), r.randrange(4), r.randrange(100), f"p{i%5}", f"k{i}") + ) +t = sum(x[0] for x in items) +C = r.randrange(t + 20) +A = r.randrange(80) +R = r.randrange(100) +print(n, C, A, R) +for x in items: + print(*x) diff --git a/problems/023-storage-evacuation/oracle.py b/problems/023-storage-evacuation/oracle.py new file mode 100644 index 0000000..bfd4cd7 --- /dev/null +++ b/problems/023-storage-evacuation/oracle.py @@ -0,0 +1,23 @@ +#!/usr/bin/env python3 +import sys + +l = sys.stdin.read().splitlines() +n, C, A, R = map(int, l[0].split()) +a = [] +for s in l[1:]: + z, p, u, x, k = s.split() + a.append([int(z), int(p), int(u), x, k]) +need = max(0, sum(x[0] for x in a) - C, R - A) +if need > sum(x[0] for x in a): + print("IMPOSSIBLE") + raise SystemExit +out = [] +freed = 0 +while freed < need: + best = min(range(len(a)), key=lambda i: (a[i][1], a[i][2], a[i][3], a[i][4])) + x = a.pop(best) + out.append((x[3], x[4])) + freed += x[0] +print(len(out), freed) +for x in out: + print(*x) diff --git a/problems/023-storage-evacuation/problem.json b/problems/023-storage-evacuation/problem.json new file mode 100644 index 0000000..78dc0a8 --- /dev/null +++ b/problems/023-storage-evacuation/problem.json @@ -0,0 +1,146 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 23, + "slug": "storage-evacuation", + "title": { + "zh-TW": "瀏覽器儲存疏散令", + "en": "Browser Storage Evacuation" + }, + "difficulty": "medium", + "tags": [ + "greedy", + "sorting", + "resource-budget" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-policy-ties-overshoot", + "kind": "adversarial", + "input": "tests/adversarial-policy-ties-overshoot.in", + "output": "tests/adversarial-policy-ties-overshoot.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 8000000, + "memoryLimitBytes": 536870912 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 1500000, + "memoryLimitBytes": 402653184 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 600000, + "memoryLimitBytes": 268435456 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "反覆搜尋下一個項目", + "en": "Repeatedly Search for the Next Item" + }, + "time": "O(N^2)", + "space": "O(N)", + "accepted": false + }, + { + "name": { + "zh-TW": "一次排序後取前綴", + "en": "Sort Once and Take a Prefix" + }, + "time": "O(N log N)", + "space": "O(N)", + "accepted": true + } + ] +} diff --git a/problems/023-storage-evacuation/solutions/c/main.c b/problems/023-storage-evacuation/solutions/c/main.c new file mode 100644 index 0000000..5b981a5 --- /dev/null +++ b/problems/023-storage-evacuation/solutions/c/main.c @@ -0,0 +1,51 @@ +#include +#include +#include +#include +#include +typedef struct { + int64_t size, last; + int pri; + char p[21], k[21]; +} Item; +static int cmp(const void *A, const void *B) { + const Item *a = A, *b = B; + if (a->pri != b->pri) + return a->pri < b->pri ? -1 : 1; + if (a->last != b->last) + return a->last < b->last ? -1 : 1; + int z = strcmp(a->p, b->p); + return z ? z : strcmp(a->k, b->k); +} +int main(void) { + int n; + int64_t C, A, R; + if (scanf("%d %" SCNd64 " %" SCNd64 " %" SCNd64, &n, &C, &A, &R) != 4) + return 0; + Item *x = malloc((size_t)n * sizeof(*x)); + int64_t total = 0; + for (int i = 0; i < n; i++) { + scanf("%" SCNd64 " %d %" SCNd64 " %20s %20s", &x[i].size, &x[i].pri, + &x[i].last, x[i].p, x[i].k); + total += x[i].size; + } + int64_t need = total - C; + if (need < 0) + need = 0; + if (R > A && R - A > need) + need = R - A; + if (need > total) { + puts("IMPOSSIBLE"); + free(x); + return 0; + } + qsort(x, n, sizeof(*x), cmp); + int k = 0; + int64_t freed = 0; + while (freed < need) + freed += x[k++].size; + printf("%d %" PRId64 "\n", k, freed); + for (int i = 0; i < k; i++) + printf("%s %s\n", x[i].p, x[i].k); + free(x); +} diff --git a/problems/023-storage-evacuation/solutions/cpp/main.cpp b/problems/023-storage-evacuation/solutions/cpp/main.cpp new file mode 100644 index 0000000..be22295 --- /dev/null +++ b/problems/023-storage-evacuation/solutions/cpp/main.cpp @@ -0,0 +1,43 @@ +#include +#include +#include +#include +#include +struct I { + std::int64_t z, u; + int p; + std::string a, k; +}; +int main() { + std::ios::sync_with_stdio(false); + std::cin.tie(nullptr); + int n; + std::int64_t C, A, R, T = 0; + std::cin >> n >> C >> A >> R; + std::vector x(n); + for (auto &v : x) { + std::cin >> v.z >> v.p >> v.u >> v.a >> v.k; + T += v.z; + } + auto need = std::max({0, T - C, R - A}); + if (need > T) { + std::cout << "IMPOSSIBLE\n"; + return 0; + } + std::sort(x.begin(), x.end(), [](const I &a, const I &b) { + if (a.p != b.p) + return a.p < b.p; + if (a.u != b.u) + return a.u < b.u; + if (a.a != b.a) + return a.a < b.a; + return a.k < b.k; + }); + std::int64_t f = 0; + int k = 0; + while (f < need) + f += x[k++].z; + std::cout << k << ' ' << f << '\n'; + for (int i = 0; i < k; i++) + std::cout << x[i].a << ' ' << x[i].k << '\n'; +} diff --git a/problems/023-storage-evacuation/solutions/go/main.go b/problems/023-storage-evacuation/solutions/go/main.go new file mode 100644 index 0000000..01d5836 --- /dev/null +++ b/problems/023-storage-evacuation/solutions/go/main.go @@ -0,0 +1,62 @@ +package main + +import ( + "bufio" + "fmt" + "os" + "sort" +) + +type I struct { + z, u int64 + p int + a, k string +} + +func main() { + in := bufio.NewReader(os.Stdin) + out := bufio.NewWriter(os.Stdout) + defer out.Flush() + var n int + var C, A, R, total int64 + fmt.Fscan(in, &n, &C, &A, &R) + v := make([]I, n) + for i := range v { + fmt.Fscan(in, &v[i].z, &v[i].p, &v[i].u, &v[i].a, &v[i].k) + total += v[i].z + } + need := total - C + if need < 0 { + need = 0 + } + if R-A > need { + need = R - A + } + if need > total { + fmt.Fprintln(out, "IMPOSSIBLE") + return + } + sort.Slice(v, func(i, j int) bool { + x, y := v[i], v[j] + if x.p != y.p { + return x.p < y.p + } + if x.u != y.u { + return x.u < y.u + } + if x.a != y.a { + return x.a < y.a + } + return x.k < y.k + }) + var freed int64 + k := 0 + for freed < need { + freed += v[k].z + k++ + } + fmt.Fprintln(out, k, freed) + for _, x := range v[:k] { + fmt.Fprintln(out, x.a, x.k) + } +} diff --git a/problems/023-storage-evacuation/solutions/javascript/main.js b/problems/023-storage-evacuation/solutions/javascript/main.js new file mode 100644 index 0000000..0f39b5b --- /dev/null +++ b/problems/023-storage-evacuation/solutions/javascript/main.js @@ -0,0 +1,35 @@ +import * as std from "std"; +const t = std.in.readAsString().trim().split(/\s+/); +let q = 0, + n = +t[q++], + C = BigInt(t[q++]), + A = BigInt(t[q++]), + R = BigInt(t[q++]), + T = 0n; +const v = []; +for (let i = 0; i < n; i++) { + const x = { + z: BigInt(t[q++]), + p: +t[q++], + u: BigInt(t[q++]), + a: t[q++], + k: t[q++], + }; + T += x.z; + v.push(x); +} +let need = T - C; +if (need < 0n) need = 0n; +if (R - A > need) need = R - A; +if (need > T) std.out.puts("IMPOSSIBLE\n"); +else { + v.sort((x, y) => + x.p - y.p || (x.u < y.u ? -1 : x.u > y.u ? 1 : 0) || + (x.a < y.a ? -1 : x.a > y.a ? 1 : 0) || (x.k < y.k ? -1 : x.k > y.k ? 1 : 0) + ); + let f = 0n, k = 0; + while (f < need) f += v[k++].z; + const out = [`${k} ${f}`]; + for (let i = 0; i < k; i++) out.push(`${v[i].a} ${v[i].k}`); + std.out.puts(out.join("\n") + "\n"); +} diff --git a/problems/023-storage-evacuation/solutions/python/main.py b/problems/023-storage-evacuation/solutions/python/main.py new file mode 100644 index 0000000..0e84401 --- /dev/null +++ b/problems/023-storage-evacuation/solutions/python/main.py @@ -0,0 +1,22 @@ +import sys + +it = iter(sys.stdin.buffer.read().split()) +n = int(next(it)) +C = int(next(it)) +A = int(next(it)) +R = int(next(it)) +v = [] +for _ in range(n): + v.append((int(next(it)), int(next(it)), int(next(it)), next(it), next(it))) +need = max(0, sum(x[0] for x in v) - C, R - A) +if need > sum(x[0] for x in v): + print("IMPOSSIBLE") +else: + v.sort(key=lambda x: (x[1], x[2], x[3], x[4])) + freed = k = 0 + while freed < need: + freed += v[k][0] + k += 1 + print(k, freed) + for x in v[:k]: + print(x[3].decode(), x[4].decode()) diff --git a/problems/023-storage-evacuation/solutions/rust/main.rs b/problems/023-storage-evacuation/solutions/rust/main.rs new file mode 100644 index 0000000..f19f542 --- /dev/null +++ b/problems/023-storage-evacuation/solutions/rust/main.rs @@ -0,0 +1,48 @@ +use std::io::{self, Read}; +struct I { + z: i64, + p: i32, + u: i64, + a: String, + k: String, +} +fn main() { + let mut s = String::new(); + io::stdin().read_to_string(&mut s).unwrap(); + let mut t = s.split_whitespace(); + let n: usize = t.next().unwrap().parse().unwrap(); + let c: i64 = t.next().unwrap().parse().unwrap(); + let a: i64 = t.next().unwrap().parse().unwrap(); + let r: i64 = t.next().unwrap().parse().unwrap(); + let mut v = Vec::with_capacity(n); + let mut total = 0; + for _ in 0..n { + let z = t.next().unwrap().parse().unwrap(); + let p = t.next().unwrap().parse().unwrap(); + let u = t.next().unwrap().parse().unwrap(); + let x = t.next().unwrap().to_string(); + let k = t.next().unwrap().to_string(); + total += z; + v.push(I { z, p, u, a: x, k }) + } + let need = 0.max(total - c).max(r - a); + if need > total { + println!("IMPOSSIBLE"); + return; + } + v.sort_by(|x, y| { + x.p.cmp(&y.p) + .then(x.u.cmp(&y.u)) + .then(x.a.cmp(&y.a)) + .then(x.k.cmp(&y.k)) + }); + let (mut f, mut k) = (0, 0); + while f < need { + f += v[k].z; + k += 1 + } + println!("{k} {f}"); + for x in &v[..k] { + println!("{} {}", x.a, x.k) + } +} diff --git a/problems/023-storage-evacuation/solutions/typescript/main.ts b/problems/023-storage-evacuation/solutions/typescript/main.ts new file mode 100644 index 0000000..0f67799 --- /dev/null +++ b/problems/023-storage-evacuation/solutions/typescript/main.ts @@ -0,0 +1,36 @@ +import * as std from "std"; +type I = { z: bigint; p: number; u: bigint; a: string; k: string }; +const t = std.in.readAsString().trim().split(/\s+/); +let q = 0, + n = +t[q++], + C = BigInt(t[q++]), + A = BigInt(t[q++]), + R = BigInt(t[q++]), + T = 0n; +const v: I[] = []; +for (let i = 0; i < n; i++) { + const x: I = { + z: BigInt(t[q++]), + p: +t[q++], + u: BigInt(t[q++]), + a: t[q++], + k: t[q++], + }; + T += x.z; + v.push(x); +} +let need = T - C; +if (need < 0n) need = 0n; +if (R - A > need) need = R - A; +if (need > T) std.out.puts("IMPOSSIBLE\n"); +else { + v.sort((x, y) => + x.p - y.p || (x.u < y.u ? -1 : x.u > y.u ? 1 : 0) || + (x.a < y.a ? -1 : x.a > y.a ? 1 : 0) || (x.k < y.k ? -1 : x.k > y.k ? 1 : 0) + ); + let f = 0n, k = 0; + while (f < need) f += v[k++].z; + const out: string[] = [`${k} ${f}`]; + for (let i = 0; i < k; i++) out.push(`${v[i].a} ${v[i].k}`); + std.out.puts(out.join("\n") + "\n"); +} diff --git a/problems/023-storage-evacuation/statement.en.md b/problems/023-storage-evacuation/statement.en.md new file mode 100644 index 0000000..c26ce99 --- /dev/null +++ b/problems/023-storage-evacuation/statement.en.md @@ -0,0 +1,95 @@ +# Browser Storage Evacuation + +When a WASM OJ stores compilation artifacts and test data in the browser, it must respect two limits at once: the cache's own logical capacity and the free space that the browser must preserve for other features. If either requirement is violated, the storage manager has to evacuate items from the cache. + +The cache currently contains `N` indivisible items and has a logical limit of `C` bytes. The browser currently has `A` bytes available, and the system requires at least `R` bytes to remain available after evacuation. If the total size of all items is `T`, at least + +`need = max(0, T - C, R - A)` + +bytes must be freed. If `need` exceeds `T`, even deleting the entire cache cannot satisfy the requirement, so evacuation is impossible. + +To make the result reproducible across devices, eviction does not choose an arbitrary combination that happens to free enough space. Each item has `size priority lastUsed participant key`, and the fixed order is: + +1. lower `priority` first; +2. for equal priority, lower (older) `lastUsed` first; +3. then ASCII-lexicographically smaller `participant`; +4. finally ASCII-lexicographically smaller `key`. + +Delete complete items in this order until the freed amount first reaches or exceeds `need`. This order is the storage policy; you may not choose a different combination that sums exactly to the target. + +## Input + +The first line contains `N C A R`, followed by `N` item lines. + +## Output + +If evacuation is impossible, output `IMPOSSIBLE`. Otherwise output `k freed` on the first line, then output `k` lines containing `participant key` in eviction order. When no deletion is needed, output `0 0` and no subsequent lines. + +## Constraints + +- `1 ≤ N ≤ 200000` +- `0 ≤ C,A,R,size,lastUsed ≤ 10^18` +- `1 ≤ size` +- The sum of all sizes is at most `9×10^18`. +- `0 ≤ priority ≤ 10^9` +- `participant` and `key` contain `1..20` lowercase alphanumeric characters. +- Every `(participant,key)` pair is unique. +- The full constraints apply to every official test. + +## Examples + + + +### Example One + +Input: + +```text +4 100 30 50 +40 2 10 alpha a +30 1 20 beta b +50 1 5 alpha c +10 1 5 alpha b +``` + +Output: + +```text +2 60 +alpha b +alpha c +``` + +### Example Two + +Input: + +```text +2 100 100 20 +10 0 1 p a +20 1 2 p b +``` + +Output: + +```text +0 0 +``` + +### Example Three + +Input: + +```text +2 100 0 1000 +10 0 1 p a +20 1 2 p b +``` + +Output: + +```text +IMPOSSIBLE +``` + + diff --git a/problems/023-storage-evacuation/statement.zh-TW.md b/problems/023-storage-evacuation/statement.zh-TW.md new file mode 100644 index 0000000..b09aa1a --- /dev/null +++ b/problems/023-storage-evacuation/statement.zh-TW.md @@ -0,0 +1,93 @@ +# 瀏覽器儲存疏散令 + +WASM OJ 在瀏覽器中保存編譯 artifact 與測試資料時,同時受到兩種限制:cache 自己設定的邏輯容量,以及瀏覽器還需要為其他功能保留的可用空間。當任一限制被突破,storage manager 就必須從 cache 中疏散項目。 + +目前 cache 保存 `N` 個不可分割的項目,邏輯上限為 `C` bytes。瀏覽器目前可用空間為 `A` bytes,而系統要求疏散後至少保留 `R` bytes 可用空間。若所有項目的總大小為 `T`,必須釋放至少 + +`need = max(0, T - C, R - A)` + +bytes。若 `need` 大於 `T`,即使刪除全部 cache 內容也無法達成要求,因此疏散不可能完成。 + +為了讓相同狀態在不同裝置上得到可重現的結果,淘汰不是任意選擇能湊足空間的組合。每個項目有 `size priority lastUsed participant key`,固定順序為: + +1. `priority` 較小者先; +2. 同 priority 時,`lastUsed` 較小(較舊)者先; +3. 再依 participant 的 ASCII 字典序; +4. 最後依 key 的 ASCII 字典序。 + +依此順序刪除完整項目,直到已釋放量第一次不少於 `need`。這個規則是 storage policy,不得另選「剛好湊滿」的組合。 + +## 輸入 + +第一行 `N C A R`,接著 N 行項目。 + +- `1 ≤ N ≤ 200000` +- `0 ≤ C,A,R,size,lastUsed ≤ 10^18`,`1 ≤ size`,所有 size 總和不超過 `9×10^18` +- `0 ≤ priority ≤ 10^9` +- participant、key 為長度 1..20 的小寫英數字;`(participant,key)` 唯一 + +## 輸出 + +不可能時輸出 `IMPOSSIBLE`。否則第一行輸出 `k freed`,接著依淘汰順序輸出 k 行 `participant key`。不需刪除時輸出 `0 0` 且沒有後續行。 + +## 限制 + +所有數量、字串格式與整數範圍均列於「輸入」段落;完整限制適用於每一筆正式測資。 + +## 範例 + + + +### 範例一 + +輸入: + +```text +4 100 30 50 +40 2 10 alpha a +30 1 20 beta b +50 1 5 alpha c +10 1 5 alpha b +``` + +輸出: + +```text +2 60 +alpha b +alpha c +``` + +### 範例二 + +輸入: + +```text +2 100 100 20 +10 0 1 p a +20 1 2 p b +``` + +輸出: + +```text +0 0 +``` + +### 範例三 + +輸入: + +```text +2 100 0 1000 +10 0 1 p a +20 1 2 p b +``` + +輸出: + +```text +IMPOSSIBLE +``` + + diff --git a/problems/023-storage-evacuation/tests/adversarial-policy-ties-overshoot.in b/problems/023-storage-evacuation/tests/adversarial-policy-ties-overshoot.in new file mode 100644 index 0000000..782052f --- /dev/null +++ b/problems/023-storage-evacuation/tests/adversarial-policy-ties-overshoot.in @@ -0,0 +1,6 @@ +5 15 100 0 +3 0 99 z k +4 1 2 a a +5 1 1 z a +7 1 1 a z +7 2 0 x q diff --git a/problems/023-storage-evacuation/tests/adversarial-policy-ties-overshoot.out b/problems/023-storage-evacuation/tests/adversarial-policy-ties-overshoot.out new file mode 100644 index 0000000..66a15e8 --- /dev/null +++ b/problems/023-storage-evacuation/tests/adversarial-policy-ties-overshoot.out @@ -0,0 +1,4 @@ +3 15 +z k +a z +z a diff --git a/problems/023-storage-evacuation/tests/sample-01.in b/problems/023-storage-evacuation/tests/sample-01.in new file mode 100644 index 0000000..8437cbf --- /dev/null +++ b/problems/023-storage-evacuation/tests/sample-01.in @@ -0,0 +1,5 @@ +4 100 30 50 +40 2 10 alpha a +30 1 20 beta b +50 1 5 alpha c +10 1 5 alpha b diff --git a/problems/023-storage-evacuation/tests/sample-01.out b/problems/023-storage-evacuation/tests/sample-01.out new file mode 100644 index 0000000..6a0ae85 --- /dev/null +++ b/problems/023-storage-evacuation/tests/sample-01.out @@ -0,0 +1,3 @@ +2 60 +alpha b +alpha c diff --git a/problems/023-storage-evacuation/tests/sample-02.in b/problems/023-storage-evacuation/tests/sample-02.in new file mode 100644 index 0000000..d7ddad8 --- /dev/null +++ b/problems/023-storage-evacuation/tests/sample-02.in @@ -0,0 +1,3 @@ +2 100 100 20 +10 0 1 p a +20 1 2 p b diff --git a/problems/023-storage-evacuation/tests/sample-02.out b/problems/023-storage-evacuation/tests/sample-02.out new file mode 100644 index 0000000..b748e2d --- /dev/null +++ b/problems/023-storage-evacuation/tests/sample-02.out @@ -0,0 +1 @@ +0 0 diff --git a/problems/023-storage-evacuation/tests/sample-03.in b/problems/023-storage-evacuation/tests/sample-03.in new file mode 100644 index 0000000..f09f84e --- /dev/null +++ b/problems/023-storage-evacuation/tests/sample-03.in @@ -0,0 +1,3 @@ +2 100 0 1000 +10 0 1 p a +20 1 2 p b diff --git a/problems/023-storage-evacuation/tests/sample-03.out b/problems/023-storage-evacuation/tests/sample-03.out new file mode 100644 index 0000000..3e36f60 --- /dev/null +++ b/problems/023-storage-evacuation/tests/sample-03.out @@ -0,0 +1 @@ +IMPOSSIBLE diff --git a/problems/023-storage-evacuation/validator.py b/problems/023-storage-evacuation/validator.py new file mode 100644 index 0000000..69c65a8 --- /dev/null +++ b/problems/023-storage-evacuation/validator.py @@ -0,0 +1,27 @@ +#!/usr/bin/env python3 +import re, sys + +try: + l = sys.stdin.read().splitlines() + h = l[0].split() + assert len(h) == 4 and all(re.fullmatch(r"0|[1-9][0-9]*", x) for x in h) + n, C, A, R = map(int, h) + assert ( + 1 <= n <= 200000 and all(x <= 10**18 for x in (C, A, R)) and len(l) == n + 1 + ) + seen = set() + total = 0 + for s in l[1:]: + p = s.split() + assert len(p) == 5 + z, pr, lu = map(int, p[:3]) + assert 1 <= z <= 10**18 and 0 <= pr <= 10**9 and 0 <= lu <= 10**18 + assert re.fullmatch(r"[a-z0-9]{1,20}", p[3]) and re.fullmatch( + r"[a-z0-9]{1,20}", p[4] + ) + assert tuple(p[3:]) not in seen + seen.add(tuple(p[3:])) + total += z + assert total <= 9 * 10**18 +except Exception: + sys.exit(1) diff --git a/problems/024-judge-ledger/editorial.en.md b/problems/024-judge-ledger/editorial.en.md new file mode 100644 index 0000000..6727974 --- /dev/null +++ b/problems/024-judge-ledger/editorial.en.md @@ -0,0 +1,26 @@ +# Editorial + +## Intuitive Approach + +Scan cases for every query, stopping early for fail-fast, while accumulating sums and maxima. One query costs `O(N)`, for `O(NQ)` total time. + +## Optimal Approach: Prefix Data and Iterative Segment Trees + +Precompute `nextBad[i]` from right to left: the first non-AC position at or after `i`, or `N+1` if none exists. This determines the actual right endpoint and verdict in `O(1)`. + +For both cost and time, build a prefix sum of known values and a prefix count of `-1` values. Output the interval sum only when its unknown count is zero. Memory and VFS also use unknown-count prefixes; when known, query their interval maxima using iterative segment trees. + +## Correctness Proof + +By definition, `nextBad[l]` is the only possible fail-fast stopping point, so the chosen right endpoint and first-failure verdict are correct. Prefix differences cover exactly the selected interval. A positive unknown count is equivalent to the statement's `null` condition; otherwise the prefix difference is the required sum. Each segment-tree query partitions the interval into disjoint nodes, whose maximum equals the maximum over all cases. Therefore all six output fields are correct. + +## Complexity + +Preprocessing takes `O(N)`. Each query performs two range-maximum queries in `O(log N)`, for total time `O(N+Q log N)`. The prefix data and segment trees use `O(N)` auxiliary space; because several reference implementations also retain the input and buffer all answers, their total resident space is `O(N+Q)`. This is the practical reference path shared by all seven languages. A theoretical static-RMQ solution could combine a Cartesian tree with linear-preprocessing RMQ for `O(N+Q)` total time, but that is not the implementation claimed by the reference solutions. + +## Common Mistakes + +- Excluding the failing case from a fail-fast range. +- Turning every metric into `null` when only one metric is unknown. +- Using an identity other than 0 for maxima, or introducing an endpoint off-by-one. +- Reporting the last failure rather than the first in a non-fail-fast query. diff --git a/problems/024-judge-ledger/editorial.zh-TW.md b/problems/024-judge-ledger/editorial.zh-TW.md new file mode 100644 index 0000000..092eda1 --- /dev/null +++ b/problems/024-judge-ledger/editorial.zh-TW.md @@ -0,0 +1,26 @@ +# 解題說明 + +## 直覺解 + +每個查詢逐 case 掃描、遇 fail-fast 停止,再累加與取最大。單次 O(N),總計 O(NQ)。 + +## 最佳實用解:prefix 與 iterative segment tree + +由右往左預計算 `nextBad[i]`,代表 i 之後(含 i)第一個非 AC 位置,沒有則為 N+1。這可 O(1) 決定實際右端點及 verdict。 + +對 cost/time 各建「已知值前綴和」和「-1 數量前綴和」;區間未知數為零才輸出區間和。memory/vfs 也有未知數前綴,已知時以 iterative segment tree 查區間最大值。 + +## 正確性證明 + +`nextBad[l]` 依定義就是 fail-fast 唯一可能的停止點,故選出的右端正確;第一失敗 verdict 也因此正確。前綴差精確涵蓋所選區間,未知計數非零恰等價於題意的 null 條件,否則前綴和值即所需總和。segment tree 將查詢區間分割為互斥節點,取這些節點最大值等於所有 case 的最大值。六個輸出欄位皆正確。 + +## 複雜度 + +建表 O(N),每查詢兩次 range maximum 為 O(log N),總時間 O(N+Q log N)。prefix 與 segment tree 的輔助空間是 O(N);由於部分 reference implementations 也會保留完整輸入並暫存所有答案,實際總駐留空間是 O(N+Q)。這是七種語言共同採用、常數與實作風險均合理的 reference 路徑;若只追求理論漸近界,static RMQ 可再用 Cartesian tree 與線性預處理 RMQ 將全體降到 O(N+Q),但那不是本題 reference solutions 宣稱實作的路徑。 + +## 常見錯誤 + +- fail-fast 忘了包含失敗 case。 +- 一個 metric 未知就把所有 metric 都變 null。 +- 最大值的 identity 用 0 以外值,或區間端點 off-by-one。 +- 非 fail-fast 的 verdict 誤取最後一個失敗。 diff --git a/problems/024-judge-ledger/generator.py b/problems/024-judge-ledger/generator.py new file mode 100644 index 0000000..5b92b6e --- /dev/null +++ b/problems/024-judge-ledger/generator.py @@ -0,0 +1,16 @@ +#!/usr/bin/env python3 +import random, sys + +seed, index = map(int, sys.argv[1:]) +r = random.Random(seed * 97 + index) +n = 12 + index % 15 +q = 15 + index % 20 +print(n, q) +for _ in range(n): + v = 0 if r.randrange(4) else r.randint(1, 3) + x = [-1 if r.randrange(8) == 0 else r.randrange(100) for _ in range(4)] + print(v, *x) +for _ in range(q): + a = r.randint(1, n) + b = r.randint(a, n) + print(a, b, r.randrange(2)) diff --git a/problems/024-judge-ledger/oracle.py b/problems/024-judge-ledger/oracle.py new file mode 100644 index 0000000..abb1c9e --- /dev/null +++ b/problems/024-judge-ledger/oracle.py @@ -0,0 +1,19 @@ +#!/usr/bin/env python3 +import sys + +it = iter(sys.stdin.read().splitlines()) +n, q = map(int, next(it).split()) +a = [list(map(int, next(it).split())) for _ in range(n)] +for _ in range(q): + l, r, f = map(int, next(it).split()) + rows = [] + for row in a[l - 1 : r]: + rows.append(row) + if f and row[0]: + break + verdict = next((x[0] for x in rows if x[0]), 0) + vals = [] + for j in range(1, 5): + z = [x[j] for x in rows] + vals.append("null" if -1 in z else str(sum(z) if j < 3 else max(z))) + print(len(rows), verdict, *vals) diff --git a/problems/024-judge-ledger/problem.json b/problems/024-judge-ledger/problem.json new file mode 100644 index 0000000..178b460 --- /dev/null +++ b/problems/024-judge-ledger/problem.json @@ -0,0 +1,146 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 24, + "slug": "judge-ledger", + "title": { + "zh-TW": "Judge 總帳區間查詢", + "en": "Judge Ledger Range Queries" + }, + "difficulty": "hard", + "tags": [ + "range-query", + "segment-tree", + "prefix-sum" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-independent-null", + "kind": "adversarial", + "input": "tests/adversarial-independent-null.in", + "output": "tests/adversarial-independent-null.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 15000000, + "memoryLimitBytes": 1073741824 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 2500000, + "memoryLimitBytes": 805306368 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 1500000, + "memoryLimitBytes": 536870912 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "逐查詢掃描 cases", + "en": "Scan Cases per Query" + }, + "time": "O(NQ)", + "space": "O(1)", + "accepted": false + }, + { + "name": { + "zh-TW": "prefix 與 iterative segment tree(實用 reference 路徑)", + "en": "Prefix Data and Iterative Segment Trees (Practical Reference Path)" + }, + "time": "O(N + Q log N)", + "space": "O(N + Q)", + "accepted": true + } + ] +} diff --git a/problems/024-judge-ledger/solutions/c/main.c b/problems/024-judge-ledger/solutions/c/main.c new file mode 100644 index 0000000..86ec269 --- /dev/null +++ b/problems/024-judge-ledger/solutions/c/main.c @@ -0,0 +1,82 @@ +#include +#include +#include +#include +static int64_t rmq(int64_t *t, int b, int l, int r) { + int64_t z = 0; + for (l = b + l - 1, r = b + r - 1; l <= r; l >>= 1, r >>= 1) { + if (l & 1) { + if (t[l] > z) + z = t[l]; + l++; + } + if (!(r & 1)) { + if (t[r] > z) + z = t[r]; + r--; + } + } + return z; +} +int main(void) { + int n, q; + if (scanf("%d %d", &n, &q) != 2) + return 0; + int *nb = malloc((n + 2) * sizeof(int)); + int *bad = calloc(n + 1, sizeof(int)); + int *unk = calloc((size_t)4 * (n + 1), sizeof(int)); + int64_t *sum = calloc((size_t)2 * (n + 1), sizeof(int64_t)); + int b = 1; + while (b < n) + b <<= 1; + int64_t *tm = calloc((size_t)2 * b, sizeof(int64_t)), + *tv = calloc((size_t)2 * b, sizeof(int64_t)); + for (int i = 1; i <= n; i++) { + int v; + int64_t x[4]; + scanf("%d %" SCNd64 " %" SCNd64 " %" SCNd64 " %" SCNd64, &v, &x[0], &x[1], + &x[2], &x[3]); + bad[i] = v; + for (int j = 0; j < 4; j++) + unk[j * (n + 1) + i] = unk[j * (n + 1) + i - 1] + (x[j] < 0); + for (int j = 0; j < 2; j++) + sum[j * (n + 1) + i] = sum[j * (n + 1) + i - 1] + (x[j] < 0 ? 0 : x[j]); + tm[b + i - 1] = x[2] < 0 ? 0 : x[2]; + tv[b + i - 1] = x[3] < 0 ? 0 : x[3]; + } + for (int i = b - 1; i; i--) { + tm[i] = tm[i * 2] > tm[i * 2 + 1] ? tm[i * 2] : tm[i * 2 + 1]; + tv[i] = tv[i * 2] > tv[i * 2 + 1] ? tv[i * 2] : tv[i * 2 + 1]; + } + nb[n + 1] = n + 1; + for (int i = n; i; i--) + nb[i] = bad[i] ? i : nb[i + 1]; + while (q--) { + int l, r, f; + scanf("%d %d %d", &l, &r, &f); + int e = f && nb[l] <= r ? nb[l] : r; + printf("%d %d", e - l + 1, nb[l] <= e ? bad[nb[l]] : 0); + for (int j = 0; j < 2; j++) { + int *u = unk + j * (n + 1); + int64_t *s = sum + j * (n + 1); + if (u[e] - u[l - 1]) + printf(" null"); + else + printf(" %" PRId64, s[e] - s[l - 1]); + } + for (int j = 2; j < 4; j++) { + int *u = unk + j * (n + 1); + if (u[e] - u[l - 1]) + printf(" null"); + else + printf(" %" PRId64, rmq(j == 2 ? tm : tv, b, l, e)); + } + putchar('\n'); + } + free(nb); + free(bad); + free(unk); + free(sum); + free(tm); + free(tv); +} diff --git a/problems/024-judge-ledger/solutions/cpp/main.cpp b/problems/024-judge-ledger/solutions/cpp/main.cpp new file mode 100644 index 0000000..3ebdb08 --- /dev/null +++ b/problems/024-judge-ledger/solutions/cpp/main.cpp @@ -0,0 +1,66 @@ +#include +#include +#include +#include +#include +std::int64_t rmq(const std::vector &t, int b, int l, int r) { + std::int64_t z = 0; + for (l = b + l - 1, r = b + r - 1; l <= r; l /= 2, r /= 2) { + if (l & 1) + z = std::max(z, t[l++]); + if (!(r & 1)) + z = std::max(z, t[r--]); + } + return z; +} +int main() { + std::ios::sync_with_stdio(false); + std::cin.tie(nullptr); + int n, q; + std::cin >> n >> q; + std::vector bad(n + 2), nb(n + 2); + std::array, 4> u; + std::array, 2> s; + for (auto &x : u) + x.assign(n + 1, 0); + for (auto &x : s) + x.assign(n + 1, 0); + int b = 1; + while (b < n) + b *= 2; + std::vector tm(2 * b), tv(2 * b); + for (int i = 1; i <= n; i++) { + std::array x; + std::cin >> bad[i] >> x[0] >> x[1] >> x[2] >> x[3]; + for (int j = 0; j < 4; j++) + u[j][i] = u[j][i - 1] + (x[j] < 0); + for (int j = 0; j < 2; j++) + s[j][i] = s[j][i - 1] + std::max(0, x[j]); + tm[b + i - 1] = std::max(0, x[2]); + tv[b + i - 1] = std::max(0, x[3]); + } + for (int i = b - 1; i; i--) { + tm[i] = std::max(tm[2 * i], tm[2 * i + 1]); + tv[i] = std::max(tv[2 * i], tv[2 * i + 1]); + } + nb[n + 1] = n + 1; + for (int i = n; i; i--) + nb[i] = bad[i] ? i : nb[i + 1]; + while (q--) { + int l, r, f; + std::cin >> l >> r >> f; + int e = f && nb[l] <= r ? nb[l] : r; + std::cout << e - l + 1 << ' ' << (nb[l] <= e ? bad[nb[l]] : 0); + for (int j = 0; j < 2; j++) + if (u[j][e] > u[j][l - 1]) + std::cout << " null"; + else + std::cout << ' ' << s[j][e] - s[j][l - 1]; + for (int j = 2; j < 4; j++) + if (u[j][e] > u[j][l - 1]) + std::cout << " null"; + else + std::cout << ' ' << rmq(j == 2 ? tm : tv, b, l, e); + std::cout << '\n'; + } +} diff --git a/problems/024-judge-ledger/solutions/go/main.go b/problems/024-judge-ledger/solutions/go/main.go new file mode 100644 index 0000000..4eca2f3 --- /dev/null +++ b/problems/024-judge-ledger/solutions/go/main.go @@ -0,0 +1,112 @@ +package main + +import ( + "bufio" + "fmt" + "os" +) + +func max(a, b int64) int64 { + if a > b { + return a + } + return b +} +func rmq(t []int64, b, l, r int) int64 { + l += b - 1 + r += b - 1 + var z int64 + for l <= r { + if l&1 == 1 { + z = max(z, t[l]) + l++ + } + if r&1 == 0 { + z = max(z, t[r]) + r-- + } + l /= 2 + r /= 2 + } + return z +} +func main() { + in := bufio.NewReader(os.Stdin) + out := bufio.NewWriter(os.Stdout) + defer out.Flush() + var n, q int + fmt.Fscan(in, &n, &q) + bad := make([]int, n+2) + nb := make([]int, n+2) + u := make([][]int, 4) + s := make([][]int64, 2) + for j := range u { + u[j] = make([]int, n+1) + } + for j := range s { + s[j] = make([]int64, n+1) + } + b := 1 + for b < n { + b *= 2 + } + tm := make([]int64, 2*b) + tv := make([]int64, 2*b) + for i := 1; i <= n; i++ { + var a [4]int64 + fmt.Fscan(in, &bad[i], &a[0], &a[1], &a[2], &a[3]) + for j := 0; j < 4; j++ { + u[j][i] = u[j][i-1] + if a[j] < 0 { + u[j][i]++ + } + } + for j := 0; j < 2; j++ { + s[j][i] = s[j][i-1] + max(0, a[j]) + } + tm[b+i-1] = max(0, a[2]) + tv[b+i-1] = max(0, a[3]) + } + for i := b - 1; i > 0; i-- { + tm[i] = max(tm[i*2], tm[i*2+1]) + tv[i] = max(tv[i*2], tv[i*2+1]) + } + nb[n+1] = n + 1 + for i := n; i > 0; i-- { + if bad[i] > 0 { + nb[i] = i + } else { + nb[i] = nb[i+1] + } + } + for ; q > 0; q-- { + var l, r, f int + fmt.Fscan(in, &l, &r, &f) + e := r + if f == 1 && nb[l] <= r { + e = nb[l] + } + v := 0 + if nb[l] <= e { + v = bad[nb[l]] + } + fmt.Fprint(out, e-l+1, " ", v) + for j := 0; j < 2; j++ { + if u[j][e] > u[j][l-1] { + fmt.Fprint(out, " null") + } else { + fmt.Fprint(out, " ", s[j][e]-s[j][l-1]) + } + } + for j := 2; j < 4; j++ { + if u[j][e] > u[j][l-1] { + fmt.Fprint(out, " null") + } else if j == 2 { + fmt.Fprint(out, " ", rmq(tm, b, l, e)) + } else { + fmt.Fprint(out, " ", rmq(tv, b, l, e)) + } + } + fmt.Fprintln(out) + } +} diff --git a/problems/024-judge-ledger/solutions/javascript/main.js b/problems/024-judge-ledger/solutions/javascript/main.js new file mode 100644 index 0000000..f183238 --- /dev/null +++ b/problems/024-judge-ledger/solutions/javascript/main.js @@ -0,0 +1,63 @@ +import * as std from "std"; +const x = std.in.readAsString().trim().split(/\s+/); +let p = 0, n = +x[p++], q = +x[p++], b = 1; +while (b < n) b *= 2; +const bad = Array(n + 2).fill(0), + nb = Array(n + 2).fill(n + 1), + u = Array.from({ length: 4 }, () => Array(n + 1).fill(0)), + s = Array.from({ length: 2 }, () => Array(n + 1).fill(0n)), + tm = Array(2 * b).fill(0n), + tv = Array(2 * b).fill(0n); +for (let i = 1; i <= n; i++) { + bad[i] = +x[p++]; + const a = [0, 1, 2, 3].map(() => BigInt(x[p++])); + for (let j = 0; j < 4; j++) u[j][i] = u[j][i - 1] + (a[j] < 0n ? 1 : 0); + for (let j = 0; j < 2; j++) s[j][i] = s[j][i - 1] + (a[j] < 0n ? 0n : a[j]); + tm[b + i - 1] = a[2] < 0n ? 0n : a[2]; + tv[b + i - 1] = a[3] < 0n ? 0n : a[3]; +} +for (let i = b - 1; i; i--) { + tm[i] = tm[2 * i] > tm[2 * i + 1] ? tm[2 * i] : tm[2 * i + 1]; + tv[i] = tv[2 * i] > tv[2 * i + 1] ? tv[2 * i] : tv[2 * i + 1]; +} +for (let i = n; i; i--) nb[i] = bad[i] ? i : nb[i + 1]; +/** + * @param {bigint[]} t + * @param {number} l + * @param {number} r + * @returns {bigint} + */ +function rmq(t, l, r) { + l += b - 1; + r += b - 1; + let z = 0n; + while (l <= r) { + if (l & 1) { + if (t[l] > z) z = t[l]; + l++; + } + if (!(r & 1)) { + if (t[r] > z) z = t[r]; + r--; + } + l >>= 1; + r >>= 1; + } + return z; +} +const out = []; +while (q--) { + const l = +x[p++], + r = +x[p++], + f = +x[p++], + e = f && nb[l] <= r ? nb[l] : r, + z = [`${e - l + 1}`, `${nb[l] <= e ? bad[nb[l]] : 0}`]; + for (let j = 0; j < 2; j++) { + z.push(u[j][e] > u[j][l - 1] ? "null" : `${s[j][e] - s[j][l - 1]}`); + } + for (let j = 2; j < 4; j++) { + z.push(u[j][e] > u[j][l - 1] ? "null" : `${rmq(j === 2 ? tm : tv, l, e)}`); + } + out.push(z.join(" ")); +} +std.out.puts(out.join("\n") + "\n"); diff --git a/problems/024-judge-ledger/solutions/python/main.py b/problems/024-judge-ledger/solutions/python/main.py new file mode 100644 index 0000000..4158801 --- /dev/null +++ b/problems/024-judge-ledger/solutions/python/main.py @@ -0,0 +1,59 @@ +import sys + +it = iter(sys.stdin.buffer.read().split()) +n = int(next(it)) +q = int(next(it)) +bad = [0] * (n + 2) +u = [[0] * (n + 1) for _ in range(4)] +s = [[0] * (n + 1) for _ in range(2)] +b = 1 +while b < n: + b *= 2 +tm = [0] * (2 * b) +tv = [0] * (2 * b) +for i in range(1, n + 1): + bad[i] = int(next(it)) + a = [int(next(it)) for _ in range(4)] + for j in range(4): + u[j][i] = u[j][i - 1] + (a[j] < 0) + for j in range(2): + s[j][i] = s[j][i - 1] + max(0, a[j]) + tm[b + i - 1] = max(0, a[2]) + tv[b + i - 1] = max(0, a[3]) +for i in range(b - 1, 0, -1): + tm[i] = max(tm[2 * i : 2 * i + 2]) + tv[i] = max(tv[2 * i : 2 * i + 2]) +nb = [n + 1] * (n + 2) +for i in range(n, 0, -1): + nb[i] = i if bad[i] else nb[i + 1] + + +def rmq(t, l, r): + l += b - 1 + r += b - 1 + z = 0 + while l <= r: + if l & 1: + z = max(z, t[l]) + l += 1 + if not r & 1: + z = max(z, t[r]) + r -= 1 + l //= 2 + r //= 2 + return z + + +out = [] +for _ in range(q): + l = int(next(it)) + r = int(next(it)) + f = int(next(it)) + e = nb[l] if f and nb[l] <= r else r + z = [str(e - l + 1), str(bad[nb[l]] if nb[l] <= e else 0)] + for j in range(2): + z.append("null" if u[j][e] > u[j][l - 1] else str(s[j][e] - s[j][l - 1])) + for j, t in ((2, tm), (3, tv)): + z.append("null" if u[j][e] > u[j][l - 1] else str(rmq(t, l, e))) + out.append(" ".join(z)) +print("\n".join(out)) diff --git a/problems/024-judge-ledger/solutions/rust/main.rs b/problems/024-judge-ledger/solutions/rust/main.rs new file mode 100644 index 0000000..c548200 --- /dev/null +++ b/problems/024-judge-ledger/solutions/rust/main.rs @@ -0,0 +1,81 @@ +use std::io::{self, Read}; +fn rmq(t: &[i64], b: usize, mut l: usize, mut r: usize) -> i64 { + l += b - 1; + r += b - 1; + let mut z = 0; + while l <= r { + if l & 1 == 1 { + z = z.max(t[l]); + l += 1 + } + if r & 1 == 0 { + z = z.max(t[r]); + r -= 1 + } + l /= 2; + r /= 2 + } + z +} +fn main() { + let mut x = String::new(); + io::stdin().read_to_string(&mut x).unwrap(); + let mut it = x.split_whitespace(); + let n: usize = it.next().unwrap().parse().unwrap(); + let q: usize = it.next().unwrap().parse().unwrap(); + let mut bad = vec![0; n + 2]; + let mut u = vec![vec![0; n + 1]; 4]; + let mut s = vec![vec![0i64; n + 1]; 2]; + let mut b = 1; + while b < n { + b *= 2 + } + let (mut tm, mut tv) = (vec![0i64; 2 * b], vec![0i64; 2 * b]); + for i in 1..=n { + bad[i] = it.next().unwrap().parse().unwrap(); + let mut a = [0i64; 4]; + for z in &mut a { + *z = it.next().unwrap().parse().unwrap() + } + for j in 0..4 { + u[j][i] = u[j][i - 1] + (a[j] < 0) as i32 + } + for j in 0..2 { + s[j][i] = s[j][i - 1] + a[j].max(0) + } + tm[b + i - 1] = a[2].max(0); + tv[b + i - 1] = a[3].max(0) + } + for i in (1..b).rev() { + tm[i] = tm[i * 2].max(tm[i * 2 + 1]); + tv[i] = tv[i * 2].max(tv[i * 2 + 1]) + } + let mut nb = vec![n + 1; n + 2]; + for i in (1..=n).rev() { + nb[i] = if bad[i] > 0 { i } else { nb[i + 1] } + } + let mut out = String::new(); + for _ in 0..q { + let l: usize = it.next().unwrap().parse().unwrap(); + let r: usize = it.next().unwrap().parse().unwrap(); + let f: i32 = it.next().unwrap().parse().unwrap(); + let e = if f == 1 && nb[l] <= r { nb[l] } else { r }; + out += &format!("{} {}", e - l + 1, if nb[l] <= e { bad[nb[l]] } else { 0 }); + for j in 0..2 { + if u[j][e] > u[j][l - 1] { + out += " null" + } else { + out += &format!(" {}", s[j][e] - s[j][l - 1]) + } + } + for j in 2..4 { + if u[j][e] > u[j][l - 1] { + out += " null" + } else { + out += &format!(" {}", rmq(if j == 2 { &tm } else { &tv }, b, l, e)) + } + } + out.push('\n') + } + print!("{out}") +} diff --git a/problems/024-judge-ledger/solutions/typescript/main.ts b/problems/024-judge-ledger/solutions/typescript/main.ts new file mode 100644 index 0000000..460d814 --- /dev/null +++ b/problems/024-judge-ledger/solutions/typescript/main.ts @@ -0,0 +1,57 @@ +import * as std from "std"; +const x = std.in.readAsString().trim().split(/\s+/); +let p = 0, n = +x[p++], q = +x[p++], b = 1; +while (b < n) b *= 2; +const bad: number[] = Array(n + 2).fill(0), + nb: number[] = Array(n + 2).fill(n + 1), + u: number[][] = Array.from({ length: 4 }, () => Array(n + 1).fill(0)), + s: bigint[][] = Array.from({ length: 2 }, () => Array(n + 1).fill(0n)), + tm: bigint[] = Array(2 * b).fill(0n), + tv: bigint[] = Array(2 * b).fill(0n); +for (let i = 1; i <= n; i++) { + bad[i] = +x[p++]; + const a = [0, 1, 2, 3].map(() => BigInt(x[p++])); + for (let j = 0; j < 4; j++) u[j][i] = u[j][i - 1] + (a[j] < 0n ? 1 : 0); + for (let j = 0; j < 2; j++) s[j][i] = s[j][i - 1] + (a[j] < 0n ? 0n : a[j]); + tm[b + i - 1] = a[2] < 0n ? 0n : a[2]; + tv[b + i - 1] = a[3] < 0n ? 0n : a[3]; +} +for (let i = b - 1; i; i--) { + tm[i] = tm[2 * i] > tm[2 * i + 1] ? tm[2 * i] : tm[2 * i + 1]; + tv[i] = tv[2 * i] > tv[2 * i + 1] ? tv[2 * i] : tv[2 * i + 1]; +} +for (let i = n; i; i--) nb[i] = bad[i] ? i : nb[i + 1]; +function rmq(t: bigint[], l: number, r: number) { + l += b - 1; + r += b - 1; + let z = 0n; + while (l <= r) { + if (l & 1) { + if (t[l] > z) z = t[l]; + l++; + } + if (!(r & 1)) { + if (t[r] > z) z = t[r]; + r--; + } + l >>= 1; + r >>= 1; + } + return z; +} +const out: string[] = []; +while (q--) { + const l = +x[p++], + r = +x[p++], + f = +x[p++], + e = f && nb[l] <= r ? nb[l] : r, + z = [`${e - l + 1}`, `${nb[l] <= e ? bad[nb[l]] : 0}`]; + for (let j = 0; j < 2; j++) { + z.push(u[j][e] > u[j][l - 1] ? "null" : `${s[j][e] - s[j][l - 1]}`); + } + for (let j = 2; j < 4; j++) { + z.push(u[j][e] > u[j][l - 1] ? "null" : `${rmq(j === 2 ? tm : tv, l, e)}`); + } + out.push(z.join(" ")); +} +std.out.puts(out.join("\n") + "\n"); diff --git a/problems/024-judge-ledger/statement.en.md b/problems/024-judge-ledger/statement.en.md new file mode 100644 index 0000000..7ea35d1 --- /dev/null +++ b/problems/024-judge-ledger/statement.en.md @@ -0,0 +1,102 @@ +# Judge Ledger Range Queries + +The final verdict of an entire submission does not contain every useful diagnostic, so a WASM OJ results interface must also let users inspect an execution summary for a selected range of test cases. One view may process the complete range, while another stops at the first failing case, so the cases included in their aggregates are different. + +Each case records `verdict cost time memory vfs` in sequence. Verdict is encoded as an integer: `0=AC, 1=WA, 2=RE, 3=TLE`. An unavailable metric is represented by `-1`. Answer several interval queries that reproduce the summary shown under each fail-fast setting. + +Each query `l r f` aggregates the 1-indexed closed interval `[l,r]`: + +- If `f=1` (fail-fast), process only through the first case in the interval whose verdict is nonzero, including that case. If no case fails, process through `r`. +- If `f=0`, process the entire interval. +- The output verdict is the first nonzero verdict in the range actually processed, or 0 if none exists. +- Sum `cost` and `time`; take the maximum of `memory` and `vfs`. +- Handle every metric independently. If any value for one metric is `-1` in the actual range, output `null` for that aggregate. Other metrics are unaffected. + +## Input + +The first line contains `N Q`. The next `N` lines contain cases, followed by `Q` query lines. + +## Output + +For every query, output `processed verdict cost time memory vfs`. `processed` is the number of cases in the actual processed range. + +## Constraints + +- `1 ≤ N,Q ≤ 200000` +- Every metric is `-1` or lies in `[0,10^12]`. +- The cost or time sum of any valid interval is at most `9×10^18`. +- `1 ≤ l ≤ r ≤ N` +- `f` is 0 or 1. +- The full constraints apply to every official test. + +## Examples + + + +### Example One + +Input: + +```text +4 4 +0 10 5 100 3 +1 20 7 120 4 +0 -1 2 80 2 +2 5 -1 200 -1 +1 4 1 +1 4 0 +3 4 1 +3 3 0 +``` + +Output: + +```text +2 1 30 12 120 4 +4 1 null null 200 null +2 2 null null 200 null +1 0 null 2 80 2 +``` + +### Example Two + +Input: + +```text +3 3 +0 1 2 3 4 +0 5 6 7 8 +0 9 10 11 12 +1 3 1 +2 3 0 +2 2 1 +``` + +Output: + +```text +3 0 15 18 11 12 +2 0 14 16 11 12 +1 0 5 6 7 8 +``` + +### Example Three + +Input: + +```text +2 2 +3 -1 -1 -1 -1 +0 7 8 9 10 +1 2 1 +1 2 0 +``` + +Output: + +```text +1 3 null null null null +2 3 null null null null +``` + + diff --git a/problems/024-judge-ledger/statement.zh-TW.md b/problems/024-judge-ledger/statement.zh-TW.md new file mode 100644 index 0000000..a167c43 --- /dev/null +++ b/problems/024-judge-ledger/statement.zh-TW.md @@ -0,0 +1,101 @@ +# Judge 總帳區間查詢 + +一份 submission 的最終 verdict 不足以呈現所有診斷資訊,因此 WASM OJ 的判題結果介面也要讓使用者檢查某一段 test cases 的執行摘要。不同檢視模式可能跑完整區間,也可能在第一個失敗 case 立刻停止;兩者實際納入統計的範圍並不相同。 + +每個 case 依序記錄 `verdict cost time memory vfs`。verdict 以整數表示:`0=AC, 1=WA, 2=RE, 3=TLE`。四個 metric 若無法取得,以 `-1` 表示。現在需要回答多個區間查詢,重現介面在不同 fail-fast 設定下應顯示的摘要。 + +每個查詢 `l r f` 要聚合 1-indexed 閉區間 `[l,r]`: + +- 若 `f=1`(fail-fast),只處理到區間中第一個 verdict 非 0 的 case(包含該 case);若沒有失敗則處理到 r。 +- 若 `f=0`,處理完整區間。 +- 輸出 verdict 為實際處理範圍內第一個非 0 verdict,若無則 0。 +- cost、time 取總和;memory、vfs 取最大值。 +- 對每一個 metric 分別處理:只要實際範圍內任一值為 -1,該 aggregate 輸出 `null`。其他 metric 不受影響。 + +## 輸入 + +第一行 `N Q`。接著 N 行 case,再接著 Q 行查詢。 + +- `1 ≤ N,Q ≤ 200000` +- metric 為 `-1` 或 `[0,10^12]`;任一合法區間的 cost/time 總和不超過 `9×10^18` +- `1 ≤ l ≤ r ≤ N`,`f` 為 0 或 1 + +## 輸出 + +每個查詢一行:`processed verdict cost time memory vfs`。`processed` 是實際處理 case 數。 + +## 限制 + +所有數量、字串格式與整數範圍均列於「輸入」段落;完整限制適用於每一筆正式測資。 + +## 範例 + + + +### 範例一 + +輸入: + +```text +4 4 +0 10 5 100 3 +1 20 7 120 4 +0 -1 2 80 2 +2 5 -1 200 -1 +1 4 1 +1 4 0 +3 4 1 +3 3 0 +``` + +輸出: + +```text +2 1 30 12 120 4 +4 1 null null 200 null +2 2 null null 200 null +1 0 null 2 80 2 +``` + +### 範例二 + +輸入: + +```text +3 3 +0 1 2 3 4 +0 5 6 7 8 +0 9 10 11 12 +1 3 1 +2 3 0 +2 2 1 +``` + +輸出: + +```text +3 0 15 18 11 12 +2 0 14 16 11 12 +1 0 5 6 7 8 +``` + +### 範例三 + +輸入: + +```text +2 2 +3 -1 -1 -1 -1 +0 7 8 9 10 +1 2 1 +1 2 0 +``` + +輸出: + +```text +1 3 null null null null +2 3 null null null null +``` + + diff --git a/problems/024-judge-ledger/tests/adversarial-independent-null.in b/problems/024-judge-ledger/tests/adversarial-independent-null.in new file mode 100644 index 0000000..92b8160 --- /dev/null +++ b/problems/024-judge-ledger/tests/adversarial-independent-null.in @@ -0,0 +1,12 @@ +5 6 +0 1 2 3 4 +1 5 -1 7 8 +2 -1 10 -1 12 +0 20 30 1 -1 +0 0 0 0 0 +1 5 1 +1 5 0 +3 5 1 +4 5 1 +4 5 0 +2 2 0 diff --git a/problems/024-judge-ledger/tests/adversarial-independent-null.out b/problems/024-judge-ledger/tests/adversarial-independent-null.out new file mode 100644 index 0000000..d93f52d --- /dev/null +++ b/problems/024-judge-ledger/tests/adversarial-independent-null.out @@ -0,0 +1,6 @@ +2 1 6 null 7 8 +5 1 null null null null +1 2 null 10 null 12 +2 0 20 30 1 null +2 0 20 30 1 null +1 1 5 null 7 8 diff --git a/problems/024-judge-ledger/tests/sample-01.in b/problems/024-judge-ledger/tests/sample-01.in new file mode 100644 index 0000000..65d8175 --- /dev/null +++ b/problems/024-judge-ledger/tests/sample-01.in @@ -0,0 +1,9 @@ +4 4 +0 10 5 100 3 +1 20 7 120 4 +0 -1 2 80 2 +2 5 -1 200 -1 +1 4 1 +1 4 0 +3 4 1 +3 3 0 diff --git a/problems/024-judge-ledger/tests/sample-01.out b/problems/024-judge-ledger/tests/sample-01.out new file mode 100644 index 0000000..c28fff6 --- /dev/null +++ b/problems/024-judge-ledger/tests/sample-01.out @@ -0,0 +1,4 @@ +2 1 30 12 120 4 +4 1 null null 200 null +2 2 null null 200 null +1 0 null 2 80 2 diff --git a/problems/024-judge-ledger/tests/sample-02.in b/problems/024-judge-ledger/tests/sample-02.in new file mode 100644 index 0000000..68f3aca --- /dev/null +++ b/problems/024-judge-ledger/tests/sample-02.in @@ -0,0 +1,7 @@ +3 3 +0 1 2 3 4 +0 5 6 7 8 +0 9 10 11 12 +1 3 1 +2 3 0 +2 2 1 diff --git a/problems/024-judge-ledger/tests/sample-02.out b/problems/024-judge-ledger/tests/sample-02.out new file mode 100644 index 0000000..4830929 --- /dev/null +++ b/problems/024-judge-ledger/tests/sample-02.out @@ -0,0 +1,3 @@ +3 0 15 18 11 12 +2 0 14 16 11 12 +1 0 5 6 7 8 diff --git a/problems/024-judge-ledger/tests/sample-03.in b/problems/024-judge-ledger/tests/sample-03.in new file mode 100644 index 0000000..030fdf8 --- /dev/null +++ b/problems/024-judge-ledger/tests/sample-03.in @@ -0,0 +1,5 @@ +2 2 +3 -1 -1 -1 -1 +0 7 8 9 10 +1 2 1 +1 2 0 diff --git a/problems/024-judge-ledger/tests/sample-03.out b/problems/024-judge-ledger/tests/sample-03.out new file mode 100644 index 0000000..eb781fc --- /dev/null +++ b/problems/024-judge-ledger/tests/sample-03.out @@ -0,0 +1,2 @@ +1 3 null null null null +2 3 null null null null diff --git a/problems/024-judge-ledger/validator.py b/problems/024-judge-ledger/validator.py new file mode 100644 index 0000000..c0cd60d --- /dev/null +++ b/problems/024-judge-ledger/validator.py @@ -0,0 +1,26 @@ +#!/usr/bin/env python3 +import re, sys + +try: + l = sys.stdin.read().splitlines() + h = l[0].split() + assert len(h) == 2 and all(re.fullmatch(r"[1-9][0-9]*", x) for x in h) + n, q = map(int, h) + assert 1 <= n <= 200000 and 1 <= q <= 200000 and len(l) == 1 + n + q + sc = st = 0 + for s in l[1 : n + 1]: + p = s.split() + assert len(p) == 5 + a = list(map(int, p)) + assert 0 <= a[0] <= 3 + assert all(x == -1 or 0 <= x <= 10**12 for x in a[1:]) + sc += max(0, a[1]) + st += max(0, a[2]) + assert sc <= 9 * 10**18 and st <= 9 * 10**18 + for s in l[n + 1 :]: + p = s.split() + assert len(p) == 3 + a, b, f = map(int, p) + assert 1 <= a <= b <= n and f in (0, 1) +except Exception: + sys.exit(1) diff --git a/problems/025-seven-matchers/editorial.en.md b/problems/025-seven-matchers/editorial.en.md new file mode 100644 index 0000000..ef4fc78 --- /dev/null +++ b/problems/025-seven-matchers/editorial.en.md @@ -0,0 +1,41 @@ +# Editorial + +## Intuitive Approach + +For `SET`, `MULTISET`, and `FILESET`, linearly search the actual array for each expected token and mark matches as used. This costs `O(K^2)` in the worst case and cannot handle a total of 200,000 tokens. + +## Advanced Approach: Canonical Comparison Sorting + +Sort both sides of every unordered matcher with a comparison sort, then compare linearly. This is deterministic and easy to implement, but performs `O(K log K)` comparisons. Even with short tokens, its worst-case time is `O(K log K+L)` and does not exploit the stated bounds on token length and byte alphabet. + +## Optimal Approach: Bounded-Byte Stable LSD Radix Sort + +`EXACT` concatenation, `LINES` trailing removal, `TOKENS`, and `FLOAT` are all linear. + +Ordinary tokens are at most 30 bytes, and `FILESET` entries at most 29. For each unordered matcher, establish canonical order with 30 passes of stable LSD byte counting sort. Process positions 29 down to 0. Use key 0 when the position is absent and `byte+1` when present. Each pass uses a 257-entry counting table. The missing sentinel is less than every real byte, so a prefix string sorts before a longer string with the same prefix; the resulting order is bytewise lexicographic. + +After sorting, deduplicate `SET` linearly before comparing the sides. Compare the sorted arrays directly for `MULTISET` and `FILESET`. The method has no hash collisions, language-specific hash behavior, or comparison-sort dependency. + +For `FLOAT`, the maximum possible difference is `2×10^18`, still within the stated signed 64-bit range. JavaScript and TypeScript should use `bigint`. + +## Correctness Proof + +`EXACT`, `LINES`, and `TOKENS` implement their specified normalization and element comparison directly. `FLOAT` checks the necessary and sufficient condition at every position. + +For radix sorting, assume inductively before position `p` that the sequence is sorted by suffix positions `p+1..29`. The counting pass groups records by their position-`p` key and, because it is stable, preserves suffix order among equal keys. The sequence is then sorted by positions `p..29`. Repeating from position 29 to 0 yields order by the complete 30-position key. Missing has key 0 while every real byte has key `byte+1`, so this is exactly bytewise lexicographic order. + +Radix sorting only permutes elements and preserves multiplicities. Therefore two sorted sequences are equal exactly when their multisets are equal. Removing adjacent duplicates produces equal sequences exactly when their sets are equal. In `FILESET`, each side has unique paths, so comparing complete-entry multisets is equivalent to comparing file mappings. Thus every matcher returns the correct result. + +## Complexity + +Let `K` be the total number of tokens on both sides of all queries, `L` their total character length, and `K_q,L_q` the corresponding values for one query. Maximum token length is constant `B=30`, and alphabet size is `A=257`. One radix canonicalization costs `O(BK_q+AB+L_q)`, which is `O(1+K_q+L_q)` because `B,A` are fixed and tokens are nonempty. Including `Q` headers, empty queries, and one output line per query, total time across all matchers is `O(Q+K+L)`. + +Per-query auxiliary space is `O(K_max+L_max)`, with `O(K_max+A)` radix scratch space. C, C++, and Go can stream by query. Rust, Python, JavaScript, and TypeScript references retain full input and buffer `Q` output lines, so their actual buffered-I/O resident space is `O(Q+K+L)`. + +## Common Mistakes + +- Inserting spaces between tokens for `EXACT`. +- Removing empty lines from the middle for `LINES`. +- Forgetting to deduplicate `SET`, or incorrectly deduplicating `MULTISET`. +- Using floating point for `FLOAT`, or overflowing during subtraction. +- Using comparison sort and obtaining `O(K log K+L)` rather than deterministic `O(K+L)`. diff --git a/problems/025-seven-matchers/editorial.zh-TW.md b/problems/025-seven-matchers/editorial.zh-TW.md new file mode 100644 index 0000000..ee03766 --- /dev/null +++ b/problems/025-seven-matchers/editorial.zh-TW.md @@ -0,0 +1,41 @@ +# 解題說明 + +## 直覺解 + +SET、MULTISET、FILESET 可對每個 expected token 線性搜尋 actual,再標記使用;最壞 O(K²),無法通過總長 200000 的測資。 + +## 次佳解 + +把無序 matcher 的兩側各自以 comparison sort 排序,再線性比較。這是 deterministic 的,也很容易實作,但比較次數為 O(K log K);即使 token 很短,最壞時間仍是 O(K log K+L),沒有利用題目給定的字串長度與 byte alphabet 上限。 + +## 最佳解 + +EXACT 串接、LINES 刪尾、TOKENS 與 FLOAT 都線性處理。 + +一般 token 最長 30 bytes,FILESET entry 最長 29 bytes。對三種無序 matcher,可用 30 趟 stable LSD byte counting sort 建立 canonical order:從位置 29 到 0,該位置不存在時令 key 為 0,存在時令 key 為 `byte+1`。每趟以大小 257 的 counting table 做穩定排序。missing sentinel 小於所有真實 byte,所以 prefix 較短的字串會排在前面;最終順序就是 byte lexicographic order。 + +SET 在排序後線性去重,再比較兩側;MULTISET/FILESET 直接比較排序結果。這個方法沒有 hash collision 或語言特定 hash 行為,也不依賴 comparison sort。 + +FLOAT 的差值最大 2×10^18,仍在題目指定的 signed 64-bit 安全範圍;JS/TS 應使用 bigint。 + +## 正確性證明 + +EXACT、LINES、TOKENS 直接實作題目定義的正規化與逐項比較。FLOAT 逐位置驗證定義中的必要且充分條件。 + +考慮 radix sort。處理位置 `p` 前,歸納假設序列已依 suffix `p+1..29` 排好。位置 `p` 的 counting pass 先依該位置 key 分組,且 stable 性保留同 key 元素原有的 suffix 順序,因此 pass 後序列依 `p..29` 排好。從位置 29 開始反覆套用,可知最後序列依完整 30-position key 排好。missing sentinel 為 0、真實 byte key 為 `byte+1`,所以此順序恰為 byte lexicographic order。 + +Radix sort 只重排元素,不改變元素或重數。於是 MULTISET 的兩個排序序列相等,當且僅當兩側多重集合相等;SET 排序後刪除相鄰重複值,所得序列相等,當且僅當兩側集合相等。FILESET 每側 path 唯一,故完整 entry 的多重集合比較等價於檔案映射相等。綜合以上,每種 matcher 的輸出皆正確。 + +## 複雜度 + +令 `K` 為全部 query 兩側 token 總數、`L` 為其字元總長,單一 query 的對應量為 `K_q,L_q`,最大 token 長度 `B=30`、alphabet 大小 `A=257`。單次 radix canonicalization 為 `O(BK_q+AB+L_q)`;`B,A` 是題目常數,且 token 非空,所以是 `O(1+K_q+L_q)`。把 `Q` 個 header、空 query 與每題一行輸出也計入後,全部 matcher 的總時間為 `O(Q+K+L)`。 + +演算法逐 query 所需 auxiliary space 為 `O(K_max+L_max)`,radix scratch 另為 `O(K_max+A)`。C、C++、Go 可逐 query 讀寫;Rust、Python、JavaScript、TypeScript reference 會保留完整輸入並緩衝 `Q` 行輸出,因此這四語言的實際 buffered I/O resident space 為 `O(Q+K+L)`。 + +## 常見錯誤 + +- EXACT 在 token 間自行加入空白。 +- LINES 刪除中間的空行。 +- SET 忘記去重或 MULTISET 錯誤去重。 +- FLOAT 使用浮點數或在相減時溢位。 +- 使用一般 comparison sort,得到 O(K log K+L) 而非 deterministic O(K+L)。 diff --git a/problems/025-seven-matchers/generator.py b/problems/025-seven-matchers/generator.py new file mode 100644 index 0000000..9a51331 --- /dev/null +++ b/problems/025-seven-matchers/generator.py @@ -0,0 +1,32 @@ +#!/usr/bin/env python3 +import random, sys + +seed, index = map(int, sys.argv[1:]) +r = random.Random(seed + index * 17) +kinds = ["EXACT", "LINES", "TOKENS", "FLOAT", "SET", "MULTISET", "FILESET"] +q = 7 +print(q) +for qi, k in enumerate(kinds): + n = r.randrange(8) + m = n if r.randrange(3) else r.randrange(8) + eps = r.randrange(5) + print(k, n, m, eps) if k == "FLOAT" else print(k, n, m) + if k == "FLOAT": + e = [str(r.randrange(-20, 21)) for _ in range(n)] + a = [str(int(e[i]) + r.randrange(-6, 7)) for i in range(min(n, m))] + [ + str(r.randrange(20)) for _ in range(max(0, m - n)) + ] + elif k == "FILESET": + e = [f"p{i}@{r.randrange(16**8):08x}" for i in range(n)] + if m == n and r.randrange(2): + a = e.copy() + r.shuffle(a) + else: + a = [f"q{i}@{r.randrange(16**8):08x}" for i in range(m)] + else: + pool = ["a", "b", "c", "#", "xy"] + e = [r.choice(pool) for _ in range(n)] + a = e[:m] + [r.choice(pool) for _ in range(max(0, m - n))] + r.shuffle(a) if k in ("SET", "MULTISET") else None + print(*e) + print(*a) diff --git a/problems/025-seven-matchers/oracle.py b/problems/025-seven-matchers/oracle.py new file mode 100644 index 0000000..e2ccdc2 --- /dev/null +++ b/problems/025-seven-matchers/oracle.py @@ -0,0 +1,42 @@ +#!/usr/bin/env python3 +import sys + +l = sys.stdin.read().splitlines() +q = int(l[0]) +at = 1 +for _ in range(q): + h = l[at].split() + at += 1 + k = h[0] + e = l[at].split() + a = l[at + 1].split() + at += 2 + ok = False + if k == "EXACT": + ok = "".join(e) == "".join(a) + elif k == "LINES": + while e and e[-1] == "#": + e.pop() + while a and a[-1] == "#": + a.pop() + ok = e == a + elif k == "TOKENS": + ok = e == a + elif k == "FLOAT": + ok = len(e) == len(a) and all( + abs(int(x) - int(y)) <= int(h[3]) for x, y in zip(e, a) + ) + elif k == "SET": + ok = all(any(x == y for y in a) for x in e) and all( + any(y == x for x in e) for y in a + ) + else: + used = [False] * len(a) + ok = len(e) == len(a) + for x in e: + j = next((j for j, y in enumerate(a) if not used[j] and x == y), None) + if j is None: + ok = False + break + used[j] = True + print("ACCEPT" if ok else "WRONG") diff --git a/problems/025-seven-matchers/problem.json b/problems/025-seven-matchers/problem.json new file mode 100644 index 0000000..c234c7b --- /dev/null +++ b/problems/025-seven-matchers/problem.json @@ -0,0 +1,155 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 25, + "slug": "seven-matchers", + "title": { + "zh-TW": "七種答案比對器", + "en": "Seven Answer Matchers" + }, + "difficulty": "medium", + "tags": [ + "sorting", + "strings", + "multiset" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-linear-dedup", + "kind": "adversarial", + "input": "tests/adversarial-linear-dedup.in", + "output": "tests/adversarial-linear-dedup.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 750000000, + "memoryLimitBytes": 1073741824 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 8500000, + "memoryLimitBytes": 805306368 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 3500000, + "memoryLimitBytes": 536870912 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "集合逐項線性搜尋", + "en": "Per-Element Linear Set Search" + }, + "time": "O(K^2)", + "space": "O(K)", + "accepted": false + }, + { + "name": { + "zh-TW": "canonical sorting", + "en": "Canonical Comparison Sorting" + }, + "time": "O(K log K + L)", + "space": "O(K + L)", + "accepted": false + }, + { + "name": { + "zh-TW": "bounded-byte LSD radix canonicalization", + "en": "Bounded-Byte LSD Radix Canonicalization" + }, + "time": "O(Q + K + L)", + "space": "O(K_max + L_max) auxiliary; O(Q + K + L) buffered I/O", + "accepted": true + } + ] +} diff --git a/problems/025-seven-matchers/solutions/c/main.c b/problems/025-seven-matchers/solutions/c/main.c new file mode 100644 index 0000000..e9518f4 --- /dev/null +++ b/problems/025-seven-matchers/solutions/c/main.c @@ -0,0 +1,134 @@ +#include +#include +#include +#include +#include +static void radix_sort(char **a, int n) { + if (n < 2) + return; + char **tmp = malloc((size_t)n * sizeof(*tmp)); + for (int pos = 29; pos >= 0; pos--) { + size_t next[257] = {0}; + for (int i = 0; i < n; i++) { + size_t len = strlen(a[i]); + unsigned key = (size_t)pos < len ? (unsigned char)a[i][pos] + 1U : 0U; + next[key]++; + } + size_t offset = 0; + for (int key = 0; key < 257; key++) { + size_t count = next[key]; + next[key] = offset; + offset += count; + } + for (int i = 0; i < n; i++) { + size_t len = strlen(a[i]); + unsigned key = (size_t)pos < len ? (unsigned char)a[i][pos] + 1U : 0U; + tmp[next[key]++] = a[i]; + } + memcpy(a, tmp, (size_t)n * sizeof(*a)); + } + free(tmp); +} +static char *word(void) { + char b[64]; + scanf("%63s", b); + size_t n = strlen(b) + 1; + char *s = malloc(n); + memcpy(s, b, n); + return s; +} +static int seq(char **a, int n, char **b, int m) { + if (n != m) + return 0; + for (int i = 0; i < n; i++) + if (strcmp(a[i], b[i])) + return 0; + return 1; +} +static int seteq(char **a, int n, char **b, int m) { + int i = 0, j = 0; + while (i < n && j < m) { + if (strcmp(a[i], b[j])) + return 0; + char *x = a[i], *y = b[j]; + while (i < n && !strcmp(a[i], x)) + i++; + while (j < m && !strcmp(b[j], y)) + j++; + } + return i == n && j == m; +} +int main(void) { + int Q; + if (scanf("%d", &Q) != 1) + return 0; + while (Q--) { + char k[16]; + int n, m; + int64_t eps = 0; + scanf("%15s%d%d", k, &n, &m); + if (!strcmp(k, "FLOAT")) + scanf("%" SCNd64, &eps); + int on = n, om = m; + char **a = malloc((size_t)n * sizeof(*a)), + **b = malloc((size_t)m * sizeof(*b)); + for (int i = 0; i < n; i++) + a[i] = word(); + for (int i = 0; i < m; i++) + b[i] = word(); + int ok = 0; + if (!strcmp(k, "EXACT")) { + size_t x = 0, y = 0; + for (int i = 0; i < n; i++) + x += strlen(a[i]); + for (int i = 0; i < m; i++) + y += strlen(b[i]); + if (x == y) { + char *A = malloc(x + 1), *B = malloc(y + 1), *p = A, *q = B; + for (int i = 0; i < n; i++) { + size_t z = strlen(a[i]); + memcpy(p, a[i], z); + p += z; + } + *p = 0; + for (int i = 0; i < m; i++) { + size_t z = strlen(b[i]); + memcpy(q, b[i], z); + q += z; + } + *q = 0; + ok = !strcmp(A, B); + free(A); + free(B); + } + } else if (!strcmp(k, "LINES")) { + while (n && strcmp(a[n - 1], "#") == 0) + n--; + while (m && strcmp(b[m - 1], "#") == 0) + m--; + ok = seq(a, n, b, m); + } else if (!strcmp(k, "TOKENS")) + ok = seq(a, n, b, m); + else if (!strcmp(k, "FLOAT")) { + ok = n == m; + for (int i = 0; i < n && ok; i++) { + int64_t x = strtoll(a[i], 0, 10), y = strtoll(b[i], 0, 10); + uint64_t d = + x >= y ? (uint64_t)x - (uint64_t)y : (uint64_t)y - (uint64_t)x; + if (d > (uint64_t)eps) + ok = 0; + } + } else { + radix_sort(a, n); + radix_sort(b, m); + ok = !strcmp(k, "SET") ? seteq(a, n, b, m) : seq(a, n, b, m); + } + puts(ok ? "ACCEPT" : "WRONG"); + for (int i = 0; i < on; i++) + free(a[i]); + for (int i = 0; i < om; i++) + free(b[i]); + free(a); + free(b); + } +} diff --git a/problems/025-seven-matchers/solutions/cpp/main.cpp b/problems/025-seven-matchers/solutions/cpp/main.cpp new file mode 100644 index 0000000..0fffcc0 --- /dev/null +++ b/problems/025-seven-matchers/solutions/cpp/main.cpp @@ -0,0 +1,84 @@ +#include +#include +#include +#include +#include +#include +static void radix_sort(std::vector &values) { + std::vector scratch(values.size()); + for (int pos = 29; pos >= 0; --pos) { + std::array next{}; + for (const auto &value : values) { + const unsigned key = static_cast(pos) < value.size() + ? static_cast(value[pos]) + 1U + : 0U; + ++next[key]; + } + std::size_t offset = 0; + for (auto &entry : next) { + const std::size_t count = entry; + entry = offset; + offset += count; + } + for (auto &value : values) { + const unsigned key = static_cast(pos) < value.size() + ? static_cast(value[pos]) + 1U + : 0U; + scratch[next[key]++] = std::move(value); + } + values.swap(scratch); + } +} +int main() { + std::ios::sync_with_stdio(false); + std::cin.tie(nullptr); + int Q; + std::cin >> Q; + while (Q--) { + std::string k; + int n, m; + std::int64_t eps = 0; + std::cin >> k >> n >> m; + if (k == "FLOAT") + std::cin >> eps; + std::vector a(n), b(m); + for (auto &x : a) + std::cin >> x; + for (auto &x : b) + std::cin >> x; + bool ok; + if (k == "EXACT") { + std::string x, y; + for (auto &s : a) + x += s; + for (auto &s : b) + y += s; + ok = x == y; + } else if (k == "LINES") { + while (!a.empty() && a.back() == "#") + a.pop_back(); + while (!b.empty() && b.back() == "#") + b.pop_back(); + ok = a == b; + } else if (k == "TOKENS") + ok = a == b; + else if (k == "FLOAT") { + ok = n == m; + for (int i = 0; i < n && ok; i++) { + auto x = std::stoll(a[i]), y = std::stoll(b[i]); + std::uint64_t d = x >= y ? (std::uint64_t)x - (std::uint64_t)y + : (std::uint64_t)y - (std::uint64_t)x; + ok = d <= (std::uint64_t)eps; + } + } else { + radix_sort(a); + radix_sort(b); + if (k == "SET") { + a.erase(std::unique(a.begin(), a.end()), a.end()); + b.erase(std::unique(b.begin(), b.end()), b.end()); + } + ok = a == b; + } + std::cout << (ok ? "ACCEPT\n" : "WRONG\n"); + } +} diff --git a/problems/025-seven-matchers/solutions/go/main.go b/problems/025-seven-matchers/solutions/go/main.go new file mode 100644 index 0000000..28cf2db --- /dev/null +++ b/problems/025-seven-matchers/solutions/go/main.go @@ -0,0 +1,122 @@ +package main + +import ( + "bufio" + "fmt" + "os" + "strconv" + "strings" +) + +func radixSort(values []string) { + scratch := make([]string, len(values)) + for pos := 29; pos >= 0; pos-- { + var next [257]int + for _, value := range values { + key := 0 + if pos < len(value) { + key = int(value[pos]) + 1 + } + next[key]++ + } + offset := 0 + for key, count := range next { + next[key] = offset + offset += count + } + for _, value := range values { + key := 0 + if pos < len(value) { + key = int(value[pos]) + 1 + } + scratch[next[key]] = value + next[key]++ + } + copy(values, scratch) + } +} + +func main() { + in := bufio.NewReader(os.Stdin) + out := bufio.NewWriter(os.Stdout) + defer out.Flush() + var Q int + fmt.Fscan(in, &Q) + for ; Q > 0; Q-- { + var k string + var n, m int + var eps int64 + fmt.Fscan(in, &k, &n, &m) + if k == "FLOAT" { + fmt.Fscan(in, &eps) + } + a := make([]string, n) + b := make([]string, m) + for i := range a { + fmt.Fscan(in, &a[i]) + } + for i := range b { + fmt.Fscan(in, &b[i]) + } + ok := false + if k == "EXACT" { + ok = strings.Join(a, "") == strings.Join(b, "") + } else if k == "LINES" { + for len(a) > 0 && a[len(a)-1] == "#" { + a = a[:len(a)-1] + } + for len(b) > 0 && b[len(b)-1] == "#" { + b = b[:len(b)-1] + } + ok = equal(a, b) + } else if k == "TOKENS" { + ok = equal(a, b) + } else if k == "FLOAT" { + ok = n == m + for i := 0; i < n && ok; i++ { + x, _ := strconv.ParseInt(a[i], 10, 64) + y, _ := strconv.ParseInt(b[i], 10, 64) + var d uint64 + if x >= y { + d = uint64(x) - uint64(y) + } else { + d = uint64(y) - uint64(x) + } + ok = d <= uint64(eps) + } + } else { + radixSort(a) + radixSort(b) + if k == "SET" { + a = dedup(a) + b = dedup(b) + } + ok = equal(a, b) + } + if ok { + fmt.Fprintln(out, "ACCEPT") + } else { + fmt.Fprintln(out, "WRONG") + } + } +} +func equal(a, b []string) bool { + if len(a) != len(b) { + return false + } + for i := range a { + if a[i] != b[i] { + return false + } + } + return true +} +func dedup(a []string) []string { + z := a[:0] + for i, x := range a { + if i == 0 || x != a[i-1] { + z = append(z, x) + } + } + return z +} diff --git a/problems/025-seven-matchers/solutions/javascript/main.js b/problems/025-seven-matchers/solutions/javascript/main.js new file mode 100644 index 0000000..1513e45 --- /dev/null +++ b/problems/025-seven-matchers/solutions/javascript/main.js @@ -0,0 +1,69 @@ +import * as std from "std"; +/** @param {string[]} a */ +function dedupSorted(a) { + let size = 0; + for (const value of a) { + if (size === 0 || a[size - 1] !== value) a[size++] = value; + } + a.length = size; +} +/** @param {string[]} values */ +function radixSort(values) { + /** @type {string[]} */ + const scratch = new Array(values.length); + for (let position = 29; position >= 0; position--) { + /** @type {number[]} */ + const next = new Array(257).fill(0); + for (const value of values) { + const key = position < value.length ? value.charCodeAt(position) + 1 : 0; + next[key]++; + } + let offset = 0; + for (let key = 0; key < 257; key++) { + const count = next[key]; + next[key] = offset; + offset += count; + } + for (const value of values) { + const key = position < value.length ? value.charCodeAt(position) + 1 : 0; + scratch[next[key]++] = value; + } + for (let i = 0; i < values.length; i++) values[i] = scratch[i]; + } +} +const t = std.in.readAsString().trim().split(/\s+/); +let p = 0, q = +t[p++]; +const out = []; +while (q--) { + const k = t[p++], + n = +t[p++], + m = +t[p++], + eps = k === "FLOAT" ? BigInt(t[p++]) : 0n; + /** @type {string[]} */ + const a = t.slice(p, p += n); + /** @type {string[]} */ + const b = t.slice(p, p += m); + let ok = false; + if (k === "EXACT") ok = a.join("") === b.join(""); + else if (k === "LINES") { + while (a[a.length - 1] === "#") a.pop(); + while (b[b.length - 1] === "#") b.pop(); + ok = JSON.stringify(a) === JSON.stringify(b); + } else if (k === "TOKENS") ok = JSON.stringify(a) === JSON.stringify(b); + else if (k === "FLOAT") { + ok = n === m && a.every((x, i) => { + const d = BigInt(x) - BigInt(b[i]); + return (d < 0n ? -d : d) <= eps; + }); + } else { + radixSort(a); + radixSort(b); + if (k === "SET") { + dedupSorted(a); + dedupSorted(b); + } + ok = JSON.stringify(a) === JSON.stringify(b); + } + out.push(ok ? "ACCEPT" : "WRONG"); +} +std.out.puts(out.join("\n") + "\n"); diff --git a/problems/025-seven-matchers/solutions/python/main.py b/problems/025-seven-matchers/solutions/python/main.py new file mode 100644 index 0000000..b548443 --- /dev/null +++ b/problems/025-seven-matchers/solutions/python/main.py @@ -0,0 +1,61 @@ +import sys + + +def dedup_sorted(values): + out = [] + for value in values: + if not out or out[-1] != value: + out.append(value) + return out + + +def radix_sort(values): + scratch = [b""] * len(values) + for position in range(29, -1, -1): + next_index = [0] * 257 + for value in values: + key = value[position] + 1 if position < len(value) else 0 + next_index[key] += 1 + offset = 0 + for key, count in enumerate(next_index): + next_index[key] = offset + offset += count + for value in values: + key = value[position] + 1 if position < len(value) else 0 + scratch[next_index[key]] = value + next_index[key] += 1 + values, scratch = scratch, values + return values + + +t = iter(sys.stdin.buffer.read().split()) +q = int(next(t)) +out = [] +for _ in range(q): + k = next(t) + n = int(next(t)) + m = int(next(t)) + eps = int(next(t)) if k == b"FLOAT" else 0 + a = [next(t) for _ in range(n)] + b = [next(t) for _ in range(m)] + if k == b"EXACT": + ok = b"".join(a) == b"".join(b) + elif k == b"LINES": + while a and a[-1] == b"#": + a.pop() + while b and b[-1] == b"#": + b.pop() + ok = a == b + elif k == b"TOKENS": + ok = a == b + elif k == b"FLOAT": + ok = n == m and all(abs(int(x) - int(y)) <= eps for x, y in zip(a, b)) + else: + a = radix_sort(a) + b = radix_sort(b) + if k == b"SET": + a = dedup_sorted(a) + b = dedup_sorted(b) + ok = a == b + out.append("ACCEPT" if ok else "WRONG") +print("\n".join(out)) diff --git a/problems/025-seven-matchers/solutions/rust/main.rs b/problems/025-seven-matchers/solutions/rust/main.rs new file mode 100644 index 0000000..355a03d --- /dev/null +++ b/problems/025-seven-matchers/solutions/rust/main.rs @@ -0,0 +1,82 @@ +use std::io::{self, Read}; +fn radix_sort(values: Vec) -> Vec { + let mut order: Vec = (0..values.len()).collect(); + let mut scratch = vec![0; values.len()]; + for position in (0..30).rev() { + let mut next = [0usize; 257]; + for &index in &order { + let key = values[index] + .as_bytes() + .get(position) + .map_or(0, |byte| *byte as usize + 1); + next[key] += 1; + } + let mut offset = 0; + for entry in &mut next { + let count = *entry; + *entry = offset; + offset += count; + } + for &index in &order { + let key = values[index] + .as_bytes() + .get(position) + .map_or(0, |byte| *byte as usize + 1); + scratch[next[key]] = index; + next[key] += 1; + } + std::mem::swap(&mut order, &mut scratch); + } + let mut slots: Vec> = values.into_iter().map(Some).collect(); + order + .into_iter() + .map(|index| slots[index].take().unwrap()) + .collect() +} +fn main() { + let mut s = String::new(); + io::stdin().read_to_string(&mut s).unwrap(); + let mut t = s.split_whitespace(); + let q: usize = t.next().unwrap().parse().unwrap(); + let mut out = String::new(); + for _ in 0..q { + let k = t.next().unwrap(); + let n: usize = t.next().unwrap().parse().unwrap(); + let m: usize = t.next().unwrap().parse().unwrap(); + let eps: i128 = if k == "FLOAT" { + t.next().unwrap().parse().unwrap() + } else { + 0 + }; + let mut a: Vec = (0..n).map(|_| t.next().unwrap().to_string()).collect(); + let mut b: Vec = (0..m).map(|_| t.next().unwrap().to_string()).collect(); + let ok = if k == "EXACT" { + a.concat() == b.concat() + } else if k == "LINES" { + while a.last().is_some_and(|x| x == "#") { + a.pop(); + } + while b.last().is_some_and(|x| x == "#") { + b.pop(); + } + a == b + } else if k == "TOKENS" { + a == b + } else if k == "FLOAT" { + n == m + && a.iter().zip(&b).all(|(x, y)| { + (x.parse::().unwrap() - y.parse::().unwrap()).abs() <= eps + }) + } else { + a = radix_sort(a); + b = radix_sort(b); + if k == "SET" { + a.dedup(); + b.dedup(); + } + a == b + }; + out += if ok { "ACCEPT\n" } else { "WRONG\n" } + } + print!("{out}") +} diff --git a/problems/025-seven-matchers/solutions/typescript/main.ts b/problems/025-seven-matchers/solutions/typescript/main.ts new file mode 100644 index 0000000..3361ea5 --- /dev/null +++ b/problems/025-seven-matchers/solutions/typescript/main.ts @@ -0,0 +1,63 @@ +import * as std from "std"; +function dedupSorted(a: string[]) { + let size = 0; + for (const value of a) { + if (size === 0 || a[size - 1] !== value) a[size++] = value; + } + a.length = size; +} +function radixSort(values: string[]) { + const scratch: string[] = new Array(values.length); + for (let position = 29; position >= 0; position--) { + const next: number[] = new Array(257).fill(0); + for (const value of values) { + const key = position < value.length ? value.charCodeAt(position) + 1 : 0; + next[key]++; + } + let offset = 0; + for (let key = 0; key < 257; key++) { + const count = next[key]; + next[key] = offset; + offset += count; + } + for (const value of values) { + const key = position < value.length ? value.charCodeAt(position) + 1 : 0; + scratch[next[key]++] = value; + } + for (let i = 0; i < values.length; i++) values[i] = scratch[i]; + } +} +const t = std.in.readAsString().trim().split(/\s+/); +let p = 0, q = +t[p++]; +const out: string[] = []; +while (q--) { + const k = t[p++], + n = +t[p++], + m = +t[p++], + eps = k === "FLOAT" ? BigInt(t[p++]) : 0n, + a = t.slice(p, p += n), + b = t.slice(p, p += m); + let ok = false; + if (k === "EXACT") ok = a.join("") === b.join(""); + else if (k === "LINES") { + while (a[a.length - 1] === "#") a.pop(); + while (b[b.length - 1] === "#") b.pop(); + ok = JSON.stringify(a) === JSON.stringify(b); + } else if (k === "TOKENS") ok = JSON.stringify(a) === JSON.stringify(b); + else if (k === "FLOAT") { + ok = n === m && a.every((x, i) => { + const d = BigInt(x) - BigInt(b[i]); + return (d < 0n ? -d : d) <= eps; + }); + } else { + radixSort(a); + radixSort(b); + if (k === "SET") { + dedupSorted(a); + dedupSorted(b); + } + ok = JSON.stringify(a) === JSON.stringify(b); + } + out.push(ok ? "ACCEPT" : "WRONG"); +} +std.out.puts(out.join("\n") + "\n"); diff --git a/problems/025-seven-matchers/statement.en.md b/problems/025-seven-matchers/statement.en.md new file mode 100644 index 0000000..db36d84 --- /dev/null +++ b/problems/025-seven-matchers/statement.en.md @@ -0,0 +1,130 @@ +# Seven Answer Matchers + +Answer validation in a WASM OJ cannot assume that “correct” always means two outputs are byte-for-byte identical. Some problems care about one complete string, some ignore set order, some preserve multiplicity, and others compare numeric tolerance or a collection of output files. + +The system therefore provides seven matchers so that every problem can select its exact judging semantics. Each query contains expected and actual token arrays and chooses one matcher. `n` and `m` may be zero; the corresponding data line is then empty. + +- `EXACT`: concatenate all tokens on each side **without separators**, then compare the two strings. +- `LINES`: token `#` represents an empty line. Remove all trailing `#` tokens from each array, then compare item by item. +- `TOKENS`: compare tokens item by item for exact equality. +- `FLOAT`: the arrays must have equal lengths. Tokens are signed integers, and the absolute difference of every pair must be at most the `eps` on the header line. +- `SET`: ignore order and multiplicity; compare the sets of distinct tokens. +- `MULTISET`: ignore order but preserve multiplicity. +- `FILESET`: every token has form `path@digest`. `path` is a lowercase alphanumeric string of length `1..20`, and `digest` is exactly eight lowercase hexadecimal characters, so a complete entry has length `10..29` bytes. Paths are unique on each side. Ignore file order; complete entries must match. + +Except for the additional `FLOAT` and `FILESET` restrictions, an ordinary token is an ASCII string of length `1..30` over `[A-Za-z0-9_#@.-]`. Every comparison is byte-exact and locale-independent. + +## Input + +The first line contains the number of queries `Q`. Each query occupies three lines: a header `type n m` (or `FLOAT n m eps`), an expected-token line, and an actual-token line. + +## Output + +For each query, output `ACCEPT` or `WRONG`. + +## Constraints + +- `1 ≤ Q ≤ 20000` +- The sum of `n+m` over all queries is at most `200000`. +- Total token length is at most `4000000`. +- `FLOAT` values lie in `[-10^18,10^18]` and `0≤eps≤10^18`. +- A `FILESET` path has length `1..20` and contains only lowercase alphanumeric characters. +- A `FILESET` digest has exactly eight lowercase hexadecimal characters; a complete entry has length `10..29` bytes. +- The full constraints apply to every official test. + +## Examples + + + +### Example One + +Input: + +```text +7 +EXACT 2 2 +ab c +a bc +LINES 3 1 +x # # +x +TOKENS 2 2 +a b +b a +FLOAT 3 3 2 +10 -5 7 +12 -6 4 +SET 3 2 +a a b +b a +MULTISET 3 2 +a a b +a b +FILESET 2 2 +a@00000001 b@00000002 +b@00000002 a@00000001 +``` + +Output: + +```text +ACCEPT +ACCEPT +WRONG +WRONG +ACCEPT +WRONG +ACCEPT +``` + +### Example Two + +Input: + +```text +3 +EXACT 0 0 + + +LINES 2 3 +# # +# # # +FLOAT 2 2 0 +-1 0 +-1 0 +``` + +Output: + +```text +ACCEPT +ACCEPT +ACCEPT +``` + +### Example Three + +Input: + +```text +3 +SET 0 1 + +x +MULTISET 3 3 +z z a +z a z +FILESET 1 1 +x@deadbeef +x@deadc0de +``` + +Output: + +```text +WRONG +ACCEPT +WRONG +``` + + diff --git a/problems/025-seven-matchers/statement.zh-TW.md b/problems/025-seven-matchers/statement.zh-TW.md new file mode 100644 index 0000000..57c159b --- /dev/null +++ b/problems/025-seven-matchers/statement.zh-TW.md @@ -0,0 +1,129 @@ +# 七種答案比對器 + +WASM OJ 的答案驗證不能假設「正確」永遠代表輸出文字逐 byte 相同。有些題目在意完整字串,有些允許忽略集合順序,有些要保留重複次數,還有些需要比較數值誤差或一組輸出檔案。 + +為了讓每題明確選擇自己的判定語意,系統提供七種 matcher。每個 query 都包含 expected 與 actual 兩個 token 陣列,並指定其中一種 matcher。`n`、`m` 可為 0;對應的資料行此時是空行。 + +- `EXACT`:將各自所有 token **不加分隔符**串接後比較。 +- `LINES`:token `#` 表示空行;先刪除陣列尾端所有 `#`,再逐項比較。 +- `TOKENS`:逐項完全相等。 +- `FLOAT`:兩陣列長度須相等;token 是帶號整數,且每對值的絕對差須不超過同一行給定的 `eps`。 +- `SET`:忽略順序與重複次數,比較不同 token 的集合。 +- `MULTISET`:忽略順序但保留重複次數。 +- `FILESET`:每個 token 形如 `path@digest`;`path` 是長度 1..20 的小寫英數字串,`digest` 恰為 8 個小寫十六進位字元,因此完整 entry 長度為 10..29 bytes。每一側 path 唯一。忽略檔案順序,完整 entry 必須相同。 + +除 FLOAT 與 FILESET 的額外限制外,一般 token 是長度 1..30 bytes 的 `[A-Za-z0-9_#@.-]` ASCII 字串。所有比較都是 byte-exact、無 locale 規則。 + +## 輸入 + +第一行 query 數 Q。每個 query 有三行:header `type n m`(FLOAT 為 `FLOAT n m eps`)、expected token 行、actual token 行。 + +- `1 ≤ Q ≤ 20000` +- 全部 query 的 `n+m` 不超過 200000,token 總長不超過 4000000 +- FLOAT 值在 `[-10^18,10^18]`,`0≤eps≤10^18` +- FILESET 的 path 長度為 1..20,只含小寫英數字;digest 恰為 8 個小寫十六進位字元,完整 entry 長度為 10..29 bytes + +## 輸出 + +每個 query 輸出 `ACCEPT` 或 `WRONG`。 + +## 限制 + +所有數量、字串格式與整數範圍均列於「輸入」段落;完整限制適用於每一筆正式測資。 + +## 範例 + + + +### 範例一 + +輸入: + +```text +7 +EXACT 2 2 +ab c +a bc +LINES 3 1 +x # # +x +TOKENS 2 2 +a b +b a +FLOAT 3 3 2 +10 -5 7 +12 -6 4 +SET 3 2 +a a b +b a +MULTISET 3 2 +a a b +a b +FILESET 2 2 +a@00000001 b@00000002 +b@00000002 a@00000001 +``` + +輸出: + +```text +ACCEPT +ACCEPT +WRONG +WRONG +ACCEPT +WRONG +ACCEPT +``` + +### 範例二 + +輸入: + +```text +3 +EXACT 0 0 + + +LINES 2 3 +# # +# # # +FLOAT 2 2 0 +-1 0 +-1 0 +``` + +輸出: + +```text +ACCEPT +ACCEPT +ACCEPT +``` + +### 範例三 + +輸入: + +```text +3 +SET 0 1 + +x +MULTISET 3 3 +z z a +z a z +FILESET 1 1 +x@deadbeef +x@deadc0de +``` + +輸出: + +```text +WRONG +ACCEPT +WRONG +``` + + diff --git a/problems/025-seven-matchers/tests/adversarial-linear-dedup.in b/problems/025-seven-matchers/tests/adversarial-linear-dedup.in new file mode 100644 index 0000000..9423e1d --- /dev/null +++ b/problems/025-seven-matchers/tests/adversarial-linear-dedup.in @@ -0,0 +1,10 @@ +3 +SET 12 11 +a a a a b c d e f g h i +a b b c c d e f g h i +SET 8 8 +a a b c d e f g +a b c d e f g h +MULTISET 6 5 +a a a b c d +a a b c d diff --git a/problems/025-seven-matchers/tests/adversarial-linear-dedup.out b/problems/025-seven-matchers/tests/adversarial-linear-dedup.out new file mode 100644 index 0000000..97a441c --- /dev/null +++ b/problems/025-seven-matchers/tests/adversarial-linear-dedup.out @@ -0,0 +1,3 @@ +ACCEPT +WRONG +WRONG diff --git a/problems/025-seven-matchers/tests/sample-01.in b/problems/025-seven-matchers/tests/sample-01.in new file mode 100644 index 0000000..bc58591 --- /dev/null +++ b/problems/025-seven-matchers/tests/sample-01.in @@ -0,0 +1,22 @@ +7 +EXACT 2 2 +ab c +a bc +LINES 3 1 +x # # +x +TOKENS 2 2 +a b +b a +FLOAT 3 3 2 +10 -5 7 +12 -6 4 +SET 3 2 +a a b +b a +MULTISET 3 2 +a a b +a b +FILESET 2 2 +a@00000001 b@00000002 +b@00000002 a@00000001 diff --git a/problems/025-seven-matchers/tests/sample-01.out b/problems/025-seven-matchers/tests/sample-01.out new file mode 100644 index 0000000..4126eaf --- /dev/null +++ b/problems/025-seven-matchers/tests/sample-01.out @@ -0,0 +1,7 @@ +ACCEPT +ACCEPT +WRONG +WRONG +ACCEPT +WRONG +ACCEPT diff --git a/problems/025-seven-matchers/tests/sample-02.in b/problems/025-seven-matchers/tests/sample-02.in new file mode 100644 index 0000000..6a35527 --- /dev/null +++ b/problems/025-seven-matchers/tests/sample-02.in @@ -0,0 +1,10 @@ +3 +EXACT 0 0 + + +LINES 2 3 +# # +# # # +FLOAT 2 2 0 +-1 0 +-1 0 diff --git a/problems/025-seven-matchers/tests/sample-02.out b/problems/025-seven-matchers/tests/sample-02.out new file mode 100644 index 0000000..7aca5bf --- /dev/null +++ b/problems/025-seven-matchers/tests/sample-02.out @@ -0,0 +1,3 @@ +ACCEPT +ACCEPT +ACCEPT diff --git a/problems/025-seven-matchers/tests/sample-03.in b/problems/025-seven-matchers/tests/sample-03.in new file mode 100644 index 0000000..dcff950 --- /dev/null +++ b/problems/025-seven-matchers/tests/sample-03.in @@ -0,0 +1,10 @@ +3 +SET 0 1 + +x +MULTISET 3 3 +z z a +z a z +FILESET 1 1 +x@deadbeef +x@deadc0de diff --git a/problems/025-seven-matchers/tests/sample-03.out b/problems/025-seven-matchers/tests/sample-03.out new file mode 100644 index 0000000..2c6b77c --- /dev/null +++ b/problems/025-seven-matchers/tests/sample-03.out @@ -0,0 +1,3 @@ +WRONG +ACCEPT +WRONG diff --git a/problems/025-seven-matchers/validator.py b/problems/025-seven-matchers/validator.py new file mode 100644 index 0000000..085d947 --- /dev/null +++ b/problems/025-seven-matchers/validator.py @@ -0,0 +1,41 @@ +#!/usr/bin/env python3 +import re, sys + +try: + l = sys.stdin.read().splitlines() + q = int(l[0]) + assert 1 <= q <= 20000 + at = 1 + cnt = chars = 0 + kinds = {"EXACT", "LINES", "TOKENS", "FLOAT", "SET", "MULTISET", "FILESET"} + for _ in range(q): + h = l[at].split() + at += 1 + assert h[0] in kinds and len(h) == (4 if h[0] == "FLOAT" else 3) + n, m = map(int, h[1:3]) + assert 0 <= n <= 200000 and 0 <= m <= 200000 + if h[0] == "FLOAT": + assert re.fullmatch(r"0|[1-9][0-9]*", h[3]) and int(h[3]) <= 10**18 + e = l[at].split() if l[at] else [] + a = l[at + 1].split() if l[at + 1] else [] + at += 2 + assert len(e) == n and len(a) == m + for side in (e, a): + if h[0] == "FLOAT": + assert all( + re.fullmatch(r"-?(0|[1-9][0-9]*)", x) and abs(int(x)) <= 10**18 + for x in side + ) + elif h[0] == "FILESET": + paths = [] + for x in side: + assert re.fullmatch(r"[a-z0-9]{1,20}@[0-9a-f]{8}", x) + paths.append(x.split("@")[0]) + assert len(paths) == len(set(paths)) + else: + assert all(re.fullmatch(r"[A-Za-z0-9_#@.\-]{1,30}", x) for x in side) + cnt += n + m + chars += sum(map(len, e + a)) + assert at == len(l) and cnt <= 200000 and chars <= 4000000 +except Exception: + sys.exit(1) diff --git a/problems/026-bidirectional-pipes/editorial.en.md b/problems/026-bidirectional-pipes/editorial.en.md new file mode 100644 index 0000000..fb80030 --- /dev/null +++ b/problems/026-bidirectional-pipes/editorial.en.md @@ -0,0 +1,24 @@ +# Editorial + +## Intuitive Approach + +Materialize each pipe as a byte queue of capacity `C` and push or pop `k` times per action. Total byte activity `B` may vastly exceed input size, while `C` can reach `10^18`, making `O(B)` time and `O(C)` space impossible. + +## Optimal Approach: Occupancy-Only Event Simulation + +Maintain only occupancies `ab` and `ba`, two program counters, and the outgoing-closed flags. Whether `W` or `R` can execute depends only on occupancy and `C`; on success, add or subtract `k` directly. In every round, call `tryStep` once for A and once for B in fixed order and track whether any action progressed. When a read lacks bytes and the peer's outgoing pipe is closed, report failure. Set a pipe closed when its program counter reaches the end. + +## Correctness Proof + +Induct over action attempts. Each occupancy equals the byte count in its actual pipe: a successful write adds `k`, a successful read subtracts `k`, and every other attempt leaves it unchanged. Since byte contents never affect any condition, these counters are indistinguishable from real queues for all future actions. Each closed flag is set exactly by `C` or natural process completion. Therefore `tryStep` classifies success, blocking, and failure exactly as specified. Calling it in the prescribed A-then-B order yields the correct final state and result. + +## Complexity + +Every successful action executes exactly once. Every progressing round completes at least one action, followed by at most one no-progress round. Time is `O(NA+NB)`, and storing all actions uses `O(NA+NB)` space. + +## Common Mistakes + +- Allowing `W` or `R` to complete partially. +- Skipping B after A blocks. +- Forgetting to close a pipe when its process ends naturally. +- Executing the other process after a failure in the same round. diff --git a/problems/026-bidirectional-pipes/editorial.zh-TW.md b/problems/026-bidirectional-pipes/editorial.zh-TW.md new file mode 100644 index 0000000..05754b3 --- /dev/null +++ b/problems/026-bidirectional-pipes/editorial.zh-TW.md @@ -0,0 +1,24 @@ +# 解題說明 + +## 直覺解 + +真的建立大小 C 的 byte queue,寫入/讀出 k 次。總 byte 動作量 B 可遠大於輸入長度,且 C 可達 10^18,因此時間 O(B)、空間 O(C) 不可行。 + +## 最佳解 + +只維護 `ab`、`ba` 兩個 occupancy、兩支 program counter 與 outgoing closed flags。W/R 的可執行條件只依 occupancy 和 C,成功時直接加減 k。每 round 依 A、B 固定順序呼叫一次 `tryStep`,記錄是否有進展;讀取不足且 peer outgoing closed 時回報 failure。program counter 到尾端時設 closed。 + +## 正確性證明 + +對每次嘗試歸納。occupancy 等於實際 pipe byte 數:成功 W 加 k、成功 R 減 k,其餘不變。因 byte 內容從不影響條件,計數器與真正 queue 對所有未來動作不可區分。closed flag 也恰在 C 或程序結束時設定。因此 tryStep 對成功、阻塞、failure 的判斷與規格一致;scheduler 又按指定順序呼叫,最終狀態與分類正確。 + +## 複雜度 + +每個成功動作只執行一次;有進展的 round 至少完成一個動作,最後最多再一個無進展 round。時間 O(NA+NB),儲存動作的空間 O(NA+NB)。 + +## 常見錯誤 + +- 把 W/R 拆成可部分完成的操作。 +- A 阻塞後不嘗試 B。 +- 程序自然結束時忘記關閉 pipe。 +- failure 後仍執行同 round 的另一程序。 diff --git a/problems/026-bidirectional-pipes/generator.py b/problems/026-bidirectional-pipes/generator.py new file mode 100644 index 0000000..8bcee5e --- /dev/null +++ b/problems/026-bidirectional-pipes/generator.py @@ -0,0 +1,30 @@ +#!/usr/bin/env python3 +import random, sys + +seed, index = map(int, sys.argv[1:]) +r = random.Random(seed * 31 + index) +C = r.randint(1, 20) +na = 8 + index % 7 +nb = 7 + (index * 3) % 8 + + +def prog(n): + out = [] + closed = False + for i in range(n): + t = r.randrange(5) + if not closed and t == 0: + out.append("C") + closed = True + elif not closed and t < 3: + out.append(f"W {r.randint(1,C)}") + else: + out.append(f"R {r.randint(1,C)}") + return out + + +a = prog(na) +b = prog(nb) +print(C, na, nb) +print(*a, sep="\n") +print(*b, sep="\n") diff --git a/problems/026-bidirectional-pipes/oracle.py b/problems/026-bidirectional-pipes/oracle.py new file mode 100644 index 0000000..69886dd --- /dev/null +++ b/problems/026-bidirectional-pipes/oracle.py @@ -0,0 +1,51 @@ +#!/usr/bin/env python3 +import sys + +l = sys.stdin.read().splitlines() +C, na, nb = map(int, l[0].split()) +acts = [l[1 : 1 + na], l[1 + na :]] +pc = [0, 0] +occ = [[], []] +closed = [na == 0, nb == 0] +steps = 0 + + +def one(who): + global steps + if pc[who] == len(acts[who]): + return "skip" + p = acts[who][pc[who]].split() + other = 1 - who + if p[0] == "W": + k = int(p[1]) + if len(occ[who]) + k > C: + return "block" + occ[who].extend([0] * k) + elif p[0] == "R": + k = int(p[1]) + if len(occ[other]) < k: + return "fail" if closed[other] else "block" + del occ[other][:k] + else: + closed[who] = True + pc[who] += 1 + steps += 1 + if pc[who] == len(acts[who]): + closed[who] = True + return "done" + + +while True: + if pc[0] == na and pc[1] == nb: + print("SUCCESS", steps, len(occ[0]), len(occ[1])) + break + progress = False + for w in (0, 1): + z = one(w) + if z == "fail": + print("FAIL", "A" if w == 0 else "B", steps, len(occ[0]), len(occ[1])) + raise SystemExit + progress |= z == "done" + if not progress: + print("DEADLOCK", steps, len(occ[0]), len(occ[1])) + break diff --git a/problems/026-bidirectional-pipes/problem.json b/problems/026-bidirectional-pipes/problem.json new file mode 100644 index 0000000..0d41851 --- /dev/null +++ b/problems/026-bidirectional-pipes/problem.json @@ -0,0 +1,146 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 26, + "slug": "bidirectional-pipes", + "title": { + "zh-TW": "雙向互動管線", + "en": "Bidirectional Interactive Pipes" + }, + "difficulty": "medium", + "tags": [ + "simulation", + "deadlock", + "state-machine" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-failure-stops-round", + "kind": "adversarial", + "input": "tests/adversarial-failure-stops-round.in", + "output": "tests/adversarial-failure-stops-round.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 9000000, + "memoryLimitBytes": 536870912 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 1000000, + "memoryLimitBytes": 402653184 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 350000, + "memoryLimitBytes": 268435456 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "逐 byte 模擬 pipe", + "en": "Per-Byte Pipe Simulation" + }, + "time": "O(B)", + "space": "O(C)", + "accepted": false + }, + { + "name": { + "zh-TW": "occupancy 事件模擬", + "en": "Occupancy-Only Event Simulation" + }, + "time": "O(NA+NB)", + "space": "O(NA+NB)", + "accepted": true + } + ] +} diff --git a/problems/026-bidirectional-pipes/solutions/c/main.c b/problems/026-bidirectional-pipes/solutions/c/main.c new file mode 100644 index 0000000..15d6e9a --- /dev/null +++ b/problems/026-bidirectional-pipes/solutions/c/main.c @@ -0,0 +1,74 @@ +#include +#include +#include +#include +typedef struct { + char t; + int64_t k; +} Act; +typedef struct { + Act *a; + int n, pc, closed; +} Prog; +static int64_t C, occ[2], steps; +static int one(Prog *p, int w) { + if (p[w].pc == p[w].n) + return 2; + Act x = p[w].a[p[w].pc]; + int o = 1 - w; + if (x.t == 'W') { + if (C - occ[w] < x.k) + return 0; + occ[w] += x.k; + } else if (x.t == 'R') { + if (occ[o] < x.k) + return p[o].closed ? -1 : 0; + occ[o] -= x.k; + } else + p[w].closed = 1; + p[w].pc++; + steps++; + if (p[w].pc == p[w].n) + p[w].closed = 1; + return 1; +} +int main(void) { + int na, nb; + if (scanf("%" SCNd64 " %d %d", &C, &na, &nb) != 3) + return 0; + Prog p[2] = {{calloc(na, sizeof(Act)), na, 0, na == 0}, + {calloc(nb, sizeof(Act)), nb, 0, nb == 0}}; + for (int w = 0; w < 2; w++) + for (int i = 0; i < p[w].n; i++) { + scanf(" %c", &p[w].a[i].t); + if (p[w].a[i].t != 'C') + scanf("%" SCNd64, &p[w].a[i].k); + } + for (;;) { + if (p[0].pc == na && p[1].pc == nb) { + printf("SUCCESS %" PRId64 " %" PRId64 " %" PRId64 "\n", steps, occ[0], + occ[1]); + break; + } + int progress = 0; + for (int w = 0; w < 2; w++) { + int z = one(p, w); + if (z < 0) { + printf("FAIL %c %" PRId64 " %" PRId64 " %" PRId64 "\n", w ? 'B' : 'A', + steps, occ[0], occ[1]); + free(p[0].a); + free(p[1].a); + return 0; + } + if (z == 1) + progress = 1; + } + if (!progress) { + printf("DEADLOCK %" PRId64 " %" PRId64 " %" PRId64 "\n", steps, occ[0], + occ[1]); + break; + } + } + free(p[0].a); + free(p[1].a); +} diff --git a/problems/026-bidirectional-pipes/solutions/cpp/main.cpp b/problems/026-bidirectional-pipes/solutions/cpp/main.cpp new file mode 100644 index 0000000..606a1e0 --- /dev/null +++ b/problems/026-bidirectional-pipes/solutions/cpp/main.cpp @@ -0,0 +1,69 @@ +#include +#include +#include +struct A { + char t; + std::int64_t k; +}; +int main() { + std::ios::sync_with_stdio(false); + std::cin.tie(nullptr); + std::int64_t C; + int n[2]; + std::cin >> C >> n[0] >> n[1]; + std::vector a[2]; + for (int w = 0; w < 2; w++) + for (int i = 0; i < n[w]; i++) { + A x; + std::cin >> x.t; + x.k = 0; + if (x.t != 'C') + std::cin >> x.k; + a[w].push_back(x); + } + int pc[2] = {}, closed[2] = {n[0] == 0, n[1] == 0}; + std::int64_t occ[2] = {}, steps = 0; + auto one = [&](int w) { + if (pc[w] == n[w]) + return 2; + A x = a[w][pc[w]]; + int o = 1 - w; + if (x.t == 'W') { + if (C - occ[w] < x.k) + return 0; + occ[w] += x.k; + } else if (x.t == 'R') { + if (occ[o] < x.k) + return closed[o] ? -1 : 0; + occ[o] -= x.k; + } else + closed[w] = 1; + pc[w]++; + steps++; + if (pc[w] == n[w]) + closed[w] = 1; + return 1; + }; + for (;;) { + if (pc[0] == n[0] && pc[1] == n[1]) { + std::cout << "SUCCESS " << steps << ' ' << occ[0] << ' ' << occ[1] + << '\n'; + break; + } + bool progress = false; + for (int w = 0; w < 2; w++) { + int z = one(w); + if (z < 0) { + std::cout << "FAIL " << (w ? 'B' : 'A') << ' ' << steps << ' ' << occ[0] + << ' ' << occ[1] << '\n'; + return 0; + } + progress |= z == 1; + } + if (!progress) { + std::cout << "DEADLOCK " << steps << ' ' << occ[0] << ' ' << occ[1] + << '\n'; + break; + } + } +} diff --git a/problems/026-bidirectional-pipes/solutions/go/main.go b/problems/026-bidirectional-pipes/solutions/go/main.go new file mode 100644 index 0000000..7851729 --- /dev/null +++ b/problems/026-bidirectional-pipes/solutions/go/main.go @@ -0,0 +1,84 @@ +package main + +import ( + "bufio" + "fmt" + "os" +) + +type A struct { + t byte + k int64 +} + +func main() { + in := bufio.NewReader(os.Stdin) + out := bufio.NewWriter(os.Stdout) + defer out.Flush() + var C int64 + var n [2]int + fmt.Fscan(in, &C, &n[0], &n[1]) + a := [2][]A{} + for w := 0; w < 2; w++ { + for i := 0; i < n[w]; i++ { + var t string + var k int64 + fmt.Fscan(in, &t) + if t != "C" { + fmt.Fscan(in, &k) + } + a[w] = append(a[w], A{t[0], k}) + } + } + pc := [2]int{} + closed := [2]bool{n[0] == 0, n[1] == 0} + occ := [2]int64{} + var steps int64 + for { + if pc == n { + fmt.Fprintln(out, "SUCCESS", steps, occ[0], occ[1]) + return + } + progress := false + for w := 0; w < 2; w++ { + if pc[w] == n[w] { + continue + } + x := a[w][pc[w]] + o := 1 - w + z := 0 + if x.t == 'W' { + if C-occ[w] >= x.k { + occ[w] += x.k + z = 1 + } + } else if x.t == 'R' { + if occ[o] >= x.k { + occ[o] -= x.k + z = 1 + } else if closed[o] { + z = -1 + } + } else { + closed[w] = true + z = 1 + } + if z < 0 { + fmt.Fprintln(out, "FAIL", string("AB"[w]), steps, occ[0], occ[1]) + return + } + if z == 1 { + pc[w]++ + steps++ + progress = true + if pc[w] == n[w] { + closed[w] = true + } + } + } + if !progress { + fmt.Fprintln(out, "DEADLOCK", steps, occ[0], occ[1]) + return + } + } +} diff --git a/problems/026-bidirectional-pipes/solutions/javascript/main.js b/problems/026-bidirectional-pipes/solutions/javascript/main.js new file mode 100644 index 0000000..033e1b0 --- /dev/null +++ b/problems/026-bidirectional-pipes/solutions/javascript/main.js @@ -0,0 +1,55 @@ +import * as std from "std"; +const x = std.in.readAsString().trim().split(/\s+/); +let p = 0, C = BigInt(x[p++]); +const n = [+x[p++], +x[p++]]; +/** @type {[string, bigint][][]} */ +const a = [[], []]; +for (let w = 0; w < 2; w++) { + for (let i = 0; i < n[w]; i++) { + const t = x[p++]; + a[w].push([t, t === "C" ? 0n : BigInt(x[p++])]); + } +} +const pc = [0, 0], closed = [n[0] === 0, n[1] === 0], occ = [0n, 0n]; +let steps = 0n, result = ""; +outer: for (;;) { + if (pc[0] === n[0] && pc[1] === n[1]) { + result = `SUCCESS ${steps} ${occ[0]} ${occ[1]}`; + break; + } + let progress = false; + for (let w = 0; w < 2; w++) { + if (pc[w] === n[w]) continue; + const [t, k] = a[w][pc[w]], o = 1 - w; + let z = 0; + if (t === "W") { + if (C - occ[w] >= k) { + occ[w] += k; + z = 1; + } + } else if (t === "R") { + if (occ[o] >= k) { + occ[o] -= k; + z = 1; + } else if (closed[o]) z = -1; + } else { + closed[w] = true; + z = 1; + } + if (z < 0) { + result = `FAIL ${"AB"[w]} ${steps} ${occ[0]} ${occ[1]}`; + break outer; + } + if (z) { + pc[w]++; + steps++; + progress = true; + if (pc[w] === n[w]) closed[w] = true; + } + } + if (!progress) { + result = `DEADLOCK ${steps} ${occ[0]} ${occ[1]}`; + break; + } +} +std.out.puts(result + "\n"); diff --git a/problems/026-bidirectional-pipes/solutions/python/main.py b/problems/026-bidirectional-pipes/solutions/python/main.py new file mode 100644 index 0000000..f84ac41 --- /dev/null +++ b/problems/026-bidirectional-pipes/solutions/python/main.py @@ -0,0 +1,49 @@ +import sys + +it = iter(sys.stdin.buffer.read().split()) +C = int(next(it)) +n = [int(next(it)), int(next(it))] +a = [[], []] +for w in range(2): + for _ in range(n[w]): + t = next(it) + a[w].append((t, 0 if t == b"C" else int(next(it)))) +pc = [0, 0] +closed = [not n[0], not n[1]] +occ = [0, 0] +steps = 0 +while True: + if pc == n: + print("SUCCESS", steps, *occ) + break + progress = False + for w in range(2): + if pc[w] == n[w]: + continue + t, k = a[w][pc[w]] + o = 1 - w + z = 0 + if t == b"W": + if C - occ[w] >= k: + occ[w] += k + z = 1 + elif t == b"R": + if occ[o] >= k: + occ[o] -= k + z = 1 + elif closed[o]: + z = -1 + else: + closed[w] = True + z = 1 + if z < 0: + print("FAIL", "AB"[w], steps, *occ) + raise SystemExit + if z: + pc[w] += 1 + steps += 1 + progress = True + closed[w] |= pc[w] == n[w] + if not progress: + print("DEADLOCK", steps, *occ) + break diff --git a/problems/026-bidirectional-pipes/solutions/rust/main.rs b/problems/026-bidirectional-pipes/solutions/rust/main.rs new file mode 100644 index 0000000..7c29012 --- /dev/null +++ b/problems/026-bidirectional-pipes/solutions/rust/main.rs @@ -0,0 +1,83 @@ +use std::io::{self, Read}; +#[derive(Clone, Copy)] +struct A { + t: u8, + k: i64, +} +fn main() { + let mut s = String::new(); + io::stdin().read_to_string(&mut s).unwrap(); + let mut it = s.split_whitespace(); + let c: i64 = it.next().unwrap().parse().unwrap(); + let n = [ + it.next().unwrap().parse::().unwrap(), + it.next().unwrap().parse::().unwrap(), + ]; + let mut a = [Vec::new(), Vec::new()]; + for w in 0..2 { + for _ in 0..n[w] { + let t = it.next().unwrap().as_bytes()[0]; + let k = if t == b'C' { + 0 + } else { + it.next().unwrap().parse().unwrap() + }; + a[w].push(A { t, k }) + } + } + let (mut pc, mut closed, mut occ, mut steps) = + ([0usize; 2], [n[0] == 0, n[1] == 0], [0i64; 2], 0i64); + loop { + if pc == n { + println!("SUCCESS {steps} {} {}", occ[0], occ[1]); + break; + } + let mut progress = false; + for w in 0..2 { + if pc[w] == n[w] { + continue; + } + let x = a[w][pc[w]]; + let o = 1 - w; + let z = if x.t == b'W' { + if c - occ[w] < x.k { + 0 + } else { + occ[w] += x.k; + 1 + } + } else if x.t == b'R' { + if occ[o] < x.k { + if closed[o] { -1 } else { 0 } + } else { + occ[o] -= x.k; + 1 + } + } else { + closed[w] = true; + 1 + }; + if z < 0 { + println!( + "FAIL {} {steps} {} {}", + if w == 0 { "A" } else { "B" }, + occ[0], + occ[1] + ); + return; + } + if z == 1 { + pc[w] += 1; + steps += 1; + progress = true; + if pc[w] == n[w] { + closed[w] = true + } + } + } + if !progress { + println!("DEADLOCK {steps} {} {}", occ[0], occ[1]); + break; + } + } +} diff --git a/problems/026-bidirectional-pipes/solutions/typescript/main.ts b/problems/026-bidirectional-pipes/solutions/typescript/main.ts new file mode 100644 index 0000000..102948a --- /dev/null +++ b/problems/026-bidirectional-pipes/solutions/typescript/main.ts @@ -0,0 +1,54 @@ +import * as std from "std"; +type Act = [string, bigint]; +const x = std.in.readAsString().trim().split(/\s+/); +let p = 0, C = BigInt(x[p++]); +const n = [+x[p++], +x[p++]], a: Act[][] = [[], []]; +for (let w = 0; w < 2; w++) { + for (let i = 0; i < n[w]; i++) { + const t = x[p++]; + a[w].push([t, t === "C" ? 0n : BigInt(x[p++])]); + } +} +const pc = [0, 0], closed = [n[0] === 0, n[1] === 0], occ = [0n, 0n]; +let steps = 0n, result = ""; +outer: for (;;) { + if (pc[0] === n[0] && pc[1] === n[1]) { + result = `SUCCESS ${steps} ${occ[0]} ${occ[1]}`; + break; + } + let progress = false; + for (let w = 0; w < 2; w++) { + if (pc[w] === n[w]) continue; + const [t, k] = a[w][pc[w]], o = 1 - w; + let z = 0; + if (t === "W") { + if (C - occ[w] >= k) { + occ[w] += k; + z = 1; + } + } else if (t === "R") { + if (occ[o] >= k) { + occ[o] -= k; + z = 1; + } else if (closed[o]) z = -1; + } else { + closed[w] = true; + z = 1; + } + if (z < 0) { + result = `FAIL ${"AB"[w]} ${steps} ${occ[0]} ${occ[1]}`; + break outer; + } + if (z) { + pc[w]++; + steps++; + progress = true; + if (pc[w] === n[w]) closed[w] = true; + } + } + if (!progress) { + result = `DEADLOCK ${steps} ${occ[0]} ${occ[1]}`; + break; + } +} +std.out.puts(result + "\n"); diff --git a/problems/026-bidirectional-pipes/statement.en.md b/problems/026-bidirectional-pipes/statement.en.md new file mode 100644 index 0000000..632b692 --- /dev/null +++ b/problems/026-bidirectional-pipes/statement.en.md @@ -0,0 +1,101 @@ +# Bidirectional Interactive Pipes + +An interactive problem requires a WASM OJ to drive the participant program and the interactor together. They exchange data through capacity-limited pipes. Unless blocking, closure, and scheduling order are modeled precisely, different hosts could produce different deadlock or failure verdicts for the same interaction. + +Call the two processes A and B. They communicate through `A→B` and `B→A`, two pipes that each have capacity `C`. Each process has a sequence of actions: + +- `W k`: atomically write to the outgoing pipe. The action completes only when at least `k` capacity remains; otherwise it blocks. +- `R k`: atomically read from the incoming pipe. The action completes only when at least `k` bytes are present. If fewer bytes are present and the incoming pipe is closed, it immediately fails; otherwise it blocks. +- `C`: close this process's outgoing pipe and complete. Each process has at most one `C`, and no `W` follows it. + +When a process finishes its final action, its outgoing pipe also closes automatically. Actions depend only on byte counts; byte contents are irrelevant. + +### Deterministic Scheduler + +To make the simulation reproducible, the scheduler uses fixed rounds: attempt A's next action once, then B's next action once. Skip a process that is already finished. A blocked attempt changes no state, but the other process is still attempted. If a read definitely produces `FAILURE`, stop immediately and do not attempt the other process in that round. + +If both processes finish, the result is `SUCCESS`. If one complete round finishes no action and causes no `FAILURE`, the result is `DEADLOCK`. Both pipes are initially empty. A process with an empty action sequence is already finished initially and has its outgoing pipe closed. + +## Input + +The first line contains `C NA NB`, followed by `NA` actions for A and `NB` actions for B. + +## Output + +Output exactly one of: + +- `SUCCESS steps ab ba` +- `DEADLOCK steps ab ba` +- `FAIL A steps ab ba` +- `FAIL B steps ab ba` + +`steps` is the number of actions completed before stopping. `ab` and `ba` are the final occupancies of the two pipes. + +## Constraints + +- `1 ≤ C ≤ 10^18` +- `0 ≤ NA,NB ≤ 200000` +- `1 ≤ NA+NB ≤ 200000` +- `1 ≤ k ≤ C` +- The full constraints apply to every official test. + +## Examples + + + +### Example One + +Input: + +```text +5 3 3 +W 3 +R 2 +C +R 3 +W 2 +C +``` + +Output: + +```text +SUCCESS 6 0 0 +``` + +### Example Two + +Input: + +```text +3 2 2 +R 1 +C +R 1 +C +``` + +Output: + +```text +DEADLOCK 0 0 0 +``` + +### Example Three + +Input: + +```text +4 2 1 +C +R 1 +C +``` + +Output: + +```text +FAIL A 2 0 0 +``` + + diff --git a/problems/026-bidirectional-pipes/statement.zh-TW.md b/problems/026-bidirectional-pipes/statement.zh-TW.md new file mode 100644 index 0000000..5bb8d9e --- /dev/null +++ b/problems/026-bidirectional-pipes/statement.zh-TW.md @@ -0,0 +1,97 @@ +# 雙向互動管線 + +互動題要求 WASM OJ 同時驅動使用者程式與 interactor。兩邊透過有容量限制的 pipe 交換資料;如果只檢查各自的動作,卻沒有精確模擬阻塞、關閉與排程順序,就可能在不同 host 上得到不同的 deadlock 或 failure 判定。 + +將兩個程序記為 A、B,它們透過 `A→B` 與 `B→A` 兩條容量同為 `C` 的 pipe 溝通。每個程序有一串動作: + +- `W k`:原子寫入 outgoing pipe。只有剩餘容量至少 k 時才整個完成,否則阻塞。 +- `R k`:原子讀取 incoming pipe。只有已有至少 k bytes 時才完成。若不足且 incoming 已關閉,立刻 FAILURE;否則阻塞。 +- `C`:關閉自己的 outgoing pipe並完成。每個程序最多一個 C,C 後不會再有 W。 + +程序執行完最後一個動作時,其 outgoing pipe 也自動關閉。動作只影響 byte 數,byte 內容不重要。 + +## 確定性 scheduler + +為了讓模擬結果可重現,scheduler 使用固定 round:先嘗試 A 的下一動作一次,再嘗試 B 的下一動作一次。已完成的程序略過。某動作阻塞時,該次嘗試不改變任何狀態;另一程序仍會被嘗試。若某個讀取確定 `FAILURE`,立刻停止,該 round 不再嘗試另一程序。 + +若兩程序都完成,結果為 `SUCCESS`;若一個完整 round 沒完成任何動作且沒有 `FAILURE`,結果為 `DEADLOCK`。兩條 pipe 初始皆為空;空動作序列在初始狀態就已完成,並關閉自己的 outgoing pipe。 + +## 輸入 + +第一行 `C NA NB`,接著 NA 行 A 的動作,再接 NB 行 B 的動作。 + +- `1≤C≤10^18`,`0≤NA,NB≤200000`,`1≤NA+NB≤200000` +- `1≤k≤C` + +## 輸出 + +- `SUCCESS steps ab ba` +- `DEADLOCK steps ab ba` +- `FAIL A steps ab ba` 或 `FAIL B ...` + +`steps` 是停止前完成的動作數;`ab`、`ba` 是兩條 pipe 最終 occupancy。 + +## 限制 + +所有數量、字串格式與整數範圍均列於「輸入」段落;完整限制適用於每一筆正式測資。 + +## 範例 + + + +### 範例一 + +輸入: + +```text +5 3 3 +W 3 +R 2 +C +R 3 +W 2 +C +``` + +輸出: + +```text +SUCCESS 6 0 0 +``` + +### 範例二 + +輸入: + +```text +3 2 2 +R 1 +C +R 1 +C +``` + +輸出: + +```text +DEADLOCK 0 0 0 +``` + +### 範例三 + +輸入: + +```text +4 2 1 +C +R 1 +C +``` + +輸出: + +```text +FAIL A 2 0 0 +``` + + diff --git a/problems/026-bidirectional-pipes/tests/adversarial-failure-stops-round.in b/problems/026-bidirectional-pipes/tests/adversarial-failure-stops-round.in new file mode 100644 index 0000000..a9002d5 --- /dev/null +++ b/problems/026-bidirectional-pipes/tests/adversarial-failure-stops-round.in @@ -0,0 +1,4 @@ +5 1 2 +R 1 +C +R 1 diff --git a/problems/026-bidirectional-pipes/tests/adversarial-failure-stops-round.out b/problems/026-bidirectional-pipes/tests/adversarial-failure-stops-round.out new file mode 100644 index 0000000..3ad112f --- /dev/null +++ b/problems/026-bidirectional-pipes/tests/adversarial-failure-stops-round.out @@ -0,0 +1 @@ +FAIL A 1 0 0 diff --git a/problems/026-bidirectional-pipes/tests/sample-01.in b/problems/026-bidirectional-pipes/tests/sample-01.in new file mode 100644 index 0000000..38f13a3 --- /dev/null +++ b/problems/026-bidirectional-pipes/tests/sample-01.in @@ -0,0 +1,7 @@ +5 3 3 +W 3 +R 2 +C +R 3 +W 2 +C diff --git a/problems/026-bidirectional-pipes/tests/sample-01.out b/problems/026-bidirectional-pipes/tests/sample-01.out new file mode 100644 index 0000000..5b5ebce --- /dev/null +++ b/problems/026-bidirectional-pipes/tests/sample-01.out @@ -0,0 +1 @@ +SUCCESS 6 0 0 diff --git a/problems/026-bidirectional-pipes/tests/sample-02.in b/problems/026-bidirectional-pipes/tests/sample-02.in new file mode 100644 index 0000000..f729f97 --- /dev/null +++ b/problems/026-bidirectional-pipes/tests/sample-02.in @@ -0,0 +1,5 @@ +3 2 2 +R 1 +C +R 1 +C diff --git a/problems/026-bidirectional-pipes/tests/sample-02.out b/problems/026-bidirectional-pipes/tests/sample-02.out new file mode 100644 index 0000000..05379d4 --- /dev/null +++ b/problems/026-bidirectional-pipes/tests/sample-02.out @@ -0,0 +1 @@ +DEADLOCK 0 0 0 diff --git a/problems/026-bidirectional-pipes/tests/sample-03.in b/problems/026-bidirectional-pipes/tests/sample-03.in new file mode 100644 index 0000000..8dda58c --- /dev/null +++ b/problems/026-bidirectional-pipes/tests/sample-03.in @@ -0,0 +1,4 @@ +4 2 1 +C +R 1 +C diff --git a/problems/026-bidirectional-pipes/tests/sample-03.out b/problems/026-bidirectional-pipes/tests/sample-03.out new file mode 100644 index 0000000..742c481 --- /dev/null +++ b/problems/026-bidirectional-pipes/tests/sample-03.out @@ -0,0 +1 @@ +FAIL A 2 0 0 diff --git a/problems/026-bidirectional-pipes/validator.py b/problems/026-bidirectional-pipes/validator.py new file mode 100644 index 0000000..3aa5eae --- /dev/null +++ b/problems/026-bidirectional-pipes/validator.py @@ -0,0 +1,32 @@ +#!/usr/bin/env python3 +import re, sys + +try: + l = sys.stdin.read().splitlines() + h = l[0].split() + assert len(h) == 3 + C, na, nb = map(int, h) + assert ( + 1 <= C <= 10**18 + and 0 <= na <= 200000 + and 0 <= nb <= 200000 + and 1 <= na + nb <= 200000 + and len(l) == 1 + na + nb + ) + for seg in (l[1 : 1 + na], l[1 + na :]): + closed = False + for s in seg: + p = s.split() + if p[0] in ("W", "R"): + assert ( + len(p) == 2 + and re.fullmatch(r"[1-9][0-9]*", p[1]) + and int(p[1]) <= C + ) + if p[0] == "W": + assert not closed + else: + assert p == ["C"] and not closed + closed = True +except Exception: + sys.exit(1) diff --git a/problems/027-chunk-independent-random/editorial.en.md b/problems/027-chunk-independent-random/editorial.en.md new file mode 100644 index 0000000..38d54d7 --- /dev/null +++ b/problems/027-chunk-independent-random/editorial.en.md @@ -0,0 +1,26 @@ +# Editorial + +## Intuitive Approach + +Maintain a conventional PRNG and generate every byte from position 0 through each chunk endpoint. Total consumption `P` may reach `9×10^18`, so `O(P)` time is impossible. + +## Optimal Approach: Counter-Based Random Access + +The formula makes word `floor(x/8)` a pure function of the seed and counter, so any byte can be accessed in `O(1)`. Maintain the consumed position `pos`. A chunk of length `k` has endpoints `pos` and `pos+k-1`; call the byte function for both, then update `pos+=k`. + +Every intermediate multiplication must retain only the low 64 bits. C, C++, Rust, and Go use unsigned 64-bit wrapping; Python masks with `2^64-1` after every step; JavaScript and TypeScript use `bigint` and a mask. + +## Correctness Proof + +The byte function implements every equation defining one stream offset. The global conversion then uniquely selects startup or user stream according to `p> 30)) * 0xBF58476D1CE4E5B9) & MASK + word = ((word ^ (word >> 27)) * 0x94D049BB133111EB) & MASK + word ^= word >> 31 + for shift in range(0, 64, 8): + yield (word >> shift) & 255 + counter += 1 + + +startup = stream(startup_seed) +user = stream(user_seed) +position = 0 + +for length in lengths: + first = last = None + for _ in range(length): + last = next(startup) if position < startup_size else next(user) + if first is None: + first = last + position += 1 + print(first, last) diff --git a/problems/027-chunk-independent-random/problem.json b/problems/027-chunk-independent-random/problem.json new file mode 100644 index 0000000..6bc1f48 --- /dev/null +++ b/problems/027-chunk-independent-random/problem.json @@ -0,0 +1,146 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 27, + "slug": "chunk-independent-random", + "title": { + "zh-TW": "分塊無關的確定性亂數", + "en": "Chunk-Independent Deterministic Randomness" + }, + "difficulty": "hard", + "tags": [ + "random-access", + "bitwise", + "prng" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-direct-stream-boundaries", + "kind": "adversarial", + "input": "tests/adversarial-direct-stream-boundaries.in", + "output": "tests/adversarial-direct-stream-boundaries.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 7500000, + "memoryLimitBytes": 536870912 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 1000000, + "memoryLimitBytes": 402653184 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 400000, + "memoryLimitBytes": 268435456 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "產生所有先前 bytes", + "en": "Generate All Preceding Bytes" + }, + "time": "O(P)", + "space": "O(1)", + "accepted": false + }, + { + "name": { + "zh-TW": "counter-based random access", + "en": "Counter-Based Random Access" + }, + "time": "O(Q)", + "space": "O(1) auxiliary; O(Q) buffered I/O", + "accepted": true + } + ] +} diff --git a/problems/027-chunk-independent-random/solutions/c/main.c b/problems/027-chunk-independent-random/solutions/c/main.c new file mode 100644 index 0000000..ed94a41 --- /dev/null +++ b/problems/027-chunk-independent-random/solutions/c/main.c @@ -0,0 +1,27 @@ +#include +#include +#include +static unsigned byte_at(uint64_t s, uint64_t x) { + uint64_t z = s + UINT64_C(0x9e3779b97f4a7c15) * (x / 8 + 1); + z = (z ^ (z >> 30)) * UINT64_C(0xbf58476d1ce4e5b9); + z = (z ^ (z >> 27)) * UINT64_C(0x94d049bb133111eb); + z ^= z >> 31; + return (unsigned)((z >> (8 * (x % 8))) & 255); +} +int main(void) { + uint64_t a, b, S; + int q; + if (scanf("%" SCNu64 " %" SCNu64 " %" SCNu64 " %d", &a, &b, &S, &q) != 4) + return 0; + uint64_t pos = 0; + while (q--) { + uint64_t k; + scanf("%" SCNu64, &k); + uint64_t p[2] = {pos, pos + k - 1}; + unsigned v[2]; + for (int i = 0; i < 2; i++) + v[i] = p[i] < S ? byte_at(a, p[i]) : byte_at(b, p[i] - S); + printf("%u %u\n", v[0], v[1]); + pos += k; + } +} diff --git a/problems/027-chunk-independent-random/solutions/cpp/main.cpp b/problems/027-chunk-independent-random/solutions/cpp/main.cpp new file mode 100644 index 0000000..dd70812 --- /dev/null +++ b/problems/027-chunk-independent-random/solutions/cpp/main.cpp @@ -0,0 +1,25 @@ +#include +#include +unsigned at(std::uint64_t s, std::uint64_t x) { + std::uint64_t z = s + UINT64_C(0x9e3779b97f4a7c15) * (x / 8 + 1); + z = (z ^ (z >> 30)) * UINT64_C(0xbf58476d1ce4e5b9); + z = (z ^ (z >> 27)) * UINT64_C(0x94d049bb133111eb); + z ^= z >> 31; + return (z >> (8 * (x % 8))) & 255; +} +int main() { + std::ios::sync_with_stdio(false); + std::cin.tie(nullptr); + std::uint64_t a, b, S, pos = 0; + int q; + std::cin >> a >> b >> S >> q; + while (q--) { + std::uint64_t k; + std::cin >> k; + unsigned f = pos < S ? at(a, pos) : at(b, pos - S); + std::uint64_t p = pos + k - 1; + unsigned l = p < S ? at(a, p) : at(b, p - S); + std::cout << f << ' ' << l << '\n'; + pos += k; + } +} diff --git a/problems/027-chunk-independent-random/solutions/go/main.go b/problems/027-chunk-independent-random/solutions/go/main.go new file mode 100644 index 0000000..cfe25cb --- /dev/null +++ b/problems/027-chunk-independent-random/solutions/go/main.go @@ -0,0 +1,36 @@ +package main + +import ( + "bufio" + "fmt" + "os" +) + +func at(s, x uint64) uint64 { + z := s + 0x9e3779b97f4a7c15*(x/8+1) + z = (z ^ (z >> 30)) * 0xbf58476d1ce4e5b9 + z = (z ^ (z >> 27)) * 0x94d049bb133111eb + z ^= z >> 31 + return (z >> (8 * (x % 8))) & 255 +} +func main() { + in := bufio.NewReader(os.Stdin) + out := bufio.NewWriter(os.Stdout) + defer out.Flush() + var a, b, S uint64 + var q int + fmt.Fscan(in, &a, &b, &S, &q) + var p uint64 + get := func(x uint64) uint64 { + if x < S { + return at(a, x) + } + return at(b, x-S) + } + for ; q > 0; q-- { + var k uint64 + fmt.Fscan(in, &k) + fmt.Fprintln(out, get(p), get(p+k-1)) + p += k + } +} diff --git a/problems/027-chunk-independent-random/solutions/javascript/main.js b/problems/027-chunk-independent-random/solutions/javascript/main.js new file mode 100644 index 0000000..47a3365 --- /dev/null +++ b/problems/027-chunk-independent-random/solutions/javascript/main.js @@ -0,0 +1,29 @@ +import * as std from "std"; +const t = std.in.readAsString().trim().split(/\s+/); +let z = 0, + a = BigInt(t[z++]), + b = BigInt(t[z++]), + S = BigInt(t[z++]), + q = +t[z++], + p = 0n; +const M = (1n << 64n) - 1n; +/** + * @param {bigint} s + * @param {bigint} x + * @returns {bigint} + */ +function byte(s, x) { + let v = (s + 0x9e3779b97f4a7c15n * (x / 8n + 1n)) & M; + v = ((v ^ (v >> 30n)) * 0xbf58476d1ce4e5b9n) & M; + v = ((v ^ (v >> 27n)) * 0x94d049bb133111ebn) & M; + v ^= v >> 31n; + return (v >> (8n * (x % 8n))) & 255n; +} +/** @param {bigint} x @returns {bigint} */ +const at = (x) => x < S ? byte(a, x) : byte(b, x - S), out = []; +while (q--) { + const k = BigInt(t[z++]); + out.push(`${at(p)} ${at(p + k - 1n)}`); + p += k; +} +std.out.puts(out.join("\n") + "\n"); diff --git a/problems/027-chunk-independent-random/solutions/python/main.py b/problems/027-chunk-independent-random/solutions/python/main.py new file mode 100644 index 0000000..9c4e2b5 --- /dev/null +++ b/problems/027-chunk-independent-random/solutions/python/main.py @@ -0,0 +1,29 @@ +import sys + +t = iter(sys.stdin.buffer.read().split()) +a = int(next(t)) +b = int(next(t)) +S = int(next(t)) +q = int(next(t)) +M = (1 << 64) - 1 + + +def byte(s, x): + z = (s + 0x9E3779B97F4A7C15 * (x // 8 + 1)) & M + z = ((z ^ (z >> 30)) * 0xBF58476D1CE4E5B9) & M + z = ((z ^ (z >> 27)) * 0x94D049BB133111EB) & M + z ^= z >> 31 + return (z >> (8 * (x % 8))) & 255 + + +def at(x): + return byte(a, x) if x < S else byte(b, x - S) + + +p = 0 +out = [] +for _ in range(q): + k = int(next(t)) + out.append(f"{at(p)} {at(p+k-1)}") + p += k +print("\n".join(out)) diff --git a/problems/027-chunk-independent-random/solutions/rust/main.rs b/problems/027-chunk-independent-random/solutions/rust/main.rs new file mode 100644 index 0000000..1593e88 --- /dev/null +++ b/problems/027-chunk-independent-random/solutions/rust/main.rs @@ -0,0 +1,32 @@ +use std::io::{self, Read}; +fn byte(s: u64, x: u64) -> u64 { + let mut z = s.wrapping_add(0x9e3779b97f4a7c15u64.wrapping_mul(x / 8 + 1)); + z = (z ^ (z >> 30)).wrapping_mul(0xbf58476d1ce4e5b9); + z = (z ^ (z >> 27)).wrapping_mul(0x94d049bb133111eb); + z ^= z >> 31; + (z >> (8 * (x % 8))) & 255 +} +fn main() { + let mut s = String::new(); + io::stdin().read_to_string(&mut s).unwrap(); + let mut t = s.split_whitespace(); + let a = t.next().unwrap().parse().unwrap(); + let b = t.next().unwrap().parse().unwrap(); + let lim = t.next().unwrap().parse().unwrap(); + let q: usize = t.next().unwrap().parse().unwrap(); + let mut p = 0u64; + let at = |x| { + if x < lim { + byte(a, x) + } else { + byte(b, x - lim) + } + }; + let mut out = String::new(); + for _ in 0..q { + let k: u64 = t.next().unwrap().parse().unwrap(); + out += &format!("{} {}\n", at(p), at(p + k - 1)); + p += k + } + print!("{out}") +} diff --git a/problems/027-chunk-independent-random/solutions/typescript/main.ts b/problems/027-chunk-independent-random/solutions/typescript/main.ts new file mode 100644 index 0000000..698ec2b --- /dev/null +++ b/problems/027-chunk-independent-random/solutions/typescript/main.ts @@ -0,0 +1,24 @@ +import * as std from "std"; +const t = std.in.readAsString().trim().split(/\s+/); +let z = 0, + a = BigInt(t[z++]), + b = BigInt(t[z++]), + S = BigInt(t[z++]), + q = +t[z++], + p = 0n; +const M = (1n << 64n) - 1n; +function byte(s: bigint, x: bigint) { + let v = (s + 0x9e3779b97f4a7c15n * (x / 8n + 1n)) & M; + v = ((v ^ (v >> 30n)) * 0xbf58476d1ce4e5b9n) & M; + v = ((v ^ (v >> 27n)) * 0x94d049bb133111ebn) & M; + v ^= v >> 31n; + return (v >> (8n * (x % 8n))) & 255n; +} +const at = (x: bigint) => x < S ? byte(a, x) : byte(b, x - S), + out: string[] = []; +while (q--) { + const k = BigInt(t[z++]); + out.push(`${at(p)} ${at(p + k - 1n)}`); + p += k; +} +std.out.puts(out.join("\n") + "\n"); diff --git a/problems/027-chunk-independent-random/statement.en.md b/problems/027-chunk-independent-random/statement.en.md new file mode 100644 index 0000000..b5c3d8a --- /dev/null +++ b/problems/027-chunk-independent-random/statement.en.md @@ -0,0 +1,94 @@ +# Chunk-Independent Deterministic Randomness + +If `random_get` uses the host's random source directly, the same WASM OJ submission may be impossible to replay deterministically. Its result also cannot depend on how the runtime divides reads into chunks: regardless of the requested length, every global position must have one value that can be computed directly. + +The system divides the conceptual random sequence into two parts. Its first `S` bytes come from the startup stream. After that, the user stream begins at its own offset 0. The `Q` calls to `random_get` consume `k_i` bytes in order, with each call beginning where the previous one ended. + +To verify the endpoints after chunking, output the first and last byte returned by every call. A chunk may be enormous, so the bytes between those endpoints do not need to be generated. + +For a stream with seed `s`, the byte at offset `x` is defined as follows, with all arithmetic reduced modulo `2^64` after each operation: + +```text +z = s + 0x9e3779b97f4a7c15 * (floor(x/8) + 1) +z = (z xor (z >> 30)) * 0xbf58476d1ce4e5b9 +z = (z xor (z >> 27)) * 0x94d049bb133111eb +w = z xor (z >> 31) +byte(x) = (w >> (8 * (x mod 8))) & 255 +``` + +Shifts are unsigned logical shifts, and bytes within a word use little-endian order. For global position `p`, use the startup seed and offset `p` when `p + +### Example One + +Input: + +```text +0 1 10 4 +1 7 5 9 +``` + +Output: + +```text +175 175 +205 226 +244 2 +137 101 +``` + +### Example Two + +Input: + +```text +18446744073709551615 0 0 3 +8 1 16 +``` + +Output: + +```text +175 226 +244 244 +101 236 +``` + +### Example Three + +Input: + +```text +42 99 17 3 +16 2 15 +``` + +Output: + +```text +149 40 +82 227 +107 8 +``` + + diff --git a/problems/027-chunk-independent-random/statement.zh-TW.md b/problems/027-chunk-independent-random/statement.zh-TW.md new file mode 100644 index 0000000..e3dc340 --- /dev/null +++ b/problems/027-chunk-independent-random/statement.zh-TW.md @@ -0,0 +1,92 @@ +# 分塊無關的確定性亂數 + +`random_get` 若直接依賴 host 的亂數來源,同一份 WASM OJ submission 就可能無法 deterministic replay。我們也不能讓結果取決於 runtime 如何把讀取拆成 chunks:無論一次要求多少 bytes,每個全域位置都必須對應到唯一且可直接計算的值。 + +系統把概念上的亂數序列分成兩段。前 `S` bytes 來自 startup stream;之後改用 user stream,並從該 stream 的 offset 0 開始。`Q` 次 `random_get` 依序消耗 `k_i` bytes,前一次呼叫結束的位置就是下一次的起點。 + +為了檢查分塊後的端點,請輸出每次呼叫所得區塊的第一個與最後一個 byte。區塊可能非常長,因此題目只要求這兩個位置,而不要求產生中間的全部內容。 + +對 seed `s` 的 stream,offset x 的 byte 定義如下(所有算術先模 `2^64`): + +``` +z = s + 0x9e3779b97f4a7c15 * (floor(x/8) + 1) +z = (z xor (z >> 30)) * 0xbf58476d1ce4e5b9 +z = (z xor (z >> 27)) * 0x94d049bb133111eb +w = z xor (z >> 31) +byte(x) = (w >> (8 * (x mod 8))) & 255 +``` + +位移為 unsigned logical shift;word 內採 little-endian byte 順序。全域位置 `p` 若 `p + +### 範例一 + +輸入: + +```text +0 1 10 4 +1 7 5 9 +``` + +輸出: + +```text +175 175 +205 226 +244 2 +137 101 +``` + +### 範例二 + +輸入: + +```text +18446744073709551615 0 0 3 +8 1 16 +``` + +輸出: + +```text +175 226 +244 244 +101 236 +``` + +### 範例三 + +輸入: + +```text +42 99 17 3 +16 2 15 +``` + +輸出: + +```text +149 40 +82 227 +107 8 +``` + + diff --git a/problems/027-chunk-independent-random/tests/adversarial-direct-stream-boundaries.in b/problems/027-chunk-independent-random/tests/adversarial-direct-stream-boundaries.in new file mode 100644 index 0000000..7e5978b --- /dev/null +++ b/problems/027-chunk-independent-random/tests/adversarial-direct-stream-boundaries.in @@ -0,0 +1,2 @@ +18446744073709551615 0 5 5 +1 4 1 7 8 diff --git a/problems/027-chunk-independent-random/tests/adversarial-direct-stream-boundaries.out b/problems/027-chunk-independent-random/tests/adversarial-direct-stream-boundaries.out new file mode 100644 index 0000000..555cf20 --- /dev/null +++ b/problems/027-chunk-independent-random/tests/adversarial-direct-stream-boundaries.out @@ -0,0 +1,5 @@ +32 32 +44 119 +175 175 +205 226 +244 110 diff --git a/problems/027-chunk-independent-random/tests/sample-01.in b/problems/027-chunk-independent-random/tests/sample-01.in new file mode 100644 index 0000000..96ce258 --- /dev/null +++ b/problems/027-chunk-independent-random/tests/sample-01.in @@ -0,0 +1,2 @@ +0 1 10 4 +1 7 5 9 diff --git a/problems/027-chunk-independent-random/tests/sample-01.out b/problems/027-chunk-independent-random/tests/sample-01.out new file mode 100644 index 0000000..ba5b850 --- /dev/null +++ b/problems/027-chunk-independent-random/tests/sample-01.out @@ -0,0 +1,4 @@ +175 175 +205 226 +244 2 +137 101 diff --git a/problems/027-chunk-independent-random/tests/sample-02.in b/problems/027-chunk-independent-random/tests/sample-02.in new file mode 100644 index 0000000..1b662e6 --- /dev/null +++ b/problems/027-chunk-independent-random/tests/sample-02.in @@ -0,0 +1,2 @@ +18446744073709551615 0 0 3 +8 1 16 diff --git a/problems/027-chunk-independent-random/tests/sample-02.out b/problems/027-chunk-independent-random/tests/sample-02.out new file mode 100644 index 0000000..2ed652f --- /dev/null +++ b/problems/027-chunk-independent-random/tests/sample-02.out @@ -0,0 +1,3 @@ +175 226 +244 244 +101 236 diff --git a/problems/027-chunk-independent-random/tests/sample-03.in b/problems/027-chunk-independent-random/tests/sample-03.in new file mode 100644 index 0000000..7c0b24f --- /dev/null +++ b/problems/027-chunk-independent-random/tests/sample-03.in @@ -0,0 +1,2 @@ +42 99 17 3 +16 2 15 diff --git a/problems/027-chunk-independent-random/tests/sample-03.out b/problems/027-chunk-independent-random/tests/sample-03.out new file mode 100644 index 0000000..b5b7c6a --- /dev/null +++ b/problems/027-chunk-independent-random/tests/sample-03.out @@ -0,0 +1,3 @@ +149 40 +82 227 +107 8 diff --git a/problems/027-chunk-independent-random/validator.py b/problems/027-chunk-independent-random/validator.py new file mode 100644 index 0000000..90c40cc --- /dev/null +++ b/problems/027-chunk-independent-random/validator.py @@ -0,0 +1,15 @@ +#!/usr/bin/env python3 +import re, sys + +try: + l = sys.stdin.read().splitlines() + assert len(l) == 2 + h = l[0].split() + assert len(h) == 4 and all(re.fullmatch(r"0|[1-9][0-9]*", x) for x in h) + a, b, S, Q = map(int, h) + assert a < 2**64 and b < 2**64 and S <= 9 * 10**18 and 1 <= Q <= 200000 + p = l[1].split() + assert len(p) == Q and all(re.fullmatch(r"[1-9][0-9]*", x) for x in p) + assert sum(map(int, p)) <= 9 * 10**18 +except Exception: + sys.exit(1) diff --git a/problems/028-canonical-replay-bundle/editorial.en.md b/problems/028-canonical-replay-bundle/editorial.en.md new file mode 100644 index 0000000..8c89571 --- /dev/null +++ b/problems/028-canonical-replay-bundle/editorial.en.md @@ -0,0 +1,37 @@ +# Editorial + +## Intuitive Approach + +Check the three local conditions first, then scan all blobs from the beginning for every reference. This preserves the required error-phase order, but the repeated searches take `O(BR)` time in the worst case. + +## Optimal Approach: Canonical Merge + +Check the phases in their prescribed order and stop immediately when a phase fails: + +1. scan adjacent blob digests for the first non-increasing position; +2. scan blob records for the first length mismatch; +3. scan adjacent reference digests for the first non-increasing position. + +After these checks, both digest sequences are strictly sorted. Use two pointers to verify references against blobs. If the blob digest is smaller, advance the blob pointer. If the digests match, advance both pointers. If the blob digest is larger, or the blobs are exhausted, the current 1-indexed reference is the first missing one. + +Perform this verification merge without summing lengths. Only after every reference is known to exist, run a second merge and add the actual length at each match. This matters because the bound on `total` is guaranteed only for valid bundles; an invalid bundle could otherwise overflow a 64-bit accumulator before its missing reference is discovered. + +## Correctness Proof + +Each of the first three scans examines records from left to right, so it reports the smallest invalid position in its phase. A later phase is entered only after every earlier phase passes, hence the mandated phase priority is respected. + +During a merge, a blob digest smaller than the current reference cannot match that reference or any earlier one, so discarding it is safe. Equal digests give the unique match because both sequences are strictly increasing. If the next blob is larger than the reference, every later blob is larger as well, so that reference is missing. Thus the first merge accepts exactly when every reference exists and reports the smallest missing reference otherwise. + +Once the first merge succeeds, the bundle satisfies all four conditions. The second merge visits the unique blob matching each reference and no unreferenced blob, so its sum is exactly the required `total`. Therefore the algorithm always produces the specified output. + +## Complexity + +Every pointer advances at most once per merge. The total running time is `O(B + R)`, and storing the input uses `O(B + R)` space. A streaming implementation can reduce the auxiliary storage to `O(B)`. + +## Common Mistakes + +- Reporting a length mismatch before a higher-priority blob-order error. +- Checking only that adjacent digests differ and accidentally accepting descending order. +- Reporting a blob position for `MISSING` instead of the reference position. +- Including unreferenced blobs in `total`. +- Accumulating before missing references have been ruled out, which can overflow on invalid input. diff --git a/problems/028-canonical-replay-bundle/editorial.zh-TW.md b/problems/028-canonical-replay-bundle/editorial.zh-TW.md new file mode 100644 index 0000000..8fc0785 --- /dev/null +++ b/problems/028-canonical-replay-bundle/editorial.zh-TW.md @@ -0,0 +1,25 @@ +# 解題說明 + +## 直覺解 + +先做三個局部 phase,再對每個 reference 從頭掃描所有 blobs;最壞 O(BR)。 + +## 最佳解 + +前三 phase 各線性掃描並嚴格依規定優先序提早輸出。通過後兩個 digest 陣列都嚴格排序;用雙指標:blob digest 小於 reference 就前進 blob,相等就前進兩者,大於或 blob 用盡代表該 reference 缺少。第一趟只驗證所有 reference 都存在;全部存在後才以第二趟 merge 累加 actual length。這避免最後才發現 missing 的無效輸入,先以不受合法 total 上限保證的 prefix 令 64-bit 累加溢位。 + +## 正確性證明 + +前三次掃描各找到其 phase 的最小違規位置,且只有前一 phase 完全合法才進入下一 phase,所以錯誤優先序正確。merge 時,當 blob 小於目前 reference,它不可能匹配目前或任何更早 reference,可安全丟棄;相等是唯一匹配;blob 大於 reference 時,排序性保證後方更大,故 reference 必缺。第一趟通過後 bundle 已合法,第二趟依相同唯一匹配累加的恰為全部引用 record 長度,且題目與 validator 此時保證 total 可用 64-bit 表示。 + +## 複雜度 + +每個指標只前進,總時間 O(B+R),空間 O(B+R)(保存輸入;可串流降至 O(B))。 + +## 常見錯誤 + +- 先回報 length 而忽略更高優先的 blob order。 +- 只檢查 digest 不相等,卻接受降序。 +- missing 時回報 blob 位置而非 reference 位置。 +- 把未引用 blob 也加入 total。 +- 在確認沒有 missing 前就累加,讓無效輸入的超大已命中 prefix 溢位。 diff --git a/problems/028-canonical-replay-bundle/generator.py b/problems/028-canonical-replay-bundle/generator.py new file mode 100644 index 0000000..bc10b4a --- /dev/null +++ b/problems/028-canonical-replay-bundle/generator.py @@ -0,0 +1,25 @@ +#!/usr/bin/env python3 +import random, sys + +seed, index = map(int, sys.argv[1:]) +r = random.Random(seed + index * 911) +b = 10 + index % 10 +vals = sorted(r.sample(range(16**8), b)) +blobs = [[f"{x:08x}", r.randrange(100), 0] for x in vals] +for x in blobs: + x[2] = x[1] +refs = sorted(f"{x:08x}" for x in r.sample(vals, r.randrange(b + 1))) +mode = index % 5 +if mode == 1 and b > 1: + blobs[1][0] = blobs[0][0] +if mode == 2: + blobs[0][2] += 1 +if mode == 3 and len(refs) > 1: + refs[1] = refs[0] +if mode == 4: + refs.append(f"{r.randrange(16**8):08x}") + refs.sort() +print(b, len(refs)) +[print(*x) for x in blobs] +if refs: + print(*refs, sep="\n") diff --git a/problems/028-canonical-replay-bundle/oracle.py b/problems/028-canonical-replay-bundle/oracle.py new file mode 100644 index 0000000..e8f511e --- /dev/null +++ b/problems/028-canonical-replay-bundle/oracle.py @@ -0,0 +1,30 @@ +#!/usr/bin/env python3 +import sys + +l = sys.stdin.read().splitlines() +b, r = map(int, l[0].split()) +blobs = [] +for s in l[1 : 1 + b]: + d, x, y = s.split() + blobs.append((d, int(x), int(y))) +refs = l[1 + b :] +for i in range(1, b): + if blobs[i][0] <= blobs[i - 1][0]: + print("INVALID BLOB_ORDER", i + 1) + raise SystemExit +for i, x in enumerate(blobs): + if x[1] != x[2]: + print("INVALID LENGTH", i + 1) + raise SystemExit +for i in range(1, r): + if refs[i] <= refs[i - 1]: + print("INVALID REF_ORDER", i + 1) + raise SystemExit +total = 0 +for i, d in enumerate(refs): + hit = next((x for x in blobs if x[0] == d), None) + if hit is None: + print("INVALID MISSING", i + 1) + raise SystemExit + total += hit[2] +print("VALID", total) diff --git a/problems/028-canonical-replay-bundle/problem.json b/problems/028-canonical-replay-bundle/problem.json new file mode 100644 index 0000000..8857b40 --- /dev/null +++ b/problems/028-canonical-replay-bundle/problem.json @@ -0,0 +1,158 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 28, + "slug": "canonical-replay-bundle", + "title": { + "zh-TW": "唯一的 Replay Bundle", + "en": "Canonical Replay Bundle" + }, + "difficulty": "medium", + "tags": [ + "two-pointers", + "canonicalization", + "validation" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-missing-after-large-prefix", + "kind": "adversarial", + "input": "tests/adversarial-missing-after-large-prefix.in", + "output": "tests/adversarial-missing-after-large-prefix.out" + }, + { + "id": "adversarial-phase-priority", + "kind": "adversarial", + "input": "tests/adversarial-phase-priority.in", + "output": "tests/adversarial-phase-priority.out" + }, + { + "id": "adversarial-total-boundary", + "kind": "adversarial", + "input": "tests/adversarial-total-boundary.in", + "output": "tests/adversarial-total-boundary.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 15000000, + "memoryLimitBytes": 536870912 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 3000000, + "memoryLimitBytes": 402653184 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 2000000, + "memoryLimitBytes": 268435456 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "每個 reference 掃描 blobs", + "en": "Scan all blobs for every reference" + }, + "time": "O(BR)", + "space": "O(1)", + "accepted": false + }, + { + "name": { + "zh-TW": "canonical merge", + "en": "Canonical merge" + }, + "time": "O(B+R)", + "space": "O(B+R)", + "accepted": true + } + ] +} diff --git a/problems/028-canonical-replay-bundle/solutions/c/main.c b/problems/028-canonical-replay-bundle/solutions/c/main.c new file mode 100644 index 0000000..e3d6802 --- /dev/null +++ b/problems/028-canonical-replay-bundle/solutions/c/main.c @@ -0,0 +1,56 @@ +#include +#include +#include +#include +#include +typedef struct { + char d[9]; + int64_t x, y; +} Blob; +int main(void) { + int b, r; + if (scanf("%d %d", &b, &r) != 2) + return 0; + Blob *a = malloc((size_t)b * sizeof(*a)); + char (*q)[9] = malloc((size_t)r * 9); + for (int i = 0; i < b; i++) + scanf("%8s %" SCNd64 " %" SCNd64, a[i].d, &a[i].x, &a[i].y); + for (int i = 0; i < r; i++) + scanf("%8s", q[i]); + for (int i = 1; i < b; i++) + if (strcmp(a[i].d, a[i - 1].d) <= 0) { + printf("INVALID BLOB_ORDER %d\n", i + 1); + goto end; + } + for (int i = 0; i < b; i++) + if (a[i].x != a[i].y) { + printf("INVALID LENGTH %d\n", i + 1); + goto end; + } + for (int i = 1; i < r; i++) + if (strcmp(q[i], q[i - 1]) <= 0) { + printf("INVALID REF_ORDER %d\n", i + 1); + goto end; + } + int j = 0; + for (int i = 0; i < r; i++) { + while (j < b && strcmp(a[j].d, q[i]) < 0) + j++; + if (j == b || strcmp(a[j].d, q[i])) { + printf("INVALID MISSING %d\n", i + 1); + goto end; + } + j++; + } + j = 0; + int64_t total = 0; + for (int i = 0; i < r; i++) { + while (strcmp(a[j].d, q[i]) < 0) + j++; + total += a[j++].y; + } + printf("VALID %" PRId64 "\n", total); +end: + free(a); + free(q); +} diff --git a/problems/028-canonical-replay-bundle/solutions/cpp/main.cpp b/problems/028-canonical-replay-bundle/solutions/cpp/main.cpp new file mode 100644 index 0000000..e415841 --- /dev/null +++ b/problems/028-canonical-replay-bundle/solutions/cpp/main.cpp @@ -0,0 +1,53 @@ +#include +#include +#include +#include +struct B { + std::string d; + std::int64_t x, y; +}; +int main() { + std::ios::sync_with_stdio(false); + std::cin.tie(nullptr); + int n, r; + std::cin >> n >> r; + std::vector a(n); + std::vector q(r); + for (auto &z : a) + std::cin >> z.d >> z.x >> z.y; + for (auto &z : q) + std::cin >> z; + for (int i = 1; i < n; i++) + if (a[i].d <= a[i - 1].d) { + std::cout << "INVALID BLOB_ORDER " << i + 1 << '\n'; + return 0; + } + for (int i = 0; i < n; i++) + if (a[i].x != a[i].y) { + std::cout << "INVALID LENGTH " << i + 1 << '\n'; + return 0; + } + for (int i = 1; i < r; i++) + if (q[i] <= q[i - 1]) { + std::cout << "INVALID REF_ORDER " << i + 1 << '\n'; + return 0; + } + int j = 0; + for (int i = 0; i < r; i++) { + while (j < n && a[j].d < q[i]) + j++; + if (j == n || a[j].d != q[i]) { + std::cout << "INVALID MISSING " << i + 1 << '\n'; + return 0; + } + j++; + } + j = 0; + std::int64_t total = 0; + for (int i = 0; i < r; i++) { + while (a[j].d < q[i]) + j++; + total += a[j++].y; + } + std::cout << "VALID " << total << '\n'; +} diff --git a/problems/028-canonical-replay-bundle/solutions/go/main.go b/problems/028-canonical-replay-bundle/solutions/go/main.go new file mode 100644 index 0000000..fa7ef0f --- /dev/null +++ b/problems/028-canonical-replay-bundle/solutions/go/main.go @@ -0,0 +1,67 @@ +package main + +import ( + "bufio" + "fmt" + "os" +) + +type B struct { + d string + x, y int64 +} + +func main() { + in := bufio.NewReader(os.Stdin) + out := bufio.NewWriter(os.Stdout) + defer out.Flush() + var n, r int + fmt.Fscan(in, &n, &r) + a := make([]B, n) + q := make([]string, r) + for i := range a { + fmt.Fscan(in, &a[i].d, &a[i].x, &a[i].y) + } + for i := range q { + fmt.Fscan(in, &q[i]) + } + for i := 1; i < n; i++ { + if a[i].d <= a[i-1].d { + fmt.Fprintln(out, "INVALID BLOB_ORDER", i+1) + return + } + } + for i, x := range a { + if x.x != x.y { + fmt.Fprintln(out, "INVALID LENGTH", i+1) + return + } + } + for i := 1; i < r; i++ { + if q[i] <= q[i-1] { + fmt.Fprintln(out, "INVALID REF_ORDER", i+1) + return + } + } + j := 0 + for i, d := range q { + for j < n && a[j].d < d { + j++ + } + if j == n || a[j].d != d { + fmt.Fprintln(out, "INVALID MISSING", i+1) + return + } + j++ + } + j = 0 + var total int64 + for _, d := range q { + for a[j].d < d { + j++ + } + total += a[j].y + j++ + } + fmt.Fprintln(out, "VALID", total) +} diff --git a/problems/028-canonical-replay-bundle/solutions/javascript/main.js b/problems/028-canonical-replay-bundle/solutions/javascript/main.js new file mode 100644 index 0000000..f985517 --- /dev/null +++ b/problems/028-canonical-replay-bundle/solutions/javascript/main.js @@ -0,0 +1,32 @@ +import * as std from "std"; +const t = std.in.readAsString().trim().split(/\s+/); +let p = 0, n = +t[p++], r = +t[p++]; +/** @type {[string, bigint, bigint][]} */ +const a = []; +for (let i = 0; i < n; i++) a.push([t[p++], BigInt(t[p++]), BigInt(t[p++])]); +const q = t.slice(p, p + r); +let ans = ""; +for (let i = 1; i < n && !ans; i++) { + if (a[i][0] <= a[i - 1][0]) ans = `INVALID BLOB_ORDER ${i + 1}`; +} +for (let i = 0; i < n && !ans; i++) { + if (a[i][1] !== a[i][2]) ans = `INVALID LENGTH ${i + 1}`; +} +for (let i = 1; i < r && !ans; i++) { + if (q[i] <= q[i - 1]) ans = `INVALID REF_ORDER ${i + 1}`; +} +let j = 0; +for (let i = 0; i < r && !ans; i++) { + while (j < n && a[j][0] < q[i]) j++; + if (j === n || a[j][0] !== q[i]) ans = `INVALID MISSING ${i + 1}`; + else j++; +} +let total = 0n; +if (!ans) { + j = 0; + for (let i = 0; i < r; i++) { + while (a[j][0] < q[i]) j++; + total += a[j++][2]; + } +} +std.out.puts((ans || `VALID ${total}`) + "\n"); diff --git a/problems/028-canonical-replay-bundle/solutions/python/main.py b/problems/028-canonical-replay-bundle/solutions/python/main.py new file mode 100644 index 0000000..0019f15 --- /dev/null +++ b/problems/028-canonical-replay-bundle/solutions/python/main.py @@ -0,0 +1,34 @@ +import sys + +t = iter(sys.stdin.buffer.read().split()) +n = int(next(t)) +r = int(next(t)) +a = [(next(t), int(next(t)), int(next(t))) for _ in range(n)] +q = [next(t) for _ in range(r)] +for i in range(1, n): + if a[i][0] <= a[i - 1][0]: + print("INVALID BLOB_ORDER", i + 1) + raise SystemExit +for i, x in enumerate(a): + if x[1] != x[2]: + print("INVALID LENGTH", i + 1) + raise SystemExit +for i in range(1, r): + if q[i] <= q[i - 1]: + print("INVALID REF_ORDER", i + 1) + raise SystemExit +j = 0 +for i, d in enumerate(q): + while j < n and a[j][0] < d: + j += 1 + if j == n or a[j][0] != d: + print("INVALID MISSING", i + 1) + raise SystemExit + j += 1 +j = total = 0 +for d in q: + while a[j][0] < d: + j += 1 + total += a[j][2] + j += 1 +print("VALID", total) diff --git a/problems/028-canonical-replay-bundle/solutions/rust/main.rs b/problems/028-canonical-replay-bundle/solutions/rust/main.rs new file mode 100644 index 0000000..63660f7 --- /dev/null +++ b/problems/028-canonical-replay-bundle/solutions/rust/main.rs @@ -0,0 +1,56 @@ +use std::io::{self, Read}; +fn main() { + let mut s = String::new(); + io::stdin().read_to_string(&mut s).unwrap(); + let mut t = s.split_whitespace(); + let n: usize = t.next().unwrap().parse().unwrap(); + let r: usize = t.next().unwrap().parse().unwrap(); + let mut a = Vec::new(); + for _ in 0..n { + a.push(( + t.next().unwrap(), + t.next().unwrap().parse::().unwrap(), + t.next().unwrap().parse::().unwrap(), + )) + } + let q: Vec<&str> = (0..r).map(|_| t.next().unwrap()).collect(); + for i in 1..n { + if a[i].0 <= a[i - 1].0 { + println!("INVALID BLOB_ORDER {}", i + 1); + return; + } + } + for (i, x) in a.iter().enumerate() { + if x.1 != x.2 { + println!("INVALID LENGTH {}", i + 1); + return; + } + } + for i in 1..r { + if q[i] <= q[i - 1] { + println!("INVALID REF_ORDER {}", i + 1); + return; + } + } + let mut j = 0; + for (i, d) in q.iter().enumerate() { + while j < n && a[j].0 < *d { + j += 1 + } + if j == n || a[j].0 != *d { + println!("INVALID MISSING {}", i + 1); + return; + } + j += 1 + } + j = 0; + let mut total = 0i64; + for d in &q { + while a[j].0 < *d { + j += 1 + } + total += a[j].2; + j += 1 + } + println!("VALID {total}") +} diff --git a/problems/028-canonical-replay-bundle/solutions/typescript/main.ts b/problems/028-canonical-replay-bundle/solutions/typescript/main.ts new file mode 100644 index 0000000..1dce163 --- /dev/null +++ b/problems/028-canonical-replay-bundle/solutions/typescript/main.ts @@ -0,0 +1,32 @@ +import * as std from "std"; +type B = [string, bigint, bigint]; +const t = std.in.readAsString().trim().split(/\s+/); +let p = 0, n = +t[p++], r = +t[p++]; +const a: B[] = []; +for (let i = 0; i < n; i++) a.push([t[p++], BigInt(t[p++]), BigInt(t[p++])]); +const q = t.slice(p, p + r); +let ans = ""; +for (let i = 1; i < n && !ans; i++) { + if (a[i][0] <= a[i - 1][0]) ans = `INVALID BLOB_ORDER ${i + 1}`; +} +for (let i = 0; i < n && !ans; i++) { + if (a[i][1] !== a[i][2]) ans = `INVALID LENGTH ${i + 1}`; +} +for (let i = 1; i < r && !ans; i++) { + if (q[i] <= q[i - 1]) ans = `INVALID REF_ORDER ${i + 1}`; +} +let j = 0; +for (let i = 0; i < r && !ans; i++) { + while (j < n && a[j][0] < q[i]) j++; + if (j === n || a[j][0] !== q[i]) ans = `INVALID MISSING ${i + 1}`; + else j++; +} +let total = 0n; +if (!ans) { + j = 0; + for (let i = 0; i < r; i++) { + while (a[j][0] < q[i]) j++; + total += a[j++][2]; + } +} +std.out.puts((ans || `VALID ${total}`) + "\n"); diff --git a/problems/028-canonical-replay-bundle/statement.en.md b/problems/028-canonical-replay-bundle/statement.en.md new file mode 100644 index 0000000..74afaec --- /dev/null +++ b/problems/028-canonical-replay-bundle/statement.en.md @@ -0,0 +1,93 @@ +# Canonical Replay Bundle + +For a WASM OJ execution to be replayed in another environment, its blobs and manifest references must be packaged as portable, verifiable text. If the same information can be represented with different orders or duplicates, two hosts may produce different bundle bytes even though they saved equivalent content, making replay and content addressing unreliable. + +The bundle must therefore have one canonical representation. A textual replay bundle contains `B` blob records followed by `R` manifest references. A blob record has the form `digest declared actual`; a reference contains only a digest. Each digest is a precomputed, collision-free, eight-character lowercase hexadecimal token. You do not need to implement hashing. + +A bundle is canonical only if all of the following conditions hold: + +1. blob digests are strictly increasing; +2. every blob's declared length equals its actual length; +3. reference digests are strictly increasing; +4. every reference digest occurs among the blobs. + +The validator must produce deterministic diagnostics. If the bundle is invalid, report only the first error phase in the order above. Within a phase, report the smallest 1-indexed record position. The possible forms are `INVALID BLOB_ORDER i`, `INVALID LENGTH i`, `INVALID REF_ORDER i`, and `INVALID MISSING i`. For an ordering error, `i` is the first record whose digest is not greater than the previous digest, so `i >= 2`. + +If the bundle is valid, output `VALID total`, where `total` is the sum of the actual lengths of all referenced blobs. Unreferenced blobs do not contribute. + +## Input + +The first line contains `B R`. The next `B` lines contain blob records, followed by `R` lines containing reference digests. + +## Output + +Output exactly one line in the format specified above. + +## Constraints + +- `0 <= B, R <= 200000` +- `B + R >= 1` +- Every length is in `[0, 10^18]`. +- For every valid bundle, `total <= 9 * 10^18`. + +The limits apply to every official test case. Error phases and record positions must follow the stated priority exactly. + +## Examples + + + +### Example One + +Input: + +```text +3 2 +00000001 5 5 +00000002 7 7 +0000000a 9 9 +00000001 +0000000a +``` + +Output: + +```text +VALID 14 +``` + +### Example Two + +Input: + +```text +2 1 +00000002 1 2 +00000001 5 5 +ffffffff +``` + +Output: + +```text +INVALID BLOB_ORDER 2 +``` + +### Example Three + +Input: + +```text +2 2 +00000001 3 3 +00000002 4 4 +00000001 +00000003 +``` + +Output: + +```text +INVALID MISSING 2 +``` + + diff --git a/problems/028-canonical-replay-bundle/statement.zh-TW.md b/problems/028-canonical-replay-bundle/statement.zh-TW.md new file mode 100644 index 0000000..5fc7f8c --- /dev/null +++ b/problems/028-canonical-replay-bundle/statement.zh-TW.md @@ -0,0 +1,91 @@ +# 唯一的 Replay Bundle + +一次 WASM OJ 執行若要能在其他環境 replay,就需要把它依賴的 blobs 與 manifest references 封裝成可攜、可驗證的文字資料。如果相同內容可以用不同排列或重複表示,兩台 host 即使保存相同資訊,也可能產生不同的 bundle bytes,讓重現與內容定址變得不可靠。 + +因此 bundle 必須採用唯一的 canonical 表示。一個文字化 replay bundle 先包含 `B` 筆 blob records,再包含 `R` 個 manifest references。blob 行為 `digest declared actual`;reference 行只有 digest。digest 是已計算完成且不碰撞的 8 位 lowercase hexadecimal token,本題不要求實作雜湊。 + +Canonical bundle 必須同時滿足: + +1. blob digest 嚴格遞增; +2. 每筆 declared length 等於 actual length; +3. reference digest 嚴格遞增; +4. 每個 reference 都能在 blobs 中找到。 + +驗證器必須提供 deterministic 診斷。若 bundle 無效,依上述 phase 順序只輸出第一種錯誤;同一 phase 取最小 1-indexed record 位置。錯誤格式為 `INVALID BLOB_ORDER i`、`INVALID LENGTH i`、`INVALID REF_ORDER i` 或 `INVALID MISSING i`。順序錯誤的位置 `i` 指第一個不大於前一筆的 record(所以 `i≥2`)。 + +若有效,輸出 `VALID total`,其中 `total` 是所有被 reference 的 blob actual length 總和;未引用 blob 不計。 + +## 輸入 + +第一行 `B R`,接著 B 行 blobs,再接 R 行 references。 + +- `0≤B,R≤200000`,`B+R≥1` +- length 在 `[0,10^18]`,合法 bundle 的 total 不超過 `9×10^18` + +## 輸出 + +依上述規格輸出一行。 + +## 限制 + +所有數量、字串格式與整數範圍均列於「輸入」段落;完整限制適用於每一筆正式測資。 + +## 範例 + + + +### 範例一 + +輸入: + +```text +3 2 +00000001 5 5 +00000002 7 7 +0000000a 9 9 +00000001 +0000000a +``` + +輸出: + +```text +VALID 14 +``` + +### 範例二 + +輸入: + +```text +2 1 +00000002 1 2 +00000001 5 5 +ffffffff +``` + +輸出: + +```text +INVALID BLOB_ORDER 2 +``` + +### 範例三 + +輸入: + +```text +2 2 +00000001 3 3 +00000002 4 4 +00000001 +00000003 +``` + +輸出: + +```text +INVALID MISSING 2 +``` + + diff --git a/problems/028-canonical-replay-bundle/tests/adversarial-missing-after-large-prefix.in b/problems/028-canonical-replay-bundle/tests/adversarial-missing-after-large-prefix.in new file mode 100644 index 0000000..45ce5c1 --- /dev/null +++ b/problems/028-canonical-replay-bundle/tests/adversarial-missing-after-large-prefix.in @@ -0,0 +1,22 @@ +10 11 +00000000 1000000000000000000 1000000000000000000 +00000001 1000000000000000000 1000000000000000000 +00000002 1000000000000000000 1000000000000000000 +00000003 1000000000000000000 1000000000000000000 +00000004 1000000000000000000 1000000000000000000 +00000005 1000000000000000000 1000000000000000000 +00000006 1000000000000000000 1000000000000000000 +00000007 1000000000000000000 1000000000000000000 +00000008 1000000000000000000 1000000000000000000 +00000009 1000000000000000000 1000000000000000000 +00000000 +00000001 +00000002 +00000003 +00000004 +00000005 +00000006 +00000007 +00000008 +00000009 +ffffffff diff --git a/problems/028-canonical-replay-bundle/tests/adversarial-missing-after-large-prefix.out b/problems/028-canonical-replay-bundle/tests/adversarial-missing-after-large-prefix.out new file mode 100644 index 0000000..ef53fa2 --- /dev/null +++ b/problems/028-canonical-replay-bundle/tests/adversarial-missing-after-large-prefix.out @@ -0,0 +1 @@ +INVALID MISSING 11 diff --git a/problems/028-canonical-replay-bundle/tests/adversarial-phase-priority.in b/problems/028-canonical-replay-bundle/tests/adversarial-phase-priority.in new file mode 100644 index 0000000..3b90e05 --- /dev/null +++ b/problems/028-canonical-replay-bundle/tests/adversarial-phase-priority.in @@ -0,0 +1,6 @@ +3 2 +00000001 1 2 +00000003 1 1 +00000002 1 1 +00000009 +00000008 diff --git a/problems/028-canonical-replay-bundle/tests/adversarial-phase-priority.out b/problems/028-canonical-replay-bundle/tests/adversarial-phase-priority.out new file mode 100644 index 0000000..4110452 --- /dev/null +++ b/problems/028-canonical-replay-bundle/tests/adversarial-phase-priority.out @@ -0,0 +1 @@ +INVALID BLOB_ORDER 3 diff --git a/problems/028-canonical-replay-bundle/tests/adversarial-total-boundary.in b/problems/028-canonical-replay-bundle/tests/adversarial-total-boundary.in new file mode 100644 index 0000000..b4a3d8b --- /dev/null +++ b/problems/028-canonical-replay-bundle/tests/adversarial-total-boundary.in @@ -0,0 +1,19 @@ +9 9 +00000000 1000000000000000000 1000000000000000000 +00000001 1000000000000000000 1000000000000000000 +00000002 1000000000000000000 1000000000000000000 +00000003 1000000000000000000 1000000000000000000 +00000004 1000000000000000000 1000000000000000000 +00000005 1000000000000000000 1000000000000000000 +00000006 1000000000000000000 1000000000000000000 +00000007 1000000000000000000 1000000000000000000 +00000008 1000000000000000000 1000000000000000000 +00000000 +00000001 +00000002 +00000003 +00000004 +00000005 +00000006 +00000007 +00000008 diff --git a/problems/028-canonical-replay-bundle/tests/adversarial-total-boundary.out b/problems/028-canonical-replay-bundle/tests/adversarial-total-boundary.out new file mode 100644 index 0000000..25fa5e6 --- /dev/null +++ b/problems/028-canonical-replay-bundle/tests/adversarial-total-boundary.out @@ -0,0 +1 @@ +VALID 9000000000000000000 diff --git a/problems/028-canonical-replay-bundle/tests/sample-01.in b/problems/028-canonical-replay-bundle/tests/sample-01.in new file mode 100644 index 0000000..21aef42 --- /dev/null +++ b/problems/028-canonical-replay-bundle/tests/sample-01.in @@ -0,0 +1,6 @@ +3 2 +00000001 5 5 +00000002 7 7 +0000000a 9 9 +00000001 +0000000a diff --git a/problems/028-canonical-replay-bundle/tests/sample-01.out b/problems/028-canonical-replay-bundle/tests/sample-01.out new file mode 100644 index 0000000..6f66cbc --- /dev/null +++ b/problems/028-canonical-replay-bundle/tests/sample-01.out @@ -0,0 +1 @@ +VALID 14 diff --git a/problems/028-canonical-replay-bundle/tests/sample-02.in b/problems/028-canonical-replay-bundle/tests/sample-02.in new file mode 100644 index 0000000..dd86893 --- /dev/null +++ b/problems/028-canonical-replay-bundle/tests/sample-02.in @@ -0,0 +1,4 @@ +2 1 +00000002 1 2 +00000001 5 5 +ffffffff diff --git a/problems/028-canonical-replay-bundle/tests/sample-02.out b/problems/028-canonical-replay-bundle/tests/sample-02.out new file mode 100644 index 0000000..55d79d6 --- /dev/null +++ b/problems/028-canonical-replay-bundle/tests/sample-02.out @@ -0,0 +1 @@ +INVALID BLOB_ORDER 2 diff --git a/problems/028-canonical-replay-bundle/tests/sample-03.in b/problems/028-canonical-replay-bundle/tests/sample-03.in new file mode 100644 index 0000000..f719278 --- /dev/null +++ b/problems/028-canonical-replay-bundle/tests/sample-03.in @@ -0,0 +1,5 @@ +2 2 +00000001 3 3 +00000002 4 4 +00000001 +00000003 diff --git a/problems/028-canonical-replay-bundle/tests/sample-03.out b/problems/028-canonical-replay-bundle/tests/sample-03.out new file mode 100644 index 0000000..404d09f --- /dev/null +++ b/problems/028-canonical-replay-bundle/tests/sample-03.out @@ -0,0 +1 @@ +INVALID MISSING 2 diff --git a/problems/028-canonical-replay-bundle/validator.py b/problems/028-canonical-replay-bundle/validator.py new file mode 100644 index 0000000..4417bdc --- /dev/null +++ b/problems/028-canonical-replay-bundle/validator.py @@ -0,0 +1,40 @@ +#!/usr/bin/env python3 +import re, sys + +try: + l = sys.stdin.read().splitlines() + h = l[0].split() + assert len(h) == 2 and all(re.fullmatch(r"0|[1-9][0-9]*", x) for x in h) + b, r = map(int, h) + assert 0 <= b <= 200000 and 0 <= r <= 200000 and b + r >= 1 and len(l) == 1 + b + r + blobs = [] + for s in l[1 : 1 + b]: + p = s.split() + assert len(p) == 3 and re.fullmatch(r"[0-9a-f]{8}", p[0]) + assert all( + re.fullmatch(r"0|[1-9][0-9]*", x) and int(x) <= 10**18 for x in p[1:] + ) + blobs.append((p[0], int(p[1]), int(p[2]))) + refs = l[1 + b :] + assert all(re.fullmatch(r"[0-9a-f]{8}", s) for s in refs) + + canonical = ( + all(blobs[i - 1][0] < blobs[i][0] for i in range(1, b)) + and all(declared == actual for _, declared, actual in blobs) + and all(refs[i - 1] < refs[i] for i in range(1, r)) + ) + if canonical: + at = 0 + total = 0 + for ref in refs: + while at < b and blobs[at][0] < ref: + at += 1 + if at == b or blobs[at][0] != ref: + canonical = False + break + total += blobs[at][2] + at += 1 + if canonical: + assert total <= 9 * 10**18 +except Exception: + sys.exit(1) diff --git a/problems/029-source-tree-evidence/editorial.en.md b/problems/029-source-tree-evidence/editorial.en.md new file mode 100644 index 0000000..74e94bd --- /dev/null +++ b/problems/029-source-tree-evidence/editorial.en.md @@ -0,0 +1,26 @@ +# Editorial + +## Intuitive Approach + +Insert each retained record into its position in an already sorted manifest. An insertion may shift the entire suffix, so reverse-sorted input takes `O(N^2)` operations in addition to reading the text. + +## Optimal Approach: Filter Then Sort + +For each record, exclude it exactly when `path == E` or when `path` starts with `E + "/"`. Including the slash in the second condition enforces the path-segment boundary and keeps paths such as `proof2` when `E` is `proof`. + +Store each retained record together with its path and unchanged output representation. Sort the retained records by bytewise path order, then emit them in that order. + +## Correctness Proof + +The filtering predicate is identical to the definition of the evidence subtree, so it excludes every record in that subtree and no record outside it. All input paths are distinct; therefore sorting the retained paths by byte order produces one unique strictly increasing sequence. Finally, the algorithm outputs the stored original record for every retained path, so it changes neither its type nor any associated field. Hence the emitted manifest is exactly the required canonical manifest. + +## Complexity + +Let `L` be the total number of input characters. Filtering costs `O(L)`. Sorting performs `O(N log N)` path comparisons, and storage is `O(N + L)`. In the comparison model, sorting arbitrary distinct ASCII paths has an `Omega(N log N)` comparison lower bound. + +## Common Mistakes + +- Using `startsWith(E)` without a segment boundary and incorrectly deleting `proof2`. +- Sorting by record type instead of path. +- Using locale-sensitive collation instead of byte order. +- Reconstructing records and losing the executable bit or symbolic-link target. diff --git a/problems/029-source-tree-evidence/editorial.zh-TW.md b/problems/029-source-tree-evidence/editorial.zh-TW.md new file mode 100644 index 0000000..4a6e12c --- /dev/null +++ b/problems/029-source-tree-evidence/editorial.zh-TW.md @@ -0,0 +1,24 @@ +# 解題說明 + +## 直覺解 + +逐筆把 record 插入目前已排序 manifest 的正確位置,需要搬移後綴,逆序輸入時 O(N²)。 + +## 最佳解 + +先用「path==E 或 path startsWith E+'/'」判斷排除項目,注意 segment 邊界。把其餘 record 連同原始輸出文字保存,以 path 使用 byte-order comparison sort,最後輸出。 + +## 正確性證明 + +filter 條件逐字等同題目對 evidence subtree 的定義,因此保留集合正確。所有 path 唯一,comparison sort 產生且只產生唯一的嚴格遞增排列;輸出保存的原 record,故除順序與指定排除外沒有欄位被改動。因此 manifest 正確且 canonical。 + +## 複雜度 + +令 L 為輸入總字元數。filter O(L),排序 O(N log N) 次比較,空間 O(N+L)。任意不同 ASCII path 的 comparison model 中,canonical 排序有 Ω(N log N) 下界。 + +## 常見錯誤 + +- 用單純 `startsWith(E)`,錯刪 `proof2`。 +- 依 record 類型而非 path 排序。 +- 使用 locale collation。 +- 重建輸出時遺失 executable 或 symlink target。 diff --git a/problems/029-source-tree-evidence/generator.py b/problems/029-source-tree-evidence/generator.py new file mode 100644 index 0000000..698140b --- /dev/null +++ b/problems/029-source-tree-evidence/generator.py @@ -0,0 +1,22 @@ +#!/usr/bin/env python3 +import random, sys + +seed, index = map(int, sys.argv[1:]) +r = random.Random(seed - index * 37) +n = 15 + index % 20 +E = "evidence" +rows = [] +for i in range(n): + path = (E + "/" if r.randrange(5) == 0 else "src/") + f"p{i}" + t = r.randrange(3) + if t == 0: + rows.append( + f"F {path} {r.randrange(2)} {r.randrange(1000)} {r.randrange(16**8):08x}" + ) + elif t == 1: + rows.append(f"L {path} target/{i}") + else: + rows.append(f"D {path}") +r.shuffle(rows) +print(n, E) +print(*rows, sep="\n") diff --git a/problems/029-source-tree-evidence/oracle.py b/problems/029-source-tree-evidence/oracle.py new file mode 100644 index 0000000..8010c85 --- /dev/null +++ b/problems/029-source-tree-evidence/oracle.py @@ -0,0 +1,14 @@ +#!/usr/bin/env python3 +import sys + +l = sys.stdin.read().splitlines() +n, E = l[0].split() +a = [] +for s in l[1:]: + path = s.split()[1] + if path != E and not path.startswith(E + "/"): + i = 0 + while i < len(a) and a[i].split()[1] < path: + i += 1 + a.insert(i, s) +sys.stdout.write(str(len(a)) + "\n" + ("\n".join(a) + "\n" if a else "")) diff --git a/problems/029-source-tree-evidence/problem.json b/problems/029-source-tree-evidence/problem.json new file mode 100644 index 0000000..9444df7 --- /dev/null +++ b/problems/029-source-tree-evidence/problem.json @@ -0,0 +1,146 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 29, + "slug": "source-tree-evidence", + "title": { + "zh-TW": "原始碼樹證據", + "en": "Source Tree Evidence" + }, + "difficulty": "medium", + "tags": [ + "sorting", + "canonicalization", + "paths" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-component-prefix-sort", + "kind": "adversarial", + "input": "tests/adversarial-component-prefix-sort.in", + "output": "tests/adversarial-component-prefix-sort.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 7000000, + "memoryLimitBytes": 1073741824 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 900000, + "memoryLimitBytes": 805306368 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 350000, + "memoryLimitBytes": 536870912 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "插入排序建立 manifest", + "en": "Build the manifest by insertion sort" + }, + "time": "O(N^2 + L)", + "space": "O(N + L)", + "accepted": false + }, + { + "name": { + "zh-TW": "filter 後 comparison sort", + "en": "Filter followed by comparison sort" + }, + "time": "O(N log N + L)", + "space": "O(N + L)", + "accepted": true + } + ] +} diff --git a/problems/029-source-tree-evidence/solutions/c/main.c b/problems/029-source-tree-evidence/solutions/c/main.c new file mode 100644 index 0000000..12f9f18 --- /dev/null +++ b/problems/029-source-tree-evidence/solutions/c/main.c @@ -0,0 +1,41 @@ +#include +#include +#include +typedef struct { + char path[121]; + char *line; +} R; +static int cmp(const void *a, const void *b) { + return strcmp(((const R *)a)->path, ((const R *)b)->path); +} +int main(void) { + int n; + char E[121], buf[512]; + if (scanf("%d %120s", &n, E) != 2) + return 0; + fgets(buf, sizeof(buf), stdin); + R *a = malloc((size_t)n * sizeof(*a)); + int m = 0; + size_t le = strlen(E); + for (int i = 0; i < n; i++) { + fgets(buf, sizeof(buf), stdin); + buf[strcspn(buf, "\r\n")] = 0; + char t; + char p[121]; + sscanf(buf, "%c %120s", &t, p); + if (!strcmp(p, E) || (!strncmp(p, E, le) && p[le] == '/')) + continue; + strcpy(a[m].path, p); + size_t z = strlen(buf) + 1; + a[m].line = malloc(z); + memcpy(a[m].line, buf, z); + m++; + } + qsort(a, m, sizeof(*a), cmp); + printf("%d\n", m); + for (int i = 0; i < m; i++) { + puts(a[i].line); + free(a[i].line); + } + free(a); +} diff --git a/problems/029-source-tree-evidence/solutions/cpp/main.cpp b/problems/029-source-tree-evidence/solutions/cpp/main.cpp new file mode 100644 index 0000000..f4e6770 --- /dev/null +++ b/problems/029-source-tree-evidence/solutions/cpp/main.cpp @@ -0,0 +1,30 @@ +#include +#include +#include +#include +struct R { + std::string p, line; +}; +int main() { + std::ios::sync_with_stdio(false); + std::cin.tie(nullptr); + int n; + std::string e, line; + std::cin >> n >> e; + std::getline(std::cin, line); + std::vector a; + while (n--) { + std::getline(std::cin, line); + std::string::size_type z = line.find(' ', 2); + std::string p = line.substr(2, z - 2); + if (p == e || (p.size() > e.size() && p.compare(0, e.size(), e) == 0 && + p[e.size()] == '/')) + continue; + a.push_back({p, line}); + } + std::sort(a.begin(), a.end(), + [](const R &x, const R &y) { return x.p < y.p; }); + std::cout << a.size() << '\n'; + for (auto &x : a) + std::cout << x.line << '\n'; +} diff --git a/problems/029-source-tree-evidence/solutions/go/main.go b/problems/029-source-tree-evidence/solutions/go/main.go new file mode 100644 index 0000000..420af95 --- /dev/null +++ b/problems/029-source-tree-evidence/solutions/go/main.go @@ -0,0 +1,36 @@ +package main + +import ( + "bufio" + "fmt" + "os" + "sort" + "strings" +) + +type R struct{ p, l string } + +func main() { + in := bufio.NewReader(os.Stdin) + out := bufio.NewWriter(os.Stdout) + defer out.Flush() + var n int + var e string + fmt.Fscan(in, &n, &e) + in.ReadString('\n') + a := make([]R, 0, n) + for ; n > 0; n-- { + line, _ := in.ReadString('\n') + line = strings.TrimRight(line, "\r\n") + p := strings.Fields(line)[1] + if p == e || strings.HasPrefix(p, e+"/") { + continue + } + a = append(a, R{p, line}) + } + sort.Slice(a, func(i, j int) bool { return a[i].p < a[j].p }) + fmt.Fprintln(out, len(a)) + for _, x := range a { + fmt.Fprintln(out, x.l) + } +} diff --git a/problems/029-source-tree-evidence/solutions/javascript/main.js b/problems/029-source-tree-evidence/solutions/javascript/main.js new file mode 100644 index 0000000..491b5ff --- /dev/null +++ b/problems/029-source-tree-evidence/solutions/javascript/main.js @@ -0,0 +1,12 @@ +import * as std from "std"; +const l = std.in.readAsString().trimEnd().split(/\r?\n/), + h = l[0].split(" "), + n = +h[0], + e = h[1], + a = []; +for (let i = 1; i <= n; i++) { + const p = l[i].split(" ")[1]; + if (p !== e && !p.startsWith(e + "/")) a.push([p, l[i]]); +} +a.sort((x, y) => x[0] < y[0] ? -1 : x[0] > y[0] ? 1 : 0); +std.out.puts([`${a.length}`, ...a.map((x) => x[1])].join("\n") + "\n"); diff --git a/problems/029-source-tree-evidence/solutions/python/main.py b/problems/029-source-tree-evidence/solutions/python/main.py new file mode 100644 index 0000000..8832267 --- /dev/null +++ b/problems/029-source-tree-evidence/solutions/python/main.py @@ -0,0 +1,13 @@ +import sys + +l = sys.stdin.buffer.read().splitlines() +n, E = l[0].split() +a = [] +for s in l[1:]: + p = s.split()[1] + if p != E and not p.startswith(E + b"/"): + a.append((p, s)) +a.sort() +sys.stdout.buffer.write( + str(len(a)).encode() + b"\n" + b"".join(s + b"\n" for _, s in a) +) diff --git a/problems/029-source-tree-evidence/solutions/rust/main.rs b/problems/029-source-tree-evidence/solutions/rust/main.rs new file mode 100644 index 0000000..cde8fc9 --- /dev/null +++ b/problems/029-source-tree-evidence/solutions/rust/main.rs @@ -0,0 +1,22 @@ +use std::io::{self, Read}; +fn main() { + let mut s = String::new(); + io::stdin().read_to_string(&mut s).unwrap(); + let mut l = s.lines(); + let h = l.next().unwrap().split_whitespace().collect::>(); + let n: usize = h[0].parse().unwrap(); + let e = h[1]; + let mut a = Vec::new(); + for line in l.take(n) { + let p = line.split_whitespace().nth(1).unwrap(); + if p == e || p.strip_prefix(e).is_some_and(|x| x.starts_with('/')) { + continue; + } + a.push((p, line)) + } + a.sort_by_key(|x| x.0); + println!("{}", a.len()); + for x in a { + println!("{}", x.1) + } +} diff --git a/problems/029-source-tree-evidence/solutions/typescript/main.ts b/problems/029-source-tree-evidence/solutions/typescript/main.ts new file mode 100644 index 0000000..08e5af5 --- /dev/null +++ b/problems/029-source-tree-evidence/solutions/typescript/main.ts @@ -0,0 +1,12 @@ +import * as std from "std"; +const l = std.in.readAsString().trimEnd().split(/\r?\n/), + h = l[0].split(" "), + n = +h[0], + e = h[1], + a: [string, string][] = []; +for (let i = 1; i <= n; i++) { + const p = l[i].split(" ")[1]; + if (p !== e && !p.startsWith(e + "/")) a.push([p, l[i]]); +} +a.sort((x, y) => x[0] < y[0] ? -1 : x[0] > y[0] ? 1 : 0); +std.out.puts([`${a.length}`, ...a.map((x) => x[1])].join("\n") + "\n"); diff --git a/problems/029-source-tree-evidence/statement.en.md b/problems/029-source-tree-evidence/statement.en.md new file mode 100644 index 0000000..5a588e3 --- /dev/null +++ b/problems/029-source-tree-evidence/statement.en.md @@ -0,0 +1,100 @@ +# Source Tree Evidence + +A reproducible WASM OJ build record needs a provenance manifest that describes the source tree compilation actually observed. The manifest must cover regular files, symbolic links, and tombstones for deleted items without depending on the order in which the tree happened to be scanned. + +The provenance evidence is itself written back into that tree. If the evidence directory were included in its own manifest, the content would depend recursively on itself, and generating one report could change the next. The designated evidence subtree must therefore be excluded completely when constructing the canonical manifest. + +The first line names the evidence root path `E`. Records have three forms: + +- `F path executable length digest` for a file; +- `L path target` for a symbolic link; +- `D path` for a tombstone representing a deleted item. + +Each digest is a precomputed eight-character lowercase hexadecimal token. All paths are normalized and pairwise distinct. Exclude a record if its path is exactly `E` or begins with `E/`. For example, when `E` is `proof`, `proof/a` is excluded but `proof2/a` is not. + +Sort all remaining records by strictly increasing UTF-8 bytes of `path` to obtain the unique order. The allowed input characters are ASCII, so this is ordinary ASCII lexicographic order. Every field other than record order must be reproduced exactly. + +## Input + +The first line contains `N E`. The next `N` lines contain records in one of the three formats above. + +## Output + +First output the number `M` of retained records. Then output the `M` retained records, unchanged, in canonical order. + +## Constraints + +- `1 <= N <= 200000` +- A path has length `1..120` and uses lowercase letters, digits, `_`, `-`, `.`, and `/`. +- A path neither starts nor ends with `/`, has no empty segment, and has no `.` or `..` segment. +- `E` follows the same path rules. +- A symbolic-link target is a nonempty token of length `1..120` using the same character set. +- `executable` is `0` or `1`. +- `0 <= length <= 10^18` + +## Examples + + + +### Example One + +Input: + +```text +5 .evidence +F src/main.c 1 12 deadbeef +D old.c +F .evidence/report 0 3 00000001 +L link src/main.c +F .evidence2/x 0 4 00000002 +``` + +Output: + +```text +4 +F .evidence2/x 0 4 00000002 +L link src/main.c +D old.c +F src/main.c 1 12 deadbeef +``` + +### Example Two + +Input: + +```text +3 proof +F proof 0 1 00000000 +F proof/a 0 2 00000001 +D proof/old +``` + +Output: + +```text +0 +``` + +### Example Three + +Input: + +```text +4 out +F out2/a 1 9 abcdef01 +L z a +D a +F out/x 0 2 12345678 +``` + +Output: + +```text +3 +D a +F out2/a 1 9 abcdef01 +L z a +``` + + diff --git a/problems/029-source-tree-evidence/statement.zh-TW.md b/problems/029-source-tree-evidence/statement.zh-TW.md new file mode 100644 index 0000000..2e29380 --- /dev/null +++ b/problems/029-source-tree-evidence/statement.zh-TW.md @@ -0,0 +1,99 @@ +# 原始碼樹證據 + +可重現的 WASM OJ 建置紀錄,需要用 provenance manifest 說明編譯實際看見的 source tree。manifest 必須涵蓋一般檔案、symbolic link 與已刪除項目的 tombstone,並且不受檔案被掃描到的先後順序影響。 + +不過 provenance evidence 本身也會寫回 tree。如果把 evidence 目錄再次收入自己的 manifest,內容就會遞迴依賴自身,每次產生證據都可能改變下一份證據。因此,產生 canonical manifest 時必須完整排除指定的 evidence subtree。 + +第一行給定 evidence 根路徑 E。record 有三種: + +- `F path executable length digest`:檔案; +- `L path target`:symbolic link; +- `D path`:已刪除項目的 tombstone。 + +digest 是已完成的 8 位小寫十六進位 token。所有 path 已 normalized、互不相同。若 record 的 path 恰等於 `E`,或以 `E/` 開頭,就排除;例如 `E=proof` 時 `proof/a` 被排除,但 `proof2/a` 不會。 + +其餘 record 依 path 的 UTF-8 bytes 嚴格遞增輸出,形成唯一順序。輸入字元限制在 ASCII,所以等價於 ASCII 字典序。輸出 record 的其他欄位完全保持不變。 + +## 輸入 + +第一行 `N E`,接著 N 行 records。 + +- `1≤N≤200000` +- path 長 1..120,由小寫英數、`_-.` 與 `/` 組成;不得以 `/` 開頭或結尾,不得有空、`.` 或 `..` segment +- E 也符合 path 規則;target 是長 1..120 的同字元集非空 token +- executable 為 0 或 1;`0≤length≤10^18` + +## 輸出 + +第一行輸出保留 record 數 M,再依 canonical 順序原樣輸出 M 行。 + +## 限制 + +所有數量、字串格式與整數範圍均列於「輸入」段落;完整限制適用於每一筆正式測資。 + +## 範例 + + + +### 範例一 + +輸入: + +```text +5 .evidence +F src/main.c 1 12 deadbeef +D old.c +F .evidence/report 0 3 00000001 +L link src/main.c +F .evidence2/x 0 4 00000002 +``` + +輸出: + +```text +4 +F .evidence2/x 0 4 00000002 +L link src/main.c +D old.c +F src/main.c 1 12 deadbeef +``` + +### 範例二 + +輸入: + +```text +3 proof +F proof 0 1 00000000 +F proof/a 0 2 00000001 +D proof/old +``` + +輸出: + +```text +0 +``` + +### 範例三 + +輸入: + +```text +4 out +F out2/a 1 9 abcdef01 +L z a +D a +F out/x 0 2 12345678 +``` + +輸出: + +```text +3 +D a +F out2/a 1 9 abcdef01 +L z a +``` + + diff --git a/problems/029-source-tree-evidence/tests/adversarial-component-prefix-sort.in b/problems/029-source-tree-evidence/tests/adversarial-component-prefix-sort.in new file mode 100644 index 0000000..351dec8 --- /dev/null +++ b/problems/029-source-tree-evidence/tests/adversarial-component-prefix-sort.in @@ -0,0 +1,8 @@ +7 proof +F proof2/a 0 1 00000000 +D proof +L proof/x target +F a 1 2 abcdef01 +D proofish +L z foo/bar +F proof/deep/x 0 0 ffffffff diff --git a/problems/029-source-tree-evidence/tests/adversarial-component-prefix-sort.out b/problems/029-source-tree-evidence/tests/adversarial-component-prefix-sort.out new file mode 100644 index 0000000..d02a345 --- /dev/null +++ b/problems/029-source-tree-evidence/tests/adversarial-component-prefix-sort.out @@ -0,0 +1,5 @@ +4 +F a 1 2 abcdef01 +F proof2/a 0 1 00000000 +D proofish +L z foo/bar diff --git a/problems/029-source-tree-evidence/tests/sample-01.in b/problems/029-source-tree-evidence/tests/sample-01.in new file mode 100644 index 0000000..2eb9137 --- /dev/null +++ b/problems/029-source-tree-evidence/tests/sample-01.in @@ -0,0 +1,6 @@ +5 .evidence +F src/main.c 1 12 deadbeef +D old.c +F .evidence/report 0 3 00000001 +L link src/main.c +F .evidence2/x 0 4 00000002 diff --git a/problems/029-source-tree-evidence/tests/sample-01.out b/problems/029-source-tree-evidence/tests/sample-01.out new file mode 100644 index 0000000..5507a8a --- /dev/null +++ b/problems/029-source-tree-evidence/tests/sample-01.out @@ -0,0 +1,5 @@ +4 +F .evidence2/x 0 4 00000002 +L link src/main.c +D old.c +F src/main.c 1 12 deadbeef diff --git a/problems/029-source-tree-evidence/tests/sample-02.in b/problems/029-source-tree-evidence/tests/sample-02.in new file mode 100644 index 0000000..37eb932 --- /dev/null +++ b/problems/029-source-tree-evidence/tests/sample-02.in @@ -0,0 +1,4 @@ +3 proof +F proof 0 1 00000000 +F proof/a 0 2 00000001 +D proof/old diff --git a/problems/029-source-tree-evidence/tests/sample-02.out b/problems/029-source-tree-evidence/tests/sample-02.out new file mode 100644 index 0000000..573541a --- /dev/null +++ b/problems/029-source-tree-evidence/tests/sample-02.out @@ -0,0 +1 @@ +0 diff --git a/problems/029-source-tree-evidence/tests/sample-03.in b/problems/029-source-tree-evidence/tests/sample-03.in new file mode 100644 index 0000000..9ec8a48 --- /dev/null +++ b/problems/029-source-tree-evidence/tests/sample-03.in @@ -0,0 +1,5 @@ +4 out +F out2/a 1 9 abcdef01 +L z a +D a +F out/x 0 2 12345678 diff --git a/problems/029-source-tree-evidence/tests/sample-03.out b/problems/029-source-tree-evidence/tests/sample-03.out new file mode 100644 index 0000000..dfd1ccc --- /dev/null +++ b/problems/029-source-tree-evidence/tests/sample-03.out @@ -0,0 +1,4 @@ +3 +D a +F out2/a 1 9 abcdef01 +L z a diff --git a/problems/029-source-tree-evidence/validator.py b/problems/029-source-tree-evidence/validator.py new file mode 100644 index 0000000..5f2380f --- /dev/null +++ b/problems/029-source-tree-evidence/validator.py @@ -0,0 +1,44 @@ +#!/usr/bin/env python3 +import re, sys + +pat = re.compile(r"[a-z0-9_.-]+(?:/[a-z0-9_.-]+)*") + + +def path(x): + return ( + pat.fullmatch(x) + and all(y not in (".", "..") for y in x.split("/")) + and len(x) <= 120 + ) + + +try: + l = sys.stdin.read().splitlines() + h = l[0].split() + assert len(h) == 2 + n = int(h[0]) + E = h[1] + assert 1 <= n <= 200000 and path(E) and len(l) == n + 1 + seen = set() + for s in l[1:]: + p = s.split() + assert ( + " ".join(p) == s + and p + and p[0] in ("F", "L", "D") + and len(p) == ({"F": 5, "L": 3, "D": 2}[p[0]]) + and path(p[1]) + and p[1] not in seen + ) + seen.add(p[1]) + if p[0] == "F": + assert ( + p[2] in ("0", "1") + and re.fullmatch(r"0|[1-9][0-9]*", p[3]) + and int(p[3]) <= 10**18 + and re.fullmatch(r"[0-9a-f]{8}", p[4]) + ) + if p[0] == "L": + assert re.fullmatch(r"[a-z0-9_./-]{1,120}", p[2]) +except Exception: + sys.exit(1) diff --git a/problems/030-cross-host-matrix/editorial.en.md b/problems/030-cross-host-matrix/editorial.en.md new file mode 100644 index 0000000..0853072 --- /dev/null +++ b/problems/030-cross-host-matrix/editorial.en.md @@ -0,0 +1,32 @@ +# Editorial + +## Intuitive Approach + +For every baseline path, linearly search the other field list, then search in the opposite direction for missing paths. A single large case can make this `O(T^2)`. + +## Optimal Approach: Merge Sorted Fields + +First compare the complete case-ID vectors. If they differ, emit `CASE_ORDER` immediately for that host. + +Otherwise, process corresponding cases in baseline order. Their field lists are already sorted, so merge them with two pointers. If one current path is smaller, it exists only on that side and is a difference. If the paths are equal, compare their values and advance both pointers. Appending the remaining suffix handles paths that exist on only one side. Processing cases and paths in this order directly produces the required output order. + +Only if every transcript matches, collect the `H` runtimes for each case, sort them, and select element `(H - 1) / 2` using integer division. + +## Correctness Proof + +Direct comparison of the case-ID vectors accepts exactly when both their lengths and every ordered ID agree, which proves the first-level classification. + +For a pair of field lists, maintain the invariant that every path before either pointer has been classified exactly once and that the smallest unclassified path is at one of the pointers. Taking the smaller path, or the common path when equal, classifies that path correctly and preserves the invariant. Thus the merge finds exactly the union of missing and unequal-valued paths without duplicates, in sorted order. Baseline case order then gives the full required difference order. + +If every host is `OK`, sorting the `H` runtimes and selecting zero-based index `floor((H - 1) / 2)` is exactly the defined lower median. Median lines are emitted only in this all-consistent case, so the complete output is correct. + +## Complexity + +Let `T` be the total number of case and field records, `D` the number of printed difference paths, and `C` the baseline case count. Shared fields are charged to `T`; a baseline-only field rescanned for different hosts produces a difference each time and is charged to `D`. Comparisons therefore take `O(T + D)`, and median sorting takes `O(CH log H)`. The reference implementations store the input and may buffer output, using `O(T + D + H)` space. The bound `D <= 200000` prevents valid output from growing impractically relative to the input. + +## Common Mistakes + +- Treating cases as a set and ignoring their order. +- Detecting changed values but missing paths present on only one side. +- Printing medians after any transcript mismatch. +- Taking the upper median when `H` is even. diff --git a/problems/030-cross-host-matrix/editorial.zh-TW.md b/problems/030-cross-host-matrix/editorial.zh-TW.md new file mode 100644 index 0000000..1b7047e --- /dev/null +++ b/problems/030-cross-host-matrix/editorial.zh-TW.md @@ -0,0 +1,26 @@ +# 解題說明 + +## 直覺解 + +對 baseline 每個 path,在另一側 field list 線性搜尋,反向再做一次以找 missing。單一大 case 可達 O(T²)。 + +## 最佳解 + +先比較 case id vector。相同時,對每對對應 case 的兩個已排序 field list 使用雙指標 merge:較小 path 只存在一側;相等時比較 value;較大則反向 missing。依 case 順序處理,自然得到規定的差異順序。 + +若完全一致,對每個 case 收集 H 個 runtime、排序並取 `(H-1)/2`。 + +## 正確性證明 + +case vector 直接比較恰判斷第一層契約。對 fields,merge 的循環不變量是:兩指標以前的所有 path 已恰好分類,且未處理部分的最小 path 位於兩指標之一;取較小者或共同者後分類必然正確且不重複。故輸出正是差異 path 聯集並具指定順序。全體 transcript 一致時,每 case 排序 runtime 後指定 index 正是 lower median。 + +## 複雜度 + +令 T 為輸入 fields 與 case records 總量、D 為輸出差異數、C 為 baseline case 數。共同 field 的掃描由 T 支付,只存在 baseline 一側而被各 host 重複掃描的 field 會各自成為一筆差異、由 D 支付,因此比較為 O(T+D);median 排序 O(CH log H)。目前 reference solutions 保存全部輸入,部分語言也緩衝輸出,故真實空間為 O(T+D+H)。題目保證 D≤200000,避免合法輸出相對輸入放大到不可執行的規模。 + +## 常見錯誤 + +- 把 case 當集合,忽略順序。 +- 只找 value 不同,漏掉只存在一側的 path。 +- transcript 不一致時仍輸出 median。 +- 偶數 host 取 upper median。 diff --git a/problems/030-cross-host-matrix/generator.py b/problems/030-cross-host-matrix/generator.py new file mode 100644 index 0000000..14f9474 --- /dev/null +++ b/problems/030-cross-host-matrix/generator.py @@ -0,0 +1,28 @@ +#!/usr/bin/env python3 +import random, sys + +seed, index = map(int, sys.argv[1:]) +r = random.Random(seed * 101 + index) +H = 3 + index % 3 +C = 4 + index % 5 +base = [] +for c in range(C): + base.append( + [f"c{c}", r.randrange(100), [(f"p{j}", f"v{r.randrange(6)}") for j in range(4)]] + ) +print(H) +for h in range(H): + cur = [[x, r.randrange(100), list(fs)] for x, _, fs in base] + mode = index % 5 + if h and mode == 1 and h == H - 1: + cur.reverse() + elif h and mode == 2 and h == H - 1: + cur[0][2][0] = (cur[0][2][0][0], "changed") + elif h and mode == 3 and h == H - 1: + cur[0][2].pop(0) + elif h and mode == 4 and h == H - 1: + cur[0][2].append(("z", "added")) + print(f"h{h}", len(cur)) + for cid, tm, fs in cur: + print(cid, tm, len(fs)) + [print(*x) for x in fs] diff --git a/problems/030-cross-host-matrix/oracle.py b/problems/030-cross-host-matrix/oracle.py new file mode 100644 index 0000000..12c7256 --- /dev/null +++ b/problems/030-cross-host-matrix/oracle.py @@ -0,0 +1,43 @@ +#!/usr/bin/env python3 +import sys + +l = sys.stdin.read().splitlines() +at = 0 +H = int(l[at]) +at += 1 +hosts = [] +for _ in range(H): + name, K = l[at].split() + at += 1 + cs = [] + for _ in range(int(K)): + cid, t, P = l[at].split() + at += 1 + fs = {} + for _ in range(int(P)): + p, v = l[at].split() + at += 1 + fs[p] = v + cs.append((cid, int(t), fs)) + hosts.append((name, cs)) +base = hosts[0][1] +allok = True +for name, cs in hosts[1:]: + if [x[0] for x in cs] != [x[0] for x in base]: + print("HOST", name, "CASE_ORDER") + allok = False + continue + d = [] + for x, y in zip(base, cs): + for p in sorted(set(x[2]) | set(y[2])): + if x[2].get(p) != y[2].get(p): + d.append(x[0] + "." + p) + if d: + print("HOST", name, len(d), *d) + allok = False + else: + print("HOST", name, "OK") +if allok: + for i, x in enumerate(base): + z = sorted(h[1][i][1] for h in hosts) + print("MEDIAN", x[0], z[(H - 1) // 2]) diff --git a/problems/030-cross-host-matrix/problem.json b/problems/030-cross-host-matrix/problem.json new file mode 100644 index 0000000..f2212c2 --- /dev/null +++ b/problems/030-cross-host-matrix/problem.json @@ -0,0 +1,146 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 30, + "slug": "cross-host-matrix", + "title": { + "zh-TW": "跨 Host 一致性矩陣", + "en": "Cross-Host Consistency Matrix" + }, + "difficulty": "hard", + "tags": [ + "merge", + "structural-diff", + "median" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-difference-accounting", + "kind": "adversarial", + "input": "tests/adversarial-difference-accounting.in", + "output": "tests/adversarial-difference-accounting.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 15000000, + "memoryLimitBytes": 1073741824 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 2000000, + "memoryLimitBytes": 805306368 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 700000, + "memoryLimitBytes": 536870912 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "每個 path 反覆線性搜尋", + "en": "Repeated linear search for every path" + }, + "time": "O(T^2 + CH log H)", + "space": "O(T)", + "accepted": false + }, + { + "name": { + "zh-TW": "sorted field merge", + "en": "Merge sorted field lists" + }, + "time": "O(T + D + CH log H)", + "space": "O(T + D + H)", + "accepted": true + } + ] +} diff --git a/problems/030-cross-host-matrix/solutions/c/main.c b/problems/030-cross-host-matrix/solutions/c/main.c new file mode 100644 index 0000000..d18aa83 --- /dev/null +++ b/problems/030-cross-host-matrix/solutions/c/main.c @@ -0,0 +1,105 @@ +#include +#include +#include +#include +#include +typedef struct { + char p[121], v[21]; +} Field; +typedef struct { + char id[21]; + uint64_t time; + int n; + Field *f; +} Case; +typedef struct { + char name[21]; + int n; + Case *c; +} Host; +static int cmpu(const void *a, const void *b) { + uint64_t x = *(const uint64_t *)a, y = *(const uint64_t *)b; + return x < y ? -1 : x > y; +} +static char *diff(const char *c, const char *p) { + size_t n = strlen(c) + strlen(p) + 2; + char *s = malloc(n); + snprintf(s, n, "%s.%s", c, p); + return s; +} +int main(void) { + int H; + if (scanf("%d", &H) != 1) + return 0; + Host *h = calloc(H, sizeof(*h)); + for (int z = 0; z < H; z++) { + scanf("%20s %d", h[z].name, &h[z].n); + h[z].c = calloc(h[z].n, sizeof(Case)); + for (int i = 0; i < h[z].n; i++) { + Case *x = &h[z].c[i]; + scanf("%20s %" SCNu64 " %d", x->id, &x->time, &x->n); + x->f = calloc(x->n, sizeof(Field)); + for (int j = 0; j < x->n; j++) + scanf("%120s %20s", x->f[j].p, x->f[j].v); + } + } + int all = 1; + for (int z = 1; z < H; z++) { + int order = h[z].n != h[0].n; + for (int i = 0; !order && i < h[0].n; i++) + order = strcmp(h[z].c[i].id, h[0].c[i].id) != 0; + if (order) { + printf("HOST %s CASE_ORDER\n", h[z].name); + all = 0; + continue; + } + size_t cap = 0; + for (int i = 0; i < h[0].n; i++) + cap += (size_t)h[0].c[i].n + h[z].c[i].n; + char **d = malloc(cap * sizeof(*d)); + int nd = 0; + for (int i = 0; i < h[0].n; i++) { + Case *a = &h[0].c[i], *b = &h[z].c[i]; + int x = 0, y = 0; + while (x < a->n || y < b->n) { + if (y == b->n || (x < a->n && strcmp(a->f[x].p, b->f[y].p) < 0)) + d[nd++] = diff(a->id, a->f[x++].p); + else if (x == a->n || strcmp(a->f[x].p, b->f[y].p) > 0) + d[nd++] = diff(a->id, b->f[y++].p); + else { + if (strcmp(a->f[x].v, b->f[y].v)) + d[nd++] = diff(a->id, a->f[x].p); + x++; + y++; + } + } + } + if (!nd) + printf("HOST %s OK\n", h[z].name); + else { + all = 0; + printf("HOST %s %d", h[z].name, nd); + for (int i = 0; i < nd; i++) + printf(" %s", d[i]); + putchar('\n'); + } + for (int i = 0; i < nd; i++) + free(d[i]); + free(d); + } + if (all) + for (int i = 0; i < h[0].n; i++) { + uint64_t *x = malloc((size_t)H * sizeof(*x)); + for (int z = 0; z < H; z++) + x[z] = h[z].c[i].time; + qsort(x, H, sizeof(*x), cmpu); + printf("MEDIAN %s %" PRIu64 "\n", h[0].c[i].id, x[(H - 1) / 2]); + free(x); + } + for (int z = 0; z < H; z++) { + for (int i = 0; i < h[z].n; i++) + free(h[z].c[i].f); + free(h[z].c); + } + free(h); +} diff --git a/problems/030-cross-host-matrix/solutions/cpp/main.cpp b/problems/030-cross-host-matrix/solutions/cpp/main.cpp new file mode 100644 index 0000000..e75cbc3 --- /dev/null +++ b/problems/030-cross-host-matrix/solutions/cpp/main.cpp @@ -0,0 +1,86 @@ +#include +#include +#include +#include +#include +struct F { + std::string p, v; +}; +struct C { + std::string id; + std::uint64_t t; + std::vector f; +}; +struct H { + std::string name; + std::vector c; +}; +int main() { + std::ios::sync_with_stdio(false); + std::cin.tie(nullptr); + int n; + std::cin >> n; + std::vector h(n); + for (auto &z : h) { + int k; + std::cin >> z.name >> k; + while (k--) { + C c; + int p; + std::cin >> c.id >> c.t >> p; + while (p--) { + F f; + std::cin >> f.p >> f.v; + c.f.push_back(f); + } + z.c.push_back(c); + } + } + bool all = true; + for (int z = 1; z < n; z++) { + bool order = h[z].c.size() != h[0].c.size(); + for (size_t i = 0; !order && i < h[0].c.size(); i++) + order = h[z].c[i].id != h[0].c[i].id; + if (order) { + std::cout << "HOST " << h[z].name << " CASE_ORDER\n"; + all = false; + continue; + } + std::vector d; + for (size_t i = 0; i < h[0].c.size(); i++) { + auto &a = h[0].c[i]; + auto &b = h[z].c[i]; + size_t x = 0, y = 0; + while (x < a.f.size() || y < b.f.size()) { + if (y == b.f.size() || (x < a.f.size() && a.f[x].p < b.f[y].p)) + d.push_back(a.id + '.' + a.f[x++].p); + else if (x == a.f.size() || a.f[x].p > b.f[y].p) + d.push_back(a.id + '.' + b.f[y++].p); + else { + if (a.f[x].v != b.f[y].v) + d.push_back(a.id + '.' + a.f[x].p); + x++; + y++; + } + } + } + std::cout << "HOST " << h[z].name; + if (d.empty()) + std::cout << " OK\n"; + else { + all = false; + std::cout << ' ' << d.size(); + for (auto &x : d) + std::cout << ' ' << x; + std::cout << '\n'; + } + } + if (all) + for (size_t i = 0; i < h[0].c.size(); i++) { + std::vector v; + for (auto &z : h) + v.push_back(z.c[i].t); + std::sort(v.begin(), v.end()); + std::cout << "MEDIAN " << h[0].c[i].id << ' ' << v[(n - 1) / 2] << '\n'; + } +} diff --git a/problems/030-cross-host-matrix/solutions/go/main.go b/problems/030-cross-host-matrix/solutions/go/main.go new file mode 100644 index 0000000..c670d0b --- /dev/null +++ b/problems/030-cross-host-matrix/solutions/go/main.go @@ -0,0 +1,90 @@ +package main + +import ( + "bufio" + "fmt" + "os" + "sort" + "strings" +) + +type F struct{ p, v string } +type C struct { + id string + t uint64 + f []F +} +type H struct { + name string + c []C +} + +func main() { + in := bufio.NewReader(os.Stdin) + out := bufio.NewWriter(os.Stdout) + defer out.Flush() + var n int + fmt.Fscan(in, &n) + h := make([]H, n) + for z := range h { + var k int + fmt.Fscan(in, &h[z].name, &k) + h[z].c = make([]C, k) + for i := range h[z].c { + var p int + fmt.Fscan(in, &h[z].c[i].id, &h[z].c[i].t, &p) + h[z].c[i].f = make([]F, p) + for j := range h[z].c[i].f { + fmt.Fscan(in, &h[z].c[i].f[j].p, &h[z].c[i].f[j].v) + } + } + } + all := true + for z := 1; z < n; z++ { + order := len(h[z].c) != len(h[0].c) + for i := 0; !order && i < len(h[0].c); i++ { + order = h[z].c[i].id != h[0].c[i].id + } + if order { + fmt.Fprintln(out, "HOST", h[z].name, "CASE_ORDER") + all = false + continue + } + d := []string{} + for i, a := range h[0].c { + b := h[z].c[i] + x, y := 0, 0 + for x < len(a.f) || y < len(b.f) { + if y == len(b.f) || (x < len(a.f) && a.f[x].p < b.f[y].p) { + d = append(d, a.id+"."+a.f[x].p) + x++ + } else if x == len(a.f) || a.f[x].p > b.f[y].p { + d = append(d, a.id+"."+b.f[y].p) + y++ + } else { + if a.f[x].v != b.f[y].v { + d = append(d, a.id+"."+a.f[x].p) + } + x++ + y++ + } + } + } + if len(d) == 0 { + fmt.Fprintln(out, "HOST", h[z].name, "OK") + } else { + all = false + fmt.Fprintln(out, "HOST", h[z].name, len(d), strings.Join(d, " ")) + } + } + if all { + for i, c := range h[0].c { + v := make([]uint64, n) + for z := range h { + v[z] = h[z].c[i].t + } + sort.Slice(v, func(a, b int) bool { return v[a] < v[b] }) + fmt.Fprintln(out, "MEDIAN", c.id, v[(n-1)/2]) + } + } +} diff --git a/problems/030-cross-host-matrix/solutions/javascript/main.js b/problems/030-cross-host-matrix/solutions/javascript/main.js new file mode 100644 index 0000000..2558925 --- /dev/null +++ b/problems/030-cross-host-matrix/solutions/javascript/main.js @@ -0,0 +1,53 @@ +import * as std from "std"; +const t = std.in.readAsString().trim().split(/\s+/); +let p = 0, H = +t[p++]; +const h = []; +for (let z = 0; z < H; z++) { + const name = t[p++], K = +t[p++], cs = []; + for (let i = 0; i < K; i++) { + const id = t[p++], tm = BigInt(t[p++]), P = +t[p++], f = []; + for (let j = 0; j < P; j++) f.push([t[p++], t[p++]]); + cs.push({ id, tm, f }); + } + h.push({ name, cs }); +} +const base = h[0].cs, out = []; +let all = true; +for (let z = 1; z < H; z++) { + const cs = h[z].cs, + order = cs.length !== base.length || cs.some((x, i) => x.id !== base[i].id); + if (order) { + out.push(`HOST ${h[z].name} CASE_ORDER`); + all = false; + continue; + } + const d = []; + for (let i = 0; i < base.length; i++) { + const a = base[i], b = cs[i]; + let x = 0, y = 0; + while (x < a.f.length || y < b.f.length) { + if (y === b.f.length || (x < a.f.length && a.f[x][0] < b.f[y][0])) { + d.push(`${a.id}.${a.f[x++][0]}`); + } else if (x === a.f.length || a.f[x][0] > b.f[y][0]) { + d.push(`${a.id}.${b.f[y++][0]}`); + } else { + if (a.f[x][1] !== b.f[y][1]) d.push(`${a.id}.${a.f[x][0]}`); + x++; + y++; + } + } + } + if (d.length) { + out.push(`HOST ${h[z].name} ${d.length} ${d.join(" ")}`); + all = false; + } else out.push(`HOST ${h[z].name} OK`); +} +if (all) { + for (let i = 0; i < base.length; i++) { + const v = h.map((x) => x.cs[i].tm).sort((a, b) => + a < b ? -1 : a > b ? 1 : 0 + ); + out.push(`MEDIAN ${base[i].id} ${v[(H - 1) >> 1]}`); + } +} +std.out.puts(out.join("\n") + "\n"); diff --git a/problems/030-cross-host-matrix/solutions/python/main.py b/problems/030-cross-host-matrix/solutions/python/main.py new file mode 100644 index 0000000..8dd89ab --- /dev/null +++ b/problems/030-cross-host-matrix/solutions/python/main.py @@ -0,0 +1,52 @@ +import sys + +t = iter(sys.stdin.buffer.read().split()) +H = int(next(t)) +h = [] +for _ in range(H): + name = next(t) + K = int(next(t)) + cs = [] + for _ in range(K): + cid = next(t) + tm = int(next(t)) + P = int(next(t)) + cs.append((cid, tm, [(next(t), next(t)) for _ in range(P)])) + h.append((name, cs)) +base = h[0][1] +out = [] +allok = True +for name, cs in h[1:]: + if [x[0] for x in cs] != [x[0] for x in base]: + out.append(b"HOST " + name + b" CASE_ORDER") + allok = False + continue + d = [] + for a, b in zip(base, cs): + i = j = 0 + while i < len(a[2]) or j < len(b[2]): + if j == len(b[2]) or i < len(a[2]) and a[2][i][0] < b[2][j][0]: + d.append(a[0] + b"." + a[2][i][0]) + i += 1 + elif i == len(a[2]) or a[2][i][0] > b[2][j][0]: + d.append(a[0] + b"." + b[2][j][0]) + j += 1 + else: + if a[2][i][1] != b[2][j][1]: + d.append(a[0] + b"." + a[2][i][0]) + i += 1 + j += 1 + if d: + out.append(b"HOST " + name + b" " + str(len(d)).encode() + b" " + b" ".join(d)) + allok = False + else: + out.append(b"HOST " + name + b" OK") +if allok: + for i, c in enumerate(base): + out.append( + b"MEDIAN " + + c[0] + + b" " + + str(sorted(x[1][i][1] for x in h)[(H - 1) // 2]).encode() + ) +sys.stdout.buffer.write(b"\n".join(out) + b"\n") diff --git a/problems/030-cross-host-matrix/solutions/rust/main.rs b/problems/030-cross-host-matrix/solutions/rust/main.rs new file mode 100644 index 0000000..0f0f681 --- /dev/null +++ b/problems/030-cross-host-matrix/solutions/rust/main.rs @@ -0,0 +1,84 @@ +use std::io::{self, Read}; +struct F { + p: String, + v: String, +} +struct C { + id: String, + t: u64, + f: Vec, +} +struct H { + name: String, + c: Vec, +} +fn main() { + let mut s = String::new(); + io::stdin().read_to_string(&mut s).unwrap(); + let mut it = s.split_whitespace(); + let n: usize = it.next().unwrap().parse().unwrap(); + let mut h = Vec::new(); + for _ in 0..n { + let name = it.next().unwrap().to_string(); + let k: usize = it.next().unwrap().parse().unwrap(); + let mut cs = Vec::new(); + for _ in 0..k { + let id = it.next().unwrap().to_string(); + let t = it.next().unwrap().parse().unwrap(); + let p: usize = it.next().unwrap().parse().unwrap(); + let mut f = Vec::new(); + for _ in 0..p { + f.push(F { + p: it.next().unwrap().to_string(), + v: it.next().unwrap().to_string(), + }) + } + cs.push(C { id, t, f }) + } + h.push(H { name, c: cs }) + } + let mut all = true; + let mut out = String::new(); + for z in 1..n { + let order = + h[z].c.len() != h[0].c.len() || h[z].c.iter().zip(&h[0].c).any(|(a, b)| a.id != b.id); + if order { + out += &format!("HOST {} CASE_ORDER\n", h[z].name); + all = false; + continue; + } + let mut d = Vec::new(); + for (a, b) in h[0].c.iter().zip(&h[z].c) { + let (mut x, mut y) = (0, 0); + while x < a.f.len() || y < b.f.len() { + if y == b.f.len() || (x < a.f.len() && a.f[x].p < b.f[y].p) { + d.push(format!("{}.{}", a.id, a.f[x].p)); + x += 1 + } else if x == a.f.len() || a.f[x].p > b.f[y].p { + d.push(format!("{}.{}", a.id, b.f[y].p)); + y += 1 + } else { + if a.f[x].v != b.f[y].v { + d.push(format!("{}.{}", a.id, a.f[x].p)) + } + x += 1; + y += 1 + } + } + } + if d.is_empty() { + out += &format!("HOST {} OK\n", h[z].name) + } else { + all = false; + out += &format!("HOST {} {} {}\n", h[z].name, d.len(), d.join(" ")) + } + } + if all { + for i in 0..h[0].c.len() { + let mut v: Vec = h.iter().map(|x| x.c[i].t).collect(); + v.sort(); + out += &format!("MEDIAN {} {}\n", h[0].c[i].id, v[(n - 1) / 2]) + } + } + print!("{out}") +} diff --git a/problems/030-cross-host-matrix/solutions/typescript/main.ts b/problems/030-cross-host-matrix/solutions/typescript/main.ts new file mode 100644 index 0000000..5b0eed0 --- /dev/null +++ b/problems/030-cross-host-matrix/solutions/typescript/main.ts @@ -0,0 +1,56 @@ +import * as std from "std"; +type F = [string, string]; +type C = { id: string; tm: bigint; f: F[] }; +type Ht = { name: string; cs: C[] }; +const t = std.in.readAsString().trim().split(/\s+/); +let p = 0, H = +t[p++]; +const h: Ht[] = []; +for (let z = 0; z < H; z++) { + const name = t[p++], K = +t[p++], cs: C[] = []; + for (let i = 0; i < K; i++) { + const id = t[p++], tm = BigInt(t[p++]), P = +t[p++], f: F[] = []; + for (let j = 0; j < P; j++) f.push([t[p++], t[p++]]); + cs.push({ id, tm, f }); + } + h.push({ name, cs }); +} +const base = h[0].cs, out: string[] = []; +let all = true; +for (let z = 1; z < H; z++) { + const cs = h[z].cs, + order = cs.length !== base.length || cs.some((x, i) => x.id !== base[i].id); + if (order) { + out.push(`HOST ${h[z].name} CASE_ORDER`); + all = false; + continue; + } + const d: string[] = []; + for (let i = 0; i < base.length; i++) { + const a = base[i], b = cs[i]; + let x = 0, y = 0; + while (x < a.f.length || y < b.f.length) { + if (y === b.f.length || (x < a.f.length && a.f[x][0] < b.f[y][0])) { + d.push(`${a.id}.${a.f[x++][0]}`); + } else if (x === a.f.length || a.f[x][0] > b.f[y][0]) { + d.push(`${a.id}.${b.f[y++][0]}`); + } else { + if (a.f[x][1] !== b.f[y][1]) d.push(`${a.id}.${a.f[x][0]}`); + x++; + y++; + } + } + } + if (d.length) { + out.push(`HOST ${h[z].name} ${d.length} ${d.join(" ")}`); + all = false; + } else out.push(`HOST ${h[z].name} OK`); +} +if (all) { + for (let i = 0; i < base.length; i++) { + const v = h.map((x) => x.cs[i].tm).sort((a, b) => + a < b ? -1 : a > b ? 1 : 0 + ); + out.push(`MEDIAN ${base[i].id} ${v[(H - 1) >> 1]}`); + } +} +std.out.puts(out.join("\n") + "\n"); diff --git a/problems/030-cross-host-matrix/statement.en.md b/problems/030-cross-host-matrix/statement.en.md new file mode 100644 index 0000000..5a85cb8 --- /dev/null +++ b/problems/030-cross-host-matrix/statement.en.md @@ -0,0 +1,113 @@ +# Cross-Host Consistency Matrix + +The same WASM OJ calibration cases must produce an identical deterministic transcript on every host, or their measurements cannot be compared directly. Runtime may vary between devices and is used only for performance aggregation. Case order, field presence, and field values must match the baseline environment. + +The first host in the input is the baseline. Every host records an **ordered** sequence of cases. Each case has an ID, a runtime, and transcript fields whose dotted paths are strictly increasing. Runtime is not part of the deterministic transcript. + +For each non-baseline host, in input order, perform the following comparison: + +1. If its case-ID sequence, including its length, is not identical to the baseline sequence, output `HOST name CASE_ORDER` and do not compare fields for that host. +2. Otherwise, find every dotted path that differs in each corresponding case. A path differs if it occurs on only one side or if its values differ. Report differences in baseline case order and then ASCII lexicographic path order. +3. If there are no differences, output `HOST name OK`. Otherwise output `HOST name k p1 ... pk`, writing each path as `caseId.fieldPath`. + +Only when every non-baseline host is `OK` can the performance data be treated as measurements of the same deterministic work. Then output the lower median runtime for every baseline case: sort all `H` runtimes, choose index `floor((H - 1) / 2)`, and output `MEDIAN caseId value`. If any host is inconsistent, output no median lines. + +## Input + +The first line contains `H`. Each host begins with `name K`, followed by `K` cases. A case header is `caseId runtime P`, followed by `P` lines of `path value`. + +## Output + +Output one line for every non-baseline host in input order. If and only if they are all `OK`, follow those lines with one median line per baseline case in baseline order. + +## Constraints + +- `2 <= H <= 200` +- Host names are globally unique; case IDs are unique within a host. +- Paths within each case are strictly increasing. +- `name`, `caseId`, and `value` contain `1..20` lowercase letters or digits. +- `path` has length `1..120` and consists of dot-separated lowercase alphanumeric segments. +- `0 <= runtime <= 10^18` +- The sum of all `K` values is at most `200000`. +- The sum of all `P` values is at most `200000`. +- Let `D` be the total number of differing paths actually printed for non-baseline hosts whose case-ID sequences are correct. Hosts reported as `CASE_ORDER` do not contribute to `D`; `D <= 200000`. + +## Examples + + + +### Example One + +Input: + +```text +3 +h0 2 +c1 10 2 +a 1 +b 2 +c2 30 1 +x 9 +h1 2 +c1 20 2 +a 1 +b 2 +c2 40 1 +x 9 +h2 2 +c1 50 2 +a 1 +b 3 +c2 60 1 +x 9 +``` + +Output: + +```text +HOST h1 OK +HOST h2 1 c1.b +``` + +### Example Two + +Input: + +```text +2 +a 1 +x 8 1 +ok yes +b 1 +x 2 1 +ok yes +``` + +Output: + +```text +HOST b OK +MEDIAN x 2 +``` + +### Example Three + +Input: + +```text +2 +a 2 +x 1 0 +y 2 0 +b 2 +y 3 0 +x 4 0 +``` + +Output: + +```text +HOST b CASE_ORDER +``` + + diff --git a/problems/030-cross-host-matrix/statement.zh-TW.md b/problems/030-cross-host-matrix/statement.zh-TW.md new file mode 100644 index 0000000..b0d2e6d --- /dev/null +++ b/problems/030-cross-host-matrix/statement.zh-TW.md @@ -0,0 +1,115 @@ +# 跨 Host 一致性矩陣 + +同一組 WASM OJ calibration cases 在不同 host 上執行時,必須產生相同的 deterministic transcript,否則量測結果不能直接比較。執行時間可以因裝置而異,因此只用來彙整效能;case 的順序、欄位集合與欄位值則必須與基準環境一致。 + +輸入中的第一個 host 是 baseline。每個 host 記錄一個**有序** case 序列;每個 case 有 id、runtime,以及按 dotted path 嚴格遞增的 transcript fields。runtime 不屬於 deterministic transcript。 + +對每個非 baseline host,依輸入順序進行以下比較: + +1. 若 case id 序列(包含長度)與 baseline 不完全相同,輸出 `HOST name CASE_ORDER`,且不比較 fields。 +2. 否則找出每個 case 中所有不同 dotted path:path 只存在一側,或兩側 value 不同,都算一次。依 baseline case 順序、再依 path ASCII 字典序輸出。 +3. 無差異輸出 `HOST name OK`;有差異輸出 `HOST name k p1 ... pk`,其中輸出 path 為 `caseId.fieldPath`。 + +只有當所有非 baseline host 都為 `OK`,效能資料才可視為來自同一份 deterministic 工作。此時再為每個 baseline case 輸出所有 `H` 個 runtime 的 lower median:排序後取 index `floor((H-1)/2)`,格式為 `MEDIAN caseId value`。若任一 host 不一致,不輸出任何 median。 + +## 輸入 + +第一行 H。每個 host 先有 `name K`,接著 K 個 case。case header 為 `caseId runtime P`,後接 P 行 `path value`。 + +- `2≤H≤200` +- 所有 host 名稱唯一;每個 host 內 caseId 唯一 +- 每個 case 內 path 嚴格遞增 +- name/caseId/value 是 1..20 小寫英數字;path 是長度 1..120、以 `.` 分隔的小寫英數 segment +- `0≤runtime≤10^18` +- 所有 K 總和及所有 P 總和各不超過 200000 +- 令 D 為所有 case id 序列正確的非 baseline host 實際輸出的差異 path + 總數(也就是各 `HOST name k ...` 的 k 總和);`D≤200000`。輸出 + `CASE_ORDER` 的 host 不計入 D + +## 輸出 + +依上述格式;非 baseline host 行按輸入順序,median 按 baseline case 順序。 + +## 限制 + +所有數量、字串格式與整數範圍均列於「輸入」段落;完整限制適用於每一筆正式測資。 + +## 範例 + + + +### 範例一 + +輸入: + +```text +3 +h0 2 +c1 10 2 +a 1 +b 2 +c2 30 1 +x 9 +h1 2 +c1 20 2 +a 1 +b 2 +c2 40 1 +x 9 +h2 2 +c1 50 2 +a 1 +b 3 +c2 60 1 +x 9 +``` + +輸出: + +```text +HOST h1 OK +HOST h2 1 c1.b +``` + +### 範例二 + +輸入: + +```text +2 +a 1 +x 8 1 +ok yes +b 1 +x 2 1 +ok yes +``` + +輸出: + +```text +HOST b OK +MEDIAN x 2 +``` + +### 範例三 + +輸入: + +```text +2 +a 2 +x 1 0 +y 2 0 +b 2 +y 3 0 +x 4 0 +``` + +輸出: + +```text +HOST b CASE_ORDER +``` + + diff --git a/problems/030-cross-host-matrix/tests/adversarial-difference-accounting.in b/problems/030-cross-host-matrix/tests/adversarial-difference-accounting.in new file mode 100644 index 0000000..3e14319 --- /dev/null +++ b/problems/030-cross-host-matrix/tests/adversarial-difference-accounting.in @@ -0,0 +1,17 @@ +3 +base 2 +c2 10 2 +a 1 +c 3 +c1 100 1 +b 2 +h1 2 +c2 20 3 +a 1 +b 9 +c 4 +c1 90 1 +a x +h2 2 +c1 1 0 +c2 2 0 diff --git a/problems/030-cross-host-matrix/tests/adversarial-difference-accounting.out b/problems/030-cross-host-matrix/tests/adversarial-difference-accounting.out new file mode 100644 index 0000000..3449164 --- /dev/null +++ b/problems/030-cross-host-matrix/tests/adversarial-difference-accounting.out @@ -0,0 +1,2 @@ +HOST h1 4 c2.b c2.c c1.a c1.b +HOST h2 CASE_ORDER diff --git a/problems/030-cross-host-matrix/tests/sample-01.in b/problems/030-cross-host-matrix/tests/sample-01.in new file mode 100644 index 0000000..3f8c5d8 --- /dev/null +++ b/problems/030-cross-host-matrix/tests/sample-01.in @@ -0,0 +1,19 @@ +3 +h0 2 +c1 10 2 +a 1 +b 2 +c2 30 1 +x 9 +h1 2 +c1 20 2 +a 1 +b 2 +c2 40 1 +x 9 +h2 2 +c1 50 2 +a 1 +b 3 +c2 60 1 +x 9 diff --git a/problems/030-cross-host-matrix/tests/sample-01.out b/problems/030-cross-host-matrix/tests/sample-01.out new file mode 100644 index 0000000..d5968ae --- /dev/null +++ b/problems/030-cross-host-matrix/tests/sample-01.out @@ -0,0 +1,2 @@ +HOST h1 OK +HOST h2 1 c1.b diff --git a/problems/030-cross-host-matrix/tests/sample-02.in b/problems/030-cross-host-matrix/tests/sample-02.in new file mode 100644 index 0000000..33acbeb --- /dev/null +++ b/problems/030-cross-host-matrix/tests/sample-02.in @@ -0,0 +1,7 @@ +2 +a 1 +x 8 1 +ok yes +b 1 +x 2 1 +ok yes diff --git a/problems/030-cross-host-matrix/tests/sample-02.out b/problems/030-cross-host-matrix/tests/sample-02.out new file mode 100644 index 0000000..055cb95 --- /dev/null +++ b/problems/030-cross-host-matrix/tests/sample-02.out @@ -0,0 +1,2 @@ +HOST b OK +MEDIAN x 2 diff --git a/problems/030-cross-host-matrix/tests/sample-03.in b/problems/030-cross-host-matrix/tests/sample-03.in new file mode 100644 index 0000000..e369f76 --- /dev/null +++ b/problems/030-cross-host-matrix/tests/sample-03.in @@ -0,0 +1,7 @@ +2 +a 2 +x 1 0 +y 2 0 +b 2 +y 3 0 +x 4 0 diff --git a/problems/030-cross-host-matrix/tests/sample-03.out b/problems/030-cross-host-matrix/tests/sample-03.out new file mode 100644 index 0000000..b61db9c --- /dev/null +++ b/problems/030-cross-host-matrix/tests/sample-03.out @@ -0,0 +1 @@ +HOST b CASE_ORDER diff --git a/problems/030-cross-host-matrix/validator.py b/problems/030-cross-host-matrix/validator.py new file mode 100644 index 0000000..027c4ff --- /dev/null +++ b/problems/030-cross-host-matrix/validator.py @@ -0,0 +1,81 @@ +#!/usr/bin/env python3 +import re, sys + +tok = re.compile(r"[a-z0-9]{1,20}") +path = re.compile(r"[a-z0-9]+(?:\.[a-z0-9]+)*") + + +def difference_count(baseline, current): + total = 0 + for (_, left), (_, right) in zip(baseline, current): + i = j = 0 + while i < len(left) or j < len(right): + if j == len(right) or (i < len(left) and left[i][0] < right[j][0]): + total += 1 + i += 1 + elif i == len(left) or right[j][0] < left[i][0]: + total += 1 + j += 1 + else: + total += left[i][1] != right[j][1] + i += 1 + j += 1 + if total > 200000: + return total + return total + + +try: + l = sys.stdin.read().splitlines() + at = 0 + H = int(l[at]) + at += 1 + assert 2 <= H <= 200 + names = set() + tc = tf = differences = 0 + baseline = None + for host_index in range(H): + h = l[at].split() + at += 1 + assert len(h) == 2 and tok.fullmatch(h[0]) + name = h[0] + K = int(h[1]) + assert name not in names and 0 <= K <= 200000 + names.add(name) + ids = set() + cases = [] + tc += K + assert tc <= 200000 + for _ in range(K): + p = l[at].split() + at += 1 + assert len(p) == 3 and tok.fullmatch(p[0]) and p[0] not in ids + ids.add(p[0]) + runtime = int(p[1]) + P = int(p[2]) + assert 0 <= runtime <= 10**18 and 0 <= P <= 200000 + tf += P + assert tf <= 200000 + prev = None + fields = [] + for _ in range(P): + x = l[at].split() + at += 1 + assert ( + len(x) == 2 + and len(x[0]) <= 120 + and path.fullmatch(x[0]) + and tok.fullmatch(x[1]) + and (prev is None or prev < x[0]) + ) + prev = x[0] + fields.append((x[0], x[1])) + cases.append((p[0], fields)) + if host_index == 0: + baseline = cases + elif [case[0] for case in cases] == [case[0] for case in baseline]: + differences += difference_count(baseline, cases) + assert differences <= 200000 + assert at == len(l) +except Exception: + sys.exit(1) diff --git a/problems/031-compile-critical-path/editorial.en.md b/problems/031-compile-critical-path/editorial.en.md new file mode 100644 index 0000000..a5d4cd8 --- /dev/null +++ b/problems/031-compile-critical-path/editorial.en.md @@ -0,0 +1,37 @@ +# Editorial + +## Intuitive Approach + +Run a DFS from every source, enumerate all source-to-sink paths, and compute each path's duration. This is direct but infeasible: repeated diamond dependencies can create exponentially many distinct paths even in a modest graph. + +## Optimal Approach: Longest-Path DP on a Topological Order + +Use Kahn's algorithm to obtain a topological order. For each stage `v`, maintain: + +- `best[v]`: the maximum duration of a path from any source to `v`; +- `ways[v]`: the number of such paths attaining `best[v]`, modulo `1,000,000,007`. + +Initialize every source with `best[v] = d_v` and `ways[v] = 1`. Process each edge `u -> v` in topological order and form `candidate = best[u] + d_v`: + +- if `candidate > best[v]`, replace `best[v]` and set `ways[v] = ways[u]`; +- if `candidate == best[v]`, add `ways[u]` to `ways[v]` modulo the modulus; +- otherwise ignore the candidate. + +Finally inspect only sinks. The largest sink value is the earliest project completion time. Sum `ways[v]` over all sinks attaining that value. + +## Correctness Proof + +Proceed by induction over the topological order. A source has exactly one source-to-itself path, of duration `d_v`, so its initialization is correct. Before a non-source `v` is processed, all its predecessors have already been processed. Every source-to-`v` path consists of a source-to-`u` path for exactly one incoming edge `u -> v`, followed by `v`. The transitions compare all such candidates, retain precisely the maximum duration, and add counts only for candidates attaining that maximum. Thus `best[v]` and `ways[v]` satisfy their definitions. + +Every complete pipeline ends at a sink, and every source-to-sink path is complete. Taking the maximum over sinks and summing the counts for tied sinks therefore yields exactly the required completion time and number of critical pipelines. + +## Complexity + +Path enumeration can require `O(2^N + M)` time and `O(N + M)` space. The topological DP processes every vertex and edge a constant number of times, using `O(N + M)` time and `O(N + M)` space. + +## Common Mistakes + +- Initializing every vertex as a source and counting paths that do not begin at a source. +- Taking the final maximum over all vertices instead of sinks only. +- Failing to add path counts on equal-duration transitions or to apply the modulus. +- Storing path durations in 32-bit integers. diff --git a/problems/031-compile-critical-path/editorial.zh-TW.md b/problems/031-compile-critical-path/editorial.zh-TW.md new file mode 100644 index 0000000..2e0a7fd --- /dev/null +++ b/problems/031-compile-critical-path/editorial.zh-TW.md @@ -0,0 +1,46 @@ +# 解題說明 + +## 直覺解法 + +從每個 source 做 DFS,列舉所有走到 sink 的路徑,計算每條路徑的時間。 +這個方法雖然直接,但菱形相依可以產生指數條路徑;即使圖只有數百個節點, +路徑數也可能遠超可執行範圍。 + +## 最佳解法 + +先以 Kahn 演算法取得拓撲序。令: + +- `best[v]`:由任一 source 到 `v` 的最大時間總和; +- `ways[v]`:達到 `best[v]` 的路徑數量。 + +每個 source 初始化為 `best[v] = d_v`、`ways[v] = 1`。依拓撲序處理邊 +`u -> v`,候選值為 `best[u] + d_v`: + +- 候選較大:取代 `best[v]`,並令 `ways[v] = ways[u]`; +- 候選相同:把 `ways[u]` 加入 `ways[v]`; +- 候選較小:忽略。 + +最後只查看 sinks。最大的 `best` 是答案時間;所有具有相同最大值的 sink +之 `ways` 相加就是完整管線數量。 + +## 正確性證明 + +依拓撲序歸納。source 只有長度為自身時間的一條 source-to-source 路徑, +初始化正確。處理 `v` 時,它的所有前驅都已處理;任何到 `v` 的路徑必定由 +某條到前驅 `u` 的路徑再接上 `v`。轉移逐一比較所有這類候選,因此得到的 +`best[v]` 是最大值;只在候選相等時加總路徑數,也恰好計算所有且僅計算 +達到最大值的路徑。歸納成立。完整管線必定終止於 sink,所以最後在 sinks +中取最大值與加總即可得到題目答案。 + +## 複雜度 + +- 列舉路徑:最壞 `O(2^N + M)` 時間、`O(N + M)` 空間。 +- 拓撲 DP:每個節點與邊各處理常數次,時間 `O(N + M)`,空間 + `O(N + M)`。 + +## 常見錯誤 + +- 把所有節點都當作初始路徑,因而計入不是從 source 開始的序列。 +- 最後對所有節點取答案,而不是只對 sinks。 +- 相同最長時間時忘記加總方法數或忘記取模。 +- 使用 32-bit integer 儲存路徑時間。 diff --git a/problems/031-compile-critical-path/generator.py b/problems/031-compile-critical-path/generator.py new file mode 100644 index 0000000..c7d95c2 --- /dev/null +++ b/problems/031-compile-critical-path/generator.py @@ -0,0 +1,19 @@ +import random +import sys + + +if len(sys.argv) != 3: + raise SystemExit("usage: generator.py SEED INDEX") +seed, index = map(int, sys.argv[1:]) +rng = random.Random((seed << 17) ^ index) +n = rng.randint(1, 10) +durations = [rng.randint(1, 20) for _ in range(n)] +edges = [] +for u in range(n): + for v in range(u + 1, n): + if rng.random() < 0.28: + edges.append((u + 1, v + 1)) +print(n, len(edges)) +print(*durations) +for edge in edges: + print(*edge) diff --git a/problems/031-compile-critical-path/oracle.py b/problems/031-compile-critical-path/oracle.py new file mode 100644 index 0000000..cf4d7e3 --- /dev/null +++ b/problems/031-compile-critical-path/oracle.py @@ -0,0 +1,38 @@ +import sys + + +MOD = 1_000_000_007 +data = list(map(int, sys.stdin.buffer.read().split())) +n, m = data[:2] +duration = data[2 : 2 + n] +graph = [[] for _ in range(n)] +indegree = [0] * n +outdegree = [0] * n +offset = 2 + n +for i in range(m): + u, v = data[offset + 2 * i] - 1, data[offset + 2 * i + 1] - 1 + graph[u].append(v) + indegree[v] += 1 + outdegree[u] += 1 + +best = -1 +ways = 0 + + +def enumerate_paths(node: int, total: int) -> None: + global best, ways + total += duration[node] + if outdegree[node] == 0: + if total > best: + best, ways = total, 1 + elif total == best: + ways = (ways + 1) % MOD + return + for target in graph[node]: + enumerate_paths(target, total) + + +for source in range(n): + if indegree[source] == 0: + enumerate_paths(source, 0) +print(best, ways % MOD) diff --git a/problems/031-compile-critical-path/problem.json b/problems/031-compile-critical-path/problem.json new file mode 100644 index 0000000..c328169 --- /dev/null +++ b/problems/031-compile-critical-path/problem.json @@ -0,0 +1,146 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 31, + "slug": "compile-critical-path", + "title": { + "zh-TW": "編譯管線的關鍵路徑", + "en": "Compile Pipeline Critical Path" + }, + "difficulty": "medium", + "tags": [ + "dag", + "dynamic-programming", + "topological-sort" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-blind-01", + "kind": "adversarial", + "input": "tests/adversarial-blind-01.in", + "output": "tests/adversarial-blind-01.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 15000000, + "memoryLimitBytes": 536870912 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 2500000, + "memoryLimitBytes": 402653184 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 950000, + "memoryLimitBytes": 268435456 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "列舉所有 source-to-sink 路徑", + "en": "Enumerate all source-to-sink paths" + }, + "time": "O(2^N + M)", + "space": "O(N + M)", + "accepted": false + }, + { + "name": { + "zh-TW": "拓撲序上的最長路徑 DP", + "en": "Longest-path DP in topological order" + }, + "time": "O(N + M)", + "space": "O(N + M)", + "accepted": true + } + ] +} diff --git a/problems/031-compile-critical-path/solutions/c/main.c b/problems/031-compile-critical-path/solutions/c/main.c new file mode 100644 index 0000000..d5d3493 --- /dev/null +++ b/problems/031-compile-critical-path/solutions/c/main.c @@ -0,0 +1,91 @@ +#include +#include +#include +#include + +enum { MOD = 1000000007 }; + +int main(void) { + int n, m; + if (scanf("%d %d", &n, &m) != 2) + return 1; + int64_t *duration = malloc((size_t)n * sizeof(*duration)); + int64_t *best = calloc((size_t)n, sizeof(*best)); + int *ways = calloc((size_t)n, sizeof(*ways)); + int *head = malloc((size_t)n * sizeof(*head)); + int *indegree = calloc((size_t)n, sizeof(*indegree)); + int *outdegree = calloc((size_t)n, sizeof(*outdegree)); + int *queue = malloc((size_t)n * sizeof(*queue)); + int *to = malloc((size_t)(m > 0 ? m : 1) * sizeof(*to)); + int *next = malloc((size_t)(m > 0 ? m : 1) * sizeof(*next)); + if (!duration || !best || !ways || !head || !indegree || !outdegree || + !queue || !to || !next) + return 1; + for (int i = 0; i < n; ++i) { + if (scanf("%" SCNd64, &duration[i]) != 1) + return 1; + head[i] = -1; + } + for (int edge = 0; edge < m; ++edge) { + int u, v; + if (scanf("%d %d", &u, &v) != 2) + return 1; + --u; + --v; + to[edge] = v; + next[edge] = head[u]; + head[u] = edge; + ++indegree[v]; + ++outdegree[u]; + } + int front = 0, back = 0; + for (int node = 0; node < n; ++node) { + if (indegree[node] == 0) { + best[node] = duration[node]; + ways[node] = 1; + queue[back++] = node; + } + } + while (front < back) { + int node = queue[front++]; + for (int edge = head[node]; edge != -1; edge = next[edge]) { + int target = to[edge]; + int64_t candidate = best[node] + duration[target]; + if (candidate > best[target]) { + best[target] = candidate; + ways[target] = ways[node]; + } else if (candidate == best[target]) { + ways[target] += ways[node]; + if (ways[target] >= MOD) + ways[target] -= MOD; + } + if (--indegree[target] == 0) + queue[back++] = target; + } + } + int64_t answer = -1; + int count = 0; + for (int node = 0; node < n; ++node) { + if (outdegree[node] != 0) + continue; + if (best[node] > answer) { + answer = best[node]; + count = ways[node]; + } else if (best[node] == answer) { + count += ways[node]; + if (count >= MOD) + count -= MOD; + } + } + printf("%" PRId64 " %d\n", answer, count); + free(next); + free(to); + free(queue); + free(outdegree); + free(indegree); + free(head); + free(ways); + free(best); + free(duration); + return 0; +} diff --git a/problems/031-compile-critical-path/solutions/cpp/main.cpp b/problems/031-compile-critical-path/solutions/cpp/main.cpp new file mode 100644 index 0000000..d8e88ff --- /dev/null +++ b/problems/031-compile-critical-path/solutions/cpp/main.cpp @@ -0,0 +1,70 @@ +#include +#include +#include +#include + +using namespace std; + +int main() { + ios::sync_with_stdio(false); + cin.tie(nullptr); + constexpr int MOD = 1'000'000'007; + int n, m; + cin >> n >> m; + vector duration(n); + for (auto &value : duration) + cin >> value; + vector> graph(n); + vector indegree(n), outdegree(n); + for (int i = 0; i < m; ++i) { + int u, v; + cin >> u >> v; + --u; + --v; + graph[u].push_back(v); + ++indegree[v]; + ++outdegree[u]; + } + vector best(n); + vector ways(n); + deque queue; + for (int node = 0; node < n; ++node) { + if (indegree[node] == 0) { + best[node] = duration[node]; + ways[node] = 1; + queue.push_back(node); + } + } + while (!queue.empty()) { + const int node = queue.front(); + queue.pop_front(); + for (const int target : graph[node]) { + const int64_t candidate = best[node] + duration[target]; + if (candidate > best[target]) { + best[target] = candidate; + ways[target] = ways[node]; + } else if (candidate == best[target]) { + ways[target] += ways[node]; + if (ways[target] >= MOD) + ways[target] -= MOD; + } + if (--indegree[target] == 0) + queue.push_back(target); + } + } + int64_t answer = -1; + int count = 0; + for (int node = 0; node < n; ++node) { + if (outdegree[node] != 0) + continue; + if (best[node] > answer) { + answer = best[node]; + count = ways[node]; + } else if (best[node] == answer) { + count += ways[node]; + if (count >= MOD) + count -= MOD; + } + } + cout << answer << ' ' << count << '\n'; +} diff --git a/problems/031-compile-critical-path/solutions/go/main.go b/problems/031-compile-critical-path/solutions/go/main.go new file mode 100644 index 0000000..a5315b6 --- /dev/null +++ b/problems/031-compile-critical-path/solutions/go/main.go @@ -0,0 +1,73 @@ +package main + +import ( + "bufio" + "fmt" + "os" +) + +const mod int64 = 1_000_000_007 + +func main() { + in := bufio.NewReaderSize(os.Stdin, 1<<20) + out := bufio.NewWriterSize(os.Stdout, 1<<20) + defer out.Flush() + var n, m int + fmt.Fscan(in, &n, &m) + duration := make([]int64, n) + for i := range duration { + fmt.Fscan(in, &duration[i]) + } + graph := make([][]int, n) + indegree := make([]int, n) + outdegree := make([]int, n) + for i := 0; i < m; i++ { + var u, v int + fmt.Fscan(in, &u, &v) + u-- + v-- + graph[u] = append(graph[u], v) + indegree[v]++ + outdegree[u]++ + } + best := make([]int64, n) + ways := make([]int64, n) + queue := make([]int, 0, n) + for node := 0; node < n; node++ { + if indegree[node] == 0 { + best[node] = duration[node] + ways[node] = 1 + queue = append(queue, node) + } + } + for head := 0; head < len(queue); head++ { + node := queue[head] + for _, target := range graph[node] { + candidate := best[node] + duration[target] + if candidate > best[target] { + best[target] = candidate + ways[target] = ways[node] + } else if candidate == best[target] { + ways[target] = (ways[target] + ways[node]) % mod + } + indegree[target]-- + if indegree[target] == 0 { + queue = append(queue, target) + } + } + } + var answer int64 = -1 + var count int64 + for node := 0; node < n; node++ { + if outdegree[node] != 0 { + continue + } + if best[node] > answer { + answer = best[node] + count = ways[node] + } else if best[node] == answer { + count = (count + ways[node]) % mod + } + } + fmt.Fprintln(out, answer, count) +} diff --git a/problems/031-compile-critical-path/solutions/javascript/main.js b/problems/031-compile-critical-path/solutions/javascript/main.js new file mode 100644 index 0000000..dab2fa2 --- /dev/null +++ b/problems/031-compile-critical-path/solutions/javascript/main.js @@ -0,0 +1,79 @@ +import * as std from "std"; + +const input = std.in.readAsString(); +let scan = 0; +function nextInt() { + while (scan < input.length && input.charCodeAt(scan) <= 32) scan++; + let value = 0; + while (scan < input.length) { + const digit = input.charCodeAt(scan) - 48; + if (digit < 0 || digit > 9) break; + value = value * 10 + digit; + scan++; + } + return value; +} +function nextBigInt() { + while (scan < input.length && input.charCodeAt(scan) <= 32) scan++; + const start = scan; + while (scan < input.length) { + const code = input.charCodeAt(scan); + if (code < 48 || code > 57) break; + scan++; + } + return BigInt(input.slice(start, scan)); +} + +const n = nextInt(), m = nextInt(); +const duration = new BigUint64Array(n); +for (let i = 0; i < n; i++) duration[i] = nextBigInt(); +const head = new Int32Array(n).fill(-1), + to = new Int32Array(m), + next = new Int32Array(m), + indegree = new Int32Array(n), + outdegree = new Int32Array(n); +for (let edge = 0; edge < m; edge++) { + const u = nextInt() - 1, v = nextInt() - 1; + to[edge] = v; + next[edge] = head[u]; + head[u] = edge; + indegree[v]++; + outdegree[u]++; +} +const MOD = 1_000_000_007; +const best = new BigUint64Array(n), + ways = new Uint32Array(n), + queue = new Int32Array(n); +let front = 0, back = 0; +for (let node = 0; node < n; node++) { + if (indegree[node] === 0) { + best[node] = duration[node]; + ways[node] = 1; + queue[back++] = node; + } +} +while (front < back) { + const node = queue[front++]; + for (let edge = head[node]; edge !== -1; edge = next[edge]) { + const target = to[edge], candidate = best[node] + duration[target]; + if (candidate > best[target]) { + best[target] = candidate; + ways[target] = ways[node]; + } else if (candidate === best[target]) { + ways[target] = (ways[target] + ways[node]) % MOD; + } + indegree[target]--; + if (indegree[target] === 0) queue[back++] = target; + } +} +let answer = -1n, count = 0; +for (let node = 0; node < n; node++) { + if (outdegree[node] !== 0) continue; + if (best[node] > answer) { + answer = best[node]; + count = ways[node]; + } else if (best[node] === answer) { + count = (count + ways[node]) % MOD; + } +} +std.out.puts(`${answer} ${count}\n`); diff --git a/problems/031-compile-critical-path/solutions/python/main.py b/problems/031-compile-critical-path/solutions/python/main.py new file mode 100644 index 0000000..9af9565 --- /dev/null +++ b/problems/031-compile-critical-path/solutions/python/main.py @@ -0,0 +1,51 @@ +from collections import deque +import sys + + +MOD = 1_000_000_007 +data = list(map(int, sys.stdin.buffer.read().split())) +n, m = data[:2] +duration = data[2 : 2 + n] +graph = [[] for _ in range(n)] +indegree = [0] * n +outdegree = [0] * n +offset = 2 + n +for index in range(m): + u = data[offset + 2 * index] - 1 + v = data[offset + 2 * index + 1] - 1 + graph[u].append(v) + indegree[v] += 1 + outdegree[u] += 1 + +best = [0] * n +ways = [0] * n +queue = deque() +for node in range(n): + if indegree[node] == 0: + best[node] = duration[node] + ways[node] = 1 + queue.append(node) + +while queue: + node = queue.popleft() + for target in graph[node]: + candidate = best[node] + duration[target] + if candidate > best[target]: + best[target] = candidate + ways[target] = ways[node] + elif candidate == best[target]: + ways[target] = (ways[target] + ways[node]) % MOD + indegree[target] -= 1 + if indegree[target] == 0: + queue.append(target) + +answer = -1 +count = 0 +for node in range(n): + if outdegree[node] != 0: + continue + if best[node] > answer: + answer, count = best[node], ways[node] + elif best[node] == answer: + count = (count + ways[node]) % MOD +print(answer, count) diff --git a/problems/031-compile-critical-path/solutions/rust/main.rs b/problems/031-compile-critical-path/solutions/rust/main.rs new file mode 100644 index 0000000..adcb36b --- /dev/null +++ b/problems/031-compile-critical-path/solutions/rust/main.rs @@ -0,0 +1,63 @@ +use std::collections::VecDeque; +use std::io::{self, Read}; + +fn main() { + const MOD: u64 = 1_000_000_007; + let mut input = String::new(); + io::stdin().read_to_string(&mut input).unwrap(); + let mut tokens = input.split_whitespace(); + let n: usize = tokens.next().unwrap().parse().unwrap(); + let m: usize = tokens.next().unwrap().parse().unwrap(); + let duration: Vec = (0..n) + .map(|_| tokens.next().unwrap().parse().unwrap()) + .collect(); + let mut graph = vec![Vec::::new(); n]; + let mut indegree = vec![0usize; n]; + let mut outdegree = vec![0usize; n]; + for _ in 0..m { + let u: usize = tokens.next().unwrap().parse::().unwrap() - 1; + let v: usize = tokens.next().unwrap().parse::().unwrap() - 1; + graph[u].push(v); + indegree[v] += 1; + outdegree[u] += 1; + } + let mut best = vec![0u64; n]; + let mut ways = vec![0u64; n]; + let mut queue = VecDeque::new(); + for node in 0..n { + if indegree[node] == 0 { + best[node] = duration[node]; + ways[node] = 1; + queue.push_back(node); + } + } + while let Some(node) = queue.pop_front() { + for &target in &graph[node] { + let candidate = best[node] + duration[target]; + if candidate > best[target] { + best[target] = candidate; + ways[target] = ways[node]; + } else if candidate == best[target] { + ways[target] = (ways[target] + ways[node]) % MOD; + } + indegree[target] -= 1; + if indegree[target] == 0 { + queue.push_back(target); + } + } + } + let mut answer = 0u64; + let mut count = 0u64; + for node in 0..n { + if outdegree[node] != 0 { + continue; + } + if best[node] > answer { + answer = best[node]; + count = ways[node]; + } else if best[node] == answer { + count = (count + ways[node]) % MOD; + } + } + println!("{answer} {count}"); +} diff --git a/problems/031-compile-critical-path/solutions/typescript/main.ts b/problems/031-compile-critical-path/solutions/typescript/main.ts new file mode 100644 index 0000000..8d04d6b --- /dev/null +++ b/problems/031-compile-critical-path/solutions/typescript/main.ts @@ -0,0 +1,79 @@ +import * as std from "std"; + +const input: string = std.in.readAsString(); +let scan = 0; +function nextInt(): number { + while (scan < input.length && input.charCodeAt(scan) <= 32) scan++; + let value = 0; + while (scan < input.length) { + const digit = input.charCodeAt(scan) - 48; + if (digit < 0 || digit > 9) break; + value = value * 10 + digit; + scan++; + } + return value; +} +function nextBigInt(): bigint { + while (scan < input.length && input.charCodeAt(scan) <= 32) scan++; + const start = scan; + while (scan < input.length) { + const code = input.charCodeAt(scan); + if (code < 48 || code > 57) break; + scan++; + } + return BigInt(input.slice(start, scan)); +} + +const n = nextInt(), m = nextInt(); +const duration = new BigUint64Array(n); +for (let i = 0; i < n; i++) duration[i] = nextBigInt(); +const head = new Int32Array(n).fill(-1), + to = new Int32Array(m), + next = new Int32Array(m), + indegree = new Int32Array(n), + outdegree = new Int32Array(n); +for (let edge = 0; edge < m; edge++) { + const u = nextInt() - 1, v = nextInt() - 1; + to[edge] = v; + next[edge] = head[u]!; + head[u] = edge; + indegree[v]!++; + outdegree[u]!++; +} +const MOD = 1_000_000_007; +const best = new BigUint64Array(n), + ways = new Uint32Array(n), + queue = new Int32Array(n); +let front = 0, back = 0; +for (let node = 0; node < n; node++) { + if (indegree[node] === 0) { + best[node] = duration[node]!; + ways[node] = 1; + queue[back++] = node; + } +} +while (front < back) { + const node = queue[front++]!; + for (let edge = head[node]!; edge !== -1; edge = next[edge]!) { + const target = to[edge]!, candidate = best[node]! + duration[target]!; + if (candidate > best[target]!) { + best[target] = candidate; + ways[target] = ways[node]!; + } else if (candidate === best[target]!) { + ways[target] = (ways[target]! + ways[node]!) % MOD; + } + indegree[target]!--; + if (indegree[target] === 0) queue[back++] = target; + } +} +let answer = -1n, count = 0; +for (let node = 0; node < n; node++) { + if (outdegree[node] !== 0) continue; + if (best[node]! > answer) { + answer = best[node]!; + count = ways[node]!; + } else if (best[node] === answer) { + count = (count + ways[node]!) % MOD; + } +} +std.out.puts(`${answer} ${count}\n`); diff --git a/problems/031-compile-critical-path/statement.en.md b/problems/031-compile-critical-path/statement.en.md new file mode 100644 index 0000000..1dcbbfc --- /dev/null +++ b/problems/031-compile-critical-path/statement.en.md @@ -0,0 +1,90 @@ +# Compile Pipeline Critical Path + +While designing the in-browser compiler for a WASM OJ, we wanted to estimate the earliest time a project could finish building before actually starting the build. Compilation jobs often depend on one another, but jobs whose prerequisites are complete can be assigned to different workers and run concurrently. + +To focus on the dependency structure itself, we use an idealized system with infinitely many workers. The project contains `N` stages, and stage `i` takes `d_i` units of time. A dependency `u v` means that stage `v` cannot start until stage `u` has finished. The dependency graph is guaranteed to be a directed acyclic graph, and every stage with no predecessor starts at time `0`. + +Besides the earliest completion time, we want to know how many distinct critical build pipelines determine that time, because each such pipeline is a bottleneck worth examining when improving the scheduler. A complete pipeline is a directed path from a stage with indegree zero to a stage with outdegree zero. The project's earliest completion time is the maximum sum of stage durations along any complete pipeline. + +Output the earliest completion time and the number of complete pipelines attaining it, modulo `1,000,000,007`. Two pipelines are the same exactly when their stage sequences are identical. An isolated stage is both a source and a sink, so it forms a complete pipeline by itself. + +## Input + +The first line contains `N M`. + +The second line contains `N` integers `d_1 ... d_N`. + +Each of the next `M` lines contains `u v`, denoting a directed dependency from `u` to `v`. There are no duplicate edges or self-loops. + +## Output + +Output two integers: the earliest completion time and the number of complete pipelines attaining that time, modulo `1,000,000,007`. + +## Constraints + +- `1 <= N <= 200000` +- `0 <= M <= 400000` +- `1 <= d_i <= 10^9` +- The sum of all stage durations is at most `9 * 10^18`. +- The input graph is a DAG. +- Stage IDs are 1-based. + +## Examples + + + +### Example One + +Input: + +```text +4 4 +2 3 3 4 +1 2 +1 3 +2 4 +3 4 + +``` + +Output: + +```text +9 2 +``` + +### Example Two + +Input: + +```text +3 0 +5 5 1 + +``` + +Output: + +```text +5 2 +``` + +### Example Three + +Input: + +```text +3 2 +1 2 3 +1 2 +2 3 + +``` + +Output: + +```text +6 1 +``` + + diff --git a/problems/031-compile-critical-path/statement.zh-TW.md b/problems/031-compile-critical-path/statement.zh-TW.md new file mode 100644 index 0000000..950bac3 --- /dev/null +++ b/problems/031-compile-critical-path/statement.zh-TW.md @@ -0,0 +1,92 @@ +# 編譯管線的關鍵路徑 + +在設計 WASM OJ 的瀏覽器內編譯器時,我們希望在真正啟動 build 之前,就能估計一個專案最早何時可以編譯完成。編譯工作之間常有相依關係,但只要相依項目都已完成,不同工作就可以交給不同 Worker 同時處理。 + +為了把問題集中在相依關係本身,我們使用擁有無限多個 Worker 的理想模型。專案由 `N` 個 stage 組成,第 `i` 個 stage 需要 `d_i` 單位時間;相依關係 `u v` 表示 stage `v` 必須等 stage `u` 完成後才能開始。相依圖保證是有向無環圖,沒有前驅的 stage 都在時間 `0` 開始。 + +除了最早完成時間,我們也想知道有多少條不同的關鍵編譯管線同時決定了這個時間,因為這些管線都是後續改善排程時需要觀察的瓶頸。一條完整管線是從入度為零的 stage 走到出度為零的 stage 的有向路徑;專案的最早完成時間等於所有完整管線中最大的 stage 時間總和。 + +請輸出最早完成時間,以及達到這個時間的完整管線數量。管線數量可能很大,請對 `1,000,000,007` 取餘數。只有經過的 stage 序列完全相同,兩條管線才視為同一條;孤立 stage 同時是 source 與 sink,因此自己構成一條完整管線。 + +## 輸入 + +第一行包含兩個整數 `N M`。 + +第二行包含 `N` 個整數 `d_1 ... d_N`。 + +接下來 `M` 行各包含兩個整數 `u v`,表示一條由 `u` 指向 `v` 的相依關係。 +不會有重複邊或 self-loop。 + +## 輸出 + +輸出兩個整數:最早完成時間,以及達到該時間的完整管線數量模 +`1,000,000,007`。 + +## 限制 + +- `1 <= N <= 200,000` +- `0 <= M <= 400,000` +- `1 <= d_i <= 10^9` +- 所有 stage 時間總和不超過 `9 × 10^18` +- 輸入圖是 DAG +- stage ID 採 1-based 編號 + +## 範例 + + + +### 範例一 + +輸入: + +```text +4 4 +2 3 3 4 +1 2 +1 3 +2 4 +3 4 + +``` + +輸出: + +```text +9 2 +``` + +### 範例二 + +輸入: + +```text +3 0 +5 5 1 + +``` + +輸出: + +```text +5 2 +``` + +### 範例三 + +輸入: + +```text +3 2 +1 2 3 +1 2 +2 3 + +``` + +輸出: + +```text +6 1 +``` + + diff --git a/problems/031-compile-critical-path/tests/adversarial-blind-01.in b/problems/031-compile-critical-path/tests/adversarial-blind-01.in new file mode 100644 index 0000000..c5b8b6a --- /dev/null +++ b/problems/031-compile-critical-path/tests/adversarial-blind-01.in @@ -0,0 +1,13 @@ +11 11 +1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 999999999 +1 2 +1 3 +2 4 +2 5 +3 4 +3 5 +4 6 +5 6 +7 8 +8 9 +9 10 diff --git a/problems/031-compile-critical-path/tests/adversarial-blind-01.out b/problems/031-compile-critical-path/tests/adversarial-blind-01.out new file mode 100644 index 0000000..e88c0fb --- /dev/null +++ b/problems/031-compile-critical-path/tests/adversarial-blind-01.out @@ -0,0 +1 @@ +4000000000 5 diff --git a/problems/031-compile-critical-path/tests/sample-01.in b/problems/031-compile-critical-path/tests/sample-01.in new file mode 100644 index 0000000..ed06901 --- /dev/null +++ b/problems/031-compile-critical-path/tests/sample-01.in @@ -0,0 +1,7 @@ +4 4 +2 3 3 4 +1 2 +1 3 +2 4 +3 4 + diff --git a/problems/031-compile-critical-path/tests/sample-01.out b/problems/031-compile-critical-path/tests/sample-01.out new file mode 100644 index 0000000..63eba86 --- /dev/null +++ b/problems/031-compile-critical-path/tests/sample-01.out @@ -0,0 +1 @@ +9 2 diff --git a/problems/031-compile-critical-path/tests/sample-02.in b/problems/031-compile-critical-path/tests/sample-02.in new file mode 100644 index 0000000..2a8f0d2 --- /dev/null +++ b/problems/031-compile-critical-path/tests/sample-02.in @@ -0,0 +1,3 @@ +3 0 +5 5 1 + diff --git a/problems/031-compile-critical-path/tests/sample-02.out b/problems/031-compile-critical-path/tests/sample-02.out new file mode 100644 index 0000000..69010fb --- /dev/null +++ b/problems/031-compile-critical-path/tests/sample-02.out @@ -0,0 +1 @@ +5 2 diff --git a/problems/031-compile-critical-path/tests/sample-03.in b/problems/031-compile-critical-path/tests/sample-03.in new file mode 100644 index 0000000..caa92c3 --- /dev/null +++ b/problems/031-compile-critical-path/tests/sample-03.in @@ -0,0 +1,5 @@ +3 2 +1 2 3 +1 2 +2 3 + diff --git a/problems/031-compile-critical-path/tests/sample-03.out b/problems/031-compile-critical-path/tests/sample-03.out new file mode 100644 index 0000000..afbc0d7 --- /dev/null +++ b/problems/031-compile-critical-path/tests/sample-03.out @@ -0,0 +1 @@ +6 1 diff --git a/problems/031-compile-critical-path/validator.py b/problems/031-compile-critical-path/validator.py new file mode 100644 index 0000000..7099e54 --- /dev/null +++ b/problems/031-compile-critical-path/validator.py @@ -0,0 +1,47 @@ +import sys + + +def fail(message: str) -> None: + raise SystemExit(message) + + +tokens = sys.stdin.buffer.read().split() +try: + values = list(map(int, tokens)) +except ValueError: + fail("input contains a non-integer token") +if len(values) < 2: + fail("missing N and M") +n, m = values[0], values[1] +if not 1 <= n <= 200_000 or not 0 <= m <= 400_000: + fail("N or M is outside its range") +if len(values) != 2 + n + 2 * m: + fail("unexpected token count") +durations = values[2 : 2 + n] +if ( + any(value < 1 or value > 10**9 for value in durations) + or sum(durations) > 9 * 10**18 +): + fail("invalid duration") +edges: list[list[int]] = [[] for _ in range(n)] +indegree = [0] * n +seen: set[tuple[int, int]] = set() +offset = 2 + n +for index in range(m): + u, v = values[offset + 2 * index] - 1, values[offset + 2 * index + 1] - 1 + if not 0 <= u < n or not 0 <= v < n or u == v or (u, v) in seen: + fail("invalid or duplicate edge") + seen.add((u, v)) + edges[u].append(v) + indegree[v] += 1 +queue = [node for node, degree in enumerate(indegree) if degree == 0] +head = 0 +while head < len(queue): + node = queue[head] + head += 1 + for target in edges[node]: + indegree[target] -= 1 + if indegree[target] == 0: + queue.append(target) +if len(queue) != n: + fail("graph is not acyclic") diff --git a/problems/032-conflict-package-cover/editorial.en.md b/problems/032-conflict-package-cover/editorial.en.md new file mode 100644 index 0000000..4087af7 --- /dev/null +++ b/problems/032-conflict-package-cover/editorial.en.md @@ -0,0 +1,32 @@ +# Editorial + +## Intuitive Approach + +Enumerating package subsets and checking whether every edge is covered is exponential. Kuhn's algorithm is better, but finding one augmenting path independently for each left vertex takes `O(LM)` in the worst case and fails on large layered graphs. + +## Optimal Approach: Hopcroft-Karp and Konig's Theorem + +The conflict graph is bipartite. Konig's theorem states that the size of a minimum vertex cover in a bipartite graph equals the size of a maximum matching, so it suffices to compute a maximum matching. + +In each Hopcroft-Karp phase, start a BFS from all unmatched left vertices. It assigns layers to left vertices and determines the shortest augmenting-path length. Then find a maximal set of vertex-disjoint shortest augmenting paths, following only edges for which the next matched left vertex is one layer deeper. + +Maintain an edge cursor for every left vertex during a phase, and invalidate a left vertex after all of its layered choices fail. This prevents repeated scans within the same phase. The reference implementations use explicit `stackU` and `stackV` structures to reconstruct augmenting paths without overflowing the call stack on deep graphs. + +The number of successful augmentations is the maximum matching size and, by Konig's theorem, the answer. + +## Correctness Proof + +BFS layers the alternating graph by shortest augmenting distance. The subsequent searches follow only valid consecutive layers. Whenever an unmatched right vertex is reached, flipping matched and unmatched edges along the recovered path increases the matching size by one and preserves the matching property. Edge cursors and failed-vertex pruning discard only edges already proved unable to complete a layered augmenting path in that phase. + +Consequently, after a phase no augmenting path of its shortest length remains. The Hopcroft-Karp theorem guarantees that repeating phases until BFS finds no augmenting path produces a maximum matching. Konig's theorem then equates its size with the minimum bipartite vertex-cover size, which is exactly the minimum number of packages whose isolation removes all conflict edges. + +## Complexity + +Hopcroft-Karp uses `O(sqrt(L + R))` phases. The implemented loops scan all left vertices and edges per phase and initialize right-side matching state, giving `O((L + R + M) sqrt(L + R))` time and `O(L + R + M)` space. The vertex terms matter when many isolated vertices coexist with a nontrivial component requiring several phases. + +## Common Mistakes + +- Applying `maximum matching = minimum vertex cover` to a non-bipartite graph. +- Following arbitrary edges after BFS and losing the layered complexity bound. +- Resetting edge cursors for every search and rescanning a phase repeatedly. +- Using recursive augmentation and overflowing the stack on a long alternating path. diff --git a/problems/032-conflict-package-cover/editorial.zh-TW.md b/problems/032-conflict-package-cover/editorial.zh-TW.md new file mode 100644 index 0000000..f4e158a --- /dev/null +++ b/problems/032-conflict-package-cover/editorial.zh-TW.md @@ -0,0 +1,30 @@ +# 解題說明 + +## 直覺解 + +枚舉所有套件子集合,檢查是否碰到每條 edge,時間指數級。較好的 Kuhn 演算法從每個左點各找一條增廣路,最壞 `O(LM)`,仍會被大型分層圖排除。 + +## 最佳解 + +這是二分圖 minimum vertex cover。Kőnig 定理指出:二分圖最小點覆蓋大小等於最大 matching 大小,所以只需求 maximum matching。 + +Hopcroft–Karp 每一 phase 先從所有未匹配左點 BFS,建立「左點層級」並找最短增廣路長;再只沿 `dist[nextU]=dist[u]+1` 的 edge 找一組 vertex-disjoint augmenting paths。實作使用每個左點的 edge cursor,失敗即把 dist 設為無效,避免同一 phase 重掃。為避免深圖造成 call stack overflow,reference solutions 以顯式 `stackU/stackV` 還原增廣路。 + +## 正確性證明 + +BFS 的 dist 使 DFS/顯式堆疊只走交錯圖中的最短增廣路;每次抵達未匹配右點,沿堆疊翻轉 matched/unmatched edges,matching 大小增加一且仍是 matching。cursor 與失敗剪枝不會刪除任何符合分層條件的尚未檢查 edge,所以一個 phase 結束時不存在該最短長度的增廣路。Hopcroft–Karp 定理保證反覆 phase 直到 BFS 找不到增廣路時 matching 為最大。最後由 Kőnig 定理,其大小等於最小點覆蓋大小,正是題目答案。 + +## 複雜度 + +Hopcroft–Karp 有 `O(sqrt(L+R))` 個 phase。Reference implementations 每個 phase +會掃過全部左點並走訪各 edge,另需初始化右點 matching,因此保守且與實際 +迴圈一致的總時間為 `O((L+R+M) sqrt(L+R))`,空間為 `O(L+R+M)`。不能省略 +vertex 項:當圖同時有大量孤立左點與需要多個 phase 的非平凡 component 時, +每個 phase 仍會掃過那些孤立點。 + +## 常見錯誤 + +- 在一般圖套用「matching=vertex cover」;此等式只保證於二分圖。 +- BFS 後仍走任意 edge,失去分層複雜度。 +- 每次 DFS 重設所有 edge cursor,造成同 phase 重掃。 +- 遞迴增廣在長交錯路上 stack overflow。 diff --git a/problems/032-conflict-package-cover/generator.py b/problems/032-conflict-package-cover/generator.py new file mode 100644 index 0000000..f126121 --- /dev/null +++ b/problems/032-conflict-package-cover/generator.py @@ -0,0 +1,10 @@ +import random, sys + +seed, index = map(int, sys.argv[1:]) +r = random.Random(seed * 10007 + index) +l = 3 + index % 5 +rr = 3 + (index // 2) % 5 +edges = [(u, v) for u in range(1, l + 1) for v in range(1, rr + 1) if r.random() < 0.35] +print(l, rr, len(edges)) +for e in edges: + print(*e) diff --git a/problems/032-conflict-package-cover/oracle.py b/problems/032-conflict-package-cover/oracle.py new file mode 100644 index 0000000..89aa5fa --- /dev/null +++ b/problems/032-conflict-package-cover/oracle.py @@ -0,0 +1,12 @@ +import sys + +a = list(map(int, sys.stdin.read().split())) +l, r, m = a[:3] +edges = [(a[i] - 1, a[i + 1] - 1) for i in range(3, len(a), 2)] +for k in range(l + r + 1): + for mask in range(1 << (l + r)): + if mask.bit_count() == k and all( + mask >> u & 1 or mask >> (l + v) & 1 for u, v in edges + ): + print(k) + raise SystemExit diff --git a/problems/032-conflict-package-cover/problem.json b/problems/032-conflict-package-cover/problem.json new file mode 100644 index 0000000..f0e3629 --- /dev/null +++ b/problems/032-conflict-package-cover/problem.json @@ -0,0 +1,156 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 32, + "slug": "conflict-package-cover", + "title": { + "zh-TW": "最少隔離的衝突套件", + "en": "Minimum Conflict Package Isolation" + }, + "difficulty": "hard", + "tags": [ + "graph", + "bipartite-matching", + "minimum-vertex-cover", + "hopcroft-karp" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-blind-01", + "kind": "adversarial", + "input": "tests/adversarial-blind-01.in", + "output": "tests/adversarial-blind-01.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 15000000, + "memoryLimitBytes": 536870912 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 1500000, + "memoryLimitBytes": 402653184 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 450000, + "memoryLimitBytes": 268435456 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "枚舉隔離集合", + "en": "Enumerate isolation sets" + }, + "time": "O(2^(L+R) M)", + "space": "O(L+R)", + "accepted": false + }, + { + "name": { + "zh-TW": "逐左點增廣", + "en": "One augmentation per left vertex" + }, + "time": "O(LM)", + "space": "O(L+R+M)", + "accepted": false + }, + { + "name": { + "zh-TW": "Hopcroft-Karp 與 Kőnig 定理", + "en": "Hopcroft-Karp and Konig's theorem" + }, + "time": "O((L+R+M) sqrt(L+R))", + "space": "O(L+R+M)", + "accepted": true + } + ] +} diff --git a/problems/032-conflict-package-cover/solutions/c/main.c b/problems/032-conflict-package-cover/solutions/c/main.c new file mode 100644 index 0000000..1c5ee74 --- /dev/null +++ b/problems/032-conflict-package-cover/solutions/c/main.c @@ -0,0 +1,98 @@ +#include +#include +int main(void) { + int L, R, M; + if (scanf("%d%d%d", &L, &R, &M) != 3) + return 0; + int *head = malloc(sizeof(int) * (size_t)L), + *to = malloc(sizeof(int) * (size_t)(M ? M : 1)), + *next = malloc(sizeof(int) * (size_t)(M ? M : 1)); + for (int i = 0; i < L; i++) + head[i] = -1; + for (int e = 0; e < M; e++) { + int u, v; + scanf("%d%d", &u, &v); + u--; + to[e] = v - 1; + next[e] = head[u]; + head[u] = e; + } + int *pu = malloc(sizeof(int) * (size_t)L), + *pv = malloc(sizeof(int) * (size_t)R), + *dist = malloc(sizeof(int) * (size_t)L), + *q = malloc(sizeof(int) * (size_t)L), + *cur = malloc(sizeof(int) * (size_t)L), + *su = malloc(sizeof(int) * (size_t)L), + *sv = malloc(sizeof(int) * (size_t)L); + for (int i = 0; i < L; i++) + pu[i] = -1; + for (int i = 0; i < R; i++) + pv[i] = -1; + int matching = 0; + for (;;) { + int l = 0, r = 0, terminal = -1; + for (int u = 0; u < L; u++) { + dist[u] = pu[u] < 0 ? 0 : -1; + if (pu[u] < 0) + q[r++] = u; + } + while (l < r) { + int u = q[l++]; + if (terminal >= 0 && dist[u] >= terminal) + continue; + for (int e = head[u]; e >= 0; e = next[e]) { + int w = pv[to[e]]; + if (w < 0) + terminal = dist[u]; + else if (dist[w] < 0) { + dist[w] = dist[u] + 1; + q[r++] = w; + } + } + } + if (terminal < 0) + break; + for (int i = 0; i < L; i++) + cur[i] = head[i]; + for (int root = 0; root < L; root++) { + if (pu[root] >= 0) + continue; + int ut = 1, vt = 0, ok = 0; + su[0] = root; + while (ut && !ok) { + int u = su[ut - 1], desc = 0; + while (cur[u] >= 0) { + int e = cur[u]; + cur[u] = next[e]; + int v = to[e], w = pv[v]; + if (w < 0 && dist[u] == terminal) { + pu[u] = v; + pv[v] = u; + for (int i = vt - 1; i >= 0; i--) { + pu[su[i]] = sv[i]; + pv[sv[i]] = su[i]; + } + ok = 1; + break; + } + if (w >= 0 && dist[u] < terminal && dist[w] == dist[u] + 1) { + sv[vt++] = v; + su[ut++] = w; + desc = 1; + break; + } + } + if (!ok && !desc) { + dist[u] = -1; + ut--; + if (vt) + vt--; + } + } + if (ok) + matching++; + } + } + printf("%d\n", matching); + return 0; +} diff --git a/problems/032-conflict-package-cover/solutions/cpp/main.cpp b/problems/032-conflict-package-cover/solutions/cpp/main.cpp new file mode 100644 index 0000000..5985723 --- /dev/null +++ b/problems/032-conflict-package-cover/solutions/cpp/main.cpp @@ -0,0 +1,84 @@ +#include +#include +#include +using namespace std; +int main() { + ios::sync_with_stdio(false); + cin.tie(nullptr); + int L, R, M; + if (!(cin >> L >> R >> M)) + return 0; + vector> g(L); + while (M--) { + int u, v; + cin >> u >> v; + g[u - 1].push_back(v - 1); + } + vector pu(L, -1), pv(R, -1), dist(L), cur(L); + int matching = 0; + for (;;) { + queue q; + for (int u = 0; u < L; u++) { + dist[u] = pu[u] < 0 ? 0 : -1; + if (pu[u] < 0) + q.push(u); + } + int terminal = -1; + while (!q.empty()) { + int u = q.front(); + q.pop(); + if (terminal >= 0 && dist[u] >= terminal) + continue; + for (int v : g[u]) { + int w = pv[v]; + if (w < 0) + terminal = dist[u]; + else if (dist[w] < 0) { + dist[w] = dist[u] + 1; + q.push(w); + } + } + } + if (terminal < 0) + break; + fill(cur.begin(), cur.end(), 0); + for (int root = 0; root < L; root++) { + if (pu[root] >= 0) + continue; + vector su{root}, sv; + bool ok = false; + while (!su.empty() && !ok) { + int u = su.back(); + bool down = false; + while (cur[u] < (int)g[u].size()) { + int v = g[u][cur[u]++], w = pv[v]; + if (w < 0 && dist[u] == terminal) { + pu[u] = v; + pv[v] = u; + for (int i = (int)sv.size() - 1; i >= 0; i--) { + pu[su[i]] = sv[i]; + pv[sv[i]] = su[i]; + } + ok = true; + break; + } + if (w >= 0 && dist[u] < terminal && dist[w] == dist[u] + 1) { + sv.push_back(v); + su.push_back(w); + down = true; + break; + } + } + if (!ok && !down) { + dist[u] = -1; + su.pop_back(); + if (!sv.empty()) + sv.pop_back(); + } + } + if (ok) + matching++; + } + } + cout << matching << '\n'; +} diff --git a/problems/032-conflict-package-cover/solutions/go/main.go b/problems/032-conflict-package-cover/solutions/go/main.go new file mode 100644 index 0000000..c4d069a --- /dev/null +++ b/problems/032-conflict-package-cover/solutions/go/main.go @@ -0,0 +1,103 @@ +package main + +import ( + "bufio" + "fmt" + "os" +) + +func main() { + in := bufio.NewReader(os.Stdin) + var L, R, M int + fmt.Fscan(in, &L, &R, &M) + g := make([][]int, L) + for ; M > 0; M-- { + var u, v int + fmt.Fscan(in, &u, &v) + g[u-1] = append(g[u-1], v-1) + } + pu := make([]int, L) + pv := make([]int, R) + dist := make([]int, L) + for i := range pu { + pu[i] = -1 + } + for i := range pv { + pv[i] = -1 + } + matching := 0 + for { + q := []int{} + for u := 0; u < L; u++ { + if pu[u] < 0 { + dist[u] = 0 + q = append(q, u) + } else { + dist[u] = -1 + } + } + terminal := -1 + for h := 0; h < len(q); h++ { + u := q[h] + if terminal >= 0 && dist[u] >= terminal { + continue + } + for _, v := range g[u] { + w := pv[v] + if w < 0 { + terminal = dist[u] + } else if dist[w] < 0 { + dist[w] = dist[u] + 1 + q = append(q, w) + } + } + } + if terminal < 0 { + break + } + cur := make([]int, L) + for root := 0; root < L; root++ { + if pu[root] >= 0 { + continue + } + su, sv := []int{root}, []int{} + ok := false + for len(su) > 0 && !ok { + u := su[len(su)-1] + down := false + for cur[u] < len(g[u]) { + v := g[u][cur[u]] + cur[u]++ + w := pv[v] + if w < 0 && dist[u] == terminal { + pu[u] = v + pv[v] = u + for i := len(sv) - 1; i >= 0; i-- { + pu[su[i]] = sv[i] + pv[sv[i]] = su[i] + } + ok = true + break + } + if w >= 0 && dist[u] < terminal && dist[w] == dist[u]+1 { + sv = append(sv, v) + su = append(su, w) + down = true + break + } + } + if !ok && !down { + dist[u] = -1 + su = su[:len(su)-1] + if len(sv) > 0 { + sv = sv[:len(sv)-1] + } + } + } + if ok { + matching++ + } + } + } + fmt.Println(matching) +} diff --git a/problems/032-conflict-package-cover/solutions/javascript/main.js b/problems/032-conflict-package-cover/solutions/javascript/main.js new file mode 100644 index 0000000..8fb650a --- /dev/null +++ b/problems/032-conflict-package-cover/solutions/javascript/main.js @@ -0,0 +1,95 @@ +import * as std from "std"; + +const input = std.in.readAsString(); +let scan = 0; +function nextInt() { + while (scan < input.length && input.charCodeAt(scan) <= 32) scan++; + let value = 0; + while (scan < input.length) { + const digit = input.charCodeAt(scan) - 48; + if (digit < 0 || digit > 9) break; + value = value * 10 + digit; + scan++; + } + return value; +} + +const left = nextInt(), right = nextInt(), edgeCount = nextInt(); +const head = new Int32Array(left).fill(-1), + to = new Int32Array(edgeCount), + next = new Int32Array(edgeCount); +for (let edge = 0; edge < edgeCount; edge++) { + const u = nextInt() - 1, v = nextInt() - 1; + to[edge] = v; + next[edge] = head[u]; + head[u] = edge; +} +const pairLeft = new Int32Array(left).fill(-1), + pairRight = new Int32Array(right).fill(-1), + distance = new Int32Array(left), + queue = new Int32Array(left), + edgeCursor = new Int32Array(left), + stackLeft = new Int32Array(left), + stackRight = new Int32Array(left); +let matching = 0; +for (;;) { + let front = 0, back = 0, terminal = -1; + for (let u = 0; u < left; u++) { + distance[u] = pairLeft[u] < 0 ? 0 : -1; + if (pairLeft[u] < 0) queue[back++] = u; + } + while (front < back) { + const u = queue[front++]; + if (terminal >= 0 && distance[u] >= terminal) continue; + for (let edge = head[u]; edge !== -1; edge = next[edge]) { + const mate = pairRight[to[edge]]; + if (mate < 0) terminal = distance[u]; + else if (distance[mate] < 0) { + distance[mate] = distance[u] + 1; + queue[back++] = mate; + } + } + } + if (terminal < 0) break; + edgeCursor.set(head); + for (let root = 0; root < left; root++) { + if (pairLeft[root] >= 0) continue; + let leftTop = 1, rightTop = 0, augmented = false; + stackLeft[0] = root; + while (leftTop > 0 && !augmented) { + const u = stackLeft[leftTop - 1]; + let descended = false; + while (edgeCursor[u] !== -1) { + const edge = edgeCursor[u]; + edgeCursor[u] = next[edge]; + const v = to[edge], mate = pairRight[v]; + if (mate < 0 && distance[u] === terminal) { + pairLeft[u] = v; + pairRight[v] = u; + for (let i = rightTop - 1; i >= 0; i--) { + pairLeft[stackLeft[i]] = stackRight[i]; + pairRight[stackRight[i]] = stackLeft[i]; + } + augmented = true; + break; + } + if ( + mate >= 0 && distance[u] < terminal && + distance[mate] === distance[u] + 1 + ) { + stackRight[rightTop++] = v; + stackLeft[leftTop++] = mate; + descended = true; + break; + } + } + if (!augmented && !descended) { + distance[u] = -1; + leftTop--; + if (rightTop > 0) rightTop--; + } + } + if (augmented) matching++; + } +} +std.out.puts(`${matching}\n`); diff --git a/problems/032-conflict-package-cover/solutions/python/main.py b/problems/032-conflict-package-cover/solutions/python/main.py new file mode 100644 index 0000000..bfeef8a --- /dev/null +++ b/problems/032-conflict-package-cover/solutions/python/main.py @@ -0,0 +1,68 @@ +import sys, collections + +a = list(map(int, sys.stdin.read().split())) +L, R, M = a[:3] +g = [[] for _ in range(L)] +p = 3 +for _ in range(M): + g[a[p] - 1].append(a[p + 1] - 1) + p += 2 +pu = [-1] * L +pv = [-1] * R +dist = [-1] * L +matching = 0 +while True: + q = collections.deque() + for u in range(L): + dist[u] = 0 if pu[u] < 0 else -1 + if pu[u] < 0: + q.append(u) + terminal = -1 + while q: + u = q.popleft() + if terminal >= 0 and dist[u] >= terminal: + continue + for v in g[u]: + w = pv[v] + if w < 0: + terminal = dist[u] + elif dist[w] < 0: + dist[w] = dist[u] + 1 + q.append(w) + if terminal < 0: + break + cur = [0] * L + for root in range(L): + if pu[root] >= 0: + continue + su = [root] + sv = [] + ok = False + while su: + u = su[-1] + while cur[u] < len(g[u]): + v = g[u][cur[u]] + cur[u] += 1 + w = pv[v] + if w < 0 and dist[u] == terminal: + pu[u] = v + pv[v] = u + for i in range(len(sv) - 1, -1, -1): + pu[su[i]] = sv[i] + pv[sv[i]] = su[i] + ok = True + break + if w >= 0 and dist[u] < terminal and dist[w] == dist[u] + 1: + sv.append(v) + su.append(w) + break + if ok: + break + if su and cur[su[-1]] >= len(g[su[-1]]): + dist[su[-1]] = -1 + su.pop() + if sv: + sv.pop() + if ok: + matching += 1 +print(matching) diff --git a/problems/032-conflict-package-cover/solutions/rust/main.rs b/problems/032-conflict-package-cover/solutions/rust/main.rs new file mode 100644 index 0000000..40c2662 --- /dev/null +++ b/problems/032-conflict-package-cover/solutions/rust/main.rs @@ -0,0 +1,91 @@ +use std::collections::VecDeque; +use std::io::{self, Read}; +fn main() { + let mut s = String::new(); + io::stdin().read_to_string(&mut s).unwrap(); + let mut it = s.split_whitespace(); + let l: usize = it.next().unwrap().parse().unwrap(); + let r: usize = it.next().unwrap().parse().unwrap(); + let m: usize = it.next().unwrap().parse().unwrap(); + let mut g = vec![vec![]; l]; + for _ in 0..m { + let u = it.next().unwrap().parse::().unwrap() - 1; + let v = it.next().unwrap().parse::().unwrap() - 1; + g[u].push(v); + } + let mut pu = vec![usize::MAX; l]; + let mut pv = vec![usize::MAX; r]; + let mut dist = vec![-1i32; l]; + let mut matching = 0; + loop { + let mut q = VecDeque::new(); + for u in 0..l { + dist[u] = if pu[u] == usize::MAX { + q.push_back(u); + 0 + } else { + -1 + } + } + let mut terminal = -1; + while let Some(u) = q.pop_front() { + if terminal >= 0 && dist[u] >= terminal { + continue; + } + for &v in &g[u] { + let w = pv[v]; + if w == usize::MAX { + terminal = dist[u] + } else if dist[w] < 0 { + dist[w] = dist[u] + 1; + q.push_back(w) + } + } + } + if terminal < 0 { + break; + } + let mut cur = vec![0; l]; + for root in 0..l { + if pu[root] != usize::MAX { + continue; + } + let (mut su, mut sv) = (vec![root], vec![]); + let mut ok = false; + while !su.is_empty() && !ok { + let u = *su.last().unwrap(); + let mut down = false; + while cur[u] < g[u].len() { + let v = g[u][cur[u]]; + cur[u] += 1; + let w = pv[v]; + if w == usize::MAX && dist[u] == terminal { + pu[u] = v; + pv[v] = u; + for i in (0..sv.len()).rev() { + pu[su[i]] = sv[i]; + pv[sv[i]] = su[i] + } + ok = true; + break; + } + if w != usize::MAX && dist[u] < terminal && dist[w] == dist[u] + 1 { + sv.push(v); + su.push(w); + down = true; + break; + } + } + if !ok && !down { + dist[u] = -1; + su.pop(); + sv.pop(); + } + } + if ok { + matching += 1 + } + } + } + println!("{matching}"); +} diff --git a/problems/032-conflict-package-cover/solutions/typescript/main.ts b/problems/032-conflict-package-cover/solutions/typescript/main.ts new file mode 100644 index 0000000..6a8ea68 --- /dev/null +++ b/problems/032-conflict-package-cover/solutions/typescript/main.ts @@ -0,0 +1,95 @@ +import * as std from "std"; + +const input: string = std.in.readAsString(); +let scan = 0; +function nextInt(): number { + while (scan < input.length && input.charCodeAt(scan) <= 32) scan++; + let value = 0; + while (scan < input.length) { + const digit = input.charCodeAt(scan) - 48; + if (digit < 0 || digit > 9) break; + value = value * 10 + digit; + scan++; + } + return value; +} + +const left = nextInt(), right = nextInt(), edgeCount = nextInt(); +const head = new Int32Array(left).fill(-1), + to = new Int32Array(edgeCount), + next = new Int32Array(edgeCount); +for (let edge = 0; edge < edgeCount; edge++) { + const u = nextInt() - 1, v = nextInt() - 1; + to[edge] = v; + next[edge] = head[u]!; + head[u] = edge; +} +const pairLeft = new Int32Array(left).fill(-1), + pairRight = new Int32Array(right).fill(-1), + distance = new Int32Array(left), + queue = new Int32Array(left), + edgeCursor = new Int32Array(left), + stackLeft = new Int32Array(left), + stackRight = new Int32Array(left); +let matching = 0; +for (;;) { + let front = 0, back = 0, terminal = -1; + for (let u = 0; u < left; u++) { + distance[u] = pairLeft[u]! < 0 ? 0 : -1; + if (pairLeft[u]! < 0) queue[back++] = u; + } + while (front < back) { + const u = queue[front++]!; + if (terminal >= 0 && distance[u]! >= terminal) continue; + for (let edge = head[u]!; edge !== -1; edge = next[edge]!) { + const mate = pairRight[to[edge]!]!; + if (mate < 0) terminal = distance[u]!; + else if (distance[mate]! < 0) { + distance[mate] = distance[u]! + 1; + queue[back++] = mate; + } + } + } + if (terminal < 0) break; + edgeCursor.set(head); + for (let root = 0; root < left; root++) { + if (pairLeft[root]! >= 0) continue; + let leftTop = 1, rightTop = 0, augmented = false; + stackLeft[0] = root; + while (leftTop > 0 && !augmented) { + const u = stackLeft[leftTop - 1]!; + let descended = false; + while (edgeCursor[u] !== -1) { + const edge = edgeCursor[u]!; + edgeCursor[u] = next[edge]!; + const v = to[edge]!, mate = pairRight[v]!; + if (mate < 0 && distance[u] === terminal) { + pairLeft[u] = v; + pairRight[v] = u; + for (let i = rightTop - 1; i >= 0; i--) { + pairLeft[stackLeft[i]!] = stackRight[i]!; + pairRight[stackRight[i]!] = stackLeft[i]!; + } + augmented = true; + break; + } + if ( + mate >= 0 && distance[u]! < terminal && + distance[mate] === distance[u]! + 1 + ) { + stackRight[rightTop++] = v; + stackLeft[leftTop++] = mate; + descended = true; + break; + } + } + if (!augmented && !descended) { + distance[u] = -1; + leftTop--; + if (rightTop > 0) rightTop--; + } + } + if (augmented) matching++; + } +} +std.out.puts(`${matching}\n`); diff --git a/problems/032-conflict-package-cover/statement.en.md b/problems/032-conflict-package-cover/statement.en.md new file mode 100644 index 0000000..685aecd --- /dev/null +++ b/problems/032-conflict-package-cover/statement.en.md @@ -0,0 +1,79 @@ +# Minimum Conflict Package Isolation + +While designing the runtime package environment for a WASM OJ, we needed to combine npm packages from the JavaScript ecosystem with lower-level native packages. Some cross-ecosystem combinations compete for the same symbols, expose incompatible ABIs, or require conflicting runtime capabilities, so both packages in such a pair cannot remain available together. + +Resolving conflicts one at a time would miss an important effect: isolating one package removes every conflict involving it. We therefore want an isolation plan that removes as few packages as possible while leaving the remaining packages mutually usable. + +Model the `L` npm packages as vertices on the left and the `R` native packages as vertices on the right. Every conflict edge connects one left package to one right package and means that its endpoints cannot both remain available. Isolating either endpoint eliminates that conflict, and isolating a package eliminates all incident conflicts. + +Find the minimum number of packages that must be isolated to eliminate every conflict. Output only the minimum size; an optimal set need not be unique, so the set itself is not required. + +## Input + +The first line contains `L R M`. Each of the next `M` lines contains `u v`, where `u` is a 1-based left-side package ID and `v` is a 1-based right-side package ID. + +## Output + +Output one integer: the minimum number of vertices required to cover every conflict edge. If `M = 0`, output `0`. + +## Constraints + +- `1 <= L, R <= 200000` +- `0 <= M <= 400000` +- There are no duplicate edges. +- Full tests include layered graphs on which one augmenting search per left vertex takes `Theta(LM)`; a layered augmenting-path algorithm is required. + +## Examples + + + +### Example One + +Input: + +```text +3 3 3 +1 1 +2 2 +3 3 +``` + +Output: + +```text +3 +``` + +### Example Two + +Input: + +```text +1 4 4 +1 1 +1 2 +1 3 +1 4 +``` + +Output: + +```text +1 +``` + +### Example Three + +Input: + +```text +4 5 0 +``` + +Output: + +```text +0 +``` + + diff --git a/problems/032-conflict-package-cover/statement.zh-TW.md b/problems/032-conflict-package-cover/statement.zh-TW.md new file mode 100644 index 0000000..ea1f09b --- /dev/null +++ b/problems/032-conflict-package-cover/statement.zh-TW.md @@ -0,0 +1,78 @@ +# 最少隔離的衝突套件 + +在設計 WASM OJ 的 runtime package 環境時,我們需要同時組合 JavaScript 生態的 npm packages 與底層的 native packages。某些跨生態的套件組合會爭用相同符號、提供不相容的 ABI,或要求彼此衝突的 runtime capability,因此不能同時開放給同一個執行環境。 + +逐一移除 conflict 並不足以解決問題,因為隔離一個套件會同時消除所有涉及它的衝突。我們希望找出影響最小的隔離方案,讓其餘套件仍能一起使用。 + +將 npm packages 視為左側的 `L` 個節點,native packages 視為右側的 `R` 個節點。每條 conflict edge 連接一個左側套件與一個右側套件,表示兩端不能同時保留;隔離任一端都會消除這條 conflict,而隔離一個套件會消除所有與它相連的 conflict。 + +請計算至少要隔離多少個套件,才能消除全部 conflict。只需輸出最小數量;最佳集合可能不唯一,因此不輸出集合本身。 + +## 輸入 + +第一行 `L R M`。接著 `M` 行 `u v`,其中 `u` 是 1-based 左側 ID,`v` 是 1-based 右側 ID。 + +## 輸出 + +輸出一個整數:覆蓋所有 conflict edges 所需的最少頂點數。`M=0` 時輸出 `0`。 + +## 限制 + +- `1 <= L,R <= 200000`,`0 <= M <= 400000`。 +- 沒有重複 edge。 +- 完整測資包含讓逐一增廣達到 `Theta(LM)` 的圖,必須使用分層增廣。 + +## 範例 + + + +### 範例一 + +輸入: + +```text +3 3 3 +1 1 +2 2 +3 3 +``` + +輸出: + +```text +3 +``` + +### 範例二 + +輸入: + +```text +1 4 4 +1 1 +1 2 +1 3 +1 4 +``` + +輸出: + +```text +1 +``` + +### 範例三 + +輸入: + +```text +4 5 0 +``` + +輸出: + +```text +0 +``` + + diff --git a/problems/032-conflict-package-cover/tests/adversarial-blind-01.in b/problems/032-conflict-package-cover/tests/adversarial-blind-01.in new file mode 100644 index 0000000..cd738bc --- /dev/null +++ b/problems/032-conflict-package-cover/tests/adversarial-blind-01.in @@ -0,0 +1,8 @@ +4 4 7 +1 1 +1 2 +2 1 +3 2 +3 3 +4 3 +4 4 diff --git a/problems/032-conflict-package-cover/tests/adversarial-blind-01.out b/problems/032-conflict-package-cover/tests/adversarial-blind-01.out new file mode 100644 index 0000000..b8626c4 --- /dev/null +++ b/problems/032-conflict-package-cover/tests/adversarial-blind-01.out @@ -0,0 +1 @@ +4 diff --git a/problems/032-conflict-package-cover/tests/sample-01.in b/problems/032-conflict-package-cover/tests/sample-01.in new file mode 100644 index 0000000..16f0fa6 --- /dev/null +++ b/problems/032-conflict-package-cover/tests/sample-01.in @@ -0,0 +1,4 @@ +3 3 3 +1 1 +2 2 +3 3 diff --git a/problems/032-conflict-package-cover/tests/sample-01.out b/problems/032-conflict-package-cover/tests/sample-01.out new file mode 100644 index 0000000..00750ed --- /dev/null +++ b/problems/032-conflict-package-cover/tests/sample-01.out @@ -0,0 +1 @@ +3 diff --git a/problems/032-conflict-package-cover/tests/sample-02.in b/problems/032-conflict-package-cover/tests/sample-02.in new file mode 100644 index 0000000..2be6f22 --- /dev/null +++ b/problems/032-conflict-package-cover/tests/sample-02.in @@ -0,0 +1,5 @@ +1 4 4 +1 1 +1 2 +1 3 +1 4 diff --git a/problems/032-conflict-package-cover/tests/sample-02.out b/problems/032-conflict-package-cover/tests/sample-02.out new file mode 100644 index 0000000..d00491f --- /dev/null +++ b/problems/032-conflict-package-cover/tests/sample-02.out @@ -0,0 +1 @@ +1 diff --git a/problems/032-conflict-package-cover/tests/sample-03.in b/problems/032-conflict-package-cover/tests/sample-03.in new file mode 100644 index 0000000..a5546c5 --- /dev/null +++ b/problems/032-conflict-package-cover/tests/sample-03.in @@ -0,0 +1 @@ +4 5 0 diff --git a/problems/032-conflict-package-cover/tests/sample-03.out b/problems/032-conflict-package-cover/tests/sample-03.out new file mode 100644 index 0000000..573541a --- /dev/null +++ b/problems/032-conflict-package-cover/tests/sample-03.out @@ -0,0 +1 @@ +0 diff --git a/problems/032-conflict-package-cover/validator.py b/problems/032-conflict-package-cover/validator.py new file mode 100644 index 0000000..cae3bcb --- /dev/null +++ b/problems/032-conflict-package-cover/validator.py @@ -0,0 +1,26 @@ +import sys + + +def main(): + a = list(map(int, sys.stdin.read().split())) + assert len(a) >= 3 + l, r, m = a[:3] + assert ( + 1 <= l <= 200000 + and 1 <= r <= 200000 + and 0 <= m <= 400000 + and len(a) == 3 + 2 * m + ) + seen = set() + p = 3 + for _ in range(m): + u, v = a[p : p + 2] + p += 2 + assert 1 <= u <= l and 1 <= v <= r and (u, v) not in seen + seen.add((u, v)) + + +try: + main() +except (AssertionError, ValueError): + sys.exit(1) diff --git a/problems/033-toolchain-mirror-network/editorial.en.md b/problems/033-toolchain-mirror-network/editorial.en.md new file mode 100644 index 0000000..a0a8e0f --- /dev/null +++ b/problems/033-toolchain-mirror-network/editorial.en.md @@ -0,0 +1,28 @@ +# Editorial + +## Intuitive Approach + +Enumerate subsets of links, test connectivity, and retain the cheapest feasible subset. This is exponential; restricting enumeration to `N - 1` links is still infeasible. + +## Optimal Approach: Kruskal's Algorithm + +If a feasible connected subgraph contains a cycle, one edge on that cycle can be removed without disconnecting it. Since all costs are nonnegative, removal cannot increase the cost. Therefore some optimum is a spanning tree, and the problem is exactly a minimum spanning tree problem. + +Sort links by nondecreasing cost. A disjoint-set union structure tracks current components. Accept an edge precisely when its endpoints are in different components, then unite them. Stop after accepting `N - 1` edges. If fewer than `N - 1` can be accepted, the graph is disconnected. Equal-cost edge order does not affect the minimum total, and no edge-set tie-break is required. + +## Correctness Proof + +At every step, Kruskal chooses a globally lightest edge joining two current components. For the cut separating those components, the cut property guarantees an MST containing such a lightest edge. Thus, inductively, all accepted edges can be extended to an MST. Once `N - 1` edges have been accepted, they are acyclic by the DSU test and connect all vertices, so they form a minimum-cost spanning tree. + +If the scan ends earlier, at least two final components have no edge between them; otherwise that edge would have joined them. No spanning tree exists, so `IMPOSSIBLE` is correct. + +## Complexity + +Sorting takes `O(M log M)` time. DSU operations take `O(M alpha(N))` total time. Storage is `O(N + M)`. + +## Common Mistakes + +- Requiring every host to connect directly to host 1. +- Keeping the first parallel edge instead of allowing the cheapest useful one. +- Accumulating the MST cost in a 32-bit integer. +- Forgetting that `N = 1` is already connected even when `M = 0`. diff --git a/problems/033-toolchain-mirror-network/editorial.zh-TW.md b/problems/033-toolchain-mirror-network/editorial.zh-TW.md new file mode 100644 index 0000000..b3c740c --- /dev/null +++ b/problems/033-toolchain-mirror-network/editorial.zh-TW.md @@ -0,0 +1,26 @@ +# 解題說明 + +## 直覺解 + +枚舉 link 子集合並檢查連通,再取最低成本,時間指數級。即使只枚舉 `N-1` 條也仍不可行。 + +## 最佳解 + +任一可行 connected subgraph 若含 cycle,因成本非負,可刪除 cycle 上一條 edge 而不變差;所以存在最佳 spanning tree,題目即 minimum spanning tree。 + +Kruskal 將 edges 依 cost 非遞減排序。DSU 判斷兩端是否已在同一 component;不同才選取並 union。選到 `N-1` 條即完成。若掃完仍不足,圖不連通。相同 cost 的處理順序不影響最小總成本,因此不需要 tie-break 或輸出 edge 集合。 + +## 正確性證明 + +在每一步,Kruskal 選的是連接兩個目前 components 的全域最輕 edge。依 cut property,對分隔這兩 components 的 cut,存在一棵 MST 含此最輕 edge;所以可在不提高最佳成本下接受它。歸納所有接受 edges 都能擴充成 MST。成功選 `N-1` 條時它們無 cycle 且連通,故是 spanning tree 且成本最小。若不足 `N-1`,原圖 components 之間沒有任何 edge,任何 spanning tree 都不存在。 + +## 複雜度 + +排序 `O(M log M)`;DSU 總計 `O(M alpha(N))`,空間 `O(N+M)`。 + +## 常見錯誤 + +- 把 toolchain 傳送誤解成每個 host 都必須直接連 host 1。 +- 平行 edge 只保留輸入第一條,而非最低成本選擇。 +- 使用 32-bit 累加 MST cost。 +- 忘記 `N=1` 即使 `M=0` 也已完成。 diff --git a/problems/033-toolchain-mirror-network/generator.py b/problems/033-toolchain-mirror-network/generator.py new file mode 100644 index 0000000..5473fa5 --- /dev/null +++ b/problems/033-toolchain-mirror-network/generator.py @@ -0,0 +1,14 @@ +import random, sys + +seed, index = map(int, sys.argv[1:]) +r = random.Random(seed * 7919 + index) +n = 2 + index % 6 +all_e = [(u, v, r.randrange(20)) for u in range(1, n + 1) for v in range(u + 1, n + 1)] +r.shuffle(all_e) +m = min(len(all_e), 5 + index % 8) +e = all_e[:m] +if index % 4 == 0: + e = [] +print(n, len(e)) +for x in e: + print(*x) diff --git a/problems/033-toolchain-mirror-network/oracle.py b/problems/033-toolchain-mirror-network/oracle.py new file mode 100644 index 0000000..a4786b8 --- /dev/null +++ b/problems/033-toolchain-mirror-network/oracle.py @@ -0,0 +1,29 @@ +import itertools, sys + +a = list(map(int, sys.stdin.read().split())) +n, m = a[:2] +e = [tuple(a[i : i + 3]) for i in range(2, len(a), 3)] +if n == 1: + print("COST 0") + raise SystemExit +best = None +for take in itertools.combinations(e, n - 1): + p = list(range(n)) + + def f(x): + while p[x] != x: + p[x] = p[p[x]] + x = p[x] + return x + + ok = True + for u, v, _ in take: + x, y = f(u - 1), f(v - 1) + if x == y: + ok = False + break + p[x] = y + if ok: + z = sum(x[2] for x in take) + best = z if best is None else min(best, z) +print("IMPOSSIBLE" if best is None else f"COST {best}") diff --git a/problems/033-toolchain-mirror-network/problem.json b/problems/033-toolchain-mirror-network/problem.json new file mode 100644 index 0000000..4a3290b --- /dev/null +++ b/problems/033-toolchain-mirror-network/problem.json @@ -0,0 +1,147 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 33, + "slug": "toolchain-mirror-network", + "title": { + "zh-TW": "Toolchain 鏡像網路", + "en": "Toolchain Mirror Network" + }, + "difficulty": "medium", + "tags": [ + "graph", + "minimum-spanning-tree", + "disjoint-set-union", + "greedy" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-blind-01", + "kind": "adversarial", + "input": "tests/adversarial-blind-01.in", + "output": "tests/adversarial-blind-01.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 15000000, + "memoryLimitBytes": 536870912 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 2000000, + "memoryLimitBytes": 402653184 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 700000, + "memoryLimitBytes": 268435456 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "枚舉傳輸連線集合", + "en": "Enumerate transfer-link subsets" + }, + "time": "O(2^M (N+M))", + "space": "O(N)", + "accepted": false + }, + { + "name": { + "zh-TW": "Kruskal 與 DSU", + "en": "Kruskal with DSU" + }, + "time": "O(M log M)", + "space": "O(N+M)", + "accepted": true + } + ] +} diff --git a/problems/033-toolchain-mirror-network/solutions/c/main.c b/problems/033-toolchain-mirror-network/solutions/c/main.c new file mode 100644 index 0000000..e8d9255 --- /dev/null +++ b/problems/033-toolchain-mirror-network/solutions/c/main.c @@ -0,0 +1,61 @@ +#include +#include +typedef unsigned long long U; +typedef struct { + int u, v; + U w; +} E; +int cmp(const void *a, const void *b) { + U x = ((const E *)a)->w, y = ((const E *)b)->w; + return x < y ? -1 : x > y; +} +int find(int *p, int x) { + int r = x; + while (p[r] != r) + r = p[r]; + while (p[x] != x) { + int y = p[x]; + p[x] = r; + x = y; + } + return r; +} +int main(void) { + int n, m; + if (scanf("%d%d", &n, &m) != 2) + return 0; + E *e = malloc(sizeof(E) * (size_t)(m ? m : 1)); + for (int i = 0; i < m; i++) { + scanf("%d%d%llu", &e[i].u, &e[i].v, &e[i].w); + e[i].u--; + e[i].v--; + } + qsort(e, (size_t)m, sizeof(E), cmp); + int *p = malloc(sizeof(int) * (size_t)n), + *sz = malloc(sizeof(int) * (size_t)n); + for (int i = 0; i < n; i++) { + p[i] = i; + sz[i] = 1; + } + U cost = 0; + int take = 0; + for (int i = 0; i < m && take < n - 1; i++) { + int u = find(p, e[i].u), v = find(p, e[i].v); + if (u == v) + continue; + if (sz[u] < sz[v]) { + int t = u; + u = v; + v = t; + } + p[v] = u; + sz[u] += sz[v]; + cost += e[i].w; + take++; + } + if (take == n - 1) + printf("COST %llu\n", cost); + else + puts("IMPOSSIBLE"); + return 0; +} diff --git a/problems/033-toolchain-mirror-network/solutions/cpp/main.cpp b/problems/033-toolchain-mirror-network/solutions/cpp/main.cpp new file mode 100644 index 0000000..86742be --- /dev/null +++ b/problems/033-toolchain-mirror-network/solutions/cpp/main.cpp @@ -0,0 +1,55 @@ +#include +#include +#include +#include +#include +using namespace std; +struct E { + int u, v; + uint64_t w; +}; +int main() { + ios::sync_with_stdio(false); + cin.tie(nullptr); + int n, m; + if (!(cin >> n >> m)) + return 0; + vector e(m); + for (auto &x : e) { + cin >> x.u >> x.v >> x.w; + --x.u; + --x.v; + } + sort(e.begin(), e.end(), [](auto &a, auto &b) { return a.w < b.w; }); + vector p(n), sz(n, 1); + iota(p.begin(), p.end(), 0); + auto find = [&](int x) { + int r = x; + while (p[r] != r) + r = p[r]; + while (p[x] != x) { + int y = p[x]; + p[x] = r; + x = y; + } + return r; + }; + uint64_t cost = 0; + int take = 0; + for (auto &x : e) { + int u = find(x.u), v = find(x.v); + if (u == v) + continue; + if (sz[u] < sz[v]) + swap(u, v); + p[v] = u; + sz[u] += sz[v]; + cost += x.w; + if (++take == n - 1) + break; + } + if (take == n - 1) + cout << "COST " << cost << '\n'; + else + cout << "IMPOSSIBLE\n"; +} diff --git a/problems/033-toolchain-mirror-network/solutions/go/main.go b/problems/033-toolchain-mirror-network/solutions/go/main.go new file mode 100644 index 0000000..40b7299 --- /dev/null +++ b/problems/033-toolchain-mirror-network/solutions/go/main.go @@ -0,0 +1,68 @@ +package main + +import ( + "bufio" + "fmt" + "os" + "sort" +) + +type E struct { + u, v int + w uint64 +} + +func main() { + in := bufio.NewReader(os.Stdin) + var n, m int + fmt.Fscan(in, &n, &m) + e := make([]E, m) + for i := range e { + fmt.Fscan(in, &e[i].u, &e[i].v, &e[i].w) + e[i].u-- + e[i].v-- + } + sort.Slice(e, func(i, j int) bool { return e[i].w < e[j].w }) + p := make([]int, n) + sz := make([]int, n) + for i := range p { + p[i] = i + sz[i] = 1 + } + find := func(x int) int { return 0 } + find = func(x int) int { + r := x + for p[r] != r { + r = p[r] + } + for p[x] != x { + y := p[x] + p[x] = r + x = y + } + return r + } + var cost uint64 + take := 0 + for _, x := range e { + u, v := find(x.u), find(x.v) + if u == v { + continue + } + if sz[u] < sz[v] { + u, v = v, u + } + p[v] = u + sz[u] += sz[v] + cost += x.w + take++ + if take == n-1 { + break + } + } + if take == n-1 { + fmt.Println("COST", cost) + } else { + fmt.Println("IMPOSSIBLE") + } +} diff --git a/problems/033-toolchain-mirror-network/solutions/javascript/main.js b/problems/033-toolchain-mirror-network/solutions/javascript/main.js new file mode 100644 index 0000000..bac01cb --- /dev/null +++ b/problems/033-toolchain-mirror-network/solutions/javascript/main.js @@ -0,0 +1,63 @@ +import * as std from "std"; + +const input = std.in.readAsString(); +let scan = 0; +function nextInt() { + while (scan < input.length && input.charCodeAt(scan) <= 32) scan++; + let value = 0; + while (scan < input.length) { + const digit = input.charCodeAt(scan) - 48; + if (digit < 0 || digit > 9) break; + value = value * 10 + digit; + scan++; + } + return value; +} +function nextBigInt() { + while (scan < input.length && input.charCodeAt(scan) <= 32) scan++; + const start = scan; + while (scan < input.length) { + const code = input.charCodeAt(scan); + if (code < 48 || code > 57) break; + scan++; + } + return BigInt(input.slice(start, scan)); +} + +const n = nextInt(), m = nextInt(); +const ENDPOINT_BITS = 18n, ENDPOINT_MASK = (1n << ENDPOINT_BITS) - 1n; +const edges = new Array(m); +for (let i = 0; i < m; i++) { + const u = nextInt() - 1, v = nextInt() - 1, cost = nextBigInt(); + edges[i] = (cost << (2n * ENDPOINT_BITS)) | (BigInt(u) << ENDPOINT_BITS) | + BigInt(v); +} +edges.sort((a, b) => a < b ? -1 : a > b ? 1 : 0); +const parent = new Int32Array(n), size = new Int32Array(n).fill(1); +for (let i = 0; i < n; i++) parent[i] = i; +/** @param {number} start @returns {number} */ +function find(start) { + let root = start; + while (parent[root] !== root) root = parent[root]; + let node = start; + while (parent[node] !== node) { + const nextNode = parent[node]; + parent[node] = root; + node = nextNode; + } + return root; +} +let total = 0n, taken = 0; +for (const packed of edges) { + const v = Number(packed & ENDPOINT_MASK), + u = Number((packed >> ENDPOINT_BITS) & ENDPOINT_MASK), + cost = packed >> (2n * ENDPOINT_BITS); + let left = find(u), right = find(v); + if (left === right) continue; + if (size[left] < size[right]) [left, right] = [right, left]; + parent[right] = left; + size[left] += size[right]; + total += cost; + if (++taken === n - 1) break; +} +std.out.puts(taken === n - 1 ? `COST ${total}\n` : "IMPOSSIBLE\n"); diff --git a/problems/033-toolchain-mirror-network/solutions/python/main.py b/problems/033-toolchain-mirror-network/solutions/python/main.py new file mode 100644 index 0000000..51faf0a --- /dev/null +++ b/problems/033-toolchain-mirror-network/solutions/python/main.py @@ -0,0 +1,31 @@ +import sys + +a = list(map(int, sys.stdin.read().split())) +n, m = a[:2] +e = [(a[i + 2], a[i] - 1, a[i + 1] - 1) for i in range(2, len(a), 3)] +e.sort() +p = list(range(n)) +sz = [1] * n + + +def f(x): + while p[x] != x: + p[x] = p[p[x]] + x = p[x] + return x + + +cost = taken = 0 +for w, u, v in e: + u, v = f(u), f(v) + if u == v: + continue + if sz[u] < sz[v]: + u, v = v, u + p[v] = u + sz[u] += sz[v] + cost += w + taken += 1 + if taken == n - 1: + break +print(f"COST {cost}" if taken == n - 1 else "IMPOSSIBLE") diff --git a/problems/033-toolchain-mirror-network/solutions/rust/main.rs b/problems/033-toolchain-mirror-network/solutions/rust/main.rs new file mode 100644 index 0000000..b5fa86e --- /dev/null +++ b/problems/033-toolchain-mirror-network/solutions/rust/main.rs @@ -0,0 +1,52 @@ +use std::io::{self, Read}; +fn find(p: &mut [usize], mut x: usize) -> usize { + let mut r = x; + while p[r] != r { + r = p[r] + } + while p[x] != x { + let y = p[x]; + p[x] = r; + x = y + } + r +} +fn main() { + let mut s = String::new(); + io::stdin().read_to_string(&mut s).unwrap(); + let mut it = s.split_whitespace(); + let n: usize = it.next().unwrap().parse().unwrap(); + let m: usize = it.next().unwrap().parse().unwrap(); + let mut e = Vec::with_capacity(m); + for _ in 0..m { + let u = it.next().unwrap().parse::().unwrap() - 1; + let v = it.next().unwrap().parse::().unwrap() - 1; + let w: u64 = it.next().unwrap().parse().unwrap(); + e.push((w, u, v)); + } + e.sort_by_key(|x| x.0); + let mut p: Vec = (0..n).collect(); + let mut sz = vec![1; n]; + let (mut cost, mut take) = (0u64, 0); + for (w, a, b) in e { + let (mut u, mut v) = (find(&mut p, a), find(&mut p, b)); + if u == v { + continue; + } + if sz[u] < sz[v] { + std::mem::swap(&mut u, &mut v) + } + p[v] = u; + sz[u] += sz[v]; + cost += w; + take += 1; + if take == n - 1 { + break; + } + } + if take == n - 1 { + println!("COST {cost}") + } else { + println!("IMPOSSIBLE") + } +} diff --git a/problems/033-toolchain-mirror-network/solutions/typescript/main.ts b/problems/033-toolchain-mirror-network/solutions/typescript/main.ts new file mode 100644 index 0000000..5a3384c --- /dev/null +++ b/problems/033-toolchain-mirror-network/solutions/typescript/main.ts @@ -0,0 +1,62 @@ +import * as std from "std"; + +const input: string = std.in.readAsString(); +let scan = 0; +function nextInt(): number { + while (scan < input.length && input.charCodeAt(scan) <= 32) scan++; + let value = 0; + while (scan < input.length) { + const digit = input.charCodeAt(scan) - 48; + if (digit < 0 || digit > 9) break; + value = value * 10 + digit; + scan++; + } + return value; +} +function nextBigInt(): bigint { + while (scan < input.length && input.charCodeAt(scan) <= 32) scan++; + const start = scan; + while (scan < input.length) { + const code = input.charCodeAt(scan); + if (code < 48 || code > 57) break; + scan++; + } + return BigInt(input.slice(start, scan)); +} + +const n = nextInt(), m = nextInt(); +const ENDPOINT_BITS = 18n, ENDPOINT_MASK = (1n << ENDPOINT_BITS) - 1n; +const edges: bigint[] = new Array(m); +for (let i = 0; i < m; i++) { + const u = nextInt() - 1, v = nextInt() - 1, cost = nextBigInt(); + edges[i] = (cost << (2n * ENDPOINT_BITS)) | (BigInt(u) << ENDPOINT_BITS) | + BigInt(v); +} +edges.sort((a, b) => a < b ? -1 : a > b ? 1 : 0); +const parent = new Int32Array(n), size = new Int32Array(n).fill(1); +for (let i = 0; i < n; i++) parent[i] = i; +function find(start: number): number { + let root = start; + while (parent[root] !== root) root = parent[root]!; + let node = start; + while (parent[node] !== node) { + const nextNode = parent[node]!; + parent[node] = root; + node = nextNode; + } + return root; +} +let total = 0n, taken = 0; +for (const packed of edges) { + const v = Number(packed & ENDPOINT_MASK), + u = Number((packed >> ENDPOINT_BITS) & ENDPOINT_MASK), + cost = packed >> (2n * ENDPOINT_BITS); + let left = find(u), right = find(v); + if (left === right) continue; + if (size[left]! < size[right]!) [left, right] = [right, left]; + parent[right] = left; + size[left]! += size[right]!; + total += cost; + if (++taken === n - 1) break; +} +std.out.puts(taken === n - 1 ? `COST ${total}\n` : "IMPOSSIBLE\n"); diff --git a/problems/033-toolchain-mirror-network/statement.en.md b/problems/033-toolchain-mirror-network/statement.en.md new file mode 100644 index 0000000..c69ac0c --- /dev/null +++ b/problems/033-toolchain-mirror-network/statement.en.md @@ -0,0 +1,85 @@ +# Toolchain Mirror Network + +While designing a distributed WASM OJ, we needed every execution host to receive the same compiler toolchain. Having every host download directly from central storage would duplicate bandwidth and could turn one source into a deployment bottleneck, so we allow a host that already has the toolchain to forward it to another host. + +Transfer costs differ between hosts: some links stay within one data center, while others cross regions. Initially only host `1` has the toolchain. We must first choose which transfer links to use and can then distribute the toolchain in any feasible order. + +An undirected link `u v cost` can transfer the toolchain once between its two hosts. As soon as either endpoint has the toolchain, the selected link can give it to the other endpoint. After the links are selected, transfers may occur in any order reachable from host `1`. + +Choose links so that every host eventually receives the toolchain while minimizing the total cost of the selected links. Equivalently, the selected links must form a connected subgraph spanning every host. + +## Input + +The first line contains `N M`. Each of the next `M` lines contains `u v cost`. Host IDs are 1-based and links are undirected. + +## Output + +If it is impossible to connect every host, output `IMPOSSIBLE`. Otherwise output `COST x`, where `x` is the minimum total cost. When `N = 1`, output `COST 0` regardless of the links. + +## Constraints + +- `1 <= N <= 200000` +- `0 <= M <= 400000` +- `u != v`; parallel links are allowed. +- `0 <= cost <= 10^12` +- The total cost of any spanning tree is at most `9 * 10^18`. +- Full tests require sublinear amortized DSU operations; subset enumeration and adjacency-matrix Prim cannot pass. + +## Examples + + + +### Example One + +Input: + +```text +4 5 +1 2 4 +2 3 1 +3 4 2 +1 4 10 +1 3 3 +``` + +Output: + +```text +COST 6 +``` + +### Example Two + +Input: + +```text +4 2 +1 2 1 +3 4 1 +``` + +Output: + +```text +IMPOSSIBLE +``` + +### Example Three + +Input: + +```text +3 4 +1 2 9 +1 2 0 +2 3 4 +1 3 8 +``` + +Output: + +```text +COST 4 +``` + + diff --git a/problems/033-toolchain-mirror-network/statement.zh-TW.md b/problems/033-toolchain-mirror-network/statement.zh-TW.md new file mode 100644 index 0000000..42aa67a --- /dev/null +++ b/problems/033-toolchain-mirror-network/statement.zh-TW.md @@ -0,0 +1,83 @@ +# Toolchain 鏡像網路 + +在設計分散式 WASM OJ 時,多個執行 host 都需要相同版本的 compiler toolchain。若每台 host 都直接從中央儲存下載,不但重複占用頻寬,也可能讓單一來源成為部署瓶頸,因此我們考慮讓已取得 toolchain 的 host 繼續轉送給其他 host。 + +不同 host 之間的傳輸成本並不相同,某些連線可能位於同一資料中心,另一些則必須跨區域傳送。部署開始時只有 host `1` 已持有 toolchain;我們需要先選出要使用的傳輸 links,再按照可行的順序完成散布。 + +每條無向 link `u v cost` 可以在兩個 host 之間傳送一次 toolchain。只要其中一端已取得 toolchain,就能沿著選定的 link 讓另一端取得。選定 links 後,傳輸可以依任一從 host `1` 可達的順序進行。 + +請選擇一組 links,使所有 host 最終都取得 toolchain,並讓選定 links 的總成本最小。換句話說,所選 links 必須形成一個涵蓋全部 host 的 connected subgraph。 + +## 輸入 + +第一行 `N M`。接著 `M` 行 `u v cost`,host ID 為 1-based,link 無向。 + +## 輸出 + +若不可能連通所有 host,輸出 `IMPOSSIBLE`;否則輸出 `COST x`,其中 `x` 是最小總成本。`N=1` 時答案為 `COST 0`,不論是否有 link。 + +## 限制 + +- `1 <= N <= 200000`,`0 <= M <= 400000`。 +- `u != v`;平行 link 允許;`0 <= cost <= 10^12`。 +- 任一 spanning tree 的成本總和保證不超過 `9*10^18`。 +- 完整測資要求次線性 amortized DSU 操作;枚舉或 adjacency matrix Prim 無法通過。 + +## 範例 + + + +### 範例一 + +輸入: + +```text +4 5 +1 2 4 +2 3 1 +3 4 2 +1 4 10 +1 3 3 +``` + +輸出: + +```text +COST 6 +``` + +### 範例二 + +輸入: + +```text +4 2 +1 2 1 +3 4 1 +``` + +輸出: + +```text +IMPOSSIBLE +``` + +### 範例三 + +輸入: + +```text +3 4 +1 2 9 +1 2 0 +2 3 4 +1 3 8 +``` + +輸出: + +```text +COST 4 +``` + + diff --git a/problems/033-toolchain-mirror-network/tests/adversarial-blind-01.in b/problems/033-toolchain-mirror-network/tests/adversarial-blind-01.in new file mode 100644 index 0000000..64e44fd --- /dev/null +++ b/problems/033-toolchain-mirror-network/tests/adversarial-blind-01.in @@ -0,0 +1,9 @@ +5 8 +1 2 1000000000000 +1 2 0 +2 3 1000000000000 +1 3 1000000000000 +3 4 999999999999 +4 5 1000000000000 +3 5 1000000000000 +2 5 1000000000000 diff --git a/problems/033-toolchain-mirror-network/tests/adversarial-blind-01.out b/problems/033-toolchain-mirror-network/tests/adversarial-blind-01.out new file mode 100644 index 0000000..74308d9 --- /dev/null +++ b/problems/033-toolchain-mirror-network/tests/adversarial-blind-01.out @@ -0,0 +1 @@ +COST 2999999999999 diff --git a/problems/033-toolchain-mirror-network/tests/sample-01.in b/problems/033-toolchain-mirror-network/tests/sample-01.in new file mode 100644 index 0000000..757aedd --- /dev/null +++ b/problems/033-toolchain-mirror-network/tests/sample-01.in @@ -0,0 +1,6 @@ +4 5 +1 2 4 +2 3 1 +3 4 2 +1 4 10 +1 3 3 diff --git a/problems/033-toolchain-mirror-network/tests/sample-01.out b/problems/033-toolchain-mirror-network/tests/sample-01.out new file mode 100644 index 0000000..01c68ad --- /dev/null +++ b/problems/033-toolchain-mirror-network/tests/sample-01.out @@ -0,0 +1 @@ +COST 6 diff --git a/problems/033-toolchain-mirror-network/tests/sample-02.in b/problems/033-toolchain-mirror-network/tests/sample-02.in new file mode 100644 index 0000000..e284799 --- /dev/null +++ b/problems/033-toolchain-mirror-network/tests/sample-02.in @@ -0,0 +1,3 @@ +4 2 +1 2 1 +3 4 1 diff --git a/problems/033-toolchain-mirror-network/tests/sample-02.out b/problems/033-toolchain-mirror-network/tests/sample-02.out new file mode 100644 index 0000000..3e36f60 --- /dev/null +++ b/problems/033-toolchain-mirror-network/tests/sample-02.out @@ -0,0 +1 @@ +IMPOSSIBLE diff --git a/problems/033-toolchain-mirror-network/tests/sample-03.in b/problems/033-toolchain-mirror-network/tests/sample-03.in new file mode 100644 index 0000000..52950e9 --- /dev/null +++ b/problems/033-toolchain-mirror-network/tests/sample-03.in @@ -0,0 +1,5 @@ +3 4 +1 2 9 +1 2 0 +2 3 4 +1 3 8 diff --git a/problems/033-toolchain-mirror-network/tests/sample-03.out b/problems/033-toolchain-mirror-network/tests/sample-03.out new file mode 100644 index 0000000..94bf80b --- /dev/null +++ b/problems/033-toolchain-mirror-network/tests/sample-03.out @@ -0,0 +1 @@ +COST 4 diff --git a/problems/033-toolchain-mirror-network/validator.py b/problems/033-toolchain-mirror-network/validator.py new file mode 100644 index 0000000..b155dca --- /dev/null +++ b/problems/033-toolchain-mirror-network/validator.py @@ -0,0 +1,19 @@ +import sys + + +def main(): + a = list(map(int, sys.stdin.read().split())) + assert len(a) >= 2 + n, m = a[:2] + assert 1 <= n <= 200000 and 0 <= m <= 400000 and len(a) == 2 + 3 * m + p = 2 + for _ in range(m): + u, v, w = a[p : p + 3] + p += 3 + assert 1 <= u <= n and 1 <= v <= n and u != v and 0 <= w <= 10**12 + + +try: + main() +except (AssertionError, ValueError): + sys.exit(1) diff --git a/problems/034-capability-cut/editorial.en.md b/problems/034-capability-cut/editorial.en.md new file mode 100644 index 0000000..3ae52f4 --- /dev/null +++ b/problems/034-capability-cut/editorial.en.md @@ -0,0 +1,32 @@ +# Editorial + +## Intuitive Approach + +Enumerate every set of blocked functions, remove it, and test reachability from all entries. This requires `O(2^N(N + M))` time. + +## Optimal Approach: Node Splitting and Minimum Cut + +Split every function `i` into `in(i)` and `out(i)`, connected by an edge of capacity `cost[i]`. Replace each original call `u -> v` with `out(u) -> in(v)` of capacity `INF`, where `INF = sum(cost) + 1`. + +Add a super-source with an `INF` edge to `in(entry)` for every entry. Add an `INF` edge from `out(dangerous)` to the super-sink for every dangerous function. Every source-to-sink path must cross the `in -> out` edge of every function it visits, so cutting such an edge is exactly blocking that function. + +Because blocking all functions costs less than `INF`, a minimum cut never uses a synthetic or call edge. Compute a maximum flow with Dinic's algorithm; by the max-flow min-cut theorem, its value is the desired minimum blocking cost. + +## Correctness Proof + +For any valid blocking set `B`, cut every `in(i) -> out(i)` edge with `i` in `B`. Since the original blocking removes every entry-to-dangerous path, this disconnects the split graph's source and sink with exactly the same cost. + +Conversely, a minimum cut cannot contain an `INF` edge: cutting all function edges is a cut of capacity at most `sum(cost) < INF`. Its finite cut edges therefore correspond only to functions. Blocking those functions removes every original entry-to-dangerous path, and its cost equals the cut capacity. These two directions prove equality between the optimal blocking cost and the minimum cut. + +Dinic computes a maximum flow, whose value equals that minimum cut. If a function is both entry and dangerous, the constructed path still crosses its own capacity edge, so length-zero dangerous paths are handled correctly. + +## Complexity + +The split graph has `V' = 2N + 2` vertices and `E' = N + M + S + T` forward edges. The general-capacity Dinic bound is `O(V'^2 E')` time and `O(V' + E')` space. + +## Common Mistakes + +- Putting node costs on call edges, which charges a function multiple times when it has several incident calls. +- Connecting the source to `out(entry)` or `in(dangerous)` to the sink, which prevents blocking endpoints correctly. +- Choosing an arbitrary fixed infinity without proving it exceeds every finite cut; `sum(cost) + 1` is sufficient. +- Storing capacities in an imprecise numeric type. diff --git a/problems/034-capability-cut/editorial.zh-TW.md b/problems/034-capability-cut/editorial.zh-TW.md new file mode 100644 index 0000000..64a7e98 --- /dev/null +++ b/problems/034-capability-cut/editorial.zh-TW.md @@ -0,0 +1,26 @@ +# 解題說明 + +## 直覺解 + +枚舉被封鎖的函式集合,刪除後從所有 entries 做 reachability 檢查。這需要 `O(2^N(N+M))`。 + +## 最佳解 + +把每個函式 `i` 拆成 `in(i)` 與 `out(i)`,加入 capacity=`cost[i]` 的 `in -> out` edge。原呼叫 `u -> v` 變成 `out(u) -> in(v)`,capacity 設為 `INF=sum(cost)+1`。加入 super source 到所有 `in(entry)` 的 INF edges,以及所有 `out(dangerous)` 到 super sink 的 INF edges。 + +任何 source-sink path 必跨過其經過函式的 `in->out` edge;切它等價於封鎖該函式。INF 大於封鎖全部函式的成本,所以 minimum cut 不會選 synthetic/call edge。用 Dinic 求 max flow,依 max-flow min-cut theorem 即得 minimum cut cost。 + +## 正確性證明 + +任一合法封鎖集合 `B` 對應切掉所有 `i in B` 的 `in(i)->out(i)` edges;它阻斷原圖所有危險路徑,故在 split graph 形成同成本 s-t cut。反之,minimum cut 不含 INF edge,因所有函式 edge 的總容量至多 `sum(cost)out`,把對應函式封鎖便阻斷每條原 entry-dangerous 路徑,且成本等於 cut。兩方向顯示最小封鎖成本等於 minimum cut capacity。Dinic 產生 maximum flow,而 max-flow min-cut theorem 保證其值等於該 minimum cut,所以輸出正確;entry=dangerous 時路徑仍跨該節點自己的 capacity edge,亦正確處理。 + +## 複雜度 + +split graph 有 `V'=2N+2`、`E'=N+M+S+T` 條正向 edge。Dinic 一般容量上界為時間 `O(V'^2 E')`、空間 `O(V'+E')`。 + +## 常見錯誤 + +- 把 node cost 直接放到 call edges,遇到多入/多出邊會重複計價。 +- source 接到 `out(entry)` 或從 `in(dangerous)` 接 sink,導致不能封鎖端點。 +- 未從限制證明固定 INF 嚴格大於所有合法 cut;直接使用 `sum(cost)+1` 最清楚。 +- JS/TS 用 `number` 保存 capacity。 diff --git a/problems/034-capability-cut/generator.py b/problems/034-capability-cut/generator.py new file mode 100644 index 0000000..700d5d9 --- /dev/null +++ b/problems/034-capability-cut/generator.py @@ -0,0 +1,20 @@ +import random, sys + +seed, index = map(int, sys.argv[1:]) +r = random.Random(seed * 65539 + index) +n = 4 + index % 4 +cost = [r.randrange(8) for _ in range(n)] +entries = r.sample(range(1, n + 1), 1 + index % 2) +danger = r.sample(range(1, n + 1), 1 + (index // 2) % 2) +edges = [ + (u, v) + for u in range(1, n + 1) + for v in range(1, n + 1) + if u != v and r.random() < 0.18 +] +print(n, len(edges), len(entries), len(danger)) +print(*cost) +print(*entries) +print(*danger) +for e in edges: + print(*e) diff --git a/problems/034-capability-cut/oracle.py b/problems/034-capability-cut/oracle.py new file mode 100644 index 0000000..095623b --- /dev/null +++ b/problems/034-capability-cut/oracle.py @@ -0,0 +1,36 @@ +import collections, itertools, sys + +a = list(map(int, sys.stdin.read().split())) +n, m, s, t = a[:4] +p = 4 +c = a[p : p + n] +p += n +entries = [x - 1 for x in a[p : p + s]] +p += s +danger = {x - 1 for x in a[p : p + t]} +p += t +g = [[] for _ in range(n)] +for _ in range(m): + u, v = a[p] - 1, a[p + 1] - 1 + p += 2 + g[u].append(v) +best = sum(c) +for mask in range(1 << n): + z = sum(c[i] for i in range(n) if mask >> i & 1) + if z >= best: + continue + q = collections.deque(x for x in entries if not (mask >> x & 1)) + seen = set(q) + bad = False + while q: + u = q.popleft() + if u in danger: + bad = True + break + for v in g[u]: + if not (mask >> v & 1) and v not in seen: + seen.add(v) + q.append(v) + if not bad: + best = z +print("COST", best) diff --git a/problems/034-capability-cut/problem.json b/problems/034-capability-cut/problem.json new file mode 100644 index 0000000..be32ab5 --- /dev/null +++ b/problems/034-capability-cut/problem.json @@ -0,0 +1,147 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 34, + "slug": "capability-cut", + "title": { + "zh-TW": "切斷危險 Capability", + "en": "Cutting Dangerous Capabilities" + }, + "difficulty": "hard", + "tags": [ + "graph", + "maximum-flow", + "minimum-cut", + "node-splitting" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-blind-01", + "kind": "adversarial", + "input": "tests/adversarial-blind-01.in", + "output": "tests/adversarial-blind-01.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 20000000, + "memoryLimitBytes": 536870912 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 2000000, + "memoryLimitBytes": 402653184 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 700000, + "memoryLimitBytes": 268435456 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "枚舉封鎖函式集合", + "en": "Enumerate blocked-function sets" + }, + "time": "O(2^N (N+M))", + "space": "O(N+M)", + "accepted": false + }, + { + "name": { + "zh-TW": "節點拆分與 Dinic min-cut", + "en": "Node splitting and Dinic minimum cut" + }, + "time": "O(V'^2 E')", + "space": "O(V'+E')", + "accepted": true + } + ] +} diff --git a/problems/034-capability-cut/solutions/c/main.c b/problems/034-capability-cut/solutions/c/main.c new file mode 100644 index 0000000..2af2ce0 --- /dev/null +++ b/problems/034-capability-cut/solutions/c/main.c @@ -0,0 +1,99 @@ +#include +#include +#include +typedef unsigned long long U; +static int *head, *to, *next, *level, *it, ec, T; +static U *cap; +void add(int u, int v, U c) { + to[ec] = v; + cap[ec] = c; + next[ec] = head[u]; + head[u] = ec++; + to[ec] = u; + cap[ec] = 0; + next[ec] = head[v]; + head[v] = ec++; +} +U dfs(int u, U f) { + if (u == T) + return f; + for (int *e = &it[u]; *e >= 0; *e = next[*e]) + if (cap[*e] && level[to[*e]] == level[u] + 1) { + U z = dfs(to[*e], f < cap[*e] ? f : cap[*e]); + if (z) { + cap[*e] -= z; + cap[*e ^ 1] += z; + return z; + } + } + return 0; +} +int main(void) { + int n, m, sn, tn; + if (scanf("%d%d%d%d", &n, &m, &sn, &tn) != 4) + return 0; + U *c = malloc(sizeof(U) * (size_t)n), sum = 0; + for (int i = 0; i < n; i++) { + scanf("%llu", &c[i]); + sum += c[i]; + } + int *en = malloc(sizeof(int) * (size_t)sn), + *dn = malloc(sizeof(int) * (size_t)tn); + for (int i = 0; i < sn; i++) { + scanf("%d", &en[i]); + en[i]--; + } + for (int i = 0; i < tn; i++) { + scanf("%d", &dn[i]); + dn[i]--; + } + int *eu = malloc(sizeof(int) * (size_t)(m ? m : 1)), + *ev = malloc(sizeof(int) * (size_t)(m ? m : 1)); + for (int i = 0; i < m; i++) { + scanf("%d%d", &eu[i], &ev[i]); + eu[i]--; + ev[i]--; + } + int V = 2 * n + 2, S = 2 * n, lim = 2 * (n + m + sn + tn) + 2; + T = S + 1; + head = malloc(sizeof(int) * (size_t)V); + to = malloc(sizeof(int) * (size_t)lim); + next = malloc(sizeof(int) * (size_t)lim); + cap = malloc(sizeof(U) * (size_t)lim); + level = malloc(sizeof(int) * (size_t)V); + it = malloc(sizeof(int) * (size_t)V); + memset(head, 255, sizeof(int) * (size_t)V); + U inf = sum + 1; + for (int i = 0; i < n; i++) + add(2 * i, 2 * i + 1, c[i]); + for (int i = 0; i < m; i++) + add(2 * eu[i] + 1, 2 * ev[i], inf); + for (int i = 0; i < sn; i++) + add(S, 2 * en[i], inf); + for (int i = 0; i < tn; i++) + add(2 * dn[i] + 1, T, inf); + int *q = malloc(sizeof(int) * (size_t)V); + U flow = 0; + for (;;) { + memset(level, 255, sizeof(int) * (size_t)V); + int l = 0, r = 0; + level[S] = 0; + q[r++] = S; + while (l < r) { + int u = q[l++]; + for (int e = head[u]; e >= 0; e = next[e]) + if (cap[e] && level[to[e]] < 0) { + level[to[e]] = level[u] + 1; + q[r++] = to[e]; + } + } + if (level[T] < 0) + break; + memcpy(it, head, sizeof(int) * (size_t)V); + U z; + while ((z = dfs(S, inf)) != 0) + flow += z; + } + printf("COST %llu\n", flow); + return 0; +} diff --git a/problems/034-capability-cut/solutions/cpp/main.cpp b/problems/034-capability-cut/solutions/cpp/main.cpp new file mode 100644 index 0000000..4e4a315 --- /dev/null +++ b/problems/034-capability-cut/solutions/cpp/main.cpp @@ -0,0 +1,90 @@ +#include +#include +#include +#include +#include +#include +using namespace std; +struct E { + int to, rev; + uint64_t cap; +}; +int main() { + ios::sync_with_stdio(false); + cin.tie(nullptr); + int n, m, sn, tn; + if (!(cin >> n >> m >> sn >> tn)) + return 0; + vector c(n); + uint64_t sum = 0; + for (auto &x : c) { + cin >> x; + sum += x; + } + vector en(sn), dn(tn); + for (int &x : en) { + cin >> x; + --x; + } + for (int &x : dn) { + cin >> x; + --x; + } + int V = 2 * n + 2, S = 2 * n, T = S + 1; + vector> g(V); + auto add = [&](int u, int v, uint64_t z) { + g[u].push_back({v, (int)g[v].size(), z}); + g[v].push_back({u, (int)g[u].size() - 1, 0}); + }; + uint64_t inf = sum + 1; + for (int i = 0; i < n; i++) + add(2 * i, 2 * i + 1, c[i]); + while (m--) { + int u, v; + cin >> u >> v; + add(2 * (u - 1) + 1, 2 * (v - 1), inf); + } + for (int x : en) + add(S, 2 * x, inf); + for (int x : dn) + add(2 * x + 1, T, inf); + uint64_t flow = 0; + vector level(V), it(V); + for (;;) { + fill(level.begin(), level.end(), -1); + queue q; + q.push(S); + level[S] = 0; + while (!q.empty()) { + int u = q.front(); + q.pop(); + for (auto &e : g[u]) + if (e.cap && level[e.to] < 0) { + level[e.to] = level[u] + 1; + q.push(e.to); + } + } + if (level[T] < 0) + break; + fill(it.begin(), it.end(), 0); + function dfs = [&](int u, uint64_t f) { + if (u == T) + return f; + for (int &i = it[u]; i < (int)g[u].size(); i++) { + E &e = g[u][i]; + if (e.cap && level[e.to] == level[u] + 1) { + uint64_t z = dfs(e.to, min(f, e.cap)); + if (z) { + e.cap -= z; + g[e.to][e.rev].cap += z; + return z; + } + } + } + return uint64_t(0); + }; + for (uint64_t z; (z = dfs(S, inf));) + flow += z; + } + cout << "COST " << flow << '\n'; +} diff --git a/problems/034-capability-cut/solutions/go/main.go b/problems/034-capability-cut/solutions/go/main.go new file mode 100644 index 0000000..7faf3d5 --- /dev/null +++ b/problems/034-capability-cut/solutions/go/main.go @@ -0,0 +1,108 @@ +package main + +import ( + "bufio" + "fmt" + "os" +) + +type E struct { + to, rev int + cap uint64 +} + +func main() { + in := bufio.NewReader(os.Stdin) + var n, m, sn, tn int + fmt.Fscan(in, &n, &m, &sn, &tn) + c := make([]uint64, n) + var sum uint64 + for i := range c { + fmt.Fscan(in, &c[i]) + sum += c[i] + } + en := make([]int, sn) + dn := make([]int, tn) + for i := range en { + fmt.Fscan(in, &en[i]) + en[i]-- + } + for i := range dn { + fmt.Fscan(in, &dn[i]) + dn[i]-- + } + V, S, T := 2*n+2, 2*n, 2*n+1 + g := make([][]E, V) + add := func(u, v int, z uint64) { + g[u] = append(g[u], E{v, len(g[v]), z}) + g[v] = append(g[v], E{u, len(g[u]) - 1, 0}) + } + inf := sum + 1 + for i, z := range c { + add(2*i, 2*i+1, z) + } + for ; m > 0; m-- { + var u, v int + fmt.Fscan(in, &u, &v) + add(2*(u-1)+1, 2*(v-1), inf) + } + for _, u := range en { + add(S, 2*u, inf) + } + for _, u := range dn { + add(2*u+1, T, inf) + } + level := make([]int, V) + it := make([]int, V) + var dfs func(int, uint64) uint64 + dfs = func(u int, f uint64) uint64 { + if u == T { + return f + } + for it[u] < len(g[u]) { + i := it[u] + e := g[u][i] + if e.cap > 0 && level[e.to] == level[u]+1 { + z := dfs(e.to, min(f, e.cap)) + if z > 0 { + g[u][i].cap -= z + g[e.to][e.rev].cap += z + return z + } + } + it[u]++ + } + return 0 + } + var flow uint64 + for { + for i := range level { + level[i] = -1 + } + level[S] = 0 + q := []int{S} + for h := 0; h < len(q); h++ { + u := q[h] + for _, e := range g[u] { + if e.cap > 0 && level[e.to] < 0 { + level[e.to] = level[u] + 1 + q = append(q, e.to) + } + } + } + if level[T] < 0 { + break + } + for i := range it { + it[i] = 0 + } + for { + z := dfs(S, inf) + if z == 0 { + break + } + flow += z + } + } + fmt.Println("COST", flow) +} diff --git a/problems/034-capability-cut/solutions/javascript/main.js b/problems/034-capability-cut/solutions/javascript/main.js new file mode 100644 index 0000000..0b97074 --- /dev/null +++ b/problems/034-capability-cut/solutions/javascript/main.js @@ -0,0 +1,100 @@ +import * as std from "std"; +/** @typedef {{ to: number, rev: number, cap: bigint }} Edge */ +const input = std.in.readAsString(); +let scan = 0; +function nextInt() { + while (scan < input.length && input.charCodeAt(scan) <= 32) scan++; + let value = 0; + while (scan < input.length) { + const digit = input.charCodeAt(scan) - 48; + if (digit < 0 || digit > 9) break; + value = value * 10 + digit; + scan++; + } + return value; +} +function nextBigInt() { + while (scan < input.length && input.charCodeAt(scan) <= 32) scan++; + const start = scan; + while (scan < input.length) { + const code = input.charCodeAt(scan); + if (code < 48 || code > 57) break; + scan++; + } + return BigInt(input.slice(start, scan)); +} +let n = nextInt(), + m = nextInt(), + sn = nextInt(), + tn = nextInt(); +/** @type {bigint[]} */ +const c = Array.from({ length: n }, () => nextBigInt()); +/** @type {number[]} */ +const en = Array.from({ length: sn }, () => nextInt() - 1); +/** @type {number[]} */ +const dn = Array.from({ length: tn }, () => nextInt() - 1); +const V = 2 * n + 2, + S = 2 * n, + T = S + 1; +/** @type {Edge[][]} */ +const g = Array.from({ length: V }, () => []); +/** + * @param {number} u + * @param {number} v + * @param {bigint} z + */ +const add = (u, v, z) => { + g[u].push({ to: v, rev: g[v].length, cap: z }); + g[v].push({ to: u, rev: g[u].length - 1, cap: 0n }); +}; +const inf = c.reduce((x, y) => x + y, 1n); +for (let i = 0; i < n; i++) add(2 * i, 2 * i + 1, c[i]); +while (m--) { + const u = nextInt() - 1, v = nextInt() - 1; + add(2 * u + 1, 2 * v, inf); +} +for (const u of en) add(S, 2 * u, inf); +for (const u of dn) add(2 * u + 1, T, inf); +let flow = 0n; +for (;;) { + const level = new Int32Array(V).fill(-1), q = [S]; + level[S] = 0; + for (let h = 0; h < q.length; h++) { + const u = q[h]; + for (const e of g[u]) { + if (e.cap > 0n && level[e.to] < 0) { + level[e.to] = level[u] + 1; + q.push(e.to); + } + } + } + if (level[T] < 0) break; + const it = new Int32Array(V); + /** + * @param {number} u + * @param {bigint} f + * @returns {bigint} + */ + const dfs = (u, f) => { + if (u === T) return f; + while (it[u] < g[u].length) { + const e = g[u][it[u]]; + if (e.cap > 0n && level[e.to] === level[u] + 1) { + const z = dfs(e.to, f < e.cap ? f : e.cap); + if (z > 0n) { + e.cap -= z; + g[e.to][e.rev].cap += z; + return z; + } + } + it[u]++; + } + return 0n; + }; + for (;;) { + const z = dfs(S, inf); + if (z === 0n) break; + flow += z; + } +} +std.out.puts(`COST ${flow}\n`); diff --git a/problems/034-capability-cut/solutions/python/main.py b/problems/034-capability-cut/solutions/python/main.py new file mode 100644 index 0000000..bda8b75 --- /dev/null +++ b/problems/034-capability-cut/solutions/python/main.py @@ -0,0 +1,69 @@ +import collections, sys + +sys.setrecursionlimit(10000) +a = list(map(int, sys.stdin.read().split())) +n, m, sn, tn = a[:4] +p = 4 +cost = a[p : p + n] +p += n +entries = [x - 1 for x in a[p : p + sn]] +p += sn +danger = [x - 1 for x in a[p : p + tn]] +p += tn +V = 2 * n + 2 +S = 2 * n +T = S + 1 +g = [[] for _ in range(V)] + + +def add(u, v, c): + g[u].append([v, len(g[v]), c]) + g[v].append([u, len(g[u]) - 1, 0]) + + +INF = sum(cost) + 1 +for i, c in enumerate(cost): + add(2 * i, 2 * i + 1, c) +for _ in range(m): + u, v = a[p] - 1, a[p + 1] - 1 + p += 2 + add(2 * u + 1, 2 * v, INF) +for x in entries: + add(S, 2 * x, INF) +for x in danger: + add(2 * x + 1, T, INF) +flow = 0 +while True: + level = [-1] * V + level[S] = 0 + q = collections.deque([S]) + while q: + u = q.popleft() + for v, _, c in g[u]: + if c and level[v] < 0: + level[v] = level[u] + 1 + q.append(v) + if level[T] < 0: + break + it = [0] * V + + def dfs(u, f): + if u == T: + return f + while it[u] < len(g[u]): + e = g[u][it[u]] + if e[2] and level[e[0]] == level[u] + 1: + z = dfs(e[0], min(f, e[2])) + if z: + e[2] -= z + g[e[0]][e[1]][2] += z + return z + it[u] += 1 + return 0 + + while True: + z = dfs(S, INF) + if not z: + break + flow += z +print("COST", flow) diff --git a/problems/034-capability-cut/solutions/rust/main.rs b/problems/034-capability-cut/solutions/rust/main.rs new file mode 100644 index 0000000..a1d1187 --- /dev/null +++ b/problems/034-capability-cut/solutions/rust/main.rs @@ -0,0 +1,115 @@ +use std::collections::VecDeque; +use std::io::{self, Read}; +#[derive(Clone, Copy)] +struct E { + to: usize, + rev: usize, + cap: u64, +} +struct Dinic { + g: Vec>, + level: Vec, + it: Vec, + t: usize, +} +impl Dinic { + fn new(n: usize, t: usize) -> Self { + Self { + g: vec![vec![]; n], + level: vec![-1; n], + it: vec![0; n], + t, + } + } + fn add(&mut self, u: usize, v: usize, c: u64) { + let (a, b) = (self.g[u].len(), self.g[v].len()); + self.g[u].push(E { + to: v, + rev: b, + cap: c, + }); + self.g[v].push(E { + to: u, + rev: a, + cap: 0, + }); + } + fn dfs(&mut self, u: usize, f: u64) -> u64 { + if u == self.t { + return f; + } + while self.it[u] < self.g[u].len() { + let i = self.it[u]; + let e = self.g[u][i]; + if e.cap > 0 && self.level[e.to] == self.level[u] + 1 { + let z = self.dfs(e.to, f.min(e.cap)); + if z > 0 { + self.g[u][i].cap -= z; + self.g[e.to][e.rev].cap += z; + return z; + } + } + self.it[u] += 1 + } + 0 + } +} +fn main() { + let mut s = String::new(); + io::stdin().read_to_string(&mut s).unwrap(); + let mut x = s.split_whitespace(); + let n: usize = x.next().unwrap().parse().unwrap(); + let m: usize = x.next().unwrap().parse().unwrap(); + let sn: usize = x.next().unwrap().parse().unwrap(); + let tn: usize = x.next().unwrap().parse().unwrap(); + let c: Vec = (0..n).map(|_| x.next().unwrap().parse().unwrap()).collect(); + let en: Vec = (0..sn) + .map(|_| x.next().unwrap().parse::().unwrap() - 1) + .collect(); + let dn: Vec = (0..tn) + .map(|_| x.next().unwrap().parse::().unwrap() - 1) + .collect(); + let (v, s, t) = (2 * n + 2, 2 * n, 2 * n + 1); + let mut d = Dinic::new(v, t); + let inf = c.iter().sum::() + 1; + for (i, &z) in c.iter().enumerate() { + d.add(2 * i, 2 * i + 1, z) + } + for _ in 0..m { + let u = x.next().unwrap().parse::().unwrap() - 1; + let w = x.next().unwrap().parse::().unwrap() - 1; + d.add(2 * u + 1, 2 * w, inf) + } + for u in en { + d.add(s, 2 * u, inf) + } + for u in dn { + d.add(2 * u + 1, t, inf) + } + let mut flow = 0; + loop { + d.level.fill(-1); + d.level[s] = 0; + let mut q = VecDeque::from([s]); + while let Some(u) = q.pop_front() { + for e in &d.g[u] { + if e.cap > 0 && d.level[e.to] < 0 { + d.level[e.to] = d.level[u] + 1; + q.push_back(e.to) + } + } + } + if d.level[t] < 0 { + break; + } + d.it.fill(0); + loop { + let z = d.dfs(s, inf); + if z == 0 { + break; + } + flow += z + } + } + println!("COST {flow}"); +} diff --git a/problems/034-capability-cut/solutions/typescript/main.ts b/problems/034-capability-cut/solutions/typescript/main.ts new file mode 100644 index 0000000..7297615 --- /dev/null +++ b/problems/034-capability-cut/solutions/typescript/main.ts @@ -0,0 +1,86 @@ +import * as std from "std"; +type E = { to: number; rev: number; cap: bigint }; +const input: string = std.in.readAsString(); +let scan = 0; +function nextInt(): number { + while (scan < input.length && input.charCodeAt(scan) <= 32) scan++; + let value = 0; + while (scan < input.length) { + const digit = input.charCodeAt(scan) - 48; + if (digit < 0 || digit > 9) break; + value = value * 10 + digit; + scan++; + } + return value; +} +function nextBigInt(): bigint { + while (scan < input.length && input.charCodeAt(scan) <= 32) scan++; + const start = scan; + while (scan < input.length) { + const code = input.charCodeAt(scan); + if (code < 48 || code > 57) break; + scan++; + } + return BigInt(input.slice(start, scan)); +} +let n = nextInt(), + m = nextInt(), + sn = nextInt(), + tn = nextInt(); +const c: bigint[] = Array.from({ length: n }, () => nextBigInt()), + en: number[] = Array.from({ length: sn }, () => nextInt() - 1), + dn: number[] = Array.from({ length: tn }, () => nextInt() - 1), + V = 2 * n + 2, + S = 2 * n, + T = S + 1, + g: E[][] = Array.from({ length: V }, () => []), + add = (u: number, v: number, z: bigint): void => { + g[u].push({ to: v, rev: g[v].length, cap: z }); + g[v].push({ to: u, rev: g[u].length - 1, cap: 0n }); + }, + inf = c.reduce((x, y) => x + y, 1n); +for (let i = 0; i < n; i++) add(2 * i, 2 * i + 1, c[i]); +while (m--) { + const u = nextInt() - 1, v = nextInt() - 1; + add(2 * u + 1, 2 * v, inf); +} +for (const u of en) add(S, 2 * u, inf); +for (const u of dn) add(2 * u + 1, T, inf); +let flow = 0n; +for (;;) { + const level = new Int32Array(V).fill(-1), q: number[] = [S]; + level[S] = 0; + for (let h = 0; h < q.length; h++) { + const u = q[h]; + for (const e of g[u]) { + if (e.cap > 0n && level[e.to] < 0) { + level[e.to] = level[u] + 1; + q.push(e.to); + } + } + } + if (level[T] < 0) break; + const it = new Int32Array(V); + const dfs = (u: number, f: bigint): bigint => { + if (u === T) return f; + while (it[u] < g[u].length) { + const e = g[u][it[u]]; + if (e.cap > 0n && level[e.to] === level[u] + 1) { + const z = dfs(e.to, f < e.cap ? f : e.cap); + if (z > 0n) { + e.cap -= z; + g[e.to][e.rev].cap += z; + return z; + } + } + it[u]++; + } + return 0n; + }; + for (;;) { + const z = dfs(S, inf); + if (z === 0n) break; + flow += z; + } +} +std.out.puts(`COST ${flow}\n`); diff --git a/problems/034-capability-cut/statement.en.md b/problems/034-capability-cut/statement.en.md new file mode 100644 index 0000000..6ca92e1 --- /dev/null +++ b/problems/034-capability-cut/statement.en.md @@ -0,0 +1,95 @@ +# Cutting Dangerous Capabilities + +While designing the capability sandbox for a WASM OJ, checking only which APIs a module imports directly was not enough. A public entry function may pass through several helper calls before reaching a function that can create a network connection, thread, or process. If any such call path exists, the user program may still reach a forbidden capability. + +We can block selected functions while loading the module, but functions have different blocking costs: some are easy to replace, while disabling others also removes substantial legitimate behavior. The goal is therefore not to block the most functions, but to cut every dangerous path at minimum total cost. + +Represent the function call relation as a directed graph. A dangerous path exists if any dangerous function is reachable from any public entry function along call edges. Blocking function `i` costs `cost[i]` and removes that function together with every incident call edge. Public entry functions and dangerous functions themselves may also be blocked. + +Find the minimum total cost required to eliminate every path from every entry function to every dangerous function. + +## Input + +The first line contains `N M S T`. The second line contains the `N` function costs. The third line contains `S` distinct entry IDs, and the fourth line contains `T` distinct dangerous IDs. Each of the next `M` lines contains a directed edge `u v`, meaning that `u` can call `v` directly. + +All sets use 1-based IDs. The entry and dangerous sets may overlap. An overlapping function forms a dangerous path of length zero unless that function is blocked. + +## Output + +Output `COST x`. If no dangerous path exists initially, `x = 0`. An optimal blocking set need not be unique, so do not output the set. + +## Constraints + +- `1 <= N <= 500` +- `0 <= M <= 5000` +- `1 <= S, T <= N` +- Edges have no self-loops or duplicates. +- `0 <= cost[i] <= 10^12` +- The sum of all costs is at most `8 * 10^18`. +- Every flow and cut value fits in an unsigned 64-bit integer. +- Full tests rule out enumerating function subsets; node costs must be transformed into cut capacities. + +## Examples + + + +### Example One + +Input: + +```text +3 2 1 1 +5 2 7 +1 +3 +1 2 +2 3 +``` + +Output: + +```text +COST 2 +``` + +### Example Two + +Input: + +```text +4 4 1 1 +10 2 3 10 +1 +4 +1 2 +2 4 +1 3 +3 4 +``` + +Output: + +```text +COST 5 +``` + +### Example Three + +Input: + +```text +4 2 1 1 +1 1 1 1 +1 +4 +1 2 +3 4 +``` + +Output: + +```text +COST 0 +``` + + diff --git a/problems/034-capability-cut/statement.zh-TW.md b/problems/034-capability-cut/statement.zh-TW.md new file mode 100644 index 0000000..b3062ce --- /dev/null +++ b/problems/034-capability-cut/statement.zh-TW.md @@ -0,0 +1,91 @@ +# 切斷危險 Capability + +在設計 WASM OJ 的 capability sandbox 時,只檢查模組直接 import 了哪些 API 並不夠。公開 entry function 可能經過多層 helper calls,間接到達能建立 network、thread 或 process 的函式;只要存在這樣的呼叫路徑,使用者程式就仍可能觸及不允許的 capability。 + +我們可以在載入模組時封鎖特定函式,但不同函式的封鎖代價不同:有些函式容易替換,有些則會連帶停用大量正常功能。因此目標不是封鎖最多函式,而是以最小代價切斷所有危險路徑。 + +將函式呼叫關係表示成一張 directed graph。若從任一公開 entry function 能沿 call edges 到達任一 dangerous function,就存在危險路徑。封鎖函式 `i` 的代價為 `cost[i]`,並會移除該函式及所有 incident call edges;entry functions 與 dangerous functions 本身也允許被封鎖。 + +請求出讓所有 entry 到 dangerous 的路徑都消失所需的最小總代價。 + +## 輸入 + +第一行 `N M S T`。第二行有 `N` 個 cost。第三行有 `S` 個互異 entry IDs;第四行有 `T` 個互異 dangerous IDs。接著 `M` 行 directed edge `u v`,表示 `u` 可直接呼叫 `v`。 + +集合使用 1-based ID;entry 與 dangerous 集合可以重疊。重疊節點形成長度 0 的危險路徑,除非該節點被封鎖。 + +## 輸出 + +輸出 `COST x`。若原本就沒有任何危險路徑,`x=0`。最佳封鎖集合可能不唯一,不輸出集合。 + +## 限制 + +- `1 <= N <= 500`,`0 <= M <= 5000`,`1 <= S,T <= N`。 +- edge 無 self-loop、無重複;`0 <= cost[i] <= 10^12`,cost 總和不超過 `8*10^18`。 +- 所有 flow/cut 值可用 unsigned 64-bit 表示。 +- 完整測資排除函式子集合枚舉;必須把 node cost 轉成 cut capacity。 + +## 範例 + + + +### 範例一 + +輸入: + +```text +3 2 1 1 +5 2 7 +1 +3 +1 2 +2 3 +``` + +輸出: + +```text +COST 2 +``` + +### 範例二 + +輸入: + +```text +4 4 1 1 +10 2 3 10 +1 +4 +1 2 +2 4 +1 3 +3 4 +``` + +輸出: + +```text +COST 5 +``` + +### 範例三 + +輸入: + +```text +4 2 1 1 +1 1 1 1 +1 +4 +1 2 +3 4 +``` + +輸出: + +```text +COST 0 +``` + + diff --git a/problems/034-capability-cut/tests/adversarial-blind-01.in b/problems/034-capability-cut/tests/adversarial-blind-01.in new file mode 100644 index 0000000..ea7e63b --- /dev/null +++ b/problems/034-capability-cut/tests/adversarial-blind-01.in @@ -0,0 +1,9 @@ +6 5 2 2 +1000000000000 7 5 6 0 1000000000000 +1 2 +2 6 +1 3 +3 6 +1 4 +4 5 +5 6 diff --git a/problems/034-capability-cut/tests/adversarial-blind-01.out b/problems/034-capability-cut/tests/adversarial-blind-01.out new file mode 100644 index 0000000..89e28bb --- /dev/null +++ b/problems/034-capability-cut/tests/adversarial-blind-01.out @@ -0,0 +1 @@ +COST 12 diff --git a/problems/034-capability-cut/tests/sample-01.in b/problems/034-capability-cut/tests/sample-01.in new file mode 100644 index 0000000..855d70a --- /dev/null +++ b/problems/034-capability-cut/tests/sample-01.in @@ -0,0 +1,6 @@ +3 2 1 1 +5 2 7 +1 +3 +1 2 +2 3 diff --git a/problems/034-capability-cut/tests/sample-01.out b/problems/034-capability-cut/tests/sample-01.out new file mode 100644 index 0000000..a6baba0 --- /dev/null +++ b/problems/034-capability-cut/tests/sample-01.out @@ -0,0 +1 @@ +COST 2 diff --git a/problems/034-capability-cut/tests/sample-02.in b/problems/034-capability-cut/tests/sample-02.in new file mode 100644 index 0000000..a4683df --- /dev/null +++ b/problems/034-capability-cut/tests/sample-02.in @@ -0,0 +1,8 @@ +4 4 1 1 +10 2 3 10 +1 +4 +1 2 +2 4 +1 3 +3 4 diff --git a/problems/034-capability-cut/tests/sample-02.out b/problems/034-capability-cut/tests/sample-02.out new file mode 100644 index 0000000..44c7d17 --- /dev/null +++ b/problems/034-capability-cut/tests/sample-02.out @@ -0,0 +1 @@ +COST 5 diff --git a/problems/034-capability-cut/tests/sample-03.in b/problems/034-capability-cut/tests/sample-03.in new file mode 100644 index 0000000..4f8978f --- /dev/null +++ b/problems/034-capability-cut/tests/sample-03.in @@ -0,0 +1,6 @@ +4 2 1 1 +1 1 1 1 +1 +4 +1 2 +3 4 diff --git a/problems/034-capability-cut/tests/sample-03.out b/problems/034-capability-cut/tests/sample-03.out new file mode 100644 index 0000000..6383e6c --- /dev/null +++ b/problems/034-capability-cut/tests/sample-03.out @@ -0,0 +1 @@ +COST 0 diff --git a/problems/034-capability-cut/validator.py b/problems/034-capability-cut/validator.py new file mode 100644 index 0000000..f1ca7ff --- /dev/null +++ b/problems/034-capability-cut/validator.py @@ -0,0 +1,34 @@ +import sys + + +def main(): + a = list(map(int, sys.stdin.read().split())) + assert len(a) >= 4 + n, m, s, t = a[:4] + assert 1 <= n <= 500 and 0 <= m <= 5000 and 1 <= s <= n and 1 <= t <= n + assert len(a) == 4 + n + s + t + 2 * m + p = 4 + c = a[p : p + n] + p += n + assert all(0 <= x <= 10**12 for x in c) and sum(c) <= 8 * 10**18 + e = a[p : p + s] + p += s + d = a[p : p + t] + p += t + assert ( + len(e) == len(set(e)) + and len(d) == len(set(d)) + and all(1 <= x <= n for x in e + d) + ) + seen = set() + for _ in range(m): + u, v = a[p : p + 2] + p += 2 + assert 1 <= u <= n and 1 <= v <= n and u != v and (u, v) not in seen + seen.add((u, v)) + + +try: + main() +except (AssertionError, ValueError): + sys.exit(1) diff --git a/problems/035-wait-for-cycles/editorial.en.md b/problems/035-wait-for-cycles/editorial.en.md new file mode 100644 index 0000000..58b3cc3 --- /dev/null +++ b/problems/035-wait-for-cycles/editorial.en.md @@ -0,0 +1,32 @@ +# Editorial + +## Intuitive Approach + +Run a graph search from every process, construct pairwise mutual reachability, and group equivalent vertices. This takes `O(N(N + M))` time; Floyd-Warshall is even worse at `O(N^3)`. + +## Optimal Approach: SCCs and the Condensation DAG + +Use iterative Kosaraju. The first traversal of the original graph uses explicit `(node, next-edge-index)` stack frames to produce finishing order. The second traversal follows reverse finishing order on the reversed graph and assigns an SCC ID to every process. Explicit stacks avoid recursion overflow on long chains. + +Collect the members of each SCC. It is a wait-cycle group exactly when it has more than one member or contains a self-loop. For every edge crossing from component `cu` to component `cv`, mark `cv` as having positive condensation indegree. + +The condensation graph is a DAG. One wake in an SCC releases that entire SCC and everything reachable downstream. Therefore the minimum number `W` is the number of condensation SCCs with indegree zero. + +Scan process IDs in increasing order when appending them to their components. This makes IDs inside each component sorted and allows components to be emitted in increasing order of their first member without an extra comparison sort. + +## Correctness Proof + +Kosaraju's theorem guarantees that the two traversals partition the graph into exactly its maximal mutually reachable sets. An SCC of size greater than one contains a directed cycle; a singleton contains a cycle exactly when it has a self-loop. Thus the reported wait-cycle groups are exactly the required groups, and sorting affects only their canonical output order. + +After contraction, every source SCC has no incoming edge from another SCC, so no wake outside it can release it. Every valid plan therefore needs at least one wake in each source SCC. Conversely, waking one process in each source SCC releases each such SCC, and every SCC in a finite DAG is reachable from some source. Release propagation consequently reaches every process. The lower and upper bounds coincide, so `W` is correct. + +## Complexity + +The two DFS passes and the condensation scan take `O(N + M)` time. Building membership lists and producing canonical order can also be done in one increasing-ID scan. Total space is `O(N + M)`. + +## Common Mistakes + +- Treating every singleton SCC as cyclic without checking for a self-loop. +- Counting condensation sinks instead of sources; release propagates in the edge direction. +- Treating duplicate condensation edges as meaningful exact indegree counts when only zero versus nonzero matters. +- Using recursive DFS on a chain of `200000` vertices. diff --git a/problems/035-wait-for-cycles/editorial.zh-TW.md b/problems/035-wait-for-cycles/editorial.zh-TW.md new file mode 100644 index 0000000..128af64 --- /dev/null +++ b/problems/035-wait-for-cycles/editorial.zh-TW.md @@ -0,0 +1,28 @@ +# 解題說明 + +## 直覺解 + +從每個 process 做一次圖搜尋,建立 mutual reachability matrix 再分組,時間 `O(N(N+M))`;Floyd–Warshall 更達 `O(N^3)`。 + +## 最佳解 + +用 iterative Kosaraju:第一趟在原圖以 `(node,next-edge-index)` stack 得到 finish order;第二趟依逆 finish order在反圖 flood fill,標出 SCC ID。這避免長鏈上的遞迴 stack overflow。 + +統計每個 SCC 的 members;size>1 或含 self-loop 就輸出為等待環群組。對每條跨 SCC edge `cu->cv`,標記 `indegree[cv]>0`。Condensation graph 是 DAG;要讓 release 從 wake seeds 覆蓋所有 components,恰需在每個 indegree=0 的 source SCC 放一個 seed,所以 `W` 是 source SCC 數。 + +## 正確性證明 + +Kosaraju 定理保證兩趟搜尋得到且只得到 maximal mutual-reachability sets,即 SCC。SCC size>1 時任兩點間路徑組成 cycle;singleton 只有 self-loop 才含 cycle,因此群組判定精確,排序只決定唯一輸出順序。 + +縮點後為 DAG。每個 source SCC 沒有其他 component 能沿 release edge到達它,所以任何方案至少要在每個 source SCC 內 wake 一點。反之,在每個 source SCC wake 一點後,SCC 內全被釋放;DAG 中每個 component 都可由某 source 沿 edge 到達,故所有 process 都會釋放。上下界相等,所以 `W` 正確。 + +## 複雜度 + +兩趟 DFS 與縮點統計皆為 `O(N+M)`。Reference solutions 再依 ID 由小到大把節點放入所屬 component,並於同一次 ID 掃描輸出 component 的最小 ID,因此不需要額外排序。總時間 `O(N+M)`,空間 `O(N+M)`。 + +## 常見錯誤 + +- 把所有 singleton SCC 都當成等待環,忽略 self-loop 條件。 +- 計算 condensation 的 sink 數;release 沿 `u->v` 正向傳播,所以需要 source。 +- 對跨 SCC 的平行 condensation edge重複計 indegree 不影響零/非零,但不應拿它當精確 indegree用途。 +- 遞迴 DFS 在 `N=200000` 長鏈爆 stack。 diff --git a/problems/035-wait-for-cycles/generator.py b/problems/035-wait-for-cycles/generator.py new file mode 100644 index 0000000..a260212 --- /dev/null +++ b/problems/035-wait-for-cycles/generator.py @@ -0,0 +1,9 @@ +import random, sys + +seed, index = map(int, sys.argv[1:]) +r = random.Random(seed * 43 + index) +n = 5 + index % 5 +edges = [(u, v) for u in range(1, n + 1) for v in range(1, n + 1) if r.random() < 0.14] +print(n, len(edges)) +for e in edges: + print(*e) diff --git a/problems/035-wait-for-cycles/oracle.py b/problems/035-wait-for-cycles/oracle.py new file mode 100644 index 0000000..209e049 --- /dev/null +++ b/problems/035-wait-for-cycles/oracle.py @@ -0,0 +1,36 @@ +import sys + +a = list(map(int, sys.stdin.read().split())) +n, m = a[:2] +reach = [[False] * n for _ in range(n)] +selfloop = [False] * n +for i in range(n): + reach[i][i] = True +for i in range(2, len(a), 2): + u, v = a[i] - 1, a[i + 1] - 1 + reach[u][v] = True + selfloop[u] |= u == v +for k in range(n): + for i in range(n): + if reach[i][k]: + for j in range(n): + reach[i][j] |= reach[k][j] +comp = [-1] * n +groups = [] +for i in range(n): + if comp[i] >= 0: + continue + g = [j for j in range(n) if reach[i][j] and reach[j][i]] + cid = len(groups) + for j in g: + comp[j] = cid + groups.append(g) +indeg = [False] * len(groups) +for i in range(2, len(a), 2): + u, v = a[i] - 1, a[i + 1] - 1 + indeg[comp[v]] |= comp[u] != comp[v] +cyc = [g for g in groups if len(g) > 1 or selfloop[g[0]]] +cyc.sort(key=lambda g: g[0]) +print(len(cyc), sum(not x for x in indeg)) +for g in cyc: + print(len(g), *(x + 1 for x in g)) diff --git a/problems/035-wait-for-cycles/problem.json b/problems/035-wait-for-cycles/problem.json new file mode 100644 index 0000000..f3fa59a --- /dev/null +++ b/problems/035-wait-for-cycles/problem.json @@ -0,0 +1,147 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 35, + "slug": "wait-for-cycles", + "title": { + "zh-TW": "互動程式的等待環", + "en": "Wait-For Cycles" + }, + "difficulty": "hard", + "tags": [ + "graph", + "strongly-connected-components", + "condensation-dag", + "kosaraju" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-blind-01", + "kind": "adversarial", + "input": "tests/adversarial-blind-01.in", + "output": "tests/adversarial-blind-01.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 20000000, + "memoryLimitBytes": 536870912 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 2000000, + "memoryLimitBytes": 402653184 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 750000, + "memoryLimitBytes": 268435456 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "每對程序做可達性", + "en": "Reachability for every process pair" + }, + "time": "O(N(N+M))", + "space": "O(N+M)", + "accepted": false + }, + { + "name": { + "zh-TW": "SCC 與縮點 DAG", + "en": "SCC decomposition and condensation DAG" + }, + "time": "O(N+M)", + "space": "O(N+M)", + "accepted": true + } + ] +} diff --git a/problems/035-wait-for-cycles/solutions/c/main.c b/problems/035-wait-for-cycles/solutions/c/main.c new file mode 100644 index 0000000..20e715a --- /dev/null +++ b/problems/035-wait-for-cycles/solutions/c/main.c @@ -0,0 +1,109 @@ +#include +#include +#include +int main(void) { + int n, m; + if (scanf("%d%d", &n, &m) != 2) + return 0; + int *eu = malloc(sizeof(int) * (size_t)(m ? m : 1)), + *ev = malloc(sizeof(int) * (size_t)(m ? m : 1)), + *h = malloc(sizeof(int) * (size_t)n), + *rh = malloc(sizeof(int) * (size_t)n), + *to = malloc(sizeof(int) * (size_t)(m ? m : 1)), + *rto = malloc(sizeof(int) * (size_t)(m ? m : 1)), + *nx = malloc(sizeof(int) * (size_t)(m ? m : 1)), + *rnx = malloc(sizeof(int) * (size_t)(m ? m : 1)); + memset(h, 255, sizeof(int) * (size_t)n); + memset(rh, 255, sizeof(int) * (size_t)n); + unsigned char *self = calloc((size_t)n, 1); + for (int e = 0; e < m; e++) { + scanf("%d%d", &eu[e], &ev[e]); + eu[e]--; + ev[e]--; + to[e] = ev[e]; + nx[e] = h[eu[e]]; + h[eu[e]] = e; + rto[e] = eu[e]; + rnx[e] = rh[ev[e]]; + rh[ev[e]] = e; + if (eu[e] == ev[e]) + self[eu[e]] = 1; + } + unsigned char *seen = calloc((size_t)n, 1); + int *iter = malloc(sizeof(int) * (size_t)n), + *st = malloc(sizeof(int) * (size_t)n), + *order = malloc(sizeof(int) * (size_t)n); + memcpy(iter, h, sizeof(int) * (size_t)n); + int os = 0; + for (int s = 0; s < n; s++) { + if (seen[s]) + continue; + int top = 1; + st[0] = s; + seen[s] = 1; + while (top) { + int u = st[top - 1], e = iter[u]; + if (e >= 0) { + iter[u] = nx[e]; + int v = to[e]; + if (!seen[v]) { + seen[v] = 1; + st[top++] = v; + } + } else { + order[os++] = u; + top--; + } + } + } + int *comp = malloc(sizeof(int) * (size_t)n); + memset(comp, 255, sizeof(int) * (size_t)n); + int cc = 0; + for (int oi = n - 1; oi >= 0; oi--) { + int s = order[oi]; + if (comp[s] >= 0) + continue; + int top = 1; + st[0] = s; + comp[s] = cc; + while (top) { + int u = st[--top]; + for (int e = rh[u]; e >= 0; e = rnx[e]) + if (comp[rto[e]] < 0) { + comp[rto[e]] = cc; + st[top++] = rto[e]; + } + } + cc++; + } + int *ch = malloc(sizeof(int) * (size_t)cc), + *mn = malloc(sizeof(int) * (size_t)n), + *sz = calloc((size_t)cc, sizeof(int)); + memset(ch, 255, sizeof(int) * (size_t)cc); + for (int i = n - 1; i >= 0; i--) { + int c = comp[i]; + mn[i] = ch[c]; + ch[c] = i; + sz[c]++; + } + unsigned char *indeg = calloc((size_t)cc, 1); + for (int e = 0; e < m; e++) + if (comp[eu[e]] != comp[ev[e]]) + indeg[comp[ev[e]]] = 1; + int groups = 0, wake = 0; + for (int c = 0; c < cc; c++) { + wake += !indeg[c]; + groups += sz[c] > 1 || self[ch[c]]; + } + printf("%d %d\n", groups, wake); + for (int i = 0; i < n; i++) { + int c = comp[i]; + if (ch[c] != i || !(sz[c] > 1 || self[i])) + continue; + printf("%d", sz[c]); + for (int v = ch[c]; v >= 0; v = mn[v]) + printf(" %d", v + 1); + putchar('\n'); + } + return 0; +} diff --git a/problems/035-wait-for-cycles/solutions/cpp/main.cpp b/problems/035-wait-for-cycles/solutions/cpp/main.cpp new file mode 100644 index 0000000..5749eda --- /dev/null +++ b/problems/035-wait-for-cycles/solutions/cpp/main.cpp @@ -0,0 +1,82 @@ +#include +#include +using namespace std; +int main() { + ios::sync_with_stdio(false); + cin.tie(nullptr); + int n, m; + if (!(cin >> n >> m)) + return 0; + vector> g(n), rg(n); + vector> edges; + vector self(n); + while (m--) { + int u, v; + cin >> u >> v; + --u; + --v; + g[u].push_back(v); + rg[v].push_back(u); + edges.push_back({u, v}); + if (u == v) + self[u] = 1; + } + vector seen(n); + vector cur(n), order; + for (int s = 0; s < n; s++) { + if (seen[s]) + continue; + vector st{s}; + seen[s] = 1; + while (!st.empty()) { + int u = st.back(); + if (cur[u] < (int)g[u].size()) { + int v = g[u][cur[u]++]; + if (!seen[v]) + seen[v] = 1, st.push_back(v); + } else { + order.push_back(u); + st.pop_back(); + } + } + } + vector comp(n, -1); + int cc = 0; + for (auto it = order.rbegin(); it != order.rend(); ++it) { + int s = *it; + if (comp[s] >= 0) + continue; + vector st{s}; + comp[s] = cc; + while (!st.empty()) { + int u = st.back(); + st.pop_back(); + for (int v : rg[u]) + if (comp[v] < 0) + comp[v] = cc, st.push_back(v); + } + cc++; + } + vector> mem(cc); + for (int i = 0; i < n; i++) + mem[comp[i]].push_back(i); + vector indeg(cc); + for (auto [u, v] : edges) + if (comp[u] != comp[v]) + indeg[comp[v]] = 1; + int groups = 0, wake = 0; + for (int c = 0; c < cc; c++) { + wake += !indeg[c]; + groups += mem[c].size() > 1 || self[mem[c][0]]; + } + cout << groups << ' ' << wake << '\n'; + for (int i = 0; i < n; i++) { + int c = comp[i]; + if (mem[c][0] != i || !(mem[c].size() > 1 || self[i])) + continue; + cout << mem[c].size(); + for (int v : mem[c]) + cout << ' ' << v + 1; + cout << '\n'; + } +} diff --git a/problems/035-wait-for-cycles/solutions/go/main.go b/problems/035-wait-for-cycles/solutions/go/main.go new file mode 100644 index 0000000..77c15a6 --- /dev/null +++ b/problems/035-wait-for-cycles/solutions/go/main.go @@ -0,0 +1,110 @@ +package main + +import ( + "bufio" + "fmt" + "os" +) + +type E struct{ u, v int } + +func main() { + in := bufio.NewReader(os.Stdin) + out := bufio.NewWriter(os.Stdout) + defer out.Flush() + var n, m int + fmt.Fscan(in, &n, &m) + g := make([][]int, n) + rg := make([][]int, n) + edges := make([]E, 0, m) + self := make([]bool, n) + for ; m > 0; m-- { + var u, v int + fmt.Fscan(in, &u, &v) + u-- + v-- + g[u] = append(g[u], v) + rg[v] = append(rg[v], u) + edges = append(edges, E{u, v}) + self[u] = self[u] || u == v + } + seen := make([]bool, n) + cur := make([]int, n) + order := []int{} + for root := 0; root < n; root++ { + if seen[root] { + continue + } + seen[root] = true + st := []int{root} + for len(st) > 0 { + u := st[len(st)-1] + if cur[u] < len(g[u]) { + v := g[u][cur[u]] + cur[u]++ + if !seen[v] { + seen[v] = true + st = append(st, v) + } + } else { + order = append(order, u) + st = st[:len(st)-1] + } + } + } + comp := make([]int, n) + for i := range comp { + comp[i] = -1 + } + cc := 0 + for oi := n - 1; oi >= 0; oi-- { + root := order[oi] + if comp[root] >= 0 { + continue + } + comp[root] = cc + st := []int{root} + for len(st) > 0 { + u := st[len(st)-1] + st = st[:len(st)-1] + for _, v := range rg[u] { + if comp[v] < 0 { + comp[v] = cc + st = append(st, v) + } + } + } + cc++ + } + mem := make([][]int, cc) + for i, c := range comp { + mem[c] = append(mem[c], i) + } + indeg := make([]bool, cc) + for _, e := range edges { + if comp[e.u] != comp[e.v] { + indeg[comp[e.v]] = true + } + } + wake := 0 + for _, x := range indeg { + if !x { + wake++ + } + } + cyc := []int{} + for i := 0; i < n; i++ { + c := comp[i] + if mem[c][0] == i && (len(mem[c]) > 1 || self[i]) { + cyc = append(cyc, c) + } + } + fmt.Fprintln(out, len(cyc), wake) + for _, c := range cyc { + fmt.Fprint(out, len(mem[c])) + for _, v := range mem[c] { + fmt.Fprint(out, " ", v+1) + } + fmt.Fprintln(out) + } +} diff --git a/problems/035-wait-for-cycles/solutions/javascript/main.js b/problems/035-wait-for-cycles/solutions/javascript/main.js new file mode 100644 index 0000000..072d83b --- /dev/null +++ b/problems/035-wait-for-cycles/solutions/javascript/main.js @@ -0,0 +1,126 @@ +import * as std from "std"; + +const input = std.in.readAsString(); +let scan = 0; +function nextInt() { + while (scan < input.length && input.charCodeAt(scan) <= 32) scan++; + let value = 0; + while (scan < input.length) { + const digit = input.charCodeAt(scan) - 48; + if (digit < 0 || digit > 9) break; + value = value * 10 + digit; + scan++; + } + return value; +} + +const n = nextInt(), m = nextInt(); +const edgeFrom = new Int32Array(m), + edgeTo = new Int32Array(m), + head = new Int32Array(n).fill(-1), + reverseHead = new Int32Array(n).fill(-1), + to = new Int32Array(m), + reverseTo = new Int32Array(m), + next = new Int32Array(m), + reverseNext = new Int32Array(m), + selfLoop = new Uint8Array(n); +for (let edge = 0; edge < m; edge++) { + const u = nextInt() - 1, v = nextInt() - 1; + edgeFrom[edge] = u; + edgeTo[edge] = v; + to[edge] = v; + next[edge] = head[u]; + head[u] = edge; + reverseTo[edge] = u; + reverseNext[edge] = reverseHead[v]; + reverseHead[v] = edge; + if (u === v) selfLoop[u] = 1; +} + +const seen = new Uint8Array(n), + iterator = new Int32Array(head), + stack = new Int32Array(n), + order = new Int32Array(n); +let orderSize = 0; +for (let root = 0; root < n; root++) { + if (seen[root]) continue; + let top = 1; + stack[0] = root; + seen[root] = 1; + while (top > 0) { + const u = stack[top - 1], edge = iterator[u]; + if (edge !== -1) { + iterator[u] = next[edge]; + const v = to[edge]; + if (!seen[v]) { + seen[v] = 1; + stack[top++] = v; + } + } else { + order[orderSize++] = u; + top--; + } + } +} + +const component = new Int32Array(n).fill(-1); +let componentCount = 0; +for (let index = n - 1; index >= 0; index--) { + const root = order[index]; + if (component[root] !== -1) continue; + let top = 1; + stack[0] = root; + component[root] = componentCount; + while (top > 0) { + const u = stack[--top]; + for (let edge = reverseHead[u]; edge !== -1; edge = reverseNext[edge]) { + const v = reverseTo[edge]; + if (component[v] === -1) { + component[v] = componentCount; + stack[top++] = v; + } + } + } + componentCount++; +} + +const componentHead = new Int32Array(componentCount).fill(-1), + memberNext = new Int32Array(n).fill(-1), + componentSize = new Int32Array(componentCount), + indegree = new Uint8Array(componentCount); +for (let node = n - 1; node >= 0; node--) { + const id = component[node]; + memberNext[node] = componentHead[id]; + componentHead[id] = node; + componentSize[id]++; +} +for (let edge = 0; edge < m; edge++) { + const from = component[edgeFrom[edge]], target = component[edgeTo[edge]]; + if (from !== target) indegree[target] = 1; +} +let groups = 0, wakes = 0; +for (let id = 0; id < componentCount; id++) { + if (!indegree[id]) wakes++; + if (componentSize[id] > 1 || selfLoop[componentHead[id]]) groups++; +} +let output = `${groups} ${wakes}\n`; +for (let node = 0; node < n; node++) { + const id = component[node]; + if ( + componentHead[id] !== node || !(componentSize[id] > 1 || selfLoop[node]) + ) continue; + output += `${componentSize[id]}`; + for ( + let member = componentHead[id]; + member !== -1; + member = memberNext[member] + ) { + output += ` ${member + 1}`; + } + output += "\n"; + if (output.length >= 1 << 20) { + std.out.puts(output); + output = ""; + } +} +if (output.length) std.out.puts(output); diff --git a/problems/035-wait-for-cycles/solutions/python/main.py b/problems/035-wait-for-cycles/solutions/python/main.py new file mode 100644 index 0000000..7831d33 --- /dev/null +++ b/problems/035-wait-for-cycles/solutions/python/main.py @@ -0,0 +1,67 @@ +import sys + +a = list(map(int, sys.stdin.read().split())) +n, m = a[:2] +g = [[] for _ in range(n)] +rg = [[] for _ in range(n)] +edges = [] +selfloop = [False] * n +p = 2 +for _ in range(m): + u, v = a[p] - 1, a[p + 1] - 1 + p += 2 + g[u].append(v) + rg[v].append(u) + edges.append((u, v)) + selfloop[u] |= u == v +seen = [False] * n +cur = [0] * n +order = [] +for s in range(n): + if seen[s]: + continue + seen[s] = True + st = [s] + while st: + u = st[-1] + if cur[u] < len(g[u]): + v = g[u][cur[u]] + cur[u] += 1 + if not seen[v]: + seen[v] = True + st.append(v) + else: + order.append(u) + st.pop() +comp = [-1] * n +members = [] +for s in reversed(order): + if comp[s] >= 0: + continue + cid = len(members) + mem = [] + comp[s] = cid + st = [s] + while st: + u = st.pop() + mem.append(u) + for v in rg[u]: + if comp[v] < 0: + comp[v] = cid + st.append(v) + members.append(mem) +members = [[] for _ in members] +for i, c in enumerate(comp): + members[c].append(i) +indeg = [False] * len(members) +for u, v in edges: + if comp[u] != comp[v]: + indeg[comp[v]] = True +cyc = [] +for i in range(n): + c = comp[i] + if members[c][0] == i and (len(members[c]) > 1 or selfloop[i]): + cyc.append(members[c]) +out = [f"{len(cyc)} {sum(not x for x in indeg)}"] +out += [str(len(x)) + " " + " ".join(str(v + 1) for v in x) for x in cyc] +print("\n".join(out)) diff --git a/problems/035-wait-for-cycles/solutions/rust/main.rs b/problems/035-wait-for-cycles/solutions/rust/main.rs new file mode 100644 index 0000000..c5c3997 --- /dev/null +++ b/problems/035-wait-for-cycles/solutions/rust/main.rs @@ -0,0 +1,88 @@ +use std::fmt::Write; +use std::io::{self, Read}; +fn main() { + let mut s = String::new(); + io::stdin().read_to_string(&mut s).unwrap(); + let mut it = s.split_whitespace(); + let n: usize = it.next().unwrap().parse().unwrap(); + let m: usize = it.next().unwrap().parse().unwrap(); + let (mut g, mut rg) = (vec![vec![]; n], vec![vec![]; n]); + let mut edges = vec![]; + let mut selfloop = vec![false; n]; + for _ in 0..m { + let u = it.next().unwrap().parse::().unwrap() - 1; + let v = it.next().unwrap().parse::().unwrap() - 1; + g[u].push(v); + rg[v].push(u); + edges.push((u, v)); + selfloop[u] |= u == v; + } + let mut seen = vec![false; n]; + let mut cur = vec![0; n]; + let mut order = vec![]; + for root in 0..n { + if seen[root] { + continue; + } + seen[root] = true; + let mut st = vec![root]; + while let Some(&u) = st.last() { + if cur[u] < g[u].len() { + let v = g[u][cur[u]]; + cur[u] += 1; + if !seen[v] { + seen[v] = true; + st.push(v) + } + } else { + order.push(u); + st.pop(); + } + } + } + let mut comp = vec![usize::MAX; n]; + let mut cc = 0; + for &root in order.iter().rev() { + if comp[root] != usize::MAX { + continue; + } + comp[root] = cc; + let mut st = vec![root]; + while let Some(u) = st.pop() { + for &v in &rg[u] { + if comp[v] == usize::MAX { + comp[v] = cc; + st.push(v) + } + } + } + cc += 1 + } + let mut mem = vec![vec![]; cc]; + for i in 0..n { + mem[comp[i]].push(i) + } + let mut indeg = vec![false; cc]; + for &(u, v) in &edges { + if comp[u] != comp[v] { + indeg[comp[v]] = true + } + } + let wake = indeg.iter().filter(|&&x| !x).count(); + let mut cyc = vec![]; + for i in 0..n { + let c = comp[i]; + if mem[c][0] == i && (mem[c].len() > 1 || selfloop[i]) { + cyc.push(c) + } + } + let mut out = format!("{} {}\n", cyc.len(), wake); + for c in cyc { + write!(out, "{}", mem[c].len()).unwrap(); + for &v in &mem[c] { + write!(out, " {}", v + 1).unwrap() + } + out.push('\n'); + } + print!("{out}"); +} diff --git a/problems/035-wait-for-cycles/solutions/typescript/main.ts b/problems/035-wait-for-cycles/solutions/typescript/main.ts new file mode 100644 index 0000000..34f0e03 --- /dev/null +++ b/problems/035-wait-for-cycles/solutions/typescript/main.ts @@ -0,0 +1,126 @@ +import * as std from "std"; + +const input: string = std.in.readAsString(); +let scan = 0; +function nextInt(): number { + while (scan < input.length && input.charCodeAt(scan) <= 32) scan++; + let value = 0; + while (scan < input.length) { + const digit = input.charCodeAt(scan) - 48; + if (digit < 0 || digit > 9) break; + value = value * 10 + digit; + scan++; + } + return value; +} + +const n = nextInt(), m = nextInt(); +const edgeFrom = new Int32Array(m), + edgeTo = new Int32Array(m), + head = new Int32Array(n).fill(-1), + reverseHead = new Int32Array(n).fill(-1), + to = new Int32Array(m), + reverseTo = new Int32Array(m), + next = new Int32Array(m), + reverseNext = new Int32Array(m), + selfLoop = new Uint8Array(n); +for (let edge = 0; edge < m; edge++) { + const u = nextInt() - 1, v = nextInt() - 1; + edgeFrom[edge] = u; + edgeTo[edge] = v; + to[edge] = v; + next[edge] = head[u]!; + head[u] = edge; + reverseTo[edge] = u; + reverseNext[edge] = reverseHead[v]!; + reverseHead[v] = edge; + if (u === v) selfLoop[u] = 1; +} + +const seen = new Uint8Array(n), + iterator = new Int32Array(head), + stack = new Int32Array(n), + order = new Int32Array(n); +let orderSize = 0; +for (let root = 0; root < n; root++) { + if (seen[root]) continue; + let top = 1; + stack[0] = root; + seen[root] = 1; + while (top > 0) { + const u = stack[top - 1]!, edge = iterator[u]!; + if (edge !== -1) { + iterator[u] = next[edge]!; + const v = to[edge]!; + if (!seen[v]) { + seen[v] = 1; + stack[top++] = v; + } + } else { + order[orderSize++] = u; + top--; + } + } +} + +const component = new Int32Array(n).fill(-1); +let componentCount = 0; +for (let index = n - 1; index >= 0; index--) { + const root = order[index]!; + if (component[root] !== -1) continue; + let top = 1; + stack[0] = root; + component[root] = componentCount; + while (top > 0) { + const u = stack[--top]!; + for (let edge = reverseHead[u]!; edge !== -1; edge = reverseNext[edge]!) { + const v = reverseTo[edge]!; + if (component[v] === -1) { + component[v] = componentCount; + stack[top++] = v; + } + } + } + componentCount++; +} + +const componentHead = new Int32Array(componentCount).fill(-1), + memberNext = new Int32Array(n).fill(-1), + componentSize = new Int32Array(componentCount), + indegree = new Uint8Array(componentCount); +for (let node = n - 1; node >= 0; node--) { + const id = component[node]!; + memberNext[node] = componentHead[id]!; + componentHead[id] = node; + componentSize[id]!++; +} +for (let edge = 0; edge < m; edge++) { + const from = component[edgeFrom[edge]!]!, target = component[edgeTo[edge]!]!; + if (from !== target) indegree[target] = 1; +} +let groups = 0, wakes = 0; +for (let id = 0; id < componentCount; id++) { + if (!indegree[id]) wakes++; + if (componentSize[id]! > 1 || selfLoop[componentHead[id]!]) groups++; +} +let output = `${groups} ${wakes}\n`; +for (let node = 0; node < n; node++) { + const id = component[node]!; + if ( + componentHead[id] !== node || !(componentSize[id]! > 1 || selfLoop[node]) + ) continue; + output += `${componentSize[id]}`; + for ( + let member = componentHead[id]!; + member !== -1; + member = memberNext[member]! + ) { + output += ` ${member + 1}`; + } + output += "\n"; + if (output.length >= 1 << 20) { + std.out.puts(output); + output = ""; + } +} +if (output.length) std.out.puts(output); diff --git a/problems/035-wait-for-cycles/statement.en.md b/problems/035-wait-for-cycles/statement.en.md new file mode 100644 index 0000000..0c4e1e9 --- /dev/null +++ b/problems/035-wait-for-cycles/statement.en.md @@ -0,0 +1,93 @@ +# Wait-For Cycles + +While designing the interactive-program runtime for a WASM OJ, we needed to handle processes that wait for events from one another. Releasing one process may let it wake other processes, but a group whose first event can only come from within the same group may otherwise remain stalled forever. + +To diagnose this situation, we want both to list the groups that contain an actual wait cycle and to determine the minimum number of external wake events needed for release events to reach the entire system. + +There are `N` processes that have not yet been released. A directed release edge `u v` means that once `u` is released, it can send an event that releases `v`. Release events continue propagating along edges. You may also inject external wake events, each into any process. + +Two processes belong to the same mutually waiting group if each is reachable from the other. A strongly connected component containing a directed cycle is a **wait-cycle group**: every SCC of size greater than `1` qualifies, while a singleton qualifies only if it has a self-loop. + +List every wait-cycle group and compute the minimum number of external wake events required to release all processes. One wake may target any process. Release propagates throughout its SCC and then downstream along condensation edges. + +## Input + +The first line contains `N M`. Each of the next `M` lines contains a directed edge `u v`. Process IDs are 1-based. + +## Output + +The first line contains `G W`: the number of wait-cycle groups and the minimum number of external wake events. Then output `G` lines, each in the form: + +```text +k id_1 ... id_k +``` + +IDs within a group must be strictly increasing. Groups must be strictly increasing by their smallest ID. If `G = 0`, output only the first line. An isolated process is a non-cyclic singleton SCC, but it is also a source of the condensation graph and therefore still requires one wake. + +## Constraints + +- `1 <= N <= 200000` +- `0 <= M <= 400000` +- Edges are distinct; self-loops are allowed. +- Full tests contain long chains on which recursive DFS may overflow the call stack; use an explicit stack. +- Pairwise mutual-reachability checks cannot pass. + +## Examples + + + +### Example One + +Input: + +```text +5 4 +1 2 +2 1 +2 3 +4 4 +``` + +Output: + +```text +2 3 +2 1 2 +1 4 +``` + +### Example Two + +Input: + +```text +3 2 +1 2 +2 3 +``` + +Output: + +```text +0 1 +``` + +### Example Three + +Input: + +```text +3 3 +1 2 +2 3 +3 1 +``` + +Output: + +```text +1 1 +3 1 2 3 +``` + + diff --git a/problems/035-wait-for-cycles/statement.zh-TW.md b/problems/035-wait-for-cycles/statement.zh-TW.md new file mode 100644 index 0000000..df78580 --- /dev/null +++ b/problems/035-wait-for-cycles/statement.zh-TW.md @@ -0,0 +1,92 @@ +# 互動程式的等待環 + +在設計 WASM OJ 的互動式程式 runtime 時,我們需要處理多個 process 彼此等待事件的情況。某個 process 被釋放後,可能送出事件喚醒其他 process;但如果一群 process 只等待群內彼此產生的事件,它們就可能永遠沒有第一個事件可執行。 + +為了診斷這類停滯,我們除了要列出真正形成等待環的群組,也要知道至少需要注入多少次 external wake event,才能讓釋放事件傳遍整個系統。 + +系統中有 `N` 個尚未釋放的 process。Directed release edge `u v` 表示 `u` 一旦被釋放,就能送出事件釋放 `v`,而釋放會沿 edges 反覆傳播。你也可以注入 external wake events,每次任選一個 process。 + +兩個 process 若彼此可達,就屬於同一個互相等待群。含 directed cycle 的 strongly connected component 稱為**等待環群組**:size 大於 `1` 的 SCC 一定符合;size 為 `1` 時,只有存在 self-loop 才符合。 + +請列出全部等待環群組,並計算讓所有 process 最終都被釋放所需的最少 external wake 數。一次 wake 可以選擇任一 process;釋放會在同一 SCC 內互相傳播,之後再沿 condensation edges 傳到下游。 + +## 輸入 + +第一行 `N M`,接著 `M` 行 directed edge `u v`。ID 為 1-based。 + +## 輸出 + +第一行 `G W`:等待環群組數與最少 external wake 數。接著 `G` 行各為: + +```text +k id_1 ... id_k +``` + +群內 ID 嚴格遞增;群組依各自最小 ID 嚴格遞增。`G=0` 時只有第一行。孤立 process 自成非循環 SCC,並且是 condensation source,故仍需要一次 wake。 + +## 限制 + +- `1 <= N <= 200000`,`0 <= M <= 400000`。 +- edge 不重複;self-loop 允許。 +- 完整測資含長鏈,遞迴 DFS 可能 stack overflow;reference solutions 使用顯式 stack。 +- 逐對檢查 mutual reachability 無法通過。 + +## 範例 + + + +### 範例一 + +輸入: + +```text +5 4 +1 2 +2 1 +2 3 +4 4 +``` + +輸出: + +```text +2 3 +2 1 2 +1 4 +``` + +### 範例二 + +輸入: + +```text +3 2 +1 2 +2 3 +``` + +輸出: + +```text +0 1 +``` + +### 範例三 + +輸入: + +```text +3 3 +1 2 +2 3 +3 1 +``` + +輸出: + +```text +1 1 +3 1 2 3 +``` + + diff --git a/problems/035-wait-for-cycles/tests/adversarial-blind-01.in b/problems/035-wait-for-cycles/tests/adversarial-blind-01.in new file mode 100644 index 0000000..bfeee6c --- /dev/null +++ b/problems/035-wait-for-cycles/tests/adversarial-blind-01.in @@ -0,0 +1,12 @@ +10 11 +1 4 +4 7 +7 1 +2 2 +3 6 +6 3 +8 8 +7 3 +2 3 +6 5 +9 8 diff --git a/problems/035-wait-for-cycles/tests/adversarial-blind-01.out b/problems/035-wait-for-cycles/tests/adversarial-blind-01.out new file mode 100644 index 0000000..26d0f30 --- /dev/null +++ b/problems/035-wait-for-cycles/tests/adversarial-blind-01.out @@ -0,0 +1,5 @@ +4 4 +3 1 4 7 +1 2 +2 3 6 +1 8 diff --git a/problems/035-wait-for-cycles/tests/sample-01.in b/problems/035-wait-for-cycles/tests/sample-01.in new file mode 100644 index 0000000..9eb74cb --- /dev/null +++ b/problems/035-wait-for-cycles/tests/sample-01.in @@ -0,0 +1,5 @@ +5 4 +1 2 +2 1 +2 3 +4 4 diff --git a/problems/035-wait-for-cycles/tests/sample-01.out b/problems/035-wait-for-cycles/tests/sample-01.out new file mode 100644 index 0000000..eca12e1 --- /dev/null +++ b/problems/035-wait-for-cycles/tests/sample-01.out @@ -0,0 +1,3 @@ +2 3 +2 1 2 +1 4 diff --git a/problems/035-wait-for-cycles/tests/sample-02.in b/problems/035-wait-for-cycles/tests/sample-02.in new file mode 100644 index 0000000..d08dd36 --- /dev/null +++ b/problems/035-wait-for-cycles/tests/sample-02.in @@ -0,0 +1,3 @@ +3 2 +1 2 +2 3 diff --git a/problems/035-wait-for-cycles/tests/sample-02.out b/problems/035-wait-for-cycles/tests/sample-02.out new file mode 100644 index 0000000..6e8183b --- /dev/null +++ b/problems/035-wait-for-cycles/tests/sample-02.out @@ -0,0 +1 @@ +0 1 diff --git a/problems/035-wait-for-cycles/tests/sample-03.in b/problems/035-wait-for-cycles/tests/sample-03.in new file mode 100644 index 0000000..57b9c35 --- /dev/null +++ b/problems/035-wait-for-cycles/tests/sample-03.in @@ -0,0 +1,4 @@ +3 3 +1 2 +2 3 +3 1 diff --git a/problems/035-wait-for-cycles/tests/sample-03.out b/problems/035-wait-for-cycles/tests/sample-03.out new file mode 100644 index 0000000..a7b548c --- /dev/null +++ b/problems/035-wait-for-cycles/tests/sample-03.out @@ -0,0 +1,2 @@ +1 1 +3 1 2 3 diff --git a/problems/035-wait-for-cycles/validator.py b/problems/035-wait-for-cycles/validator.py new file mode 100644 index 0000000..99df1e7 --- /dev/null +++ b/problems/035-wait-for-cycles/validator.py @@ -0,0 +1,21 @@ +import sys + + +def main(): + a = list(map(int, sys.stdin.read().split())) + assert len(a) >= 2 + n, m = a[:2] + assert 1 <= n <= 200000 and 0 <= m <= 400000 and len(a) == 2 + 2 * m + seen = set() + p = 2 + for _ in range(m): + u, v = a[p : p + 2] + p += 2 + assert 1 <= u <= n and 1 <= v <= n and (u, v) not in seen + seen.add((u, v)) + + +try: + main() +except (AssertionError, ValueError): + sys.exit(1) diff --git a/problems/036-artifact-cache-knapsack/editorial.en.md b/problems/036-artifact-cache-knapsack/editorial.en.md new file mode 100644 index 0000000..59c474d --- /dev/null +++ b/problems/036-artifact-cache-knapsack/editorial.en.md @@ -0,0 +1,34 @@ +# Editorial + +## Intuitive Approach + +Enumerating whether to keep each artifact takes `O(2^N N)` time. A standard two-dimensional table `dp[i][c]` reduces the time to `O(NC)`, but its `O(NC)` memory exceeds the full memory limit. + +## Optimal Approach: One-Dimensional 0/1 Knapsack + +Let `dp[c]` be the maximum value obtainable from the artifacts processed so far with total size at most `c`. Initially all entries are zero, representing the empty subset. + +For an artifact `(w, v)`, iterate `c` downward from `C` to `w` and apply + +```text +dp[c] = max(dp[c], dp[c - w] + v) +``` + +Descending capacity ensures that the source state still belongs to the previous artifact set, so the current artifact cannot be used more than once. The answer is `dp[C]`. + +## Correctness Proof + +Induct on the number of processed artifacts. Initially, only the empty subset is available and every `dp[c] = 0` is correct. For a new artifact `(w, v)`, an optimal subset for capacity `c` either excludes it, retaining the old `dp[c]`, or includes it, in which case the remaining artifacts occupy at most `c - w` and contribute at most the old `dp[c - w]`. The transition takes the better of exactly these two exhaustive, disjoint cases. + +Because capacities are updated in descending order, every source on the right excludes the current artifact. Thus the 0/1 restriction is preserved, the invariant holds after each artifact, and `dp[C]` is the optimum. + +## Complexity + +The algorithm uses `O(NC)` time and `O(C)` space. This is the standard pseudo-polynomial optimization for 0/1 knapsack; the general binary-encoded problem is NP-hard. + +## Common Mistakes + +- Iterating capacity upward and turning the problem into unbounded knapsack. +- Applying a value-to-size greedy rule, which is not valid for 0/1 knapsack. +- Mishandling `C = 0` or zero-valued artifacts. +- Accumulating values in a 32-bit integer. diff --git a/problems/036-artifact-cache-knapsack/editorial.zh-TW.md b/problems/036-artifact-cache-knapsack/editorial.zh-TW.md new file mode 100644 index 0000000..b010bb9 --- /dev/null +++ b/problems/036-artifact-cache-knapsack/editorial.zh-TW.md @@ -0,0 +1,30 @@ +# 解題說明 + +## 直覺解法 + +列舉每個 artifact 選或不選需 `O(2^N N)`。經典二維 DP `dp[i][c]` 可降為 `O(NC)` 時間,但需 `O(NC)` 空間,在完整限制下超過 memory limit。 + +## 最佳解法 + +令 `dp[c]` 為目前看過的 artifact 中、總 size 不超過 `c` 時的最大 value。對一個 `(w,v)`,令 `c` 從 `C` 遞減到 `w`: + +```text +dp[c] = max(dp[c], dp[c-w] + v) +``` + +反向迭代保證右側仍是加入本 artifact 前的狀態,因此每件最多使用一次。答案為 `dp[C]`。 + +## 正確性證明 + +以處理 artifact 數歸納。初始只可選空集合,所有 `dp[c]=0` 正確。加入 `(w,v)` 後,容量 `c` 的最優解要嘛不選它,值為舊 `dp[c]`;要嘛選它,其餘 artifact 佔用至多 `c-w`,最佳值為舊 `dp[c-w]+v`。轉移取兩者最大,涵蓋且只涵蓋合法解。反向更新確保「舊」狀態未含當前 artifact。故最後 `dp[C]` 為全體最優值。 + +## 複雜度 + +時間 `O(NC)`,空間 `O(C)`。這是標準 pseudo-polynomial 0/1 knapsack 最佳化;一般二進位編碼版本為 NP-hard。 + +## 常見錯誤 + +- 容量正向更新,讓同一 artifact 被重複選成 unbounded knapsack。 +- 以 value/size 比值貪心;0/1 背包不具該貪心性質。 +- 忘記 `C=0` 或 value 為零。 +- 用 32-bit 儲存累積 value。 diff --git a/problems/036-artifact-cache-knapsack/generator.py b/problems/036-artifact-cache-knapsack/generator.py new file mode 100644 index 0000000..b37a2d5 --- /dev/null +++ b/problems/036-artifact-cache-knapsack/generator.py @@ -0,0 +1,11 @@ +import random, sys + +if len(sys.argv) != 3: + raise SystemExit("usage: generator.py SEED INDEX") +r = random.Random((int(sys.argv[1]) << 32) ^ int(sys.argv[2])) +idx = int(sys.argv[2]) +N = r.randint(1, min(18, 5 + idx % 14)) +C = r.randint(0, 45) +print(N, C) +for _ in range(N): + print(r.randint(1, 55), r.randint(0, 100)) diff --git a/problems/036-artifact-cache-knapsack/oracle.py b/problems/036-artifact-cache-knapsack/oracle.py new file mode 100644 index 0000000..33936ea --- /dev/null +++ b/problems/036-artifact-cache-knapsack/oracle.py @@ -0,0 +1,15 @@ +import sys + +t = list(map(int, sys.stdin.buffer.read().split())) +N, C = t[:2] +a = list(zip(t[2::2], t[3::2])) +best = 0 +for mask in range(1 << N): + w = v = 0 + for i, (x, y) in enumerate(a): + if mask >> i & 1: + w += x + v += y + if w <= C: + best = max(best, v) +print(best) diff --git a/problems/036-artifact-cache-knapsack/problem.json b/problems/036-artifact-cache-knapsack/problem.json new file mode 100644 index 0000000..3b8256b --- /dev/null +++ b/problems/036-artifact-cache-knapsack/problem.json @@ -0,0 +1,155 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 36, + "slug": "artifact-cache-knapsack", + "title": { + "zh-TW": "Artifact Cache 的取捨", + "en": "Artifact Cache Trade-offs" + }, + "difficulty": "medium", + "tags": [ + "dynamic-programming", + "knapsack", + "cache" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-blind-01", + "kind": "adversarial", + "input": "tests/adversarial-blind-01.in", + "output": "tests/adversarial-blind-01.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 8000000, + "memoryLimitBytes": 134217728 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 1500000, + "memoryLimitBytes": 100663296 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 400000, + "memoryLimitBytes": 67108864 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "列舉所有 artifact 子集合", + "en": "Enumerate all artifact subsets" + }, + "time": "O(2^N N)", + "space": "O(N)", + "accepted": false + }, + { + "name": { + "zh-TW": "二維 0/1 背包", + "en": "Two-dimensional 0/1 knapsack table" + }, + "time": "O(NC)", + "space": "O(NC)", + "accepted": false + }, + { + "name": { + "zh-TW": "容量反向的一維 0/1 背包", + "en": "One-dimensional 0/1 knapsack with descending capacity" + }, + "time": "O(NC)", + "space": "O(C)", + "accepted": true + } + ] +} diff --git a/problems/036-artifact-cache-knapsack/solutions/c/main.c b/problems/036-artifact-cache-knapsack/solutions/c/main.c new file mode 100644 index 0000000..e8d442f --- /dev/null +++ b/problems/036-artifact-cache-knapsack/solutions/c/main.c @@ -0,0 +1,21 @@ +#include +#include +#include +int main(void) { + int n, c; + if (scanf("%d%d", &n, &c) != 2) + return 0; + uint64_t *dp = calloc((size_t)c + 1, sizeof(*dp)); + while (n--) { + int w; + unsigned long long v; + scanf("%d%llu", &w, &v); + for (int x = c; x >= w; x--) { + uint64_t q = dp[x - w] + v; + if (q > dp[x]) + dp[x] = q; + } + } + printf("%llu\n", (unsigned long long)dp[c]); + free(dp); +} diff --git a/problems/036-artifact-cache-knapsack/solutions/cpp/main.cpp b/problems/036-artifact-cache-knapsack/solutions/cpp/main.cpp new file mode 100644 index 0000000..36f6ed4 --- /dev/null +++ b/problems/036-artifact-cache-knapsack/solutions/cpp/main.cpp @@ -0,0 +1,21 @@ +#include +#include +#include +#include +using namespace std; +int main() { + ios::sync_with_stdio(false); + cin.tie(nullptr); + int n, c; + if (!(cin >> n >> c)) + return 0; + vector dp(c + 1); + while (n--) { + int w; + uint64_t v; + cin >> w >> v; + for (int x = c; x >= w; x--) + dp[x] = max(dp[x], dp[x - w] + v); + } + cout << dp[c] << '\n'; +} diff --git a/problems/036-artifact-cache-knapsack/solutions/go/main.go b/problems/036-artifact-cache-knapsack/solutions/go/main.go new file mode 100644 index 0000000..4f8410d --- /dev/null +++ b/problems/036-artifact-cache-knapsack/solutions/go/main.go @@ -0,0 +1,29 @@ +package main + +import ( + "bufio" + "fmt" + "os" +) + +func main() { + in := bufio.NewReader(os.Stdin) + out := bufio.NewWriter(os.Stdout) + defer out.Flush() + var n, c int + if _, e := fmt.Fscan(in, &n, &c); e != nil { + return + } + dp := make([]uint64, c+1) + for ; n > 0; n-- { + var w int + var v uint64 + fmt.Fscan(in, &w, &v) + for x := c; x >= w; x-- { + if q := dp[x-w] + v; q > dp[x] { + dp[x] = q + } + } + } + fmt.Fprintln(out, dp[c]) +} diff --git a/problems/036-artifact-cache-knapsack/solutions/javascript/main.js b/problems/036-artifact-cache-knapsack/solutions/javascript/main.js new file mode 100644 index 0000000..90eb584 --- /dev/null +++ b/problems/036-artifact-cache-knapsack/solutions/javascript/main.js @@ -0,0 +1,37 @@ +import * as std from "std"; + +const input = std.in.readAsString(); +let scan = 0; +function nextInt() { + while (scan < input.length && input.charCodeAt(scan) <= 32) scan++; + let value = 0; + while (scan < input.length) { + const digit = input.charCodeAt(scan) - 48; + if (digit < 0 || digit > 9) break; + value = value * 10 + digit; + scan++; + } + return value; +} +function nextBigInt() { + while (scan < input.length && input.charCodeAt(scan) <= 32) scan++; + const start = scan; + while (scan < input.length) { + const code = input.charCodeAt(scan); + if (code < 48 || code > 57) break; + scan++; + } + return BigInt(input.slice(start, scan)); +} + +const itemCount = nextInt(), + capacity = nextInt(), + dp = new BigUint64Array(capacity + 1); +for (let item = 0; item < itemCount; item++) { + const size = nextInt(), value = nextBigInt(); + for (let current = capacity; current >= size; current--) { + const candidate = dp[current - size] + value; + if (candidate > dp[current]) dp[current] = candidate; + } +} +std.out.puts(`${dp[capacity]}\n`); diff --git a/problems/036-artifact-cache-knapsack/solutions/python/main.py b/problems/036-artifact-cache-knapsack/solutions/python/main.py new file mode 100644 index 0000000..0a604c8 --- /dev/null +++ b/problems/036-artifact-cache-knapsack/solutions/python/main.py @@ -0,0 +1,11 @@ +import sys + +t = list(map(int, sys.stdin.buffer.read().split())) +it = iter(t) +N, C = next(it), next(it) +dp = [0] * (C + 1) +for _ in range(N): + w, v = next(it), next(it) + for c in range(C, w - 1, -1): + dp[c] = max(dp[c], dp[c - w] + v) +print(dp[C]) diff --git a/problems/036-artifact-cache-knapsack/solutions/rust/main.rs b/problems/036-artifact-cache-knapsack/solutions/rust/main.rs new file mode 100644 index 0000000..2c6d2ce --- /dev/null +++ b/problems/036-artifact-cache-knapsack/solutions/rust/main.rs @@ -0,0 +1,17 @@ +use std::io::{self, Read}; +fn main() { + let mut s = String::new(); + io::stdin().read_to_string(&mut s).unwrap(); + let mut t = s.split_whitespace(); + let n: usize = t.next().unwrap().parse().unwrap(); + let c: usize = t.next().unwrap().parse().unwrap(); + let mut dp = vec![0u64; c + 1]; + for _ in 0..n { + let w: usize = t.next().unwrap().parse().unwrap(); + let v: u64 = t.next().unwrap().parse().unwrap(); + for x in (w..=c).rev() { + dp[x] = dp[x].max(dp[x - w] + v); + } + } + println!("{}", dp[c]); +} diff --git a/problems/036-artifact-cache-knapsack/solutions/typescript/main.ts b/problems/036-artifact-cache-knapsack/solutions/typescript/main.ts new file mode 100644 index 0000000..72d3339 --- /dev/null +++ b/problems/036-artifact-cache-knapsack/solutions/typescript/main.ts @@ -0,0 +1,37 @@ +import * as std from "std"; + +const input: string = std.in.readAsString(); +let scan = 0; +function nextInt(): number { + while (scan < input.length && input.charCodeAt(scan) <= 32) scan++; + let value = 0; + while (scan < input.length) { + const digit = input.charCodeAt(scan) - 48; + if (digit < 0 || digit > 9) break; + value = value * 10 + digit; + scan++; + } + return value; +} +function nextBigInt(): bigint { + while (scan < input.length && input.charCodeAt(scan) <= 32) scan++; + const start = scan; + while (scan < input.length) { + const code = input.charCodeAt(scan); + if (code < 48 || code > 57) break; + scan++; + } + return BigInt(input.slice(start, scan)); +} + +const itemCount = nextInt(), + capacity = nextInt(), + dp = new BigUint64Array(capacity + 1); +for (let item = 0; item < itemCount; item++) { + const size = nextInt(), value = nextBigInt(); + for (let current = capacity; current >= size; current--) { + const candidate = dp[current - size]! + value; + if (candidate > dp[current]!) dp[current] = candidate; + } +} +std.out.puts(`${dp[capacity]}\n`); diff --git a/problems/036-artifact-cache-knapsack/statement.en.md b/problems/036-artifact-cache-knapsack/statement.en.md new file mode 100644 index 0000000..22a9a9b --- /dev/null +++ b/problems/036-artifact-cache-knapsack/statement.en.md @@ -0,0 +1,87 @@ +# Artifact Cache Trade-offs + +While designing an incremental compilation cache for a WASM OJ, we found that keeping every build artifact was not practical. Browser storage is limited, and artifacts differ greatly in both size and reconstruction cost: one large artifact may save little time on the next build, while a small artifact may be very valuable to retain. + +To decide what should survive a cache cleanup, we record the cache space used by each artifact and the build time that reusing it would save. This problem first considers independent artifacts, so retaining one does not require retaining any other artifact. + +There are `N` build artifacts. Artifact `i` consumes `size_i` units of cache and saves `value_i` units of time during the next build if retained. Each artifact may be retained at most once, and the cache has total capacity `C`. + +Choose a subset whose total size does not exceed `C` and whose total saved time is maximum. Output only the maximum value, not the subset. The empty subset is always valid. + +## Input + +The first line contains `N C`. Each of the next `N` lines contains `size_i value_i`. + +## Output + +Output one line containing the maximum total saved time. + +## Constraints + +- `1 <= N <= 200` +- `0 <= C <= 100000` +- `1 <= size_i <= 100000` +- `0 <= value_i <= 10^12` +- The sum of all values is at most `9 * 10^18`. + +Artifacts are indivisible. An artifact with `size_i > C` can never be selected. The full limits and the 64 MiB memory limit rule out subset enumeration and an `O(NC)`-space table. + +## Examples + + + +### Example One + +Input: + +```text +4 7 +6 13 +4 8 +3 6 +5 12 +``` + +Output: + +```text +14 +``` + +### Example Two + +Input: + +```text +3 0 +1 100 +2 200 +3 300 +``` + +Output: + +```text +0 +``` + +### Example Three + +Input: + +```text +5 10 +2 4 +2 5 +6 12 +5 11 +4 8 +``` + +Output: + +```text +21 +``` + + diff --git a/problems/036-artifact-cache-knapsack/statement.zh-TW.md b/problems/036-artifact-cache-knapsack/statement.zh-TW.md new file mode 100644 index 0000000..abb1f47 --- /dev/null +++ b/problems/036-artifact-cache-knapsack/statement.zh-TW.md @@ -0,0 +1,87 @@ +# Artifact Cache 的取捨 + +在設計 WASM OJ 的增量編譯快取時,我們發現「把所有編譯產物都留下來」並不是可行策略。瀏覽器提供的持久化空間有限,而不同 artifact 的大小與重建成本差異很大:有些檔案占用大量 cache,下一次 build 卻只節省很少時間;另一些小型 artifact 則非常值得保留。 + +為了決定一次清理後應該留下哪些內容,我們替每個 artifact 記錄它占用的 cache size,以及下次 build 重用它能節省的時間。這一題先考慮彼此獨立的 artifact,因此保留其中一個不會要求同時保留其他項目。 + +共有 `N` 個編譯 artifact。第 `i` 個占用 `size_i` 單位 cache,若保留則能在下一次 build 節省 `value_i` 單位時間。每個 artifact 最多保留一次,cache 總容量為 `C`。 + +請選擇一個子集合,使總 size 不超過 `C`,並最大化總節省時間。只需輸出最大值,不需輸出集合;空集合永遠合法。 + +## 輸入 + +第一行 `N C`,接下來 `N` 行各為 `size_i value_i`。 + +## 輸出 + +一行最大總節省時間。 + +## 限制 + +- `1 ≤ N ≤ 200` +- `0 ≤ C ≤ 100000` +- `1 ≤ size_i ≤ 100000` +- `0 ≤ value_i ≤ 10^12` +- 所有 value 總和不超過 `9×10^18` + +artifact 不可切割;size 大於 `C` 的 artifact 永遠不能選。完整限制與 64 MiB memory limit 排除子集合列舉及 `O(NC)` 儲存空間。 + +## 範例 + + + +### 範例一 + +輸入: + +```text +4 7 +6 13 +4 8 +3 6 +5 12 +``` + +輸出: + +```text +14 +``` + +### 範例二 + +輸入: + +```text +3 0 +1 100 +2 200 +3 300 +``` + +輸出: + +```text +0 +``` + +### 範例三 + +輸入: + +```text +5 10 +2 4 +2 5 +6 12 +5 11 +4 8 +``` + +輸出: + +```text +21 +``` + + diff --git a/problems/036-artifact-cache-knapsack/tests/adversarial-blind-01.in b/problems/036-artifact-cache-knapsack/tests/adversarial-blind-01.in new file mode 100644 index 0000000..2470216 --- /dev/null +++ b/problems/036-artifact-cache-knapsack/tests/adversarial-blind-01.in @@ -0,0 +1,7 @@ +6 10 +6 13 +4 8 +3 8 +5 11 +10 20 +11 1000 diff --git a/problems/036-artifact-cache-knapsack/tests/adversarial-blind-01.out b/problems/036-artifact-cache-knapsack/tests/adversarial-blind-01.out new file mode 100644 index 0000000..aabe6ec --- /dev/null +++ b/problems/036-artifact-cache-knapsack/tests/adversarial-blind-01.out @@ -0,0 +1 @@ +21 diff --git a/problems/036-artifact-cache-knapsack/tests/sample-01.in b/problems/036-artifact-cache-knapsack/tests/sample-01.in new file mode 100644 index 0000000..bd998f2 --- /dev/null +++ b/problems/036-artifact-cache-knapsack/tests/sample-01.in @@ -0,0 +1,5 @@ +4 7 +6 13 +4 8 +3 6 +5 12 diff --git a/problems/036-artifact-cache-knapsack/tests/sample-01.out b/problems/036-artifact-cache-knapsack/tests/sample-01.out new file mode 100644 index 0000000..8351c19 --- /dev/null +++ b/problems/036-artifact-cache-knapsack/tests/sample-01.out @@ -0,0 +1 @@ +14 diff --git a/problems/036-artifact-cache-knapsack/tests/sample-02.in b/problems/036-artifact-cache-knapsack/tests/sample-02.in new file mode 100644 index 0000000..6e0c7a7 --- /dev/null +++ b/problems/036-artifact-cache-knapsack/tests/sample-02.in @@ -0,0 +1,4 @@ +3 0 +1 100 +2 200 +3 300 diff --git a/problems/036-artifact-cache-knapsack/tests/sample-02.out b/problems/036-artifact-cache-knapsack/tests/sample-02.out new file mode 100644 index 0000000..573541a --- /dev/null +++ b/problems/036-artifact-cache-knapsack/tests/sample-02.out @@ -0,0 +1 @@ +0 diff --git a/problems/036-artifact-cache-knapsack/tests/sample-03.in b/problems/036-artifact-cache-knapsack/tests/sample-03.in new file mode 100644 index 0000000..f501304 --- /dev/null +++ b/problems/036-artifact-cache-knapsack/tests/sample-03.in @@ -0,0 +1,6 @@ +5 10 +2 4 +2 5 +6 12 +5 11 +4 8 diff --git a/problems/036-artifact-cache-knapsack/tests/sample-03.out b/problems/036-artifact-cache-knapsack/tests/sample-03.out new file mode 100644 index 0000000..aabe6ec --- /dev/null +++ b/problems/036-artifact-cache-knapsack/tests/sample-03.out @@ -0,0 +1 @@ +21 diff --git a/problems/036-artifact-cache-knapsack/validator.py b/problems/036-artifact-cache-knapsack/validator.py new file mode 100644 index 0000000..a15e308 --- /dev/null +++ b/problems/036-artifact-cache-knapsack/validator.py @@ -0,0 +1,30 @@ +import re, sys + + +def fail(): + raise SystemExit(1) + + +try: + t = sys.stdin.buffer.read().decode("utf-8").split() + p = 0 + + def u(a, b): + global p + if p >= len(t) or re.fullmatch(r"0|[1-9][0-9]*", t[p]) is None: + fail() + v = int(t[p]) + p += 1 + if not a <= v <= b: + fail() + return v + + N, C = u(1, 200), u(0, 100000) + total = 0 + for _ in range(N): + u(1, 100000) + total += u(0, 10**12) + if total > 9 * 10**18 or p != len(t): + fail() +except (UnicodeDecodeError, ValueError, OverflowError): + fail() diff --git a/problems/037-dependency-tree-knapsack/editorial.en.md b/problems/037-dependency-tree-knapsack/editorial.en.md new file mode 100644 index 0000000..10b8643 --- /dev/null +++ b/problems/037-dependency-tree-knapsack/editorial.en.md @@ -0,0 +1,37 @@ +# Editorial + +## Intuitive Approach + +Enumerating all subsets and validating every selected node's ancestors takes `O(2^N N)` time. A conventional tree knapsack that convolves a capacity table for every child takes `O(NC^2)` in the worst case. + +## Optimal Approach: Preorder and Skip-Subtree DP + +Attach every forest root to a virtual node `0` that is always selected and has zero size and value. Run DFS preorder over the real nodes, producing `order[0..N-1]`. For every preorder position `i`, record `after[i]`, the first position after the entire subtree rooted at `order[i]`. + +Define `dp[i][c]` as the maximum value obtainable from preorder position `i` onward with capacity `c`, under the precondition that the parent of `order[i]` has been selected. Let `u = order[i]`. There are two choices: + +- Skip `u`: dependency closure forbids every descendant of `u`, so continue at `dp[after[i]][c]`. +- Select `u`: pay its size, gain its value, and continue at the next preorder position. + +```text +dp[i][c] = max(dp[after[i]][c], value[u] + dp[i + 1][c - size[u]]) +``` + +The second term exists only when `size[u] <= c`. Compute positions from `N - 1` down to `0`; the answer is `dp[0][C]`. + +## Correctness Proof + +Consider state `(i, c)` and node `u`, whose parent is selected by the state invariant. Every dependency-closed solution falls into exactly one of two cases. If it omits `u`, it must omit every descendant, and preorder continuation is exactly `after[i]`. If it includes `u`, closure is satisfied at `u`; after paying for it, the next preorder position may be decided under the same ancestor preconditions. The cases are disjoint and exhaustive, and each transition uses the optimal remainder for its case. + +Backward induction therefore proves every `dp[i][c]` correct. The virtual root makes each forest root independently selectable or skippable, so `dp[0][C]` is the optimum over the entire forest. + +## Complexity + +DFS takes `O(N)` time. There are `N(C + 1)` constant-time DP states, so both time and space are `O(NC)`, improving on the `O(NC^2)` child-convolution approach. + +## Common Mistakes + +- Reversing the dependency: selecting a parent does not require selecting every child. +- Advancing only to `i + 1` after skipping a node, which permits descendants without their prerequisite. +- Assuming the input IDs already form a DFS preorder. +- Forgetting the virtual-root semantics needed to combine independent trees. diff --git a/problems/037-dependency-tree-knapsack/editorial.zh-TW.md b/problems/037-dependency-tree-knapsack/editorial.zh-TW.md new file mode 100644 index 0000000..e4ee4d4 --- /dev/null +++ b/problems/037-dependency-tree-knapsack/editorial.zh-TW.md @@ -0,0 +1,35 @@ +# 解題說明 + +## 直覺解法 + +列舉子集合後檢查每個被選節點的 ancestors,需 `O(2^N N)`。一般 tree knapsack 把各 child 的容量表逐一卷積,最壞 `O(NC^2)`。 + +## 最佳解法:preorder 跳過子樹 + +加入一個永遠已選、size/value 皆為零的 virtual root 0,把 forest roots 接在其下。對真實節點做 DFS preorder,得到陣列 `order[0..N-1]`;另記 `after[i]`,即 `order[i]` 整個 subtree 結束後的第一個 preorder 索引。 + +定義 `dp[i][c]`:已確定 `order[i]` 的 parent 被選時,從 preorder 位置 `i` 之後且容量為 `c` 的最大收益。兩種選擇: + +- 不選此節點:其 descendants 都不可能選,直接到 `dp[after[i]][c]`; +- 選此節點:支付 size、取得 value,下一位置 `i+1` 可繼續決定。 + +```text +dp[i][c] = max(dp[after[i]][c], value[u] + dp[i+1][c-size[u]]) +``` + +第二項只在容量足夠時存在。由 `i=N-1..0` 計算;答案為 `dp[0][C]`。 + +## 正確性證明 + +考慮狀態中的目前節點 `u`,其 parent 已選。任何合法解對 `u` 恰有兩類:若不選 `u`,closure 規則禁止選它的任何 descendant,preorder 中必跳到 `after[i]`;若選 `u`,closure 在 `u` 處滿足,扣除它後可從下一 preorder 節點繼續,所有 ancestors 的選擇前提仍成立。兩類互斥且涵蓋全部合法解,轉移各取其最佳再取最大。因此由倒序歸納,所有 `dp` 正確。virtual root 讓每棵樹 root 都可獨立選或不選,所以 `dp[0][C]` 即整座 forest 的最優值。 + +## 複雜度 + +DFS `O(N)`;共有 `N(C+1)` 個常數時間狀態,時間與空間皆 `O(NC)`,優於容量卷積的 `O(NC^2)`。 + +## 常見錯誤 + +- 把 edge 方向反過來,誤成選 parent 必須選所有 children。 +- 不選節點後只前進 `i+1`,讓 descendant 在缺 prerequisite 時被選。 +- 假設輸入 ID 已是 DFS preorder。 +- 忘記 forest 需要 virtual root 語意;實作不必真的把 root 放進 DP。 diff --git a/problems/037-dependency-tree-knapsack/generator.py b/problems/037-dependency-tree-knapsack/generator.py new file mode 100644 index 0000000..f2e812b --- /dev/null +++ b/problems/037-dependency-tree-knapsack/generator.py @@ -0,0 +1,11 @@ +import random, sys + +if len(sys.argv) != 3: + raise SystemExit("usage: generator.py SEED INDEX") +r = random.Random((int(sys.argv[1]) << 32) ^ int(sys.argv[2])) +idx = int(sys.argv[2]) +N = r.randint(1, min(18, 5 + idx % 14)) +C = r.randint(0, 40) +print(N, C) +for i in range(1, N + 1): + print(r.randint(0, i - 1), r.randint(1, 20), r.randint(0, 70)) diff --git a/problems/037-dependency-tree-knapsack/oracle.py b/problems/037-dependency-tree-knapsack/oracle.py new file mode 100644 index 0000000..55da2a2 --- /dev/null +++ b/problems/037-dependency-tree-knapsack/oracle.py @@ -0,0 +1,20 @@ +import sys + +t = list(map(int, sys.stdin.buffer.read().split())) +it = iter(t) +N, C = next(it), next(it) +a = [(next(it), next(it), next(it)) for _ in range(N)] +best = 0 +for mask in range(1 << N): + ok = True + w = v = 0 + for i, (p, s, x) in enumerate(a): + if mask >> i & 1: + if p and not (mask >> (p - 1) & 1): + ok = False + break + w += s + v += x + if ok and w <= C: + best = max(best, v) +print(best) diff --git a/problems/037-dependency-tree-knapsack/problem.json b/problems/037-dependency-tree-knapsack/problem.json new file mode 100644 index 0000000..3902fbf --- /dev/null +++ b/problems/037-dependency-tree-knapsack/problem.json @@ -0,0 +1,156 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 37, + "slug": "dependency-tree-knapsack", + "title": { + "zh-TW": "有依賴的快取背包", + "en": "Dependency-Aware Cache Knapsack" + }, + "difficulty": "hard", + "tags": [ + "tree", + "dynamic-programming", + "knapsack", + "dfs-order" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-blind-01", + "kind": "adversarial", + "input": "tests/adversarial-blind-01.in", + "output": "tests/adversarial-blind-01.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 15000000, + "memoryLimitBytes": 536870912 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 1500000, + "memoryLimitBytes": 402653184 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 650000, + "memoryLimitBytes": 268435456 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "列舉所有節點子集合再驗證 closure", + "en": "Enumerate node subsets and validate closure" + }, + "time": "O(2^N N)", + "space": "O(N)", + "accepted": false + }, + { + "name": { + "zh-TW": "逐子樹容量卷積", + "en": "Capacity convolution for every subtree" + }, + "time": "O(NC^2)", + "space": "O(NC)", + "accepted": false + }, + { + "name": { + "zh-TW": "preorder 與 skip-subtree DP", + "en": "Preorder skip-subtree DP" + }, + "time": "O(NC)", + "space": "O(NC)", + "accepted": true + } + ] +} diff --git a/problems/037-dependency-tree-knapsack/solutions/c/main.c b/problems/037-dependency-tree-knapsack/solutions/c/main.c new file mode 100644 index 0000000..b4d037e --- /dev/null +++ b/problems/037-dependency-tree-knapsack/solutions/c/main.c @@ -0,0 +1,58 @@ +#include +#include +#include +static int *head, *next, *to, *order, *after, cnt; +static void dfs(int u) { + int pos = cnt; + order[cnt++] = u; + for (int e = head[u]; e != -1; e = next[e]) + dfs(to[e]); + after[pos] = cnt; +} +int main(void) { + int n, C; + if (scanf("%d%d", &n, &C) != 2) + return 0; + int *sz = calloc(n + 1, sizeof(*sz)); + uint64_t *val = calloc(n + 1, sizeof(*val)); + head = malloc((n + 1) * sizeof(*head)); + next = malloc(n * sizeof(*next)); + to = malloc(n * sizeof(*to)); + order = malloc(n * sizeof(*order)); + after = malloc(n * sizeof(*after)); + for (int i = 0; i <= n; i++) + head[i] = -1; + for (int i = 1, p; i <= n; i++) { + unsigned long long v; + scanf("%d%d%llu", &p, &sz[i], &v); + val[i] = v; + to[i - 1] = i; + next[i - 1] = head[p]; + head[p] = i - 1; + } + for (int e = head[0]; e != -1; e = next[e]) + dfs(to[e]); + size_t w = (size_t)C + 1; + uint64_t *dp = calloc((size_t)(n + 1) * w, sizeof(*dp)); + for (int i = n - 1; i >= 0; i--) { + int u = order[i]; + for (int c = 0; c <= C; c++) { + uint64_t best = dp[(size_t)after[i] * w + c]; + if (c >= sz[u]) { + uint64_t q = val[u] + dp[(size_t)(i + 1) * w + c - sz[u]]; + if (q > best) + best = q; + } + dp[(size_t)i * w + c] = best; + } + } + printf("%llu\n", (unsigned long long)dp[C]); + free(sz); + free(val); + free(head); + free(next); + free(to); + free(order); + free(after); + free(dp); +} diff --git a/problems/037-dependency-tree-knapsack/solutions/cpp/main.cpp b/problems/037-dependency-tree-knapsack/solutions/cpp/main.cpp new file mode 100644 index 0000000..468282b --- /dev/null +++ b/problems/037-dependency-tree-knapsack/solutions/cpp/main.cpp @@ -0,0 +1,41 @@ +#include +#include +#include +#include +#include +using namespace std; +int main() { + ios::sync_with_stdio(false); + cin.tie(nullptr); + int n, C; + if (!(cin >> n >> C)) + return 0; + vector> ch(n + 1); + vector sz(n + 1); + vector val(n + 1); + for (int i = 1, p; i <= n; i++) { + cin >> p >> sz[i] >> val[i]; + ch[p].push_back(i); + } + vector order, after; + function dfs = [&](int u) { + int pos = order.size(); + order.push_back(u); + after.push_back(0); + for (int v : ch[u]) + dfs(v); + after[pos] = order.size(); + }; + for (int u : ch[0]) + dfs(u); + vector> dp(n + 1, vector(C + 1)); + for (int i = n - 1; i >= 0; i--) { + int u = order[i]; + for (int c = 0; c <= C; c++) { + dp[i][c] = dp[after[i]][c]; + if (c >= sz[u]) + dp[i][c] = max(dp[i][c], val[u] + dp[i + 1][c - sz[u]]); + } + } + cout << dp[0][C] << '\n'; +} diff --git a/problems/037-dependency-tree-knapsack/solutions/go/main.go b/problems/037-dependency-tree-knapsack/solutions/go/main.go new file mode 100644 index 0000000..35c0c81 --- /dev/null +++ b/problems/037-dependency-tree-knapsack/solutions/go/main.go @@ -0,0 +1,57 @@ +package main + +import ( + "bufio" + "fmt" + "os" +) + +func main() { + in := bufio.NewReader(os.Stdin) + out := bufio.NewWriter(os.Stdout) + defer out.Flush() + var n, C int + if _, e := fmt.Fscan(in, &n, &C); e != nil { + return + } + ch := make([][]int, n+1) + size := make([]int, n+1) + value := make([]uint64, n+1) + for i := 1; i <= n; i++ { + var p int + fmt.Fscan(in, &p, &size[i], &value[i]) + ch[p] = append(ch[p], i) + } + order := []int{} + after := []int{} + var dfs func(int) + dfs = func(u int) { + pos := len(order) + order = append(order, u) + after = append(after, 0) + for _, v := range ch[u] { + dfs(v) + } + after[pos] = len(order) + } + for _, u := range ch[0] { + dfs(u) + } + dp := make([][]uint64, n+1) + for i := range dp { + dp[i] = make([]uint64, C+1) + } + for i := n - 1; i >= 0; i-- { + u := order[i] + for c := 0; c <= C; c++ { + dp[i][c] = dp[after[i]][c] + if c >= size[u] { + q := value[u] + dp[i+1][c-size[u]] + if q > dp[i][c] { + dp[i][c] = q + } + } + } + } + fmt.Fprintln(out, dp[0][C]) +} diff --git a/problems/037-dependency-tree-knapsack/solutions/javascript/main.js b/problems/037-dependency-tree-knapsack/solutions/javascript/main.js new file mode 100644 index 0000000..67cb3ed --- /dev/null +++ b/problems/037-dependency-tree-knapsack/solutions/javascript/main.js @@ -0,0 +1,67 @@ +import * as std from "std"; + +const input = std.in.readAsString(); +let scan = 0; +function nextInt() { + while (scan < input.length && input.charCodeAt(scan) <= 32) scan++; + let value = 0; + while (scan < input.length) { + const digit = input.charCodeAt(scan) - 48; + if (digit < 0 || digit > 9) break; + value = value * 10 + digit; + scan++; + } + return value; +} +function nextBigInt() { + while (scan < input.length && input.charCodeAt(scan) <= 32) scan++; + const start = scan; + while (scan < input.length) { + const code = input.charCodeAt(scan); + if (code < 48 || code > 57) break; + scan++; + } + return BigInt(input.slice(start, scan)); +} + +const nodeCount = nextInt(), + capacity = nextInt(); +/** @type {number[][]} */ +const children = Array.from({ length: nodeCount + 1 }, () => []), + size = new Int32Array(nodeCount + 1), + value = new BigUint64Array(nodeCount + 1); +for (let node = 1; node <= nodeCount; node++) { + const parent = nextInt(); + size[node] = nextInt(); + value[node] = nextBigInt(); + children[parent].push(node); +} +/** @type {number[]} */ +const order = []; +/** @type {number[]} */ +const after = []; +/** @param {number} node */ +function dfs(node) { + const position = order.length; + order.push(node); + after.push(0); + for (const child of children[node]) dfs(child); + after[position] = order.length; +} +for (const root of children[0]) dfs(root); +const width = capacity + 1, dp = new BigUint64Array((nodeCount + 1) * width); +for (let position = nodeCount - 1; position >= 0; position--) { + const node = order[position], + row = position * width, + selectedTail = (position + 1) * width, + skippedTail = after[position] * width; + for (let current = 0; current <= capacity; current++) { + let best = dp[skippedTail + current]; + if (current >= size[node]) { + const candidate = value[node] + dp[selectedTail + current - size[node]]; + if (candidate > best) best = candidate; + } + dp[row + current] = best; + } +} +std.out.puts(`${dp[capacity]}\n`); diff --git a/problems/037-dependency-tree-knapsack/solutions/python/main.py b/problems/037-dependency-tree-knapsack/solutions/python/main.py new file mode 100644 index 0000000..0725bec --- /dev/null +++ b/problems/037-dependency-tree-knapsack/solutions/python/main.py @@ -0,0 +1,37 @@ +import sys + +t = list(map(int, sys.stdin.buffer.read().split())) +it = iter(t) +N, C = next(it), next(it) +ch = [[] for _ in range(N + 1)] +size = [0] * (N + 1) +value = [0] * (N + 1) +for i in range(1, N + 1): + p, size[i], value[i] = next(it), next(it), next(it) + ch[p].append(i) +order = [] +after = [] + + +def dfs(u): + pos = len(order) + order.append(u) + after.append(0) + for v in ch[u]: + dfs(v) + after[pos] = len(order) + + +for u in ch[0]: + dfs(u) +dp = [[0] * (C + 1) for _ in range(N + 1)] +for i in range(N - 1, -1, -1): + u = order[i] + skip = dp[after[i]] + take = dp[i + 1] + row = dp[i] + w = size[u] + v = value[u] + for c in range(C + 1): + row[c] = max(skip[c], v + take[c - w] if c >= w else 0) +print(dp[0][C]) diff --git a/problems/037-dependency-tree-knapsack/solutions/rust/main.rs b/problems/037-dependency-tree-knapsack/solutions/rust/main.rs new file mode 100644 index 0000000..f65fc23 --- /dev/null +++ b/problems/037-dependency-tree-knapsack/solutions/rust/main.rs @@ -0,0 +1,41 @@ +use std::io::{self, Read}; +fn dfs(u: usize, ch: &Vec>, order: &mut Vec, after: &mut Vec) { + let pos = order.len(); + order.push(u); + after.push(0); + for &v in &ch[u] { + dfs(v, ch, order, after); + } + after[pos] = order.len(); +} +fn main() { + let mut s = String::new(); + io::stdin().read_to_string(&mut s).unwrap(); + let mut t = s.split_whitespace(); + let n: usize = t.next().unwrap().parse().unwrap(); + let cmax: usize = t.next().unwrap().parse().unwrap(); + let mut ch = vec![Vec::new(); n + 1]; + let mut size = vec![0usize; n + 1]; + let mut value = vec![0u64; n + 1]; + for i in 1..=n { + let p: usize = t.next().unwrap().parse().unwrap(); + size[i] = t.next().unwrap().parse().unwrap(); + value[i] = t.next().unwrap().parse().unwrap(); + ch[p].push(i); + } + let (mut order, mut after) = (Vec::new(), Vec::new()); + for &u in &ch[0] { + dfs(u, &ch, &mut order, &mut after); + } + let mut dp = vec![vec![0u64; cmax + 1]; n + 1]; + for i in (0..n).rev() { + let u = order[i]; + for c in 0..=cmax { + dp[i][c] = dp[after[i]][c]; + if c >= size[u] { + dp[i][c] = dp[i][c].max(value[u] + dp[i + 1][c - size[u]]); + } + } + } + println!("{}", dp[0][cmax]); +} diff --git a/problems/037-dependency-tree-knapsack/solutions/typescript/main.ts b/problems/037-dependency-tree-knapsack/solutions/typescript/main.ts new file mode 100644 index 0000000..89e4679 --- /dev/null +++ b/problems/037-dependency-tree-knapsack/solutions/typescript/main.ts @@ -0,0 +1,63 @@ +import * as std from "std"; + +const input: string = std.in.readAsString(); +let scan = 0; +function nextInt(): number { + while (scan < input.length && input.charCodeAt(scan) <= 32) scan++; + let value = 0; + while (scan < input.length) { + const digit = input.charCodeAt(scan) - 48; + if (digit < 0 || digit > 9) break; + value = value * 10 + digit; + scan++; + } + return value; +} +function nextBigInt(): bigint { + while (scan < input.length && input.charCodeAt(scan) <= 32) scan++; + const start = scan; + while (scan < input.length) { + const code = input.charCodeAt(scan); + if (code < 48 || code > 57) break; + scan++; + } + return BigInt(input.slice(start, scan)); +} + +const nodeCount = nextInt(), + capacity = nextInt(), + children: number[][] = Array.from({ length: nodeCount + 1 }, () => []), + size = new Int32Array(nodeCount + 1), + value = new BigUint64Array(nodeCount + 1); +for (let node = 1; node <= nodeCount; node++) { + const parent = nextInt(); + size[node] = nextInt(); + value[node] = nextBigInt(); + children[parent]!.push(node); +} +const order: number[] = [], after: number[] = []; +function dfs(node: number): void { + const position = order.length; + order.push(node); + after.push(0); + for (const child of children[node]!) dfs(child); + after[position] = order.length; +} +for (const root of children[0]!) dfs(root); +const width = capacity + 1, dp = new BigUint64Array((nodeCount + 1) * width); +for (let position = nodeCount - 1; position >= 0; position--) { + const node = order[position]!, + row = position * width, + selectedTail = (position + 1) * width, + skippedTail = after[position]! * width; + for (let current = 0; current <= capacity; current++) { + let best = dp[skippedTail + current]!; + if (current >= size[node]!) { + const candidate = value[node]! + + dp[selectedTail + current - size[node]!]!; + if (candidate > best) best = candidate; + } + dp[row + current] = best; + } +} +std.out.puts(`${dp[capacity]}\n`); diff --git a/problems/037-dependency-tree-knapsack/statement.en.md b/problems/037-dependency-tree-knapsack/statement.en.md new file mode 100644 index 0000000..c066a68 --- /dev/null +++ b/problems/037-dependency-tree-knapsack/statement.en.md @@ -0,0 +1,87 @@ +# Dependency-Aware Cache Knapsack + +While designing cache cleanup for a WASM OJ compiler, we could not compare artifacts only by their individual sizes and values. Some cached results are derived from other artifacts. Keeping a derived result after deleting a prerequisite needed to rebuild or validate it would leave an incomplete cache entry that cannot be reused safely. + +We restrict these dependencies to a dependency forest. Each artifact has at most one direct prerequisite, but retaining any node requires retaining its entire ancestor chain up to a root. + +There are `N` cache artifacts. Node `i` has direct prerequisite `parent_i`; `parent_i = 0` means it has no prerequisite. Every node has a cache size and a reuse value, and the available capacity is `C`. + +Choose a dependency-closed subset with total size at most `C` and maximum total value. Any selection missing a required ancestor is invalid. The empty subset is valid. Output only the maximum value. + +## Input + +The first line contains `N C`. For IDs `1..N`, the next `N` lines contain `parent_i size_i value_i`. + +The input guarantees `0 <= parent_i < i`, so the structure is a forest with no cycle. ID order is not necessarily DFS order. Children of the same parent have increasing ID as their fixed order, although this order does not affect the optimum. + +## Output + +Output one line containing the maximum total value. + +## Constraints + +- `1 <= N <= 200` +- `0 <= C <= 10000` +- `1 <= size_i <= 10000` +- `0 <= value_i <= 10^12` +- The sum of all values is at most `9 * 10^18`. + +Full tests rule out subset enumeration. The intended solution also avoids an `O(C^2)` capacity convolution for every child. + +## Examples + + + +### Example One + +Input: + +```text +4 7 +0 2 3 +1 3 5 +1 4 8 +2 2 4 +``` + +Output: + +```text +12 +``` + +### Example Two + +Input: + +```text +3 0 +0 1 10 +1 1 20 +0 1 30 +``` + +Output: + +```text +0 +``` + +### Example Three + +Input: + +```text +3 3 +0 5 5 +1 1 100 +0 2 10 +``` + +Output: + +```text +10 +``` + + diff --git a/problems/037-dependency-tree-knapsack/statement.zh-TW.md b/problems/037-dependency-tree-knapsack/statement.zh-TW.md new file mode 100644 index 0000000..ca379a4 --- /dev/null +++ b/problems/037-dependency-tree-knapsack/statement.zh-TW.md @@ -0,0 +1,87 @@ +# 有依賴的快取背包 + +在設計 WASM OJ 的編譯快取清理策略時,我們不能只比較單一 artifact 的大小與收益。某些快取項目是由其他 artifact 衍生而來;如果只保留衍生結果,卻刪除了重建或驗證它所需的 prerequisite,這份快取就不再完整,也不能安全重用。 + +我們把這些相依關係限制成一座 dependency forest。每個 artifact 最多只有一個直接 prerequisite,但保留某個節點時,必須連同它一路到 root 的完整 ancestor chain 一起保留。 + +系統共有 `N` 個 cache artifacts。節點 `i` 的 `parent_i` 是它的直接 prerequisite;`parent_i = 0` 表示它沒有 prerequisite。每個節點都有 cache size 與重用收益,而可用容量為 `C`。 + +請在容量 `C` 內選擇一個 dependency-closed 子集合,使總收益最大。缺少任何必要 ancestor 的選擇都不合法。空集合合法,只需輸出最大收益。 + +## 輸入 + +第一行 `N C`。接下來依 ID `1..N` 各一行 `parent_i size_i value_i`。 + +輸入保證 `0 ≤ parent_i < i`,因此結構必為 forest,且不存在 cycle。ID 順序不保證是 DFS 順序;同一 parent 的 children 以 ID 遞增視為固定順序,但答案不受此順序影響。 + +## 輸出 + +一行最大總收益。 + +## 限制 + +- `1 ≤ N ≤ 200` +- `0 ≤ C ≤ 10000` +- `1 ≤ size_i ≤ 10000` +- `0 ≤ value_i ≤ 10^12` +- 所有 value 總和不超過 `9×10^18` + +完整限制排除子集合列舉;預期解也不做每個 child 的 `O(C^2)` 容量卷積。 + +## 範例 + + + +### 範例一 + +輸入: + +```text +4 7 +0 2 3 +1 3 5 +1 4 8 +2 2 4 +``` + +輸出: + +```text +12 +``` + +### 範例二 + +輸入: + +```text +3 0 +0 1 10 +1 1 20 +0 1 30 +``` + +輸出: + +```text +0 +``` + +### 範例三 + +輸入: + +```text +3 3 +0 5 5 +1 1 100 +0 2 10 +``` + +輸出: + +```text +10 +``` + + diff --git a/problems/037-dependency-tree-knapsack/tests/adversarial-blind-01.in b/problems/037-dependency-tree-knapsack/tests/adversarial-blind-01.in new file mode 100644 index 0000000..2dc9f30 --- /dev/null +++ b/problems/037-dependency-tree-knapsack/tests/adversarial-blind-01.in @@ -0,0 +1,9 @@ +8 8 +0 6 1 +1 1 100 +0 2 8 +1 1 100 +3 3 20 +2 1 100 +0 4 25 +5 1 20 diff --git a/problems/037-dependency-tree-knapsack/tests/adversarial-blind-01.out b/problems/037-dependency-tree-knapsack/tests/adversarial-blind-01.out new file mode 100644 index 0000000..3bc92d4 --- /dev/null +++ b/problems/037-dependency-tree-knapsack/tests/adversarial-blind-01.out @@ -0,0 +1 @@ +201 diff --git a/problems/037-dependency-tree-knapsack/tests/sample-01.in b/problems/037-dependency-tree-knapsack/tests/sample-01.in new file mode 100644 index 0000000..ecfb651 --- /dev/null +++ b/problems/037-dependency-tree-knapsack/tests/sample-01.in @@ -0,0 +1,5 @@ +4 7 +0 2 3 +1 3 5 +1 4 8 +2 2 4 diff --git a/problems/037-dependency-tree-knapsack/tests/sample-01.out b/problems/037-dependency-tree-knapsack/tests/sample-01.out new file mode 100644 index 0000000..48082f7 --- /dev/null +++ b/problems/037-dependency-tree-knapsack/tests/sample-01.out @@ -0,0 +1 @@ +12 diff --git a/problems/037-dependency-tree-knapsack/tests/sample-02.in b/problems/037-dependency-tree-knapsack/tests/sample-02.in new file mode 100644 index 0000000..eee07b9 --- /dev/null +++ b/problems/037-dependency-tree-knapsack/tests/sample-02.in @@ -0,0 +1,4 @@ +3 0 +0 1 10 +1 1 20 +0 1 30 diff --git a/problems/037-dependency-tree-knapsack/tests/sample-02.out b/problems/037-dependency-tree-knapsack/tests/sample-02.out new file mode 100644 index 0000000..573541a --- /dev/null +++ b/problems/037-dependency-tree-knapsack/tests/sample-02.out @@ -0,0 +1 @@ +0 diff --git a/problems/037-dependency-tree-knapsack/tests/sample-03.in b/problems/037-dependency-tree-knapsack/tests/sample-03.in new file mode 100644 index 0000000..ebe8d1b --- /dev/null +++ b/problems/037-dependency-tree-knapsack/tests/sample-03.in @@ -0,0 +1,4 @@ +3 3 +0 5 5 +1 1 100 +0 2 10 diff --git a/problems/037-dependency-tree-knapsack/tests/sample-03.out b/problems/037-dependency-tree-knapsack/tests/sample-03.out new file mode 100644 index 0000000..f599e28 --- /dev/null +++ b/problems/037-dependency-tree-knapsack/tests/sample-03.out @@ -0,0 +1 @@ +10 diff --git a/problems/037-dependency-tree-knapsack/validator.py b/problems/037-dependency-tree-knapsack/validator.py new file mode 100644 index 0000000..d857ebf --- /dev/null +++ b/problems/037-dependency-tree-knapsack/validator.py @@ -0,0 +1,31 @@ +import re, sys + + +def fail(): + raise SystemExit(1) + + +try: + t = sys.stdin.buffer.read().decode("utf-8").split() + p = 0 + + def u(a, b): + global p + if p >= len(t) or re.fullmatch(r"0|[1-9][0-9]*", t[p]) is None: + fail() + v = int(t[p]) + p += 1 + if not a <= v <= b: + fail() + return v + + N, C = u(1, 200), u(0, 10000) + total = 0 + for i in range(1, N + 1): + u(0, i - 1) + u(1, 10000) + total += u(0, 10**12) + if total > 9 * 10**18 or p != len(t): + fail() +except (UnicodeDecodeError, ValueError, OverflowError): + fail() diff --git a/problems/038-conformance-feature-coverage/editorial.en.md b/problems/038-conformance-feature-coverage/editorial.en.md new file mode 100644 index 0000000..801c9f5 --- /dev/null +++ b/problems/038-conformance-feature-coverage/editorial.en.md @@ -0,0 +1,34 @@ +# Editorial + +## Intuitive Approach + +Enumerating whether to select each test and combining coverage takes `O(2^N(N + F))` time. Greedily choosing the best new-coverage-to-cost ratio is also incorrect because overlaps change every later marginal gain. + +## Optimal Approach: Minimum Cost per Coverage Mask + +Since `F <= 20`, represent a feature set by an `F`-bit mask. Let `dp[mask]` be the minimum cost of a subset of the tests processed so far whose union is exactly `mask`. Mark unreachable states with a true infinity and initialize only `dp[0] = 0`. + +For a test `(cost, testMask)`, first copy `next = dp`, representing omission. For every reachable `mask`, update + +```text +next[mask | testMask] = min(next[mask | testMask], dp[mask] + cost) +``` + +After all tests, inspect every `mask` with `dp[mask] <= B` and take the maximum population count. + +## Correctness Proof + +Induct on the processed tests. Initially, the empty subset is the unique possibility, so only mask zero is reachable at cost zero. For a new test, every subset either omits it, in which case the old state is preserved, or includes it. Removing the new test from the latter leaves some old union `mask`; restoring it creates exactly `mask | testMask` and adds exactly its cost. The transition enumerates both exhaustive cases and takes the minimum cost for every resulting union. + +Thus the final DP gives the minimum cost for every achievable coverage set. Masks whose minimum cost is at most `B` correspond exactly to legal selections, and the maximum popcount among them is the required answer. + +## Complexity + +There are `2^F` masks and each test scans them once, for `O(N 2^F)` time and `O(2^F)` space. + +## Common Mistakes + +- Counting repeated coverage more than once and producing an answer greater than `F`. +- Using `sum(cost) + 1` as an unreachable sentinel and then accepting every value at most `B`; when `B > sum(cost)`, that sentinel appears feasible. Use a value beyond both the budget and every reachable cost, and never transition from it. +- Masking tests rather than features and returning to `2^N` enumeration. +- Ignoring zero-cost tests or tests with empty coverage. diff --git a/problems/038-conformance-feature-coverage/editorial.zh-TW.md b/problems/038-conformance-feature-coverage/editorial.zh-TW.md new file mode 100644 index 0000000..ef331c4 --- /dev/null +++ b/problems/038-conformance-feature-coverage/editorial.zh-TW.md @@ -0,0 +1,34 @@ +# 解題說明 + +## 直覺解法 + +列舉每個測試選或不選,再合併 coverage,需 `O(2^N(N+F))`。依「新覆蓋數/成本」貪心也不正確,因集合重疊會改變後續邊際收益。 + +## 最佳解法:bitmask 最小成本 + +因 `F≤20`,以 `F` bits 表示 coverage。令 `dp[mask]` 為目前測試中,恰能得到 union `mask` 的最小成本;不可達為無限大,初始只有 `dp[0]=0`。 + +處理測試 `(cost,testMask)` 時先複製 `next=dp`(不選),再對每個可達 `mask` 更新: + +```text +next[mask | testMask] = min(next[mask | testMask], dp[mask] + cost) +``` + +完成後,在 `dp[mask]≤B` 的 mask 中取 popcount 最大者。 + +## 正確性證明 + +以處理測試數歸納。初始空集合唯一,狀態正確。加入一個測試後,任何子集合要嘛不含它,其最小成本由舊 `dp` 保留;要嘛含它,移除該測試後有某舊 union `mask`,新 union 正是 `mask|testMask`,成本多 `cost`。轉移枚舉兩類所有可能並取最小,所以 `next` 對每個 union 仍正確。最後 cost 不超過 budget 的狀態恰為所有合法選擇,最大 popcount 即答案。 + +## 複雜度 + +共有 `2^F` 個 mask,每個測試掃描一次,時間 `O(N2^F)`、空間 `O(2^F)`。 + +## 常見錯誤 + +- 把重複覆蓋也累加,答案超過 `F`。 +- 把「不可達」設成 `sum(cost)+1` 後又只用 `dp[mask]≤B` 判斷;若 + `B>sum(cost)`,這個 sentinel 本身會被誤認為可行。應使用真正大於 budget + 與所有可達成本的值,並在轉移時排除 sentinel。 +- 以測試數 `N` 做 bitmask,回到 `2^N` 的暴力。 +- 忽略 cost 為零或 coverage 為空的測試。 diff --git a/problems/038-conformance-feature-coverage/generator.py b/problems/038-conformance-feature-coverage/generator.py new file mode 100644 index 0000000..45d64a7 --- /dev/null +++ b/problems/038-conformance-feature-coverage/generator.py @@ -0,0 +1,13 @@ +import random, sys + +if len(sys.argv) != 3: + raise SystemExit("usage: generator.py SEED INDEX") +r = random.Random((int(sys.argv[1]) << 32) ^ int(sys.argv[2])) +idx = int(sys.argv[2]) +F = r.randint(1, min(10, 3 + idx % 8)) +N = r.randint(1, min(15, 5 + idx % 11)) +B = r.randint(0, 35) +print(F, N, B) +for _ in range(N): + a = [x for x in range(1, F + 1) if r.random() < 0.4] + print(r.randint(0, 15), len(a), *a) diff --git a/problems/038-conformance-feature-coverage/oracle.py b/problems/038-conformance-feature-coverage/oracle.py new file mode 100644 index 0000000..7f88125 --- /dev/null +++ b/problems/038-conformance-feature-coverage/oracle.py @@ -0,0 +1,22 @@ +import sys + +t = list(map(int, sys.stdin.buffer.read().split())) +it = iter(t) +F, N, B = next(it), next(it), next(it) +a = [] +for _ in range(N): + c, k = next(it), next(it) + m = 0 + for _ in range(k): + m |= 1 << (next(it) - 1) + a.append((c, m)) +best = 0 +for s in range(1 << N): + c = m = 0 + for i, (x, y) in enumerate(a): + if s >> i & 1: + c += x + m |= y + if c <= B: + best = max(best, m.bit_count()) +print(best) diff --git a/problems/038-conformance-feature-coverage/problem.json b/problems/038-conformance-feature-coverage/problem.json new file mode 100644 index 0000000..228fdd0 --- /dev/null +++ b/problems/038-conformance-feature-coverage/problem.json @@ -0,0 +1,146 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 38, + "slug": "conformance-feature-coverage", + "title": { + "zh-TW": "最划算的 Conformance Suite", + "en": "Best-Value Conformance Suite" + }, + "difficulty": "hard", + "tags": [ + "bitmask", + "dynamic-programming", + "maximum-coverage" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-blind-01", + "kind": "adversarial", + "input": "tests/adversarial-blind-01.in", + "output": "tests/adversarial-blind-01.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 15000000, + "memoryLimitBytes": 268435456 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 1500000, + "memoryLimitBytes": 201326592 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 550000, + "memoryLimitBytes": 134217728 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "列舉測試子集合", + "en": "Enumerate test subsets" + }, + "time": "O(2^N(N+F))", + "space": "O(F)", + "accepted": false + }, + { + "name": { + "zh-TW": "coverage mask 最小成本 DP", + "en": "Minimum-cost DP by coverage mask" + }, + "time": "O(N 2^F)", + "space": "O(2^F)", + "accepted": true + } + ] +} diff --git a/problems/038-conformance-feature-coverage/solutions/c/main.c b/problems/038-conformance-feature-coverage/solutions/c/main.c new file mode 100644 index 0000000..afe7f2d --- /dev/null +++ b/problems/038-conformance-feature-coverage/solutions/c/main.c @@ -0,0 +1,52 @@ +#include +#include +#include +#include +static int pc(unsigned x) { + int n = 0; + while (x) { + x &= x - 1; + n++; + } + return n; +} +int main(void) { + int F, N; + unsigned long long B; + if (scanf("%d%d%llu", &F, &N, &B) != 3) + return 0; + int S = 1 << F; + uint64_t *dp = malloc((size_t)S * sizeof(*dp)), + *nx = malloc((size_t)S * sizeof(*nx)); + const uint64_t INF = UINT64_MAX / 4; + for (int i = 0; i < S; i++) + dp[i] = INF; + dp[0] = 0; + while (N--) { + unsigned long long cost; + int k, m = 0, x; + scanf("%llu%d", &cost, &k); + while (k--) { + scanf("%d", &x); + m |= 1 << (x - 1); + } + memcpy(nx, dp, (size_t)S * sizeof(*dp)); + for (int s = 0; s < S; s++) + if (dp[s] != INF) { + int q = s | m; + uint64_t v = dp[s] + cost; + if (v < nx[q]) + nx[q] = v; + } + uint64_t *tmp = dp; + dp = nx; + nx = tmp; + } + int ans = 0; + for (int s = 0; s < S; s++) + if (dp[s] <= B && pc((unsigned)s) > ans) + ans = pc((unsigned)s); + printf("%d\n", ans); + free(dp); + free(nx); +} diff --git a/problems/038-conformance-feature-coverage/solutions/cpp/main.cpp b/problems/038-conformance-feature-coverage/solutions/cpp/main.cpp new file mode 100644 index 0000000..8c3f994 --- /dev/null +++ b/problems/038-conformance-feature-coverage/solutions/cpp/main.cpp @@ -0,0 +1,38 @@ +#include +#include +#include +#include +#include +#include +using namespace std; +int main() { + ios::sync_with_stdio(false); + cin.tie(nullptr); + int F, N; + uint64_t B; + if (!(cin >> F >> N >> B)) + return 0; + int S = 1 << F; + const uint64_t INF = numeric_limits::max() / 4; + vector dp(S, INF); + dp[0] = 0; + while (N--) { + uint64_t cost; + int k, m = 0, x; + cin >> cost >> k; + while (k--) { + cin >> x; + m |= 1 << (x - 1); + } + auto nx = dp; + for (int s = 0; s < S; s++) + if (dp[s] != INF) + nx[s | m] = min(nx[s | m], dp[s] + cost); + dp.swap(nx); + } + int ans = 0; + for (int s = 0; s < S; s++) + if (dp[s] <= B) + ans = max(ans, popcount((unsigned)s)); + cout << ans << '\n'; +} diff --git a/problems/038-conformance-feature-coverage/solutions/go/main.go b/problems/038-conformance-feature-coverage/solutions/go/main.go new file mode 100644 index 0000000..2635ac6 --- /dev/null +++ b/problems/038-conformance-feature-coverage/solutions/go/main.go @@ -0,0 +1,52 @@ +package main + +import ( + "bufio" + "fmt" + "math" + "math/bits" + "os" +) + +func main() { + in := bufio.NewReader(os.Stdin) + out := bufio.NewWriter(os.Stdout) + defer out.Flush() + var f, n int + var b uint64 + if _, e := fmt.Fscan(in, &f, &n, &b); e != nil { + return + } + S := 1 << f + inf := uint64(math.MaxUint64 / 4) + dp := make([]uint64, S) + for i := range dp { + dp[i] = inf + } + dp[0] = 0 + for ; n > 0; n-- { + var cost uint64 + var k int + fmt.Fscan(in, &cost, &k) + m := 0 + for ; k > 0; k-- { + var x int + fmt.Fscan(in, &x) + m |= 1 << (x - 1) + } + next := append([]uint64(nil), dp...) + for s, v := range dp { + if v != inf && v+cost < next[s|m] { + next[s|m] = v + cost + } + } + dp = next + } + ans := 0 + for s, v := range dp { + if v <= b && bits.OnesCount(uint(s)) > ans { + ans = bits.OnesCount(uint(s)) + } + } + fmt.Fprintln(out, ans) +} diff --git a/problems/038-conformance-feature-coverage/solutions/javascript/main.js b/problems/038-conformance-feature-coverage/solutions/javascript/main.js new file mode 100644 index 0000000..cc9f613 --- /dev/null +++ b/problems/038-conformance-feature-coverage/solutions/javascript/main.js @@ -0,0 +1,50 @@ +import * as std from "std"; + +const input = std.in.readAsString(); +let scan = 0; +function nextInt() { + while (scan < input.length && input.charCodeAt(scan) <= 32) scan++; + let value = 0; + while (scan < input.length) { + const digit = input.charCodeAt(scan) - 48; + if (digit < 0 || digit > 9) break; + value = value * 10 + digit; + scan++; + } + return value; +} +/** @param {number} value @returns {number} */ +function popcount(value) { + let count = 0; + while (value) { + value &= value - 1; + count++; + } + return count; +} + +const featureCount = nextInt(), + testCount = nextInt(), + budget = nextInt(), + states = 1 << featureCount; +let dp = new Float64Array(states), next = new Float64Array(states); +dp.fill(Number.POSITIVE_INFINITY); +dp[0] = 0; +for (let test = 0; test < testCount; test++) { + const cost = nextInt(), coveredCount = nextInt(); + let covered = 0; + for (let i = 0; i < coveredCount; i++) covered |= 1 << (nextInt() - 1); + next.set(dp); + for (let mask = 0; mask < states; mask++) { + if (dp[mask] !== Number.POSITIVE_INFINITY) { + const union = mask | covered, candidate = dp[mask] + cost; + if (candidate < next[union]) next[union] = candidate; + } + } + [dp, next] = [next, dp]; +} +let answer = 0; +for (let mask = 0; mask < states; mask++) { + if (dp[mask] <= budget) answer = Math.max(answer, popcount(mask)); +} +std.out.puts(`${answer}\n`); diff --git a/problems/038-conformance-feature-coverage/solutions/python/main.py b/problems/038-conformance-feature-coverage/solutions/python/main.py new file mode 100644 index 0000000..e0df3f3 --- /dev/null +++ b/problems/038-conformance-feature-coverage/solutions/python/main.py @@ -0,0 +1,21 @@ +import sys + +t = list(map(int, sys.stdin.buffer.read().split())) +it = iter(t) +F, N, B = next(it), next(it), next(it) +S = 1 << F +inf = 10**30 +dp = [inf] * S +dp[0] = 0 +for _ in range(N): + cost, k = next(it), next(it) + m = 0 + for _ in range(k): + m |= 1 << (next(it) - 1) + ndp = dp[:] + for s, v in enumerate(dp): + if v != inf: + q = s | m + ndp[q] = min(ndp[q], v + cost) + dp = ndp +print(max(s.bit_count() for s, v in enumerate(dp) if v <= B)) diff --git a/problems/038-conformance-feature-coverage/solutions/rust/main.rs b/problems/038-conformance-feature-coverage/solutions/rust/main.rs new file mode 100644 index 0000000..7927d2e --- /dev/null +++ b/problems/038-conformance-feature-coverage/solutions/rust/main.rs @@ -0,0 +1,37 @@ +use std::io::{self, Read}; +fn main() { + let mut s = String::new(); + io::stdin().read_to_string(&mut s).unwrap(); + let mut t = s.split_whitespace(); + let f: usize = t.next().unwrap().parse().unwrap(); + let n: usize = t.next().unwrap().parse().unwrap(); + let b: u64 = t.next().unwrap().parse().unwrap(); + let states = 1usize << f; + let inf = u64::MAX / 4; + let mut dp = vec![inf; states]; + dp[0] = 0; + for _ in 0..n { + let cost: u64 = t.next().unwrap().parse().unwrap(); + let k: usize = t.next().unwrap().parse().unwrap(); + let mut m = 0usize; + for _ in 0..k { + let x: usize = t.next().unwrap().parse().unwrap(); + m |= 1 << (x - 1); + } + let mut next = dp.clone(); + for mask in 0..states { + if dp[mask] != inf { + let q = mask | m; + next[q] = next[q].min(dp[mask] + cost); + } + } + dp = next; + } + let mut ans = 0; + for mask in 0..states { + if dp[mask] <= b { + ans = ans.max(mask.count_ones()); + } + } + println!("{}", ans); +} diff --git a/problems/038-conformance-feature-coverage/solutions/typescript/main.ts b/problems/038-conformance-feature-coverage/solutions/typescript/main.ts new file mode 100644 index 0000000..75324b1 --- /dev/null +++ b/problems/038-conformance-feature-coverage/solutions/typescript/main.ts @@ -0,0 +1,49 @@ +import * as std from "std"; + +const input: string = std.in.readAsString(); +let scan = 0; +function nextInt(): number { + while (scan < input.length && input.charCodeAt(scan) <= 32) scan++; + let value = 0; + while (scan < input.length) { + const digit = input.charCodeAt(scan) - 48; + if (digit < 0 || digit > 9) break; + value = value * 10 + digit; + scan++; + } + return value; +} +function popcount(value: number): number { + let count = 0; + while (value) { + value &= value - 1; + count++; + } + return count; +} + +const featureCount = nextInt(), + testCount = nextInt(), + budget = nextInt(), + states = 1 << featureCount; +let dp = new Float64Array(states), next = new Float64Array(states); +dp.fill(Number.POSITIVE_INFINITY); +dp[0] = 0; +for (let test = 0; test < testCount; test++) { + const cost = nextInt(), coveredCount = nextInt(); + let covered = 0; + for (let i = 0; i < coveredCount; i++) covered |= 1 << (nextInt() - 1); + next.set(dp); + for (let mask = 0; mask < states; mask++) { + if (dp[mask] !== Number.POSITIVE_INFINITY) { + const union = mask | covered, candidate = dp[mask]! + cost; + if (candidate < next[union]!) next[union] = candidate; + } + } + [dp, next] = [next, dp]; +} +let answer = 0; +for (let mask = 0; mask < states; mask++) { + if (dp[mask]! <= budget) answer = Math.max(answer, popcount(mask)); +} +std.out.puts(`${answer}\n`); diff --git a/problems/038-conformance-feature-coverage/statement.en.md b/problems/038-conformance-feature-coverage/statement.en.md new file mode 100644 index 0000000..455d03f --- /dev/null +++ b/problems/038-conformance-feature-coverage/statement.en.md @@ -0,0 +1,93 @@ +# Best-Value Conformance Suite + +While designing a runtime conformance suite for a WASM OJ, we accumulated many candidate tests but could not run all of them before every release. Tests have different instruction costs, and one test may validate several runtime features at once. If multiple tests validate the same feature, that feature still counts as only one covered feature. + +Under a limited execution budget, we therefore want to choose the most useful collection of tests so that as many distinct features as possible are actually validated before release. + +The runtime has `F` features to validate, numbered `1..F`. Candidate test `i` has execution cost `cost_i` and covers a set of features. A feature is validated if at least one selected test covers it. + +Choose any subset of tests with total cost at most budget `B`, maximizing the number of distinct covered features. A test cannot be selected more than once, and the empty subset is valid. Covering a feature repeatedly gives no additional benefit. Output only the maximum coverage count, not the subset. + +## Input + +The first line contains `F N B`. Each of the next `N` lines has the form: + +```text +cost k feature1 ... featurek +``` + +Feature IDs within one test are distinct. `k = 0` is allowed. + +## Output + +Output one line containing the maximum number of features that can be covered. + +## Constraints + +- `1 <= F <= 20` +- `1 <= N <= 25` +- `0 <= B <= 10^12` +- `0 <= cost_i <= 10^9` +- `0 <= k <= F` +- `1 <= feature_j <= F` +- The sum of all costs is at most `2.5 * 10^10` and can be represented exactly. +- Full tests rule out enumerating up to `2^25` test subsets. + +## Examples + + + +### Example One + +Input: + +```text +4 3 5 +3 2 1 2 +2 2 2 3 +4 1 4 +``` + +Output: + +```text +3 +``` + +### Example Two + +Input: + +```text +3 3 0 +0 1 2 +0 2 1 3 +1 3 1 2 3 +``` + +Output: + +```text +3 +``` + +### Example Three + +Input: + +```text +5 5 6 +2 2 1 2 +2 2 1 2 +3 2 3 4 +3 1 5 +7 5 1 2 3 4 5 +``` + +Output: + +```text +4 +``` + + diff --git a/problems/038-conformance-feature-coverage/statement.zh-TW.md b/problems/038-conformance-feature-coverage/statement.zh-TW.md new file mode 100644 index 0000000..31784dc --- /dev/null +++ b/problems/038-conformance-feature-coverage/statement.zh-TW.md @@ -0,0 +1,92 @@ +# 最划算的 Conformance Suite + +在設計 WASM OJ 的 runtime conformance suite 時,我們累積了許多候選測試,但無法在每一次發布前全部執行。不同測試的 instruction cost 不同,而且一個測試可能同時驗證多項 runtime features;若多個測試驗證了同一項 feature,並不會讓這項 feature 算成多次覆蓋。 + +因此,在有限的執行 budget 下,我們想挑出一批最有價值的測試,讓發布前實際驗證到的不同 features 儘可能多。 + +Runtime 有 `F` 個待驗證 feature,編號為 `1..F`。候選測試 `i` 的執行成本為 `cost_i`,並覆蓋一個 feature 集合。只要至少選到一個覆蓋某 feature 的測試,該 feature 就算被驗證。 + +請在總成本 budget `B` 內選擇任意測試子集合,使被覆蓋的不同 feature 數量最大。每個測試不可重複選擇,空集合合法;重複覆蓋同一 feature 沒有額外收益。只需輸出最大覆蓋數,不需輸出集合。 + +## 輸入 + +第一行 `F N B`。接下來 `N` 行各為: + +```text +cost k feature1 ... featurek +``` + +同一測試內的 feature ID 互不相同,`k=0` 合法。 + +## 輸出 + +一行最大可覆蓋 feature 數。 + +## 限制 + +- `1 ≤ F ≤ 20` +- `1 ≤ N ≤ 25` +- `0 ≤ B ≤ 10^12` +- `0 ≤ cost_i ≤ 10^9` +- `0 ≤ k ≤ F`,`1 ≤ feature_j ≤ F` + +所有成本加總不超過 `2.5×10^10`,可安全存於精確整數。完整限制排除列舉最多 `2^25` 個測試子集合。 + +## 範例 + + + +### 範例一 + +輸入: + +```text +4 3 5 +3 2 1 2 +2 2 2 3 +4 1 4 +``` + +輸出: + +```text +3 +``` + +### 範例二 + +輸入: + +```text +3 3 0 +0 1 2 +0 2 1 3 +1 3 1 2 3 +``` + +輸出: + +```text +3 +``` + +### 範例三 + +輸入: + +```text +5 5 6 +2 2 1 2 +2 2 1 2 +3 2 3 4 +3 1 5 +7 5 1 2 3 4 5 +``` + +輸出: + +```text +4 +``` + + diff --git a/problems/038-conformance-feature-coverage/tests/adversarial-blind-01.in b/problems/038-conformance-feature-coverage/tests/adversarial-blind-01.in new file mode 100644 index 0000000..d2b7ea3 --- /dev/null +++ b/problems/038-conformance-feature-coverage/tests/adversarial-blind-01.in @@ -0,0 +1,6 @@ +7 5 1000 +0 2 1 2 +0 2 2 3 +5 2 4 5 +7 1 6 +0 0 diff --git a/problems/038-conformance-feature-coverage/tests/adversarial-blind-01.out b/problems/038-conformance-feature-coverage/tests/adversarial-blind-01.out new file mode 100644 index 0000000..1e8b314 --- /dev/null +++ b/problems/038-conformance-feature-coverage/tests/adversarial-blind-01.out @@ -0,0 +1 @@ +6 diff --git a/problems/038-conformance-feature-coverage/tests/sample-01.in b/problems/038-conformance-feature-coverage/tests/sample-01.in new file mode 100644 index 0000000..480a9c7 --- /dev/null +++ b/problems/038-conformance-feature-coverage/tests/sample-01.in @@ -0,0 +1,4 @@ +4 3 5 +3 2 1 2 +2 2 2 3 +4 1 4 diff --git a/problems/038-conformance-feature-coverage/tests/sample-01.out b/problems/038-conformance-feature-coverage/tests/sample-01.out new file mode 100644 index 0000000..00750ed --- /dev/null +++ b/problems/038-conformance-feature-coverage/tests/sample-01.out @@ -0,0 +1 @@ +3 diff --git a/problems/038-conformance-feature-coverage/tests/sample-02.in b/problems/038-conformance-feature-coverage/tests/sample-02.in new file mode 100644 index 0000000..5aa7a79 --- /dev/null +++ b/problems/038-conformance-feature-coverage/tests/sample-02.in @@ -0,0 +1,4 @@ +3 3 0 +0 1 2 +0 2 1 3 +1 3 1 2 3 diff --git a/problems/038-conformance-feature-coverage/tests/sample-02.out b/problems/038-conformance-feature-coverage/tests/sample-02.out new file mode 100644 index 0000000..00750ed --- /dev/null +++ b/problems/038-conformance-feature-coverage/tests/sample-02.out @@ -0,0 +1 @@ +3 diff --git a/problems/038-conformance-feature-coverage/tests/sample-03.in b/problems/038-conformance-feature-coverage/tests/sample-03.in new file mode 100644 index 0000000..9854b6a --- /dev/null +++ b/problems/038-conformance-feature-coverage/tests/sample-03.in @@ -0,0 +1,6 @@ +5 5 6 +2 2 1 2 +2 2 1 2 +3 2 3 4 +3 1 5 +7 5 1 2 3 4 5 diff --git a/problems/038-conformance-feature-coverage/tests/sample-03.out b/problems/038-conformance-feature-coverage/tests/sample-03.out new file mode 100644 index 0000000..b8626c4 --- /dev/null +++ b/problems/038-conformance-feature-coverage/tests/sample-03.out @@ -0,0 +1 @@ +4 diff --git a/problems/038-conformance-feature-coverage/validator.py b/problems/038-conformance-feature-coverage/validator.py new file mode 100644 index 0000000..4e008f8 --- /dev/null +++ b/problems/038-conformance-feature-coverage/validator.py @@ -0,0 +1,35 @@ +import re, sys + + +def fail(): + raise SystemExit(1) + + +try: + t = sys.stdin.buffer.read().decode("utf-8").split() + p = 0 + + def u(a, b): + global p + if p >= len(t) or re.fullmatch(r"0|[1-9][0-9]*", t[p]) is None: + fail() + v = int(t[p]) + p += 1 + if not a <= v <= b: + fail() + return v + + F, N, B = u(1, 20), u(1, 25), u(0, 10**12) + for _ in range(N): + u(0, 10**9) + k = u(0, F) + seen = set() + for _ in range(k): + x = u(1, F) + if x in seen: + fail() + seen.add(x) + if p != len(t): + fail() +except (UnicodeDecodeError, ValueError, OverflowError): + fail() diff --git a/problems/039-calibration-multiple-choice-knapsack/editorial.en.md b/problems/039-calibration-multiple-choice-knapsack/editorial.en.md new file mode 100644 index 0000000..c585a23 --- /dev/null +++ b/problems/039-calibration-multiple-choice-knapsack/editorial.en.md @@ -0,0 +1,32 @@ +# Editorial + +## Intuitive Approach + +Each group contributes either no plan or one of `K_g` plans, yielding `product(K_g + 1)` combinations. A two-dimensional `dp[g][c]` reduces time to `O(C sum K_g)` but consumes `O(GC)` space, exceeding the full memory limit. + +## Optimal Approach: Rolling Multiple-Choice Knapsack + +Let `dp[c]` be the maximum confidence obtainable from processed profiles with total time at most `c`. When processing one profile, initialize `next = dp` to represent skipping it. Then, for every plan `(time, value)` in that profile and every `c >= time`, update + +```text +next[c] = max(next[c], dp[c - time] + value) +``` + +Every source must come from the previous profile's `dp`, not from `next`. Replace `dp` with `next` only after the entire profile is processed. This enforces mutual exclusion even for plans with zero execution time. + +## Correctness Proof + +Induct on the number of processed profiles. For a new profile, every legal schedule either skips it, which is represented by retaining old `dp[c]`, or selects exactly one of its plans. Removing that selected plan leaves a schedule using only earlier profiles, whose best value is old `dp[c - time_j]`; adding the plan contributes `value_j`. The transition examines every mutually exclusive choice and takes the best. + +Since no transition reads from `next`, no state can contain two plans from the same profile. Therefore the invariant holds after each group, and final `dp[C]` is the best valid schedule. + +## Complexity + +Every plan scans `C + 1` capacities, so time is `O(C sum K_g)`. Two one-dimensional arrays use `O(C)` space. + +## Common Mistakes + +- Flattening all plans into ordinary 0/1 knapsack and selecting multiple plans from one profile. +- Transitioning from `next`, especially when `time = 0`. +- Requiring one plan from every profile even though skipping is allowed. +- Storing accumulated confidence in a 32-bit integer. diff --git a/problems/039-calibration-multiple-choice-knapsack/editorial.zh-TW.md b/problems/039-calibration-multiple-choice-knapsack/editorial.zh-TW.md new file mode 100644 index 0000000..e27059a --- /dev/null +++ b/problems/039-calibration-multiple-choice-knapsack/editorial.zh-TW.md @@ -0,0 +1,26 @@ +# 解題說明 + +## 直覺解法 + +每組選「不選或某一方案」,組合數為 `product(K_g+1)`。二維 `dp[g][c]` 雖將時間降為 `O(C ΣK_g)`,卻需 `O(GC)` 空間,完整限制下超過 memory limit。 + +## 最佳解法 + +令 `dp[c]` 為已處理 profiles 在時間不超過 `c` 時的最大收益。處理一組時先令 `next=dp`,代表不選此組;對組內每個 `(time,value)` 與每個 `c≥time`,用**上一組**的 `dp[c-time]+value` 更新 `next[c]`。整組結束後才令 `dp=next`。 + +不可在同一 `next` 上繼續取來源,否則會同時選到同組多個方案。time 為零時也遵守同一規則。 + +## 正確性證明 + +以處理組數歸納。對新 profile,任何合法排程恰有兩類:跳過它,收益由舊 `dp[c]` 表示;或選它的唯一某方案 `j`,其餘排程只來自舊 profiles,最佳收益為舊 `dp[c-time_j]+value_j`。轉移枚舉所有互斥選項並取最大,既不漏解也不會同組複選。因此每輪後 `dp` 定義成立,最終 `dp[C]` 即最佳排程。 + +## 複雜度 + +每個方案掃描 `C+1` 容量,時間 `O(C ΣK_g)`,兩個一維陣列使空間為 `O(C)`。 + +## 常見錯誤 + +- 把所有方案攤平成普通 0/1 背包,允許同 profile 選多種。 +- 從 `next` 而非上一輪 `dp` 轉移,尤其 time=0 時會錯。 +- 強迫每個 profile 一定選一種;本題允許跳過。 +- 用 32-bit 儲存可信度總和。 diff --git a/problems/039-calibration-multiple-choice-knapsack/generator.py b/problems/039-calibration-multiple-choice-knapsack/generator.py new file mode 100644 index 0000000..25ea4b7 --- /dev/null +++ b/problems/039-calibration-multiple-choice-knapsack/generator.py @@ -0,0 +1,15 @@ +import random, sys + +if len(sys.argv) != 3: + raise SystemExit("usage: generator.py SEED INDEX") +r = random.Random((int(sys.argv[1]) << 32) ^ int(sys.argv[2])) +idx = int(sys.argv[2]) +G = r.randint(1, min(8, 3 + idx % 6)) +C = r.randint(0, 35) +print(G, C) +for _ in range(G): + k = r.randint(1, 4) + a = [] + for _ in range(k): + a.extend((r.randint(0, 40), r.randint(0, 80))) + print(k, *a) diff --git a/problems/039-calibration-multiple-choice-knapsack/oracle.py b/problems/039-calibration-multiple-choice-knapsack/oracle.py new file mode 100644 index 0000000..4eb8251 --- /dev/null +++ b/problems/039-calibration-multiple-choice-knapsack/oracle.py @@ -0,0 +1,26 @@ +import sys + +t = list(map(int, sys.stdin.buffer.read().split())) +it = iter(t) +G, C = next(it), next(it) +groups = [] +for _ in range(G): + k = next(it) + groups.append([(next(it), next(it)) for _ in range(k)]) +best = 0 + + +def dfs(g, time, value): + global best + if time > C: + return + if g == G: + best = max(best, value) + return + dfs(g + 1, time, value) + for w, v in groups[g]: + dfs(g + 1, time + w, value + v) + + +dfs(0, 0, 0) +print(best) diff --git a/problems/039-calibration-multiple-choice-knapsack/problem.json b/problems/039-calibration-multiple-choice-knapsack/problem.json new file mode 100644 index 0000000..4d466a0 --- /dev/null +++ b/problems/039-calibration-multiple-choice-knapsack/problem.json @@ -0,0 +1,155 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 39, + "slug": "calibration-multiple-choice-knapsack", + "title": { + "zh-TW": "Calibration 實驗排程", + "en": "Calibration Experiment Scheduling" + }, + "difficulty": "medium", + "tags": [ + "dynamic-programming", + "multiple-choice-knapsack", + "scheduling" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-blind-01", + "kind": "adversarial", + "input": "tests/adversarial-blind-01.in", + "output": "tests/adversarial-blind-01.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 9500000, + "memoryLimitBytes": 134217728 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 1500000, + "memoryLimitBytes": 100663296 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 500000, + "memoryLimitBytes": 67108864 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "列舉每組選項或不選", + "en": "Enumerate one option or omission per group" + }, + "time": "O(product(K_g+1))", + "space": "O(G)", + "accepted": false + }, + { + "name": { + "zh-TW": "二維分組背包", + "en": "Two-dimensional grouped knapsack" + }, + "time": "O(C sum K_g)", + "space": "O(GC)", + "accepted": false + }, + { + "name": { + "zh-TW": "rolling multiple-choice knapsack", + "en": "Rolling multiple-choice knapsack" + }, + "time": "O(C sum K_g)", + "space": "O(C)", + "accepted": true + } + ] +} diff --git a/problems/039-calibration-multiple-choice-knapsack/solutions/c/main.c b/problems/039-calibration-multiple-choice-knapsack/solutions/c/main.c new file mode 100644 index 0000000..cc57d52 --- /dev/null +++ b/problems/039-calibration-multiple-choice-knapsack/solutions/c/main.c @@ -0,0 +1,37 @@ +#include +#include +#include +#include +int main(void) { + int G, C; + if (scanf("%d%d", &G, &C) != 2) + return 0; + uint64_t *dp = calloc((size_t)C + 1, sizeof(*dp)), + *nx = malloc(((size_t)C + 1) * sizeof(*nx)); + while (G--) { + int k; + scanf("%d", &k); + int *w = malloc((size_t)k * sizeof(*w)); + uint64_t *v = malloc((size_t)k * sizeof(*v)); + for (int i = 0; i < k; i++) { + unsigned long long x; + scanf("%d%llu", &w[i], &x); + v[i] = x; + } + memcpy(nx, dp, ((size_t)C + 1) * sizeof(*dp)); + for (int i = 0; i < k; i++) + for (int c = w[i]; c <= C; c++) { + uint64_t q = dp[c - w[i]] + v[i]; + if (q > nx[c]) + nx[c] = q; + } + uint64_t *tmp = dp; + dp = nx; + nx = tmp; + free(w); + free(v); + } + printf("%llu\n", (unsigned long long)dp[C]); + free(dp); + free(nx); +} diff --git a/problems/039-calibration-multiple-choice-knapsack/solutions/cpp/main.cpp b/problems/039-calibration-multiple-choice-knapsack/solutions/cpp/main.cpp new file mode 100644 index 0000000..afa51b2 --- /dev/null +++ b/problems/039-calibration-multiple-choice-knapsack/solutions/cpp/main.cpp @@ -0,0 +1,27 @@ +#include +#include +#include +#include +#include +using namespace std; +int main() { + ios::sync_with_stdio(false); + cin.tie(nullptr); + int G, C; + if (!(cin >> G >> C)) + return 0; + vector dp(C + 1); + while (G--) { + int k; + cin >> k; + vector> a(k); + for (auto &[w, v] : a) + cin >> w >> v; + auto next = dp; + for (auto [w, v] : a) + for (int c = w; c <= C; c++) + next[c] = max(next[c], dp[c - w] + v); + dp.swap(next); + } + cout << dp[C] << '\n'; +} diff --git a/problems/039-calibration-multiple-choice-knapsack/solutions/go/main.go b/problems/039-calibration-multiple-choice-knapsack/solutions/go/main.go new file mode 100644 index 0000000..b568e05 --- /dev/null +++ b/problems/039-calibration-multiple-choice-knapsack/solutions/go/main.go @@ -0,0 +1,41 @@ +package main + +import ( + "bufio" + "fmt" + "os" +) + +type option struct { + w int + v uint64 +} + +func main() { + in := bufio.NewReader(os.Stdin) + out := bufio.NewWriter(os.Stdout) + defer out.Flush() + var g, C int + if _, e := fmt.Fscan(in, &g, &C); e != nil { + return + } + dp := make([]uint64, C+1) + for ; g > 0; g-- { + var k int + fmt.Fscan(in, &k) + a := make([]option, k) + for i := range a { + fmt.Fscan(in, &a[i].w, &a[i].v) + } + next := append([]uint64(nil), dp...) + for _, q := range a { + for c := q.w; c <= C; c++ { + if v := dp[c-q.w] + q.v; v > next[c] { + next[c] = v + } + } + } + dp = next + } + fmt.Fprintln(out, dp[C]) +} diff --git a/problems/039-calibration-multiple-choice-knapsack/solutions/javascript/main.js b/problems/039-calibration-multiple-choice-knapsack/solutions/javascript/main.js new file mode 100644 index 0000000..077b2ae --- /dev/null +++ b/problems/039-calibration-multiple-choice-knapsack/solutions/javascript/main.js @@ -0,0 +1,48 @@ +import * as std from "std"; + +const input = std.in.readAsString(); +let scan = 0; +function nextInt() { + while (scan < input.length && input.charCodeAt(scan) <= 32) scan++; + let value = 0; + while (scan < input.length) { + const digit = input.charCodeAt(scan) - 48; + if (digit < 0 || digit > 9) break; + value = value * 10 + digit; + scan++; + } + return value; +} +function nextBigInt() { + while (scan < input.length && input.charCodeAt(scan) <= 32) scan++; + const start = scan; + while (scan < input.length) { + const code = input.charCodeAt(scan); + if (code < 48 || code > 57) break; + scan++; + } + return BigInt(input.slice(start, scan)); +} + +const groupCount = nextInt(), capacity = nextInt(); +let dp = new BigUint64Array(capacity + 1), + next = new BigUint64Array(capacity + 1); +for (let group = 0; group < groupCount; group++) { + const optionCount = nextInt(), + times = new Int32Array(optionCount), + values = new BigUint64Array(optionCount); + for (let option = 0; option < optionCount; option++) { + times[option] = nextInt(); + values[option] = nextBigInt(); + } + next.set(dp); + for (let option = 0; option < optionCount; option++) { + const time = times[option], value = values[option]; + for (let current = time; current <= capacity; current++) { + const candidate = dp[current - time] + value; + if (candidate > next[current]) next[current] = candidate; + } + } + [dp, next] = [next, dp]; +} +std.out.puts(`${dp[capacity]}\n`); diff --git a/problems/039-calibration-multiple-choice-knapsack/solutions/python/main.py b/problems/039-calibration-multiple-choice-knapsack/solutions/python/main.py new file mode 100644 index 0000000..c279e3e --- /dev/null +++ b/problems/039-calibration-multiple-choice-knapsack/solutions/python/main.py @@ -0,0 +1,15 @@ +import sys + +t = list(map(int, sys.stdin.buffer.read().split())) +it = iter(t) +G, C = next(it), next(it) +dp = [0] * (C + 1) +for _ in range(G): + k = next(it) + a = [(next(it), next(it)) for _ in range(k)] + ndp = dp[:] + for w, v in a: + for c in range(w, C + 1): + ndp[c] = max(ndp[c], dp[c - w] + v) + dp = ndp +print(dp[C]) diff --git a/problems/039-calibration-multiple-choice-knapsack/solutions/rust/main.rs b/problems/039-calibration-multiple-choice-knapsack/solutions/rust/main.rs new file mode 100644 index 0000000..0519ac6 --- /dev/null +++ b/problems/039-calibration-multiple-choice-knapsack/solutions/rust/main.rs @@ -0,0 +1,27 @@ +use std::io::{self, Read}; +fn main() { + let mut s = String::new(); + io::stdin().read_to_string(&mut s).unwrap(); + let mut t = s.split_whitespace(); + let g: usize = t.next().unwrap().parse().unwrap(); + let cmax: usize = t.next().unwrap().parse().unwrap(); + let mut dp = vec![0u64; cmax + 1]; + for _ in 0..g { + let k: usize = t.next().unwrap().parse().unwrap(); + let mut a = Vec::with_capacity(k); + for _ in 0..k { + a.push(( + t.next().unwrap().parse::().unwrap(), + t.next().unwrap().parse::().unwrap(), + )); + } + let mut next = dp.clone(); + for (w, v) in a { + for c in w..=cmax { + next[c] = next[c].max(dp[c - w] + v); + } + } + dp = next; + } + println!("{}", dp[cmax]); +} diff --git a/problems/039-calibration-multiple-choice-knapsack/solutions/typescript/main.ts b/problems/039-calibration-multiple-choice-knapsack/solutions/typescript/main.ts new file mode 100644 index 0000000..164f324 --- /dev/null +++ b/problems/039-calibration-multiple-choice-knapsack/solutions/typescript/main.ts @@ -0,0 +1,48 @@ +import * as std from "std"; + +const input: string = std.in.readAsString(); +let scan = 0; +function nextInt(): number { + while (scan < input.length && input.charCodeAt(scan) <= 32) scan++; + let value = 0; + while (scan < input.length) { + const digit = input.charCodeAt(scan) - 48; + if (digit < 0 || digit > 9) break; + value = value * 10 + digit; + scan++; + } + return value; +} +function nextBigInt(): bigint { + while (scan < input.length && input.charCodeAt(scan) <= 32) scan++; + const start = scan; + while (scan < input.length) { + const code = input.charCodeAt(scan); + if (code < 48 || code > 57) break; + scan++; + } + return BigInt(input.slice(start, scan)); +} + +const groupCount = nextInt(), capacity = nextInt(); +let dp = new BigUint64Array(capacity + 1), + next = new BigUint64Array(capacity + 1); +for (let group = 0; group < groupCount; group++) { + const optionCount = nextInt(), + times = new Int32Array(optionCount), + values = new BigUint64Array(optionCount); + for (let option = 0; option < optionCount; option++) { + times[option] = nextInt(); + values[option] = nextBigInt(); + } + next.set(dp); + for (let option = 0; option < optionCount; option++) { + const time = times[option]!, value = values[option]!; + for (let current = time; current <= capacity; current++) { + const candidate = dp[current - time]! + value; + if (candidate > next[current]!) next[current] = candidate; + } + } + [dp, next] = [next, dp]; +} +std.out.puts(`${dp[capacity]}\n`); diff --git a/problems/039-calibration-multiple-choice-knapsack/statement.en.md b/problems/039-calibration-multiple-choice-knapsack/statement.en.md new file mode 100644 index 0000000..1abde63 --- /dev/null +++ b/problems/039-calibration-multiple-choice-knapsack/statement.en.md @@ -0,0 +1,89 @@ +# Calibration Experiment Scheduling + +While designing instruction-cost calibration for a WASM OJ, we needed to measure different language and toolchain profiles regularly. For one profile, we might run a fast plan that provides limited evidence or spend more time on a broader benchmark. These plans are alternative ways to perform the same calibration, so they cannot both be selected for one profile. + +Calibration time before a release is limited. We may skip some profiles and choose different measurement depths for others. Choices for different profiles do not exclude one another, but all experiments share the same total time limit. + +There are `G` calibration profiles. Profile `g` offers `K_g` mutually exclusive measurement plans, each with an execution time and a confidence value. At most one plan may be chosen from a profile, and a profile may be skipped entirely. + +Maximize total confidence subject to total time at most `C`. Plans are indivisible and cannot be repeated. The empty schedule is valid. Output only the maximum value. + +## Input + +The first line contains `G C`. Each profile is then given on one line: + +```text +K time1 value1 time2 value2 ... timeK valueK +``` + +## Output + +Output one line containing the maximum total confidence. + +## Constraints + +- `1 <= G <= 100` +- `0 <= C <= 100000` +- `1 <= K_g` +- `sum K_g <= 200` +- `0 <= time <= 100000` +- `0 <= value <= 10^12` +- The sum of all values is at most `9 * 10^18`. + +Even if two plans have identical time and value, they remain alternatives in the same profile and cannot both be selected. The full limits and the 64 MiB memory limit rule out combination enumeration and a complete `O(GC)` table. + +## Examples + + + +### Example One + +Input: + +```text +3 7 +2 2 4 4 8 +2 3 7 5 10 +1 2 5 +``` + +Output: + +```text +16 +``` + +### Example Two + +Input: + +```text +2 0 +3 0 5 0 7 1 100 +2 0 4 0 3 +``` + +Output: + +```text +11 +``` + +### Example Three + +Input: + +```text +3 5 +1 6 100 +1 5 9 +2 2 3 3 4 +``` + +Output: + +```text +9 +``` + + diff --git a/problems/039-calibration-multiple-choice-knapsack/statement.zh-TW.md b/problems/039-calibration-multiple-choice-knapsack/statement.zh-TW.md new file mode 100644 index 0000000..f8aa2ca --- /dev/null +++ b/problems/039-calibration-multiple-choice-knapsack/statement.zh-TW.md @@ -0,0 +1,88 @@ +# Calibration 實驗排程 + +在設計 WASM OJ 的 instruction cost calibration 時,我們需要定期測量不同語言與 toolchain profile。對同一個 profile,可以選擇快速但證據較少的測量方案,也可以投入更多時間執行較完整的 benchmark;這些方案代表同一次 calibration 的替代做法,不能同時採用。 + +發布前可用的校準時間有限,因此我們可能跳過某些 profile,也可能為不同 profile 選擇不同深度的測量。不同 profile 之間互不排斥,但所有實驗的執行時間必須共享同一個總上限。 + +共有 `G` 個 calibration profiles。Profile `g` 提供 `K_g` 種互斥測量方案,每個方案都有執行時間與可信度收益。同一個 profile 最多選擇一種方案,也可以完全跳過。 + +請在總時間上限 `C` 內,最大化所選方案的可信度總和。方案不可切割或重複,空排程合法;只需輸出最大值。 + +## 輸入 + +第一行 `G C`。接下來每個 profile 一行: + +```text +K time1 value1 time2 value2 ... timeK valueK +``` + +## 輸出 + +一行最大可信度總和。 + +## 限制 + +- `1 ≤ G ≤ 100` +- `0 ≤ C ≤ 100000` +- `1 ≤ K_g`,且 `ΣK_g ≤ 200` +- `0 ≤ time ≤ 100000` +- `0 ≤ value ≤ 10^12` +- 所有 value 加總不超過 `9×10^18` + +即使兩個方案的 time/value 相同,它們仍只是同一組中的替代品,不能同時選。完整限制與 64 MiB memory limit 排除組合列舉及完整 `O(GC)` table。 + +## 範例 + + + +### 範例一 + +輸入: + +```text +3 7 +2 2 4 4 8 +2 3 7 5 10 +1 2 5 +``` + +輸出: + +```text +16 +``` + +### 範例二 + +輸入: + +```text +2 0 +3 0 5 0 7 1 100 +2 0 4 0 3 +``` + +輸出: + +```text +11 +``` + +### 範例三 + +輸入: + +```text +3 5 +1 6 100 +1 5 9 +2 2 3 3 4 +``` + +輸出: + +```text +9 +``` + + diff --git a/problems/039-calibration-multiple-choice-knapsack/tests/adversarial-blind-01.in b/problems/039-calibration-multiple-choice-knapsack/tests/adversarial-blind-01.in new file mode 100644 index 0000000..5020a70 --- /dev/null +++ b/problems/039-calibration-multiple-choice-knapsack/tests/adversarial-blind-01.in @@ -0,0 +1,5 @@ +4 5 +3 0 5 0 7 5 20 +2 0 4 3 10 +2 2 8 5 30 +1 1 9 diff --git a/problems/039-calibration-multiple-choice-knapsack/tests/adversarial-blind-01.out b/problems/039-calibration-multiple-choice-knapsack/tests/adversarial-blind-01.out new file mode 100644 index 0000000..87523dd --- /dev/null +++ b/problems/039-calibration-multiple-choice-knapsack/tests/adversarial-blind-01.out @@ -0,0 +1 @@ +41 diff --git a/problems/039-calibration-multiple-choice-knapsack/tests/sample-01.in b/problems/039-calibration-multiple-choice-knapsack/tests/sample-01.in new file mode 100644 index 0000000..af17dc9 --- /dev/null +++ b/problems/039-calibration-multiple-choice-knapsack/tests/sample-01.in @@ -0,0 +1,4 @@ +3 7 +2 2 4 4 8 +2 3 7 5 10 +1 2 5 diff --git a/problems/039-calibration-multiple-choice-knapsack/tests/sample-01.out b/problems/039-calibration-multiple-choice-knapsack/tests/sample-01.out new file mode 100644 index 0000000..b6a7d89 --- /dev/null +++ b/problems/039-calibration-multiple-choice-knapsack/tests/sample-01.out @@ -0,0 +1 @@ +16 diff --git a/problems/039-calibration-multiple-choice-knapsack/tests/sample-02.in b/problems/039-calibration-multiple-choice-knapsack/tests/sample-02.in new file mode 100644 index 0000000..6e8aa3a --- /dev/null +++ b/problems/039-calibration-multiple-choice-knapsack/tests/sample-02.in @@ -0,0 +1,3 @@ +2 0 +3 0 5 0 7 1 100 +2 0 4 0 3 diff --git a/problems/039-calibration-multiple-choice-knapsack/tests/sample-02.out b/problems/039-calibration-multiple-choice-knapsack/tests/sample-02.out new file mode 100644 index 0000000..b4de394 --- /dev/null +++ b/problems/039-calibration-multiple-choice-knapsack/tests/sample-02.out @@ -0,0 +1 @@ +11 diff --git a/problems/039-calibration-multiple-choice-knapsack/tests/sample-03.in b/problems/039-calibration-multiple-choice-knapsack/tests/sample-03.in new file mode 100644 index 0000000..0632b2b --- /dev/null +++ b/problems/039-calibration-multiple-choice-knapsack/tests/sample-03.in @@ -0,0 +1,4 @@ +3 5 +1 6 100 +1 5 9 +2 2 3 3 4 diff --git a/problems/039-calibration-multiple-choice-knapsack/tests/sample-03.out b/problems/039-calibration-multiple-choice-knapsack/tests/sample-03.out new file mode 100644 index 0000000..ec63514 --- /dev/null +++ b/problems/039-calibration-multiple-choice-knapsack/tests/sample-03.out @@ -0,0 +1 @@ +9 diff --git a/problems/039-calibration-multiple-choice-knapsack/validator.py b/problems/039-calibration-multiple-choice-knapsack/validator.py new file mode 100644 index 0000000..afc74c4 --- /dev/null +++ b/problems/039-calibration-multiple-choice-knapsack/validator.py @@ -0,0 +1,33 @@ +import re, sys + + +def fail(): + raise SystemExit(1) + + +try: + t = sys.stdin.buffer.read().decode("utf-8").split() + p = 0 + + def u(a, b): + global p + if p >= len(t) or re.fullmatch(r"0|[1-9][0-9]*", t[p]) is None: + fail() + v = int(t[p]) + p += 1 + if not a <= v <= b: + fail() + return v + + G, C = u(1, 100), u(0, 100000) + count = total = 0 + for _ in range(G): + k = u(1, 200) + count += k + for _ in range(k): + u(0, 100000) + total += u(0, 10**12) + if count > 200 or total > 9 * 10**18 or p != len(t): + fail() +except (UnicodeDecodeError, ValueError, OverflowError): + fail() diff --git a/problems/040-dual-quota-output-knapsack/editorial.en.md b/problems/040-dual-quota-output-knapsack/editorial.en.md new file mode 100644 index 0000000..0b0ce9d --- /dev/null +++ b/problems/040-dual-quota-output-knapsack/editorial.en.md @@ -0,0 +1,34 @@ +# Editorial + +## Intuitive Approach + +Enumerating all bundle subsets takes `O(2^N N)` time. A three-dimensional table `dp[item][bytes][entries]` solves the problem in `O(NBI)` time but uses `O(NBI)` space, exceeding 64 MiB at the full limits. + +## Optimal Approach: Two-Dimensional 0/1 Knapsack + +Let `dp[e][b]` be the maximum value obtainable from the bundles processed so far using at most `e` entries and at most `b` bytes. For a bundle `(w, k, v)`, iterate `e` downward from `I` to `k` and `b` downward from `B` to `w`: + +```text +dp[e][b] = max(dp[e][b], dp[e - k][b - w] + v) +``` + +Both dimensions descend, so the source state belongs to the state before the current bundle was added. Each bundle is therefore used at most once. The answer is `dp[I][B]`. + +When the quota ranges are huge but reachable states are sparse, a Pareto frontier may be useful. Under this problem's explicit capacity bounds, dense DP provides a simpler deterministic worst-case bound. + +## Correctness Proof + +Induct on the number of processed bundles. Any optimal solution for quotas `(e, b)` either excludes the new bundle, preserving old `dp[e][b]`, or includes it. Removing it from the second case leaves a legal solution for `(e - k, b - w)`, whose best old value plus `v` is exactly the transition candidate. These cases are exhaustive and disjoint, so their maximum is correct. + +Descending iteration in both quota dimensions prevents the new bundle from appearing in a source state during the same iteration, preserving the 0/1 restriction even when `w = 0`. Thus final `dp[I][B]` is the maximum legal importance. + +## Complexity + +Time is `O(NBI)`, and space is `O(BI)`. + +## Common Mistakes + +- Solving only a one-dimensional bytes knapsack and ignoring the entry quota. +- Updating the entry dimension upward; with `bytes = 0`, this can reuse the same bundle in one iteration. Descend in both dimensions. +- Skipping zero-byte bundles even though they can have value and still consume entries. +- Optimizing the two quotas separately and intersecting the chosen sets, which need not be globally optimal. diff --git a/problems/040-dual-quota-output-knapsack/editorial.zh-TW.md b/problems/040-dual-quota-output-knapsack/editorial.zh-TW.md new file mode 100644 index 0000000..e9d7949 --- /dev/null +++ b/problems/040-dual-quota-output-knapsack/editorial.zh-TW.md @@ -0,0 +1,31 @@ +# 解題說明 + +## 直覺解法 + +列舉所有 bundle 子集合需 `O(2^N N)`。三維 `dp[item][bytes][entries]` 可在 `O(NBI)` 時間解出,但空間 `O(NBI)` 在完整限制下超過 64 MiB。 + +## 最佳解法 + +令 `dp[e][b]` 為目前看過的 bundle 中,在 entries 不超過 `e`、bytes 不超過 `b` 時的最大 value。處理 `(w,k,v)` 時,令 `e` 從 `I` 遞減至 `k`,並令 `b` 從 `B` 遞減至 `w`: + +```text +dp[e][b] = max(dp[e][b], dp[e-k][b-w] + v) +``` + +兩個維度都反向,右側必是加入本 bundle 前的狀態,所以每個 bundle 最多使用一次。答案為 `dp[I][B]`。當 B/I 很大但可達狀態稀疏時可維護 Pareto frontier;在本題明確的容量上限下,dense DP 有更好的確定性 worst-case bound。 + +## 正確性證明 + +以已處理 bundle 數歸納。新 bundle 的任何合法最優解要嘛不含它,保留舊 `dp[e][b]`;要嘛含它,移除後剩餘解必符合 `(e-k,b-w)`,最佳值為舊狀態加 `v`。轉移取兩類最大,涵蓋全部且不含非法解。反向迭代使同一輪的本 bundle 不會出現在來源狀態,因此保持 0/1 限制。最終狀態即兩 quota 內最大重要度。 + +## 複雜度 + +時間 `O(NBI)`,空間 `O(BI)`。 + +## 常見錯誤 + +- 只按 bytes 做一維背包,忽略 entries quota。 +- 讓 entries 維正向更新,尤其遇到 `bytes=0` 時會從本輪剛更新的狀態再次取用 + 同一 bundle。兩維都反向是最直接且不易出錯的寫法。 +- bytes 為零時跳過 item;它仍可能有價值並消耗 entries。 +- 分別求兩個 quota 下的最佳集合再取交集;這不保證全域最優。 diff --git a/problems/040-dual-quota-output-knapsack/generator.py b/problems/040-dual-quota-output-knapsack/generator.py new file mode 100644 index 0000000..b49aaf4 --- /dev/null +++ b/problems/040-dual-quota-output-knapsack/generator.py @@ -0,0 +1,12 @@ +import random, sys + +if len(sys.argv) != 3: + raise SystemExit("usage: generator.py SEED INDEX") +r = random.Random((int(sys.argv[1]) << 32) ^ int(sys.argv[2])) +idx = int(sys.argv[2]) +N = r.randint(1, min(18, 5 + idx % 14)) +B = r.randint(0, 35) +I = r.randint(0, 10) +print(N, B, I) +for _ in range(N): + print(r.randint(0, 40), r.randint(1, 12), r.randint(0, 100)) diff --git a/problems/040-dual-quota-output-knapsack/oracle.py b/problems/040-dual-quota-output-knapsack/oracle.py new file mode 100644 index 0000000..d78641a --- /dev/null +++ b/problems/040-dual-quota-output-knapsack/oracle.py @@ -0,0 +1,16 @@ +import sys + +t = list(map(int, sys.stdin.buffer.read().split())) +N, B, I = t[:3] +a = list(zip(t[3::3], t[4::3], t[5::3])) +best = 0 +for mask in range(1 << N): + b = e = v = 0 + for i, (x, y, z) in enumerate(a): + if mask >> i & 1: + b += x + e += y + v += z + if b <= B and e <= I: + best = max(best, v) +print(best) diff --git a/problems/040-dual-quota-output-knapsack/problem.json b/problems/040-dual-quota-output-knapsack/problem.json new file mode 100644 index 0000000..c6febc6 --- /dev/null +++ b/problems/040-dual-quota-output-knapsack/problem.json @@ -0,0 +1,155 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 40, + "slug": "dual-quota-output-knapsack", + "title": { + "zh-TW": "雙限制輸出蒐集", + "en": "Dual-Quota Output Collection" + }, + "difficulty": "hard", + "tags": [ + "dynamic-programming", + "two-dimensional-knapsack", + "quota" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-blind-01", + "kind": "adversarial", + "input": "tests/adversarial-blind-01.in", + "output": "tests/adversarial-blind-01.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 15000000, + "memoryLimitBytes": 134217728 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 1500000, + "memoryLimitBytes": 100663296 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 500000, + "memoryLimitBytes": 67108864 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "列舉輸出 bundle 子集合", + "en": "Enumerate output-bundle subsets" + }, + "time": "O(2^N N)", + "space": "O(N)", + "accepted": false + }, + { + "name": { + "zh-TW": "item × bytes × entries 三維 DP", + "en": "Three-dimensional item-by-bytes-by-entries DP" + }, + "time": "O(NBI)", + "space": "O(NBI)", + "accepted": false + }, + { + "name": { + "zh-TW": "反向更新的二維 0/1 背包", + "en": "Two-dimensional 0/1 knapsack with descending updates" + }, + "time": "O(NBI)", + "space": "O(BI)", + "accepted": true + } + ] +} diff --git a/problems/040-dual-quota-output-knapsack/solutions/c/main.c b/problems/040-dual-quota-output-knapsack/solutions/c/main.c new file mode 100644 index 0000000..9cc09da --- /dev/null +++ b/problems/040-dual-quota-output-knapsack/solutions/c/main.c @@ -0,0 +1,23 @@ +#include +#include +#include +int main(void) { + int n, B, I; + if (scanf("%d%d%d", &n, &B, &I) != 3) + return 0; + size_t w = (size_t)B + 1; + uint64_t *dp = calloc(((size_t)I + 1) * w, sizeof(*dp)); + while (n--) { + int b, e; + unsigned long long v; + scanf("%d%d%llu", &b, &e, &v); + for (int x = I; x >= e; x--) + for (int y = B; y >= b; y--) { + uint64_t q = dp[(size_t)(x - e) * w + y - b] + v; + if (q > dp[(size_t)x * w + y]) + dp[(size_t)x * w + y] = q; + } + } + printf("%llu\n", (unsigned long long)dp[(size_t)I * w + B]); + free(dp); +} diff --git a/problems/040-dual-quota-output-knapsack/solutions/cpp/main.cpp b/problems/040-dual-quota-output-knapsack/solutions/cpp/main.cpp new file mode 100644 index 0000000..b69c68e --- /dev/null +++ b/problems/040-dual-quota-output-knapsack/solutions/cpp/main.cpp @@ -0,0 +1,22 @@ +#include +#include +#include +#include +using namespace std; +int main() { + ios::sync_with_stdio(false); + cin.tie(nullptr); + int n, B, I; + if (!(cin >> n >> B >> I)) + return 0; + vector> dp(I + 1, vector(B + 1)); + while (n--) { + int b, e; + uint64_t v; + cin >> b >> e >> v; + for (int x = I; x >= e; x--) + for (int y = B; y >= b; y--) + dp[x][y] = max(dp[x][y], dp[x - e][y - b] + v); + } + cout << dp[I][B] << '\n'; +} diff --git a/problems/040-dual-quota-output-knapsack/solutions/go/main.go b/problems/040-dual-quota-output-knapsack/solutions/go/main.go new file mode 100644 index 0000000..14ef9eb --- /dev/null +++ b/problems/040-dual-quota-output-knapsack/solutions/go/main.go @@ -0,0 +1,34 @@ +package main + +import ( + "bufio" + "fmt" + "os" +) + +func main() { + in := bufio.NewReader(os.Stdin) + out := bufio.NewWriter(os.Stdout) + defer out.Flush() + var n, B, I int + if _, e := fmt.Fscan(in, &n, &B, &I); e != nil { + return + } + dp := make([][]uint64, I+1) + for i := range dp { + dp[i] = make([]uint64, B+1) + } + for ; n > 0; n-- { + var b, e int + var v uint64 + fmt.Fscan(in, &b, &e, &v) + for x := I; x >= e; x-- { + for y := B; y >= b; y-- { + if q := dp[x-e][y-b] + v; q > dp[x][y] { + dp[x][y] = q + } + } + } + } + fmt.Fprintln(out, dp[I][B]) +} diff --git a/problems/040-dual-quota-output-knapsack/solutions/javascript/main.js b/problems/040-dual-quota-output-knapsack/solutions/javascript/main.js new file mode 100644 index 0000000..535929c --- /dev/null +++ b/problems/040-dual-quota-output-knapsack/solutions/javascript/main.js @@ -0,0 +1,48 @@ +import * as std from "std"; + +const input = std.in.readAsString(); +let scan = 0; +function nextInt() { + while (scan < input.length && input.charCodeAt(scan) <= 32) scan++; + let value = 0; + while (scan < input.length) { + const digit = input.charCodeAt(scan) - 48; + if (digit < 0 || digit > 9) break; + value = value * 10 + digit; + scan++; + } + return value; +} +function nextBigInt() { + while (scan < input.length && input.charCodeAt(scan) <= 32) scan++; + const start = scan; + while (scan < input.length) { + const code = input.charCodeAt(scan); + if (code < 48 || code > 57) break; + scan++; + } + return BigInt(input.slice(start, scan)); +} + +const bundleCount = nextInt(), + byteLimit = nextInt(), + entryLimit = nextInt(), + width = byteLimit + 1, + dp = new BigUint64Array((entryLimit + 1) * width); +for (let bundle = 0; bundle < bundleCount; bundle++) { + const bytes = nextInt(), entries = nextInt(), value = nextBigInt(); + for ( + let currentEntries = entryLimit; + currentEntries >= entries; + currentEntries-- + ) { + const row = currentEntries * width, + previous = (currentEntries - entries) * width; + for (let currentBytes = byteLimit; currentBytes >= bytes; currentBytes--) { + const index = row + currentBytes, + candidate = dp[previous + currentBytes - bytes] + value; + if (candidate > dp[index]) dp[index] = candidate; + } + } +} +std.out.puts(`${dp[entryLimit * width + byteLimit]}\n`); diff --git a/problems/040-dual-quota-output-knapsack/solutions/python/main.py b/problems/040-dual-quota-output-knapsack/solutions/python/main.py new file mode 100644 index 0000000..8f8bbf9 --- /dev/null +++ b/problems/040-dual-quota-output-knapsack/solutions/python/main.py @@ -0,0 +1,13 @@ +import sys + +t = list(map(int, sys.stdin.buffer.read().split())) +it = iter(t) +N, B, I = next(it), next(it), next(it) +dp = [[0] * (B + 1) for _ in range(I + 1)] +for _ in range(N): + b, e, v = next(it), next(it), next(it) + for x in range(I, e - 1, -1): + row, old = dp[x], dp[x - e] + for y in range(B, b - 1, -1): + row[y] = max(row[y], old[y - b] + v) +print(dp[I][B]) diff --git a/problems/040-dual-quota-output-knapsack/solutions/rust/main.rs b/problems/040-dual-quota-output-knapsack/solutions/rust/main.rs new file mode 100644 index 0000000..db7dde9 --- /dev/null +++ b/problems/040-dual-quota-output-knapsack/solutions/rust/main.rs @@ -0,0 +1,21 @@ +use std::io::{self, Read}; +fn main() { + let mut s = String::new(); + io::stdin().read_to_string(&mut s).unwrap(); + let mut t = s.split_whitespace(); + let n: usize = t.next().unwrap().parse().unwrap(); + let bmax: usize = t.next().unwrap().parse().unwrap(); + let imax: usize = t.next().unwrap().parse().unwrap(); + let mut dp = vec![vec![0u64; bmax + 1]; imax + 1]; + for _ in 0..n { + let b: usize = t.next().unwrap().parse().unwrap(); + let e: usize = t.next().unwrap().parse().unwrap(); + let v: u64 = t.next().unwrap().parse().unwrap(); + for x in (e..=imax).rev() { + for y in (b..=bmax).rev() { + dp[x][y] = dp[x][y].max(dp[x - e][y - b] + v); + } + } + } + println!("{}", dp[imax][bmax]); +} diff --git a/problems/040-dual-quota-output-knapsack/solutions/typescript/main.ts b/problems/040-dual-quota-output-knapsack/solutions/typescript/main.ts new file mode 100644 index 0000000..c3a44f3 --- /dev/null +++ b/problems/040-dual-quota-output-knapsack/solutions/typescript/main.ts @@ -0,0 +1,48 @@ +import * as std from "std"; + +const input: string = std.in.readAsString(); +let scan = 0; +function nextInt(): number { + while (scan < input.length && input.charCodeAt(scan) <= 32) scan++; + let value = 0; + while (scan < input.length) { + const digit = input.charCodeAt(scan) - 48; + if (digit < 0 || digit > 9) break; + value = value * 10 + digit; + scan++; + } + return value; +} +function nextBigInt(): bigint { + while (scan < input.length && input.charCodeAt(scan) <= 32) scan++; + const start = scan; + while (scan < input.length) { + const code = input.charCodeAt(scan); + if (code < 48 || code > 57) break; + scan++; + } + return BigInt(input.slice(start, scan)); +} + +const bundleCount = nextInt(), + byteLimit = nextInt(), + entryLimit = nextInt(), + width = byteLimit + 1, + dp = new BigUint64Array((entryLimit + 1) * width); +for (let bundle = 0; bundle < bundleCount; bundle++) { + const bytes = nextInt(), entries = nextInt(), value = nextBigInt(); + for ( + let currentEntries = entryLimit; + currentEntries >= entries; + currentEntries-- + ) { + const row = currentEntries * width, + previous = (currentEntries - entries) * width; + for (let currentBytes = byteLimit; currentBytes >= bytes; currentBytes--) { + const index = row + currentBytes, + candidate = dp[previous + currentBytes - bytes]! + value; + if (candidate > dp[index]!) dp[index] = candidate; + } + } +} +std.out.puts(`${dp[entryLimit * width + byteLimit]}\n`); diff --git a/problems/040-dual-quota-output-knapsack/statement.en.md b/problems/040-dual-quota-output-knapsack/statement.en.md new file mode 100644 index 0000000..8743fb7 --- /dev/null +++ b/problems/040-dual-quota-output-knapsack/statement.en.md @@ -0,0 +1,90 @@ +# Dual-Quota Output Collection + +While designing failure diagnostics for a WASM OJ, we wanted to retain stdout, error logs, coverage data, and other outputs that help users understand why a submission failed. Output stored in the browser is constrained in two ways: file contents must stay within a shared byte quota, and the number of virtual-file-system entries must also remain bounded. + +One submission may produce several optional diagnostic bundles. Each bundle has its own space requirement, entry count, and diagnostic importance. A bundle is useful only when retained in full, so it cannot be partially selected. + +There are `N` optional bundles. Bundle `i` consumes `bytes_i` bytes of shared output space and `entries_i` VFS entries, and has diagnostic importance `value_i`. Each bundle is indivisible and cannot be selected more than once. + +The system permits at most `B` bytes and `I` entries. Choose any subset that stays within both quotas and maximizes total importance. The empty subset is valid. Output only the maximum importance, not the subset. + +## Input + +The first line contains `N B I`. Each of the next `N` lines contains `bytes_i entries_i value_i`. + +## Output + +Output one line containing the maximum total importance. + +## Constraints + +- `1 <= N <= 100` +- `0 <= B <= 3000` +- `0 <= I <= 30` +- `0 <= bytes_i <= 3000` +- `1 <= entries_i <= 30` +- `0 <= value_i <= 10^12` +- The sum of all values is at most `9 * 10^18`. + +An empty bundle with zero bytes still consumes at least one entry. The full limits and the 64 MiB memory limit rule out subset enumeration and a full three-dimensional table retaining the item dimension. + +## Examples + + + +### Example One + +Input: + +```text +4 7 3 +4 1 8 +3 2 7 +2 1 5 +5 3 20 +``` + +Output: + +```text +20 +``` + +### Example Two + +Input: + +```text +4 0 2 +0 1 5 +0 1 7 +0 2 9 +1 1 100 +``` + +Output: + +```text +12 +``` + +### Example Three + +Input: + +```text +5 10 4 +6 2 12 +4 2 9 +5 1 10 +3 3 8 +10 4 25 +``` + +Output: + +```text +25 +``` + + diff --git a/problems/040-dual-quota-output-knapsack/statement.zh-TW.md b/problems/040-dual-quota-output-knapsack/statement.zh-TW.md new file mode 100644 index 0000000..3448d72 --- /dev/null +++ b/problems/040-dual-quota-output-knapsack/statement.zh-TW.md @@ -0,0 +1,90 @@ +# 雙限制輸出蒐集 + +在設計 WASM OJ 的失敗診斷功能時,我們希望保存 stdout、錯誤紀錄、coverage 資料與其他輸出,協助使用者理解 submission 為什麼失敗。然而瀏覽器內的輸出空間同時受到兩種限制:檔案內容不能超過共享 byte quota,虛擬檔案系統中的 entry 數量也不能無限制增加。 + +一次 submission 可能產生多個可選的診斷 bundles。每個 bundle 都有自己的空間需求、entry 數量與診斷重要度,而且必須完整保留才有意義,不能只保存其中一部分。 + +共有 `N` 個可選 bundle。Bundle `i` 會消耗 `bytes_i` bytes 的共享輸出空間及 `entries_i` 個 VFS entries,並帶來 `value_i` 的診斷重要度。每個 bundle 不可拆分,也不可重複選擇。 + +系統最多允許 `B` bytes 與 `I` entries。請選擇任意子集合,在兩種 quota 都不超限時最大化總重要度。空集合合法;只需輸出最大重要度,不需輸出集合。 + +## 輸入 + +第一行 `N B I`。接下來 `N` 行各為 `bytes_i entries_i value_i`。 + +## 輸出 + +一行最大重要度總和。 + +## 限制 + +- `1 ≤ N ≤ 100` +- `0 ≤ B ≤ 3000` +- `0 ≤ I ≤ 30` +- `0 ≤ bytes_i ≤ 3000` +- `1 ≤ entries_i ≤ 30` +- `0 ≤ value_i ≤ 10^12` +- 所有 value 總和不超過 `9×10^18` + +bytes 為零的空 bundle 仍消耗至少一個 entry。完整限制與 64 MiB memory limit 排除子集合列舉與保留 item 維度的完整三維 table。 + +## 範例 + + + +### 範例一 + +輸入: + +```text +4 7 3 +4 1 8 +3 2 7 +2 1 5 +5 3 20 +``` + +輸出: + +```text +20 +``` + +### 範例二 + +輸入: + +```text +4 0 2 +0 1 5 +0 1 7 +0 2 9 +1 1 100 +``` + +輸出: + +```text +12 +``` + +### 範例三 + +輸入: + +```text +5 10 4 +6 2 12 +4 2 9 +5 1 10 +3 3 8 +10 4 25 +``` + +輸出: + +```text +25 +``` + + diff --git a/problems/040-dual-quota-output-knapsack/tests/adversarial-blind-01.in b/problems/040-dual-quota-output-knapsack/tests/adversarial-blind-01.in new file mode 100644 index 0000000..11cfc36 --- /dev/null +++ b/problems/040-dual-quota-output-knapsack/tests/adversarial-blind-01.in @@ -0,0 +1,7 @@ +6 7 4 +0 1 5 +0 1 10 +4 2 12 +3 2 11 +7 4 30 +8 1 100 diff --git a/problems/040-dual-quota-output-knapsack/tests/adversarial-blind-01.out b/problems/040-dual-quota-output-knapsack/tests/adversarial-blind-01.out new file mode 100644 index 0000000..64bb6b7 --- /dev/null +++ b/problems/040-dual-quota-output-knapsack/tests/adversarial-blind-01.out @@ -0,0 +1 @@ +30 diff --git a/problems/040-dual-quota-output-knapsack/tests/sample-01.in b/problems/040-dual-quota-output-knapsack/tests/sample-01.in new file mode 100644 index 0000000..16df59f --- /dev/null +++ b/problems/040-dual-quota-output-knapsack/tests/sample-01.in @@ -0,0 +1,5 @@ +4 7 3 +4 1 8 +3 2 7 +2 1 5 +5 3 20 diff --git a/problems/040-dual-quota-output-knapsack/tests/sample-01.out b/problems/040-dual-quota-output-knapsack/tests/sample-01.out new file mode 100644 index 0000000..209e3ef --- /dev/null +++ b/problems/040-dual-quota-output-knapsack/tests/sample-01.out @@ -0,0 +1 @@ +20 diff --git a/problems/040-dual-quota-output-knapsack/tests/sample-02.in b/problems/040-dual-quota-output-knapsack/tests/sample-02.in new file mode 100644 index 0000000..3b5efcc --- /dev/null +++ b/problems/040-dual-quota-output-knapsack/tests/sample-02.in @@ -0,0 +1,5 @@ +4 0 2 +0 1 5 +0 1 7 +0 2 9 +1 1 100 diff --git a/problems/040-dual-quota-output-knapsack/tests/sample-02.out b/problems/040-dual-quota-output-knapsack/tests/sample-02.out new file mode 100644 index 0000000..48082f7 --- /dev/null +++ b/problems/040-dual-quota-output-knapsack/tests/sample-02.out @@ -0,0 +1 @@ +12 diff --git a/problems/040-dual-quota-output-knapsack/tests/sample-03.in b/problems/040-dual-quota-output-knapsack/tests/sample-03.in new file mode 100644 index 0000000..278588e --- /dev/null +++ b/problems/040-dual-quota-output-knapsack/tests/sample-03.in @@ -0,0 +1,6 @@ +5 10 4 +6 2 12 +4 2 9 +5 1 10 +3 3 8 +10 4 25 diff --git a/problems/040-dual-quota-output-knapsack/tests/sample-03.out b/problems/040-dual-quota-output-knapsack/tests/sample-03.out new file mode 100644 index 0000000..7273c0f --- /dev/null +++ b/problems/040-dual-quota-output-knapsack/tests/sample-03.out @@ -0,0 +1 @@ +25 diff --git a/problems/040-dual-quota-output-knapsack/validator.py b/problems/040-dual-quota-output-knapsack/validator.py new file mode 100644 index 0000000..647a671 --- /dev/null +++ b/problems/040-dual-quota-output-knapsack/validator.py @@ -0,0 +1,31 @@ +import re, sys + + +def fail(): + raise SystemExit(1) + + +try: + t = sys.stdin.buffer.read().decode("utf-8").split() + p = 0 + + def u(a, b): + global p + if p >= len(t) or re.fullmatch(r"0|[1-9][0-9]*", t[p]) is None: + fail() + v = int(t[p]) + p += 1 + if not a <= v <= b: + fail() + return v + + N, B, I = u(1, 100), u(0, 3000), u(0, 30) + total = 0 + for _ in range(N): + u(0, 3000) + u(1, 30) + total += u(0, 10**12) + if total > 9 * 10**18 or p != len(t): + fail() +except (UnicodeDecodeError, ValueError, OverflowError): + fail() diff --git a/problems/041-progressive-cost-budget/editorial.en.md b/problems/041-progressive-cost-budget/editorial.en.md new file mode 100644 index 0000000..0468cf2 --- /dev/null +++ b/problems/041-progressive-cost-budget/editorial.en.md @@ -0,0 +1,45 @@ +# Editorial + +## Intuitive Approach: Restart Every Scan + +For each budget, start at the first stage and accumulate costs until the next stage would exceed the budget. One query can inspect all `N` stages, so the total time is `O(NQ)`. Because the budgets appear after the costs in the input, retaining the costs takes `O(N)` space. This directly follows the definition, but it cannot finish when `N,Q=200000`. + +## Efficient Approach: Prefix Sums and Binary Search + +Build a prefix-sum array: + +```text +prefix[0] = 0 +prefix[k] = cost_1 + cost_2 + ... + cost_k +``` + +All costs are nonnegative, so `prefix` is nondecreasing. For a budget `B`, find the last position in `prefix` whose value is at most `B`; that position is the answer. Use upper bound—the first value greater than `B`—rather than an arbitrary matching position. Zero-cost stages can create equal prefix sums, and stopping at an earlier equal value would miss stages that are free to complete. + +Building the array takes `O(N)`. Each binary search takes `O(log N)`, for `O(N+Q log N)` total time and `O(N)` auxiliary space. + +## Optimal Approach: Two Pointers over Monotone Budgets + +The budgets are nondecreasing, so the answer for one query can never shrink for the next query. Maintain: + +- `completed`, the number of stages currently completed; +- `spent`, the total cost of those stages. + +For the current budget `B`, repeatedly complete the next stage while it exists and `cost[completed] <= B - spent`. Comparing with the remaining budget avoids a potentially overflowing `spent + cost` expression. Output `completed` when the loop stops. + +## Correctness Proof + +Before each budget is processed, maintain the invariant that `completed` is the maximum prefix allowed by the previous budget and `spent` is exactly that prefix's cost. + +The current budget is no smaller than the previous one, so the existing prefix remains valid. Every loop iteration adds the next stage only when it is affordable, hence the enlarged prefix remains valid; zero-cost stages are covered by the same test. The loop stops only after every stage is complete or when the next stage would exceed the current budget. In the latter case, no longer prefix can be valid because stages cannot be skipped. Therefore `completed` is exactly the maximum valid answer for the current budget, and the invariant holds for the next query. By induction, every reported answer is correct. + +## Complexity + +Every budget is handled once, and `completed` advances from `0` to `N` at most once over the whole algorithm. Total time is `O(N+Q)`, and storing the stage costs takes `O(N)` auxiliary space. Some reference implementations buffer `Q` output lines to reduce output calls, making their resident space `O(N+Q)`. + +## Common Mistakes + +- Resetting the stage pointer for each budget, which degrades to `O(NQ)`. +- Failing to advance over zero-cost stages. +- Using lower bound in the binary-search approach and missing later equal prefix sums. +- Assuming budgets are strictly increasing; adjacent budgets may be equal. +- Using 32-bit integers, or imprecise JavaScript/TypeScript `number` values. diff --git a/problems/041-progressive-cost-budget/editorial.zh-TW.md b/problems/041-progressive-cost-budget/editorial.zh-TW.md new file mode 100644 index 0000000..ae60614 --- /dev/null +++ b/problems/041-progressive-cost-budget/editorial.zh-TW.md @@ -0,0 +1,45 @@ +# 解題說明 + +## 直覺解法:每次重新掃描 + +對每個 budget 都從第一個 stage 開始累加,直到下一個 stage 會超出 budget。單一查詢最多檢查 `N` 個 stage,總時間為 `O(NQ)`;由於讀完 cost 後才會讀到 budget,必須保留 `N` 個成本,空間為 `O(N)`。這個方法直接反映題意,但在 `N,Q=200000` 時無法完成。 + +## 進階解法:前綴和與二分搜尋 + +建立前綴和陣列: + +```text +prefix[0] = 0 +prefix[k] = cost_1 + cost_2 + ... + cost_k +``` + +因為成本皆非負,`prefix` 不遞減。對 budget `B`,在 `prefix` 中尋找最後一個 `<= B` 的位置,其索引就是答案。必須使用 upper bound(第一個 `> B` 的位置),而不是只找任意一個等於 `B` 的元素,否則零成本 stage 造成的重複前綴和會讓答案太小。 + +建表花費 `O(N)`,每個查詢二分搜尋花費 `O(log N)`,總時間為 `O(N+Q log N)`,輔助空間為 `O(N)`。 + +## 最佳解法:利用單調 budget 的雙指標 + +budget 已保證不遞減,因此前一個答案不可能在下一次查詢時縮短。維護: + +- `completed`:目前已完成的 stage 數量; +- `spent`:這些 stage 的總成本。 + +處理 budget `B` 時,只要還有下一個 stage,且 `cost[completed] <= B - spent`,就完成該 stage 並更新兩個狀態。使用減法形式的比較,可以避免先計算 `spent + cost` 所可能造成的整數溢位。當迴圈停止時輸出 `completed`。 + +## 正確性證明 + +在處理每個 budget 前,維持以下不變量:`completed` 是先前 budget 可完成的最大 stage 數,且 `spent` 正好是這段前綴的成本。 + +目前 budget 不小於先前 budget,所以既有前綴仍合法。迴圈每次只在下一個 stage 的成本仍可支付時將它加入,因此加入後的前綴合法;這也包含成本為零的 stage。迴圈停止只可能是全部 stage 都已完成,或下一個 stage 會使成本超過目前 budget。由於 stage 不可跳過,後一種情況下任何更長前綴都不合法。因此輸出的 `completed` 正是目前 budget 的最大合法答案,不變量也對下一次查詢成立。依數學歸納法,所有答案皆正確。 + +## 複雜度 + +每個 budget 處理一次,而 `completed` 在整個演算法中只會從 `0` 增加到 `N`,所以總時間為 `O(N+Q)`。儲存 stage 成本需要 `O(N)` 輔助空間。部分 reference 為了減少輸出呼叫會額外緩衝 `Q` 個答案,因此這些實作的 resident 空間為 `O(N+Q)`。 + +## 常見錯誤 + +- 對每個 budget 都把 stage 指標重設為零,退化成 `O(NQ)`。 +- 遇到成本為零的 stage 時沒有繼續前進。 +- 二分搜尋使用 lower bound,漏掉具有相同前綴和的後續 stage。 +- 假設 budget 嚴格遞增;相等的相鄰 budget 也是合法輸入。 +- 使用 32-bit 整數,或在 JavaScript/TypeScript 使用不精確的 `number`。 diff --git a/problems/041-progressive-cost-budget/generator.py b/problems/041-progressive-cost-budget/generator.py new file mode 100644 index 0000000..6813982 --- /dev/null +++ b/problems/041-progressive-cost-budget/generator.py @@ -0,0 +1,48 @@ +import random +import sys + + +if len(sys.argv) != 3: + raise SystemExit("usage: generator.py SEED INDEX") + +seed = int(sys.argv[1]) +index = int(sys.argv[2]) +if index == 999_999: + n = q = 200_000 + costs = [999_999_999_999] * 10_001 + [0] * 189_999 + total = sum(costs) + print(n, q) + for offset in range(0, n, 1_000): + print(*costs[offset : offset + 1_000]) + budgets = [total] * q + for offset in range(0, q, 1_000): + print(*budgets[offset : offset + 1_000]) + raise SystemExit(0) + +randomizer = random.Random((seed << 32) ^ index) +n = randomizer.randint(1, min(80, 8 + index % 73)) +q = randomizer.randint(1, min(80, 8 + (index * 7) % 73)) + +costs = [] +for stage in range(n): + selector = randomizer.randrange(8) + if selector < 2: + costs.append(0) + elif selector == 2: + costs.append(10**12 - randomizer.randrange(1000)) + else: + costs.append(randomizer.randrange(1, 10001)) + +total = sum(costs) +budgets = [randomizer.randrange(total + 10001) for _ in range(q)] +if q >= 1: + budgets[0] = 0 +if q >= 2: + budgets[1] = total +if q >= 3: + budgets[2] = max(0, total - 1) +budgets.sort() + +print(n, q) +print(*costs) +print(*budgets) diff --git a/problems/041-progressive-cost-budget/oracle.py b/problems/041-progressive-cost-budget/oracle.py new file mode 100644 index 0000000..602b249 --- /dev/null +++ b/problems/041-progressive-cost-budget/oracle.py @@ -0,0 +1,15 @@ +from bisect import bisect_right +import sys + + +values = list(map(int, sys.stdin.buffer.read().split())) +n, q = values[:2] +costs = values[2:2 + n] +budgets = values[2 + n:2 + n + q] + +prefix = [0] +for cost in costs: + prefix.append(prefix[-1] + cost) + +answers = (str(bisect_right(prefix, budget) - 1) for budget in budgets) +sys.stdout.write("\n".join(answers) + "\n") diff --git a/problems/041-progressive-cost-budget/problem.json b/problems/041-progressive-cost-budget/problem.json new file mode 100644 index 0000000..e1e25a1 --- /dev/null +++ b/problems/041-progressive-cost-budget/problem.json @@ -0,0 +1,155 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 41, + "slug": "progressive-cost-budget", + "title": { + "zh-TW": "逐步放寬的 Cost Budget", + "en": "Progressive Cost Budget" + }, + "difficulty": "easy", + "tags": [ + "prefix-sum", + "binary-search", + "two-pointers" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-blind-01", + "kind": "adversarial", + "input": "tests/adversarial-blind-01.in", + "output": "tests/adversarial-blind-01.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 30000000000, + "memoryLimitBytes": 134217728 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 30000000000, + "memoryLimitBytes": 100663296 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 15000000000, + "memoryLimitBytes": 67108864 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "每個 budget 重新掃描", + "en": "Restart the scan for every budget" + }, + "time": "O(NQ)", + "space": "O(N)", + "accepted": false + }, + { + "name": { + "zh-TW": "前綴和搭配二分搜尋", + "en": "Prefix sums with binary search" + }, + "time": "O(N + Q log N)", + "space": "O(N)", + "accepted": true + }, + { + "name": { + "zh-TW": "利用單調 budget 的雙指標", + "en": "Two pointers over monotone budgets" + }, + "time": "O(N + Q)", + "space": "O(N + Q)", + "accepted": true + } + ] +} diff --git a/problems/041-progressive-cost-budget/solutions/c/main.c b/problems/041-progressive-cost-budget/solutions/c/main.c new file mode 100644 index 0000000..2764c98 --- /dev/null +++ b/problems/041-progressive-cost-budget/solutions/c/main.c @@ -0,0 +1,34 @@ +#include +#include +#include +#include + +int main(void) { + size_t n, q; + if (scanf("%zu %zu", &n, &q) != 2) { + return 0; + } + + uint64_t *costs = malloc(n * sizeof(*costs)); + if (costs == NULL) { + return 1; + } + for (size_t i = 0; i < n; ++i) { + scanf("%" SCNu64, &costs[i]); + } + + size_t completed = 0; + uint64_t spent = 0; + for (size_t query = 0; query < q; ++query) { + uint64_t budget; + scanf("%" SCNu64, &budget); + while (completed < n && costs[completed] <= budget - spent) { + spent += costs[completed]; + ++completed; + } + printf("%zu\n", completed); + } + + free(costs); + return 0; +} diff --git a/problems/041-progressive-cost-budget/solutions/cpp/main.cpp b/problems/041-progressive-cost-budget/solutions/cpp/main.cpp new file mode 100644 index 0000000..331b9bc --- /dev/null +++ b/problems/041-progressive-cost-budget/solutions/cpp/main.cpp @@ -0,0 +1,26 @@ +#include +#include +#include + +int main() { + std::ios::sync_with_stdio(false); + std::cin.tie(nullptr); + + std::size_t n, q; + std::cin >> n >> q; + std::vector costs(n); + for (auto &cost : costs) { + std::cin >> cost; + } + + std::size_t completed = 0; + std::uint64_t spent = 0; + for (std::size_t query = 0; query < q; ++query) { + std::uint64_t budget; + std::cin >> budget; + while (completed < n && costs[completed] <= budget - spent) { + spent += costs[completed++]; + } + std::cout << completed << '\n'; + } +} diff --git a/problems/041-progressive-cost-budget/solutions/go/main.go b/problems/041-progressive-cost-budget/solutions/go/main.go new file mode 100644 index 0000000..541a397 --- /dev/null +++ b/problems/041-progressive-cost-budget/solutions/go/main.go @@ -0,0 +1,32 @@ +package main + +import ( + "bufio" + "fmt" + "os" +) + +func main() { + in := bufio.NewReaderSize(os.Stdin, 1<<20) + out := bufio.NewWriterSize(os.Stdout, 1<<20) + defer out.Flush() + + var n, q int + fmt.Fscan(in, &n, &q) + costs := make([]uint64, n) + for index := range costs { + fmt.Fscan(in, &costs[index]) + } + + completed := 0 + var spent uint64 + for query := 0; query < q; query++ { + var budget uint64 + fmt.Fscan(in, &budget) + for completed < n && costs[completed] <= budget-spent { + spent += costs[completed] + completed++ + } + fmt.Fprintln(out, completed) + } +} diff --git a/problems/041-progressive-cost-budget/solutions/javascript/main.js b/problems/041-progressive-cost-budget/solutions/javascript/main.js new file mode 100644 index 0000000..a8701d5 --- /dev/null +++ b/problems/041-progressive-cost-budget/solutions/javascript/main.js @@ -0,0 +1,20 @@ +import * as std from "std"; + +const tokens = std.in.readAsString().trim().split(/\s+/); +let position = 0; +const n = Number(tokens[position++]); +const q = Number(tokens[position++]); +const costs = Array.from({ length: n }, () => BigInt(tokens[position++])); + +let completed = 0; +let spent = 0n; +const answers = []; +for (let query = 0; query < q; query++) { + const budget = BigInt(tokens[position++]); + while (completed < n && costs[completed] <= budget - spent) { + spent += costs[completed++]; + } + answers.push(String(completed)); +} + +std.out.puts(answers.join("\n") + "\n"); diff --git a/problems/041-progressive-cost-budget/solutions/python/main.py b/problems/041-progressive-cost-budget/solutions/python/main.py new file mode 100644 index 0000000..a693e38 --- /dev/null +++ b/problems/041-progressive-cost-budget/solutions/python/main.py @@ -0,0 +1,18 @@ +import sys + + +values = list(map(int, sys.stdin.buffer.read().split())) +n, q = values[:2] +costs = values[2:2 + n] +budgets = values[2 + n:2 + n + q] + +completed = 0 +spent = 0 +answers = [] +for budget in budgets: + while completed < n and costs[completed] <= budget - spent: + spent += costs[completed] + completed += 1 + answers.append(str(completed)) + +sys.stdout.write("\n".join(answers) + "\n") diff --git a/problems/041-progressive-cost-budget/solutions/rust/main.rs b/problems/041-progressive-cost-budget/solutions/rust/main.rs new file mode 100644 index 0000000..6c6c287 --- /dev/null +++ b/problems/041-progressive-cost-budget/solutions/rust/main.rs @@ -0,0 +1,26 @@ +use std::io::{self, Read}; + +fn main() { + let mut input = String::new(); + io::stdin().read_to_string(&mut input).unwrap(); + let mut tokens = input.split_whitespace(); + let n: usize = tokens.next().unwrap().parse().unwrap(); + let q: usize = tokens.next().unwrap().parse().unwrap(); + let costs: Vec = (0..n) + .map(|_| tokens.next().unwrap().parse().unwrap()) + .collect(); + + let mut completed = 0usize; + let mut spent = 0u64; + let mut output = String::new(); + for _ in 0..q { + let budget: u64 = tokens.next().unwrap().parse().unwrap(); + while completed < n && costs[completed] <= budget - spent { + spent += costs[completed]; + completed += 1; + } + output.push_str(&completed.to_string()); + output.push('\n'); + } + print!("{output}"); +} diff --git a/problems/041-progressive-cost-budget/solutions/typescript/main.ts b/problems/041-progressive-cost-budget/solutions/typescript/main.ts new file mode 100644 index 0000000..a781054 --- /dev/null +++ b/problems/041-progressive-cost-budget/solutions/typescript/main.ts @@ -0,0 +1,20 @@ +import * as std from "std"; + +const tokens: string[] = std.in.readAsString().trim().split(/\s+/); +let position = 0; +const n = Number(tokens[position++]); +const q = Number(tokens[position++]); +const costs: bigint[] = Array.from({ length: n }, () => BigInt(tokens[position++])); + +let completed = 0; +let spent = 0n; +const answers: string[] = []; +for (let query = 0; query < q; query++) { + const budget = BigInt(tokens[position++]); + while (completed < n && costs[completed] <= budget - spent) { + spent += costs[completed++]; + } + answers.push(String(completed)); +} + +std.out.puts(answers.join("\n") + "\n"); diff --git a/problems/041-progressive-cost-budget/statement.en.md b/problems/041-progressive-cost-budget/statement.en.md new file mode 100644 index 0000000..159d075 --- /dev/null +++ b/problems/041-progressive-cost-budget/statement.en.md @@ -0,0 +1,100 @@ +# Progressive Cost Budget + +While designing a WASM OJ, we needed to limit how much computation a user program could consume. Relying only on wall-clock time was not ideal: the same program can produce very different timings across browsers, devices, and system loads. We therefore record instruction cost during WebAssembly execution, making resource limits more stable and reproducible. + +A complete judging workflow is divided into `N` stages that run in order. Stage `i` costs `cost_i` instruction-cost points. Later stages depend on earlier results, so intermediate stages cannot be skipped: completing stage `k` requires completing the preceding `k-1` stages first. + +Before choosing the cost limit used in production, we prepare `Q` progressively relaxed candidate budgets `budget_1, budget_2, ..., budget_Q`, guaranteed to be nondecreasing. Each budget starts from the first stage and independently evaluates the same workflow. + +For every `budget_j`, output the greatest number of consecutive stages from the beginning that can be completed. In other words, find the largest `k` such that: + +```text +cost_1 + cost_2 + ... + cost_k <= budget_j +``` + +`k=0` is always allowed. A zero-cost stage can still be completed and must be included in the answer. + +## Input + +The first line contains two integers, `N Q`. + +The second line contains `N` integers, `cost_1, cost_2, ..., cost_N`. + +The third line contains `Q` nondecreasing integers, `budget_1, budget_2, ..., budget_Q`. + +## Output + +For each budget in order, output one line containing the maximum number of stages that can be completed. + +## Constraints + +- `1 <= N,Q <= 200000` +- `0 <= cost_i <= 10^12` +- `0 <= budget_j <= 9 * 10^18` +- `budget_1 <= budget_2 <= ... <= budget_Q` +- The sum of all stage costs is at most `9 * 10^18` +- The full constraints apply to every official test +- JavaScript and TypeScript solutions must use `bigint` for costs, budgets, and accumulated values + +## Examples + + + +### Example One + +Input: + +```text +5 4 +4 2 7 1 3 +0 6 10 17 +``` + +Output: + +```text +0 +2 +2 +5 +``` + +### Example Two + +Input: + +```text +4 5 +0 5 0 2 +0 4 5 6 7 +``` + +Output: + +```text +1 +1 +3 +3 +4 +``` + +### Example Three + +Input: + +```text +1 3 +9 +8 9 100 +``` + +Output: + +```text +0 +1 +1 +``` + + diff --git a/problems/041-progressive-cost-budget/statement.zh-TW.md b/problems/041-progressive-cost-budget/statement.zh-TW.md new file mode 100644 index 0000000..fc01461 --- /dev/null +++ b/problems/041-progressive-cost-budget/statement.zh-TW.md @@ -0,0 +1,100 @@ +# 逐步放寬的 Cost Budget + +在設計 WASM OJ 時,我們需要限制使用者程式可以消耗的計算資源。單純使用實際執行時間並不理想:同一份程式在不同瀏覽器、裝置或系統負載下,可能得到差異很大的結果。因此,我們選擇記錄 WebAssembly 執行過程中的 instruction cost,讓資源限制更穩定,也更容易重現。 + +一次完整的判題流程可以拆成 `N` 個依序執行的 stage。第 `i` 個 stage 需要 `cost_i` 點 instruction cost。後面的 stage 依賴前面的執行結果,因此不能跳過中間步驟;若要完成第 `k` 個 stage,就必須先完成前 `k-1` 個 stage。 + +在決定正式使用哪個 cost limit 前,我們準備了 `Q` 個逐步放寬的候選 budget `budget_1, budget_2, ..., budget_Q`,並保證它們不遞減。每個 budget 都會從第一個 stage 開始,獨立評估同一份工作流程。 + +對每個 `budget_j`,請輸出最多能完整執行多少個開頭連續的 stage;也就是找出最大的 `k`,使得: + +```text +cost_1 + cost_2 + ... + cost_k <= budget_j +``` + +`k=0` 永遠合法。成本為零的 stage 仍然是可完成的 stage,因此也必須計入答案。 + +## 輸入 + +第一行包含兩個整數 `N Q`。 + +第二行包含 `N` 個整數 `cost_1, cost_2, ..., cost_N`。 + +第三行包含 `Q` 個不遞減的整數 `budget_1, budget_2, ..., budget_Q`。 + +## 輸出 + +對每個 budget 依序輸出一行,內容是可完整執行的最大 stage 數量。 + +## 限制 + +- `1 <= N,Q <= 200000` +- `0 <= cost_i <= 10^12` +- `0 <= budget_j <= 9 * 10^18` +- `budget_1 <= budget_2 <= ... <= budget_Q` +- 所有 stage 的成本總和不超過 `9 * 10^18` +- 所有官方測資都符合完整限制 +- JavaScript 與 TypeScript 必須使用 `bigint` 儲存成本、budget 與累計值 + +## 範例 + + + +### 範例一 + +輸入: + +```text +5 4 +4 2 7 1 3 +0 6 10 17 +``` + +輸出: + +```text +0 +2 +2 +5 +``` + +### 範例二 + +輸入: + +```text +4 5 +0 5 0 2 +0 4 5 6 7 +``` + +輸出: + +```text +1 +1 +3 +3 +4 +``` + +### 範例三 + +輸入: + +```text +1 3 +9 +8 9 100 +``` + +輸出: + +```text +0 +1 +1 +``` + + diff --git a/problems/041-progressive-cost-budget/tests/adversarial-blind-01.in b/problems/041-progressive-cost-budget/tests/adversarial-blind-01.in new file mode 100644 index 0000000..3b1aa66 --- /dev/null +++ b/problems/041-progressive-cost-budget/tests/adversarial-blind-01.in @@ -0,0 +1,401 @@ +200000 200000 +999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 999999999999 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b/problems/041-progressive-cost-budget/tests/sample-01.in @@ -0,0 +1,3 @@ +5 4 +4 2 7 1 3 +0 6 10 17 diff --git a/problems/041-progressive-cost-budget/tests/sample-01.out b/problems/041-progressive-cost-budget/tests/sample-01.out new file mode 100644 index 0000000..3717457 --- /dev/null +++ b/problems/041-progressive-cost-budget/tests/sample-01.out @@ -0,0 +1,4 @@ +0 +2 +2 +5 diff --git a/problems/041-progressive-cost-budget/tests/sample-02.in b/problems/041-progressive-cost-budget/tests/sample-02.in new file mode 100644 index 0000000..576cb9a --- /dev/null +++ b/problems/041-progressive-cost-budget/tests/sample-02.in @@ -0,0 +1,3 @@ +4 5 +0 5 0 2 +0 4 5 6 7 diff --git a/problems/041-progressive-cost-budget/tests/sample-02.out b/problems/041-progressive-cost-budget/tests/sample-02.out new file mode 100644 index 0000000..1569a84 --- /dev/null +++ b/problems/041-progressive-cost-budget/tests/sample-02.out @@ -0,0 +1,5 @@ +1 +1 +3 +3 +4 diff --git a/problems/041-progressive-cost-budget/tests/sample-03.in b/problems/041-progressive-cost-budget/tests/sample-03.in new file mode 100644 index 0000000..f1962ee --- /dev/null +++ b/problems/041-progressive-cost-budget/tests/sample-03.in @@ -0,0 +1,3 @@ +1 3 +9 +8 9 100 diff --git a/problems/041-progressive-cost-budget/tests/sample-03.out b/problems/041-progressive-cost-budget/tests/sample-03.out new file mode 100644 index 0000000..986394f --- /dev/null +++ b/problems/041-progressive-cost-budget/tests/sample-03.out @@ -0,0 +1,3 @@ +0 +1 +1 diff --git a/problems/041-progressive-cost-budget/validator.py b/problems/041-progressive-cost-budget/validator.py new file mode 100644 index 0000000..667e1fb --- /dev/null +++ b/problems/041-progressive-cost-budget/validator.py @@ -0,0 +1,41 @@ +import re +import sys + + +def fail(): + raise SystemExit(1) + + +try: + tokens = sys.stdin.buffer.read().decode("utf-8").split() + position = 0 + + def unsigned(lower, upper): + global position + if position >= len(tokens) or re.fullmatch(r"0|[1-9][0-9]*", tokens[position]) is None: + fail() + value = int(tokens[position]) + position += 1 + if not lower <= value <= upper: + fail() + return value + + n = unsigned(1, 200000) + q = unsigned(1, 200000) + total = 0 + for _ in range(n): + total += unsigned(0, 10**12) + if total > 9 * 10**18: + fail() + + previous = -1 + for _ in range(q): + budget = unsigned(0, 9 * 10**18) + if budget < previous: + fail() + previous = budget + + if position != len(tokens): + fail() +except (UnicodeDecodeError, ValueError, OverflowError): + fail() diff --git a/problems/042-first-duplicate-test/editorial.en.md b/problems/042-first-duplicate-test/editorial.en.md new file mode 100644 index 0000000..ea6a496 --- /dev/null +++ b/problems/042-first-duplicate-test/editorial.en.md @@ -0,0 +1,38 @@ +# Editorial + +Let `L` be the maximum fingerprint length and `S` the sum of all fingerprint lengths. + +## Intuitive Approach + +Store every fingerprint already seen. For arrival `i`, compare its exact token with positions `1` through `i - 1` and stop at the first match. This directly implements the definition, but an all-distinct input performs `O(N^2)` comparisons. Its time is `O(N^2 L)` and its space is `O(S)`. + +## Improved Approach: Sorting + +Store `(fingerprint, index)` pairs and sort them by fingerprint, then by index. Equal fingerprints become one contiguous group. The first two indices of each repeated group are that fingerprint's first arrival and first duplicate. Take the group whose second index is smallest. + +This takes `O(N log N * L)` time under length-bounded string comparison and `O(S)` space. It is deterministic, but sorting does more work than necessary because arrival order already tells us when an answer becomes final. + +## Optimal Approach: First-Occurrence Hash Map + +Scan the fingerprints from left to right and maintain a hash map from each exact token to its first index. + +- If the current token is absent, insert its current index. +- If it is present, the current index is the smallest possible duplicate index because all earlier arrivals have already been checked. The stored value is the earliest matching index. Output both and stop. + +Hashing may choose a bucket, but equality must still compare the complete token. Never parse fingerprints as hexadecimal integers. + +## Correctness Proof + +Before processing index `i`, the map contains exactly one entry for every distinct fingerprint in positions `1..i-1`, and each entry stores its earliest position. This holds initially because the prefix is empty. If fingerprint `i` is new, inserting `i` establishes the invariant for the next prefix. If it is already present, the stored index `j` is its earliest earlier occurrence by the invariant. No index smaller than `i` can be the answer because all of them were processed without finding a duplicate. Therefore the algorithm outputs exactly the required pair `(i, j)`. If the scan ends, no position duplicated an earlier token, so `NONE` is correct. + +## Complexity + +With expected constant-time hash-table operations, the time is `O(S)` and the space is `O(S)`. Exact comparisons resolve hash collisions, so collisions affect performance but never correctness. + +## Common Mistakes + +- Parsing tokens as numbers, which incorrectly makes `0` equal to `00`. +- Replacing an existing map value and then reporting the most recent occurrence instead of the first. +- Sorting and returning the lexicographically first repeated fingerprint rather than the one with the smallest duplicate index. +- Trusting equal hash values without comparing the complete fingerprint. +- Using zero-based indices in the output. diff --git a/problems/042-first-duplicate-test/editorial.zh-TW.md b/problems/042-first-duplicate-test/editorial.zh-TW.md new file mode 100644 index 0000000..e53e410 --- /dev/null +++ b/problems/042-first-duplicate-test/editorial.zh-TW.md @@ -0,0 +1,38 @@ +# 解題說明 + +令 `L` 為 fingerprint 最大長度,`S` 為所有 fingerprint 長度總和。 + +## 直覺解法 + +保存所有看過的 fingerprint。處理抵達位置 `i` 時,依序與位置 `1` 到 `i - 1` 的完整 token 比較,第一個相同者就是所需的 `j`。這直接實作定義,但所有 token 皆不同時會執行 `O(N^2)` 次比較。時間為 `O(N^2 L)`,空間為 `O(S)`。 + +## 進階解法:排序 + +保存 `(fingerprint, index)` 並依 fingerprint、index 排序。相同 fingerprint 會形成連續群組;每個重複群組最小的兩個 index 分別是第一次出現與第一次重複。最後選擇第二個 index 最小的群組。 + +在字串長度有上限的比較模型下,時間為 `O(N log N * L)`,空間為 `O(S)`。此法有確定性的界線,但抵達順序其實已足以判斷答案,排序做了不必要的額外工作。 + +## 最佳解法:首次位置 Hash Map + +由左至右掃描,以 hash map 保存每個完整 token 第一次出現的 index。 + +- 當前 token 尚未出現時,記錄目前 index。 +- 已出現時,所有更早位置都已檢查完畢,因此目前 index 必是最小的重複 index;map 中的值則是最早的相同位置。輸出後即可停止。 + +Hash 可以用來選擇 bucket,但相等判斷仍必須比較完整 token。絕對不能把 fingerprint 解析成十六進位整數。 + +## 正確性證明 + +處理 index `i` 之前,map 恰好包含位置 `1..i-1` 中每種不同 fingerprint,且值為它的最早位置。空前綴時性質成立。若第 `i` 個 fingerprint 尚未出現,插入 `i` 後性質仍成立;若已出現,依不變量,map 中的 `j` 正是最早的相同位置。所有小於 `i` 的位置都已處理且未回報重複,因此不存在更小的答案 index。故演算法輸出的 `(i,j)` 完全符合題意。若掃描結束仍未回報,代表每個位置都沒有相同的前項,輸出 `NONE` 正確。 + +## 複雜度 + +在 hash table 操作期望為常數時間時,時間 `O(S)`,空間 `O(S)`。Hash collision 必須以完整 token 比較解決,所以 collision 只影響效能、不影響正確性。 + +## 常見錯誤 + +- 將 token 解析成數字,錯誤地認為 `0` 與 `00` 相同。 +- token 再次出現時覆寫 map,導致回報最近位置而非最早位置。 +- 排序後回傳字典序最小的重複 fingerprint,而非 duplicate index 最小者。 +- 只比較 hash 值而未比較完整 fingerprint。 +- 輸出零起算 index。 diff --git a/problems/042-first-duplicate-test/generator.py b/problems/042-first-duplicate-test/generator.py new file mode 100644 index 0000000..a9126a0 --- /dev/null +++ b/problems/042-first-duplicate-test/generator.py @@ -0,0 +1,40 @@ +import random +import sys + + +if len(sys.argv) != 3: + raise SystemExit("usage: generator.py SEED INDEX") + +seed = int(sys.argv[1]) +index = int(sys.argv[2]) +if index == 999_999: + n = 200_000 + fingerprints = [format(value, "x") for value in range(1, n + 1)] + fingerprints[-1] = format(123_457, "x") + print(n) + print(*fingerprints) + raise SystemExit(0) + +rng = random.Random((seed << 32) ^ index) +n = rng.randint(1, min(36, 8 + index % 29)) + + +def fresh(used): + while True: + width = rng.randint(1, 8) + token = "".join(rng.choice("0123456789abcdef") for _ in range(width)) + if token not in used: + used.add(token) + return token + + +used = set() +fingerprints = [fresh(used) for _ in range(n)] +if n >= 2 and index % 4 != 0: + duplicate_at = rng.randint(1, n - 1) + fingerprints[duplicate_at] = fingerprints[rng.randrange(duplicate_at)] +if n >= 4 and index % 3 == 0: + fingerprints[-1] = fingerprints[0] + +print(n) +print(*fingerprints) diff --git a/problems/042-first-duplicate-test/oracle.py b/problems/042-first-duplicate-test/oracle.py new file mode 100644 index 0000000..e623f12 --- /dev/null +++ b/problems/042-first-duplicate-test/oracle.py @@ -0,0 +1,22 @@ +import sys + + +tokens = sys.stdin.buffer.read().split() +n = int(tokens[0]) +ordered = sorted((fingerprint, index) for index, fingerprint in enumerate(tokens[1:n + 1], 1)) +answer = None +start = 0 +while start < n: + end = start + 1 + while end < n and ordered[end][0] == ordered[start][0]: + end += 1 + if end - start >= 2: + candidate = (ordered[start + 1][1], ordered[start][1]) + if answer is None or candidate[0] < answer[0]: + answer = candidate + start = end + +if answer is None: + print("NONE") +else: + print(*answer) diff --git a/problems/042-first-duplicate-test/problem.json b/problems/042-first-duplicate-test/problem.json new file mode 100644 index 0000000..c4903f5 --- /dev/null +++ b/problems/042-first-duplicate-test/problem.json @@ -0,0 +1,156 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 42, + "slug": "first-duplicate-test", + "title": { + "zh-TW": "第一份重複測資", + "en": "First Duplicate Test" + }, + "difficulty": "easy", + "tags": [ + "hash-map", + "sorting", + "strings", + "exact-match" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-blind-01", + "kind": "adversarial", + "input": "tests/adversarial-blind-01.in", + "output": "tests/adversarial-blind-01.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 20000000000, + "memoryLimitBytes": 134217728 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 7500000000, + "memoryLimitBytes": 100663296 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 3000000000, + "memoryLimitBytes": 67108864 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "逐一比較所有先前 fingerprint", + "en": "Compare every previous fingerprint" + }, + "time": "O(N^2 L)", + "space": "O(S)", + "accepted": false + }, + { + "name": { + "zh-TW": "排序 fingerprint 與 index", + "en": "Sort fingerprints with indices" + }, + "time": "O(N log N * L)", + "space": "O(S)", + "accepted": false + }, + { + "name": { + "zh-TW": "首次位置 hash map", + "en": "First-occurrence hash map" + }, + "time": "O(S) expected", + "space": "O(S)", + "accepted": true + } + ] +} diff --git a/problems/042-first-duplicate-test/solutions/c/main.c b/problems/042-first-duplicate-test/solutions/c/main.c new file mode 100644 index 0000000..3bd03c7 --- /dev/null +++ b/problems/042-first-duplicate-test/solutions/c/main.c @@ -0,0 +1,53 @@ +#include +#include +#include +#include + +typedef struct { + char key[33]; + int first_index; +} Entry; + +static uint64_t hash_token(const char *token) { + uint64_t hash = UINT64_C(14695981039346656037); + while (*token != '\0') { + hash ^= (unsigned char)*token++; + hash *= UINT64_C(1099511628211); + } + return hash; +} + +int main(void) { + int n; + if (scanf("%d", &n) != 1) + return 0; + + size_t capacity = 1; + while (capacity < (size_t)n * 2) + capacity <<= 1; + Entry *table = calloc(capacity, sizeof(*table)); + if (table == NULL) + return 1; + + for (int index = 1; index <= n; index++) { + char token[33]; + if (scanf("%32s", token) != 1) { + free(table); + return 0; + } + size_t slot = (size_t)hash_token(token) & (capacity - 1); + while (table[slot].first_index != 0 && strcmp(table[slot].key, token) != 0) + slot = (slot + 1) & (capacity - 1); + if (table[slot].first_index != 0) { + printf("%d %d\n", index, table[slot].first_index); + free(table); + return 0; + } + strcpy(table[slot].key, token); + table[slot].first_index = index; + } + + puts("NONE"); + free(table); + return 0; +} diff --git a/problems/042-first-duplicate-test/solutions/cpp/main.cpp b/problems/042-first-duplicate-test/solutions/cpp/main.cpp new file mode 100644 index 0000000..bcfaf59 --- /dev/null +++ b/problems/042-first-duplicate-test/solutions/cpp/main.cpp @@ -0,0 +1,25 @@ +#include +#include +#include +using namespace std; + +int main() { + ios::sync_with_stdio(false); + cin.tie(nullptr); + + int n; + if (!(cin >> n)) + return 0; + unordered_map first_index; + first_index.reserve(static_cast(n) * 2); + for (int index = 1; index <= n; ++index) { + string fingerprint; + cin >> fingerprint; + auto [it, inserted] = first_index.emplace(fingerprint, index); + if (!inserted) { + cout << index << ' ' << it->second << '\n'; + return 0; + } + } + cout << "NONE\n"; +} diff --git a/problems/042-first-duplicate-test/solutions/go/main.go b/problems/042-first-duplicate-test/solutions/go/main.go new file mode 100644 index 0000000..b111e48 --- /dev/null +++ b/problems/042-first-duplicate-test/solutions/go/main.go @@ -0,0 +1,29 @@ +package main + +import ( + "bufio" + "fmt" + "os" +) + +func main() { + in := bufio.NewReaderSize(os.Stdin, 1<<20) + out := bufio.NewWriter(os.Stdout) + defer out.Flush() + + var n int + if _, err := fmt.Fscan(in, &n); err != nil { + return + } + firstIndex := make(map[string]int, n) + for index := 1; index <= n; index++ { + var fingerprint string + fmt.Fscan(in, &fingerprint) + if earliest, found := firstIndex[fingerprint]; found { + fmt.Fprintln(out, index, earliest) + return + } + firstIndex[fingerprint] = index + } + fmt.Fprintln(out, "NONE") +} diff --git a/problems/042-first-duplicate-test/solutions/javascript/main.js b/problems/042-first-duplicate-test/solutions/javascript/main.js new file mode 100644 index 0000000..fc14378 --- /dev/null +++ b/problems/042-first-duplicate-test/solutions/javascript/main.js @@ -0,0 +1,24 @@ +import * as std from "std"; + +const input = std.in.readAsString(); +let cursor = 0; +function nextToken() { + while (cursor < input.length && input.charCodeAt(cursor) <= 32) cursor++; + const start = cursor; + while (cursor < input.length && input.charCodeAt(cursor) > 32) cursor++; + return input.slice(start, cursor); +} + +const count = Number(nextToken()); +const firstIndex = new Map(); +let answer = "NONE"; +for (let index = 1; index <= count; index++) { + const fingerprint = nextToken(); + const earliest = firstIndex.get(fingerprint); + if (earliest !== undefined) { + answer = `${index} ${earliest}`; + break; + } + firstIndex.set(fingerprint, index); +} +std.out.puts(`${answer}\n`); diff --git a/problems/042-first-duplicate-test/solutions/python/main.py b/problems/042-first-duplicate-test/solutions/python/main.py new file mode 100644 index 0000000..1879d05 --- /dev/null +++ b/problems/042-first-duplicate-test/solutions/python/main.py @@ -0,0 +1,20 @@ +import sys + + +def input_tokens(): + for line in sys.stdin.buffer: + yield from line.split() + + +tokens = input_tokens() +n = int(next(tokens)) +first_index = {} +for index in range(1, n + 1): + fingerprint = next(tokens) + earliest = first_index.get(fingerprint) + if earliest is not None: + print(index, earliest) + break + first_index[fingerprint] = index +else: + print("NONE") diff --git a/problems/042-first-duplicate-test/solutions/rust/main.rs b/problems/042-first-duplicate-test/solutions/rust/main.rs new file mode 100644 index 0000000..3111fac --- /dev/null +++ b/problems/042-first-duplicate-test/solutions/rust/main.rs @@ -0,0 +1,20 @@ +use std::collections::HashMap; +use std::io::{self, Read}; + +fn main() { + let mut input = String::new(); + io::stdin().read_to_string(&mut input).unwrap(); + let mut tokens = input.split_whitespace(); + let n: usize = tokens.next().unwrap().parse().unwrap(); + let mut first_index: HashMap<&str, usize> = HashMap::with_capacity(n * 2); + + for index in 1..=n { + let fingerprint = tokens.next().unwrap(); + if let Some(&earliest) = first_index.get(fingerprint) { + println!("{} {}", index, earliest); + return; + } + first_index.insert(fingerprint, index); + } + println!("NONE"); +} diff --git a/problems/042-first-duplicate-test/solutions/typescript/main.ts b/problems/042-first-duplicate-test/solutions/typescript/main.ts new file mode 100644 index 0000000..3cca7ff --- /dev/null +++ b/problems/042-first-duplicate-test/solutions/typescript/main.ts @@ -0,0 +1,24 @@ +import * as std from "std"; + +const input: string = std.in.readAsString(); +let cursor = 0; +function nextToken(): string { + while (cursor < input.length && input.charCodeAt(cursor) <= 32) cursor++; + const start = cursor; + while (cursor < input.length && input.charCodeAt(cursor) > 32) cursor++; + return input.slice(start, cursor); +} + +const count = Number(nextToken()); +const firstIndex = new Map(); +let answer = "NONE"; +for (let index = 1; index <= count; index++) { + const fingerprint = nextToken(); + const earliest = firstIndex.get(fingerprint); + if (earliest !== undefined) { + answer = `${index} ${earliest}`; + break; + } + firstIndex.set(fingerprint, index); +} +std.out.puts(`${answer}\n`); diff --git a/problems/042-first-duplicate-test/statement.en.md b/problems/042-first-duplicate-test/statement.en.md new file mode 100644 index 0000000..d5dd8b6 --- /dev/null +++ b/problems/042-first-duplicate-test/statement.en.md @@ -0,0 +1,79 @@ +# First Duplicate Test + +While designing the problem-import pipeline for a WASM OJ, we needed to prevent the same test case from being added more than once. Every test already has a fingerprint before entering storage, so full file contents do not need to be compared again. For reproducible diagnostics, however, we want not only to detect a duplicate but also to identify the earliest duplicate and its original source. + +The system receives `N` test-case fingerprints in arrival order. Each fingerprint is a non-empty lowercase hexadecimal token. Fingerprints are compared as exact token strings, not as hexadecimal numbers: for example, `0` and `00` are different fingerprints. + +Find the earliest arrival that duplicates an earlier fingerprint. More precisely, find the smallest index `i` for which an index `j < i` has the same fingerprint, and report `i` together with the earliest such index `j` for that fingerprint. All indices are one-based. + +If every fingerprint is distinct, report `NONE`. + +## Input + +The first line contains an integer `N`. + +The remaining input contains `N` whitespace-separated fingerprints in arrival order. + +## Output + +If a duplicate exists, output `i j`, where `i` is the smallest duplicate index and `j` is the first index containing the same token. + +Otherwise, output `NONE`. + +## Constraints + +- `1 <= N <= 200000` +- Every fingerprint has length from `1` to `32`. +- Every character is one of `0`–`9` or `a`–`f`. +- Comparisons are exact token comparisons; fingerprints are not numbers. + +## Examples + + + +### Example One + +Input: + +```text +5 +aa bb cc bb aa +``` + +Output: + +```text +4 2 +``` + +### Example Two + +Input: + +```text +4 +0 a 00 f0 +``` + +Output: + +```text +NONE +``` + +### Example Three + +Input: + +```text +6 +0 a 00 a ff 0 +``` + +Output: + +```text +4 2 +``` + + diff --git a/problems/042-first-duplicate-test/statement.zh-TW.md b/problems/042-first-duplicate-test/statement.zh-TW.md new file mode 100644 index 0000000..6c804a5 --- /dev/null +++ b/problems/042-first-duplicate-test/statement.zh-TW.md @@ -0,0 +1,79 @@ +# 第一份重複測資 + +在設計 WASM OJ 的題庫匯入流程時,我們需要避免同一份 test case 被重複加入。每份測資在進入儲存系統前都已計算出 fingerprint,因此不必再次比較完整檔案內容;但為了讓錯誤訊息可重現,我們不只想知道是否有重複,還要找出最早發生重複的位置及其原始來源。 + +系統依抵達順序收到 `N` 個 test case fingerprints。每個 fingerprint 都是非空的小寫十六進位 token。Fingerprint 必須按照 token 字串精確比較,而不是當成十六進位數值;例如 `0` 與 `00` 是不同的 fingerprint。 + +請找出最早與先前資料重複的一筆。更精確地說,找出最小的 index `i`,使得存在 `j < i` 且兩者 fingerprint 相同,並同時輸出這個 fingerprint 最早出現的 index `j`。所有 index 從 `1` 開始。 + +若所有 fingerprint 都互不相同,請輸出 `NONE`。 + +## 輸入 + +第一行包含整數 `N`。 + +其餘輸入依抵達順序包含 `N` 個以空白分隔的 fingerprint。 + +## 輸出 + +若存在重複,輸出 `i j`,其中 `i` 是最小的重複 index,`j` 是相同 token 第一次出現的 index。 + +否則輸出 `NONE`。 + +## 限制 + +- `1 ≤ N ≤ 200000` +- 每個 fingerprint 長度介於 `1` 到 `32`。 +- 每個字元皆為 `0`–`9` 或 `a`–`f`。 +- 必須精確比較 token;fingerprint 不是數字。 + +## 範例 + + + +### 範例一 + +輸入: + +```text +5 +aa bb cc bb aa +``` + +輸出: + +```text +4 2 +``` + +### 範例二 + +輸入: + +```text +4 +0 a 00 f0 +``` + +輸出: + +```text +NONE +``` + +### 範例三 + +輸入: + +```text +6 +0 a 00 a ff 0 +``` + +輸出: + +```text +4 2 +``` + + diff --git a/problems/042-first-duplicate-test/tests/adversarial-blind-01.in b/problems/042-first-duplicate-test/tests/adversarial-blind-01.in new file mode 100644 index 0000000..4b74fba --- /dev/null +++ b/problems/042-first-duplicate-test/tests/adversarial-blind-01.in @@ -0,0 +1,2 @@ +200000 +1 2 3 4 5 6 7 8 9 a b c d e f 10 11 12 13 14 15 16 17 18 19 1a 1b 1c 1d 1e 1f 20 21 22 23 24 25 26 27 28 29 2a 2b 2c 2d 2e 2f 30 31 32 33 34 35 36 37 38 39 3a 3b 3c 3d 3e 3f 40 41 42 43 44 45 46 47 48 49 4a 4b 4c 4d 4e 4f 50 51 52 53 54 55 56 57 58 59 5a 5b 5c 5d 5e 5f 60 61 62 63 64 65 66 67 68 69 6a 6b 6c 6d 6e 6f 70 71 72 73 74 75 76 77 78 79 7a 7b 7c 7d 7e 7f 80 81 82 83 84 85 86 87 88 89 8a 8b 8c 8d 8e 8f 90 91 92 93 94 95 96 97 98 99 9a 9b 9c 9d 9e 9f a0 a1 a2 a3 a4 a5 a6 a7 a8 a9 aa ab ac ad ae af b0 b1 b2 b3 b4 b5 b6 b7 b8 b9 ba bb bc bd be bf c0 c1 c2 c3 c4 c5 c6 c7 c8 c9 ca cb cc cd ce cf d0 d1 d2 d3 d4 d5 d6 d7 d8 d9 da db dc dd de df e0 e1 e2 e3 e4 e5 e6 e7 e8 e9 ea eb ec ed ee ef f0 f1 f2 f3 f4 f5 f6 f7 f8 f9 fa fb fc fd fe ff 100 101 102 103 104 105 106 107 108 109 10a 10b 10c 10d 10e 10f 110 111 112 113 114 115 116 117 118 119 11a 11b 11c 11d 11e 11f 120 121 122 123 124 125 126 127 128 129 12a 12b 12c 12d 12e 12f 130 131 132 133 134 135 136 137 138 139 13a 13b 13c 13d 13e 13f 140 141 142 143 144 145 146 147 148 149 14a 14b 14c 14d 14e 14f 150 151 152 153 154 155 156 157 158 159 15a 15b 15c 15d 15e 15f 160 161 162 163 164 165 166 167 168 169 16a 16b 16c 16d 16e 16f 170 171 172 173 174 175 176 177 178 179 17a 17b 17c 17d 17e 17f 180 181 182 183 184 185 186 187 188 189 18a 18b 18c 18d 18e 18f 190 191 192 193 194 195 196 197 198 199 19a 19b 19c 19d 19e 19f 1a0 1a1 1a2 1a3 1a4 1a5 1a6 1a7 1a8 1a9 1aa 1ab 1ac 1ad 1ae 1af 1b0 1b1 1b2 1b3 1b4 1b5 1b6 1b7 1b8 1b9 1ba 1bb 1bc 1bd 1be 1bf 1c0 1c1 1c2 1c3 1c4 1c5 1c6 1c7 1c8 1c9 1ca 1cb 1cc 1cd 1ce 1cf 1d0 1d1 1d2 1d3 1d4 1d5 1d6 1d7 1d8 1d9 1da 1db 1dc 1dd 1de 1df 1e0 1e1 1e2 1e3 1e4 1e5 1e6 1e7 1e8 1e9 1ea 1eb 1ec 1ed 1ee 1ef 1f0 1f1 1f2 1f3 1f4 1f5 1f6 1f7 1f8 1f9 1fa 1fb 1fc 1fd 1fe 1ff 200 201 202 203 204 205 206 207 208 209 20a 20b 20c 20d 20e 20f 210 211 212 213 214 215 216 217 218 219 21a 21b 21c 21d 21e 21f 220 221 222 223 224 225 226 227 228 229 22a 22b 22c 22d 22e 22f 230 231 232 233 234 235 236 237 238 239 23a 23b 23c 23d 23e 23f 240 241 242 243 244 245 246 247 248 249 24a 24b 24c 24d 24e 24f 250 251 252 253 254 255 256 257 258 259 25a 25b 25c 25d 25e 25f 260 261 262 263 264 265 266 267 268 269 26a 26b 26c 26d 26e 26f 270 271 272 273 274 275 276 277 278 279 27a 27b 27c 27d 27e 27f 280 281 282 283 284 285 286 287 288 289 28a 28b 28c 28d 28e 28f 290 291 292 293 294 295 296 297 298 299 29a 29b 29c 29d 29e 29f 2a0 2a1 2a2 2a3 2a4 2a5 2a6 2a7 2a8 2a9 2aa 2ab 2ac 2ad 2ae 2af 2b0 2b1 2b2 2b3 2b4 2b5 2b6 2b7 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b82 b83 b84 b85 b86 b87 b88 b89 b8a b8b b8c b8d b8e b8f b90 b91 b92 b93 b94 b95 b96 b97 b98 b99 b9a b9b b9c b9d b9e b9f ba0 ba1 ba2 ba3 ba4 ba5 ba6 ba7 ba8 ba9 baa bab bac bad bae baf bb0 bb1 bb2 bb3 bb4 bb5 bb6 bb7 bb8 bb9 bba bbb bbc bbd bbe bbf bc0 bc1 bc2 bc3 bc4 bc5 bc6 bc7 bc8 bc9 bca bcb bcc bcd bce bcf bd0 bd1 bd2 bd3 bd4 bd5 bd6 bd7 bd8 bd9 bda bdb bdc bdd bde bdf be0 be1 be2 be3 be4 be5 be6 be7 be8 be9 bea beb bec bed bee bef bf0 bf1 bf2 bf3 bf4 bf5 bf6 bf7 bf8 bf9 bfa bfb bfc bfd bfe bff c00 c01 c02 c03 c04 c05 c06 c07 c08 c09 c0a c0b c0c c0d c0e c0f c10 c11 c12 c13 c14 c15 c16 c17 c18 c19 c1a c1b c1c c1d c1e c1f c20 c21 c22 c23 c24 c25 c26 c27 c28 c29 c2a c2b c2c c2d c2e c2f c30 c31 c32 c33 c34 c35 c36 c37 c38 c39 c3a c3b c3c c3d c3e c3f c40 c41 c42 c43 c44 c45 c46 c47 c48 c49 c4a c4b c4c c4d c4e c4f c50 c51 c52 c53 c54 c55 c56 c57 c58 c59 c5a c5b c5c c5d c5e c5f c60 c61 c62 c63 c64 c65 c66 c67 c68 c69 c6a c6b c6c c6d c6e c6f c70 c71 c72 c73 c74 c75 c76 c77 c78 c79 c7a c7b c7c c7d c7e c7f c80 c81 c82 c83 c84 c85 c86 c87 c88 c89 c8a c8b c8c c8d c8e c8f c90 c91 c92 c93 c94 c95 c96 c97 c98 c99 c9a c9b c9c c9d c9e c9f ca0 ca1 ca2 ca3 ca4 ca5 ca6 ca7 ca8 ca9 caa cab cac cad cae caf cb0 cb1 cb2 cb3 cb4 cb5 cb6 cb7 cb8 cb9 cba cbb cbc cbd cbe cbf cc0 cc1 cc2 cc3 cc4 cc5 cc6 cc7 cc8 cc9 cca ccb ccc ccd cce ccf cd0 cd1 cd2 cd3 cd4 cd5 cd6 cd7 cd8 cd9 cda cdb cdc cdd cde cdf ce0 ce1 ce2 ce3 ce4 ce5 ce6 ce7 ce8 ce9 cea ceb cec ced cee cef cf0 cf1 cf2 cf3 cf4 cf5 cf6 cf7 cf8 cf9 cfa cfb cfc cfd cfe cff d00 d01 d02 d03 d04 d05 d06 d07 d08 d09 d0a d0b d0c d0d d0e d0f d10 d11 d12 d13 d14 d15 d16 d17 d18 d19 d1a d1b d1c d1d d1e d1f d20 d21 d22 d23 d24 d25 d26 d27 d28 d29 d2a d2b d2c d2d d2e d2f d30 d31 d32 d33 d34 d35 d36 d37 d38 d39 d3a d3b d3c d3d d3e d3f d40 d41 d42 d43 d44 d45 d46 d47 d48 d49 d4a d4b d4c d4d d4e d4f d50 d51 d52 d53 d54 d55 d56 d57 d58 d59 d5a d5b d5c d5d d5e d5f d60 d61 d62 d63 d64 d65 d66 d67 d68 d69 d6a d6b d6c d6d d6e d6f d70 d71 d72 d73 d74 d75 d76 d77 d78 d79 d7a d7b d7c d7d d7e d7f d80 d81 d82 d83 d84 d85 d86 d87 d88 d89 d8a d8b d8c d8d d8e d8f d90 d91 d92 d93 d94 d95 d96 d97 d98 d99 d9a d9b d9c d9d d9e d9f da0 da1 da2 da3 da4 da5 da6 da7 da8 da9 daa dab dac dad dae daf db0 db1 db2 db3 db4 db5 db6 db7 db8 db9 dba dbb dbc dbd dbe dbf dc0 dc1 dc2 dc3 dc4 dc5 dc6 dc7 dc8 dc9 dca dcb dcc dcd dce dcf dd0 dd1 dd2 dd3 dd4 dd5 dd6 dd7 dd8 dd9 dda ddb ddc ddd dde ddf de0 de1 de2 de3 de4 de5 de6 de7 de8 de9 dea deb dec ded dee def df0 df1 df2 df3 df4 df5 df6 df7 df8 df9 dfa dfb dfc dfd dfe dff e00 e01 e02 e03 e04 e05 e06 e07 e08 e09 e0a e0b e0c e0d e0e e0f e10 e11 e12 e13 e14 e15 e16 e17 e18 e19 e1a e1b e1c e1d e1e e1f e20 e21 e22 e23 e24 e25 e26 e27 e28 e29 e2a e2b e2c e2d e2e e2f e30 e31 e32 e33 e34 e35 e36 e37 e38 e39 e3a e3b e3c e3d e3e e3f e40 e41 e42 e43 e44 e45 e46 e47 e48 e49 e4a e4b e4c e4d e4e e4f e50 e51 e52 e53 e54 e55 e56 e57 e58 e59 e5a e5b e5c e5d e5e e5f e60 e61 e62 e63 e64 e65 e66 e67 e68 e69 e6a e6b e6c e6d e6e e6f e70 e71 e72 e73 e74 e75 e76 e77 e78 e79 e7a e7b e7c e7d e7e e7f e80 e81 e82 e83 e84 e85 e86 e87 e88 e89 e8a e8b e8c e8d e8e e8f e90 e91 e92 e93 e94 e95 e96 e97 e98 e99 e9a e9b e9c e9d e9e e9f ea0 ea1 ea2 ea3 ea4 ea5 ea6 ea7 ea8 ea9 eaa eab eac ead eae eaf eb0 eb1 eb2 eb3 eb4 eb5 eb6 eb7 eb8 eb9 eba ebb ebc ebd ebe ebf ec0 ec1 ec2 ec3 ec4 ec5 ec6 ec7 ec8 ec9 eca ecb ecc ecd ece ecf ed0 ed1 ed2 ed3 ed4 ed5 ed6 ed7 ed8 ed9 eda edb edc edd ede edf ee0 ee1 ee2 ee3 ee4 ee5 ee6 ee7 ee8 ee9 eea eeb eec eed eee eef ef0 ef1 ef2 ef3 ef4 ef5 ef6 ef7 ef8 ef9 efa efb efc efd efe eff f00 f01 f02 f03 f04 f05 f06 f07 f08 f09 f0a f0b f0c f0d f0e f0f f10 f11 f12 f13 f14 f15 f16 f17 f18 f19 f1a f1b f1c f1d f1e f1f f20 f21 f22 f23 f24 f25 f26 f27 f28 f29 f2a f2b f2c f2d f2e f2f f30 f31 f32 f33 f34 f35 f36 f37 f38 f39 f3a f3b f3c f3d f3e f3f f40 f41 f42 f43 f44 f45 f46 f47 f48 f49 f4a f4b f4c f4d f4e f4f f50 f51 f52 f53 f54 f55 f56 f57 f58 f59 f5a f5b f5c f5d f5e f5f f60 f61 f62 f63 f64 f65 f66 f67 f68 f69 f6a f6b f6c f6d f6e f6f f70 f71 f72 f73 f74 f75 f76 f77 f78 f79 f7a f7b f7c f7d f7e f7f f80 f81 f82 f83 f84 f85 f86 f87 f88 f89 f8a f8b f8c f8d f8e f8f f90 f91 f92 f93 f94 f95 f96 f97 f98 f99 f9a f9b f9c f9d f9e f9f fa0 fa1 fa2 fa3 fa4 fa5 fa6 fa7 fa8 fa9 faa fab fac fad fae faf fb0 fb1 fb2 fb3 fb4 fb5 fb6 fb7 fb8 fb9 fba fbb fbc fbd fbe fbf fc0 fc1 fc2 fc3 fc4 fc5 fc6 fc7 fc8 fc9 fca fcb fcc fcd fce fcf fd0 fd1 fd2 fd3 fd4 fd5 fd6 fd7 fd8 fd9 fda fdb fdc fdd fde fdf fe0 fe1 fe2 fe3 fe4 fe5 fe6 fe7 fe8 fe9 fea feb fec fed fee fef ff0 ff1 ff2 ff3 ff4 ff5 ff6 ff7 ff8 ff9 ffa ffb ffc ffd ffe fff 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 100a 100b 100c 100d 100e 100f 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 101a 101b 101c 101d 101e 101f 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 102a 102b 102c 102d 102e 102f 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 103a 103b 103c 103d 103e 103f 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 104a 104b 104c 104d 104e 104f 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 105a 105b 105c 105d 105e 105f 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 106a 106b 106c 106d 106e 106f 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 107a 107b 107c 107d 107e 107f 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 108a 108b 108c 108d 108e 108f 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 109a 109b 109c 109d 109e 109f 10a0 10a1 10a2 10a3 10a4 10a5 10a6 10a7 10a8 10a9 10aa 10ab 10ac 10ad 10ae 10af 10b0 10b1 10b2 10b3 10b4 10b5 10b6 10b7 10b8 10b9 10ba 10bb 10bc 10bd 10be 10bf 10c0 10c1 10c2 10c3 10c4 10c5 10c6 10c7 10c8 10c9 10ca 10cb 10cc 10cd 10ce 10cf 10d0 10d1 10d2 10d3 10d4 10d5 10d6 10d7 10d8 10d9 10da 10db 10dc 10dd 10de 10df 10e0 10e1 10e2 10e3 10e4 10e5 10e6 10e7 10e8 10e9 10ea 10eb 10ec 10ed 10ee 10ef 10f0 10f1 10f2 10f3 10f4 10f5 10f6 10f7 10f8 10f9 10fa 10fb 10fc 10fd 10fe 10ff 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 110a 110b 110c 110d 110e 110f 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 111a 111b 111c 111d 111e 111f 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 112a 112b 112c 112d 112e 112f 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 113a 113b 113c 113d 113e 113f 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 114a 114b 114c 114d 114e 114f 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 115a 115b 115c 115d 115e 115f 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 116a 116b 116c 116d 116e 116f 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 117a 117b 117c 117d 117e 117f 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 118a 118b 118c 118d 118e 118f 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 119a 119b 119c 119d 119e 119f 11a0 11a1 11a2 11a3 11a4 11a5 11a6 11a7 11a8 11a9 11aa 11ab 11ac 11ad 11ae 11af 11b0 11b1 11b2 11b3 11b4 11b5 11b6 11b7 11b8 11b9 11ba 11bb 11bc 11bd 11be 11bf 11c0 11c1 11c2 11c3 11c4 11c5 11c6 11c7 11c8 11c9 11ca 11cb 11cc 11cd 11ce 11cf 11d0 11d1 11d2 11d3 11d4 11d5 11d6 11d7 11d8 11d9 11da 11db 11dc 11dd 11de 11df 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12a8 12a9 12aa 12ab 12ac 12ad 12ae 12af 12b0 12b1 12b2 12b3 12b4 12b5 12b6 12b7 12b8 12b9 12ba 12bb 12bc 12bd 12be 12bf 12c0 12c1 12c2 12c3 12c4 12c5 12c6 12c7 12c8 12c9 12ca 12cb 12cc 12cd 12ce 12cf 12d0 12d1 12d2 12d3 12d4 12d5 12d6 12d7 12d8 12d9 12da 12db 12dc 12dd 12de 12df 12e0 12e1 12e2 12e3 12e4 12e5 12e6 12e7 12e8 12e9 12ea 12eb 12ec 12ed 12ee 12ef 12f0 12f1 12f2 12f3 12f4 12f5 12f6 12f7 12f8 12f9 12fa 12fb 12fc 12fd 12fe 12ff 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 130a 130b 130c 130d 130e 130f 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319 131a 131b 131c 131d 131e 131f 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 132a 132b 132c 132d 132e 132f 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 133a 133b 133c 133d 133e 133f 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 134a 134b 134c 134d 134e 134f 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 135a 135b 135c 135d 135e 135f 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 136a 136b 136c 136d 136e 136f 1370 1371 1372 1373 1374 1375 1376 1377 1378 1379 137a 137b 137c 137d 137e 137f 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 138a 138b 138c 138d 138e 138f 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399 139a 139b 139c 139d 139e 139f 13a0 13a1 13a2 13a3 13a4 13a5 13a6 13a7 13a8 13a9 13aa 13ab 13ac 13ad 13ae 13af 13b0 13b1 13b2 13b3 13b4 13b5 13b6 13b7 13b8 13b9 13ba 13bb 13bc 13bd 13be 13bf 13c0 13c1 13c2 13c3 13c4 13c5 13c6 13c7 13c8 13c9 13ca 13cb 13cc 13cd 13ce 13cf 13d0 13d1 13d2 13d3 13d4 13d5 13d6 13d7 13d8 13d9 13da 13db 13dc 13dd 13de 13df 13e0 13e1 13e2 13e3 13e4 13e5 13e6 13e7 13e8 13e9 13ea 13eb 13ec 13ed 13ee 13ef 13f0 13f1 13f2 13f3 13f4 13f5 13f6 13f7 13f8 13f9 13fa 13fb 13fc 13fd 13fe 13ff 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 140a 140b 140c 140d 140e 140f 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 141a 141b 141c 141d 141e 141f 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 142a 142b 142c 142d 142e 142f 1430 1431 1432 1433 1434 1435 1436 1437 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1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 150a 150b 150c 150d 150e 150f 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 151a 151b 151c 151d 151e 151f 1520 1521 1522 1523 1524 1525 1526 1527 1528 1529 152a 152b 152c 152d 152e 152f 1530 1531 1532 1533 1534 1535 1536 1537 1538 1539 153a 153b 153c 153d 153e 153f 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 154a 154b 154c 154d 154e 154f 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 155a 155b 155c 155d 155e 155f 1560 1561 1562 1563 1564 1565 1566 1567 1568 1569 156a 156b 156c 156d 156e 156f 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579 157a 157b 157c 157d 157e 157f 1580 1581 1582 1583 1584 1585 1586 1587 1588 1589 158a 158b 158c 158d 158e 158f 1590 1591 1592 1593 1594 1595 1596 1597 1598 1599 159a 159b 159c 159d 159e 159f 15a0 15a1 15a2 15a3 15a4 15a5 15a6 15a7 15a8 15a9 15aa 15ab 15ac 15ad 15ae 15af 15b0 15b1 15b2 15b3 15b4 15b5 15b6 15b7 15b8 15b9 15ba 15bb 15bc 15bd 15be 15bf 15c0 15c1 15c2 15c3 15c4 15c5 15c6 15c7 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0000000..ed56506 --- /dev/null +++ b/problems/042-first-duplicate-test/tests/adversarial-blind-01.out @@ -0,0 +1 @@ +200000 123457 diff --git a/problems/042-first-duplicate-test/tests/sample-01.in b/problems/042-first-duplicate-test/tests/sample-01.in new file mode 100644 index 0000000..f6e7466 --- /dev/null +++ b/problems/042-first-duplicate-test/tests/sample-01.in @@ -0,0 +1,2 @@ +5 +aa bb cc bb aa diff --git a/problems/042-first-duplicate-test/tests/sample-01.out b/problems/042-first-duplicate-test/tests/sample-01.out new file mode 100644 index 0000000..805e7f5 --- /dev/null +++ b/problems/042-first-duplicate-test/tests/sample-01.out @@ -0,0 +1 @@ +4 2 diff --git a/problems/042-first-duplicate-test/tests/sample-02.in b/problems/042-first-duplicate-test/tests/sample-02.in new file mode 100644 index 0000000..b86598b --- /dev/null +++ b/problems/042-first-duplicate-test/tests/sample-02.in @@ -0,0 +1,2 @@ +4 +0 a 00 f0 diff --git a/problems/042-first-duplicate-test/tests/sample-02.out b/problems/042-first-duplicate-test/tests/sample-02.out new file mode 100644 index 0000000..7a2d820 --- /dev/null +++ b/problems/042-first-duplicate-test/tests/sample-02.out @@ -0,0 +1 @@ +NONE diff --git a/problems/042-first-duplicate-test/tests/sample-03.in b/problems/042-first-duplicate-test/tests/sample-03.in new file mode 100644 index 0000000..80a32b7 --- /dev/null +++ b/problems/042-first-duplicate-test/tests/sample-03.in @@ -0,0 +1,2 @@ +6 +0 a 00 a ff 0 diff --git a/problems/042-first-duplicate-test/tests/sample-03.out b/problems/042-first-duplicate-test/tests/sample-03.out new file mode 100644 index 0000000..805e7f5 --- /dev/null +++ b/problems/042-first-duplicate-test/tests/sample-03.out @@ -0,0 +1 @@ +4 2 diff --git a/problems/042-first-duplicate-test/validator.py b/problems/042-first-duplicate-test/validator.py new file mode 100644 index 0000000..feb435c --- /dev/null +++ b/problems/042-first-duplicate-test/validator.py @@ -0,0 +1,20 @@ +import re +import sys + + +def fail(): + raise SystemExit(1) + + +try: + tokens = sys.stdin.buffer.read().decode("utf-8").split() + if not tokens or re.fullmatch(r"[1-9][0-9]*", tokens[0]) is None: + fail() + n = int(tokens[0]) + if not 1 <= n <= 200_000 or len(tokens) != n + 1: + fail() + fingerprint = re.compile(r"[0-9a-f]{1,32}") + if any(fingerprint.fullmatch(token) is None for token in tokens[1:]): + fail() +except (UnicodeDecodeError, ValueError, OverflowError): + fail() diff --git a/problems/043-verdict-range-counts/editorial.en.md b/problems/043-verdict-range-counts/editorial.en.md new file mode 100644 index 0000000..df78bc4 --- /dev/null +++ b/problems/043-verdict-range-counts/editorial.en.md @@ -0,0 +1,30 @@ +# Editorial + +## Intuitive Approach + +Scanning `[L,R]` for every query takes `O(NQ)` time in the worst case. An intermediate method stores sorted positions for each verdict and uses two binary searches per query, improving the total to `O(N + Q log N)`. + +## Optimal Approach: Four Prefix Counts + +Let `pref[v][i]` be the number of verdict `v` values among the first `i` positions. Build the table from left to right by copying the previous column and incrementing the current verdict. A query is: + +```text +pref[V][R] - pref[V][L - 1] +``` + +The fixed four-verdict alphabet maps directly to a four-element array; a general dictionary is unnecessary. + +## Correctness Proof + +By definition, `pref[V][R]` counts every `V` in positions `1..R`, while `pref[V][L-1]` counts exactly those left of the query in positions `1..L-1`. Their difference contains precisely `[L,R]`, with no omitted or repeated position. Construction adds each position's verdict exactly once, so the prefix definition holds everywhere. + +## Complexity + +Building takes `O(N)`, and each query takes `O(1)`, for `O(N+Q)` total time. The four prefix arrays and input/output buffers have a common `O(N+Q)` space bound. + +## Common Mistakes + +- Using `pref[R] - pref[L]` for a closed interval. +- Mixing zero-based and one-based indices. +- Reallocating or copying the verdict string for every query. +- Mapping an unvalidated query character to a valid verdict accidentally. diff --git a/problems/043-verdict-range-counts/editorial.zh-TW.md b/problems/043-verdict-range-counts/editorial.zh-TW.md new file mode 100644 index 0000000..14f854a --- /dev/null +++ b/problems/043-verdict-range-counts/editorial.zh-TW.md @@ -0,0 +1,30 @@ +# 解題說明 + +## 直覺解法 + +每次直接掃描 `[L,R]`,最壞時間為 `O(NQ)`。也可以為每種 verdict 儲存排序後的位置,利用兩次二分搜尋計數,總時間改善為 `O(N + Q log N)`。 + +## 最佳解法:四組前綴計數 + +令 `pref[v][i]` 表示前 `i` 個位置中 verdict `v` 的數量。從左到右複製前一欄,並把目前 verdict 的計數加一。查詢答案為: + +```text +pref[V][R] - pref[V][L - 1] +``` + +固定四種 verdict 可直接映射到大小為四的陣列,不需要一般字典。 + +## 正確性證明 + +依定義,`pref[V][R]` 計算位置 `1..R` 中所有 `V`,`pref[V][L-1]` 則計算查詢區間左側 `1..L-1` 中所有 `V`。兩者相減恰好留下 `[L,R]`,沒有漏算或重算。前綴表逐位置把目前字元加入一次,因此其定義對所有位置成立。 + +## 複雜度 + +建表 `O(N)`,每個查詢 `O(1)`,總時間 `O(N+Q)`。四組前綴與輸入/輸出緩衝的共同空間上界為 `O(N+Q)`。 + +## 常見錯誤 + +- 把閉區間公式寫成 `pref[R] - pref[L]`。 +- 混用 0-based 與 1-based index。 +- 為每個查詢重新配置或複製 verdict 字串。 +- 未驗證查詢字元,錯把未知字元映射到某個合法 verdict。 diff --git a/problems/043-verdict-range-counts/generator.py b/problems/043-verdict-range-counts/generator.py new file mode 100644 index 0000000..675abf7 --- /dev/null +++ b/problems/043-verdict-range-counts/generator.py @@ -0,0 +1,27 @@ +import random +import sys + + +if len(sys.argv) != 3: + raise SystemExit("usage: generator.py SEED INDEX") +seed, index = int(sys.argv[1]), int(sys.argv[2]) +randomizer = random.Random((seed << 32) ^ index) +alphabet = "AWRT" +if index == 999_999: + n, q = 100_000, 80_000 + verdicts = "".join(alphabet[((i * 37) ^ (i >> 3)) & 3] for i in range(n)) + print(n, q) + print(verdicts) + for i in range(q): + left = (i * 7_919) % n + 1 + length = (i * 104_729) % (n - left + 1) + 1 + print(left, left + length - 1, alphabet[i & 3]) +else: + n, q = randomizer.randint(1, 40), randomizer.randint(1, 40) + verdicts = "".join(randomizer.choice(alphabet) for _ in range(n)) + print(n, q) + print(verdicts) + for _ in range(q): + left = randomizer.randint(1, n) + right = randomizer.randint(left, n) + print(left, right, randomizer.choice(alphabet)) diff --git a/problems/043-verdict-range-counts/oracle.py b/problems/043-verdict-range-counts/oracle.py new file mode 100644 index 0000000..7f805f9 --- /dev/null +++ b/problems/043-verdict-range-counts/oracle.py @@ -0,0 +1,19 @@ +import bisect +import sys + + +tokens = sys.stdin.buffer.read().split() +n, q = map(int, tokens[:2]) +verdicts = tokens[2].decode() +positions = {value: [] for value in "AWRT"} +for index, value in enumerate(verdicts, 1): + positions[value].append(index) +output = [] +cursor = 3 +for _ in range(q): + left, right = int(tokens[cursor]), int(tokens[cursor + 1]) + verdict = tokens[cursor + 2].decode() + cursor += 3 + locations = positions[verdict] + output.append(str(bisect.bisect_right(locations, right) - bisect.bisect_left(locations, left))) +print("\n".join(output)) diff --git a/problems/043-verdict-range-counts/problem.json b/problems/043-verdict-range-counts/problem.json new file mode 100644 index 0000000..fc172d1 --- /dev/null +++ b/problems/043-verdict-range-counts/problem.json @@ -0,0 +1,155 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 43, + "slug": "verdict-range-counts", + "title": { + "zh-TW": "判決區間計數", + "en": "Verdict Range Counts" + }, + "difficulty": "easy", + "tags": [ + "prefix-sum", + "range-query", + "static-data" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-01", + "kind": "adversarial", + "input": "tests/adversarial-01.in", + "output": "tests/adversarial-01.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 30000000000, + "memoryLimitBytes": 134217728 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 10000000000, + "memoryLimitBytes": 100663296 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 5000000000, + "memoryLimitBytes": 67108864 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "每次查詢掃描整個區間", + "en": "Scan the entire range for every query" + }, + "time": "O(NQ)", + "space": "O(1) auxiliary", + "accepted": false + }, + { + "name": { + "zh-TW": "每種判決的位置表搭配二分搜尋", + "en": "Position lists with binary search" + }, + "time": "O(N + Q log N)", + "space": "O(N)", + "accepted": true + }, + { + "name": { + "zh-TW": "四組前綴計數", + "en": "Four prefix-count arrays" + }, + "time": "O(N + Q)", + "space": "O(N + Q)", + "accepted": true + } + ] +} diff --git a/problems/043-verdict-range-counts/solutions/c/main.c b/problems/043-verdict-range-counts/solutions/c/main.c new file mode 100644 index 0000000..4406601 --- /dev/null +++ b/problems/043-verdict-range-counts/solutions/c/main.c @@ -0,0 +1,39 @@ +#include +#include +#include + +static int verdict_index(char value) { + if (value == 'A') return 0; + if (value == 'W') return 1; + if (value == 'R') return 2; + return 3; +} + +int main(void) { + int n, q; + if (scanf("%d%d", &n, &q) != 2) return 1; + char *verdicts = malloc((size_t)n + 1U); + uint32_t *prefix = calloc((size_t)4 * ((size_t)n + 1U), sizeof(*prefix)); + if (verdicts == NULL || prefix == NULL) return 1; + if (scanf("%s", verdicts) != 1) return 1; + size_t stride = (size_t)n + 1U; + for (int i = 1; i <= n; i++) { + for (int kind = 0; kind < 4; kind++) { + prefix[(size_t)kind * stride + (size_t)i] = prefix[(size_t)kind * stride + (size_t)(i - 1)]; + } + int kind = verdict_index(verdicts[i - 1]); + prefix[(size_t)kind * stride + (size_t)i]++; + } + for (int query = 0; query < q; query++) { + int left, right; + char verdict[2]; + if (scanf("%d%d%1s", &left, &right, verdict) != 3) return 1; + int kind = verdict_index(verdict[0]); + uint32_t answer = prefix[(size_t)kind * stride + (size_t)right] + - prefix[(size_t)kind * stride + (size_t)(left - 1)]; + printf("%u\n", answer); + } + free(prefix); + free(verdicts); + return 0; +} diff --git a/problems/043-verdict-range-counts/solutions/cpp/main.cpp b/problems/043-verdict-range-counts/solutions/cpp/main.cpp new file mode 100644 index 0000000..5b3c821 --- /dev/null +++ b/problems/043-verdict-range-counts/solutions/cpp/main.cpp @@ -0,0 +1,35 @@ +#include +#include +#include +#include +#include + +static int verdict_index(char value) { + if (value == 'A') return 0; + if (value == 'W') return 1; + if (value == 'R') return 2; + return 3; +} + +int main() { + std::ios::sync_with_stdio(false); + std::cin.tie(nullptr); + int n, q; + std::string verdicts; + if (!(std::cin >> n >> q >> verdicts)) return 1; + std::vector> prefix(static_cast(n) + 1); + for (int i = 1; i <= n; ++i) { + prefix[static_cast(i)] = prefix[static_cast(i - 1)]; + ++prefix[static_cast(i)][static_cast(verdict_index(verdicts[static_cast(i - 1)]))]; + } + for (int query = 0; query < q; ++query) { + int left, right; + char verdict; + std::cin >> left >> right >> verdict; + const auto kind = static_cast(verdict_index(verdict)); + std::cout << prefix[static_cast(right)][kind] + - prefix[static_cast(left - 1)][kind] + << '\n'; + } + return 0; +} diff --git a/problems/043-verdict-range-counts/solutions/go/main.go b/problems/043-verdict-range-counts/solutions/go/main.go new file mode 100644 index 0000000..0fd4e8b --- /dev/null +++ b/problems/043-verdict-range-counts/solutions/go/main.go @@ -0,0 +1,43 @@ +package main + +import ( + "bufio" + "fmt" + "os" +) + +func verdictIndex(value byte) int { + switch value { + case 'A': + return 0 + case 'W': + return 1 + case 'R': + return 2 + default: + return 3 + } +} + +func main() { + in := bufio.NewReaderSize(os.Stdin, 1<<20) + out := bufio.NewWriterSize(os.Stdout, 1<<20) + defer out.Flush() + var n, q int + var verdicts string + if _, err := fmt.Fscan(in, &n, &q, &verdicts); err != nil { + return + } + prefix := make([][4]uint32, n+1) + for i := 1; i <= n; i++ { + prefix[i] = prefix[i-1] + prefix[i][verdictIndex(verdicts[i-1])]++ + } + for query := 0; query < q; query++ { + var left, right int + var verdict string + fmt.Fscan(in, &left, &right, &verdict) + kind := verdictIndex(verdict[0]) + fmt.Fprintln(out, prefix[right][kind]-prefix[left-1][kind]) + } +} diff --git a/problems/043-verdict-range-counts/solutions/javascript/main.js b/problems/043-verdict-range-counts/solutions/javascript/main.js new file mode 100644 index 0000000..7348b0a --- /dev/null +++ b/problems/043-verdict-range-counts/solutions/javascript/main.js @@ -0,0 +1,42 @@ +import * as std from "std"; + +const input = std.in.readAsString(); +let cursor = 0; +function nextToken() { + while (cursor < input.length && input.charCodeAt(cursor) <= 32) cursor++; + const start = cursor; + while (cursor < input.length && input.charCodeAt(cursor) > 32) cursor++; + return input.slice(start, cursor); +} +/** @param {string} value */ +function verdictIndex(value) { + if (value === "A") return 0; + if (value === "W") return 1; + if (value === "R") return 2; + return 3; +} + +const n = Number(nextToken()); +const q = Number(nextToken()); +const verdicts = nextToken(); +const prefix = Array.from({ length: 4 }, () => new Uint32Array(n + 1)); +for (let index = 1; index <= n; index++) { + for (let kind = 0; kind < 4; kind++) prefix[kind][index] = prefix[kind][index - 1]; + prefix[verdictIndex(verdicts[index - 1])][index]++; +} +let output = ""; +/** @param {number} line */ +function emit(line) { + output += `${line}\n`; + if (output.length >= 65536) { + std.out.puts(output); + output = ""; + } +} +for (let query = 0; query < q; query++) { + const left = Number(nextToken()); + const right = Number(nextToken()); + const kind = verdictIndex(nextToken()); + emit(prefix[kind][right] - prefix[kind][left - 1]); +} +if (output) std.out.puts(output); diff --git a/problems/043-verdict-range-counts/solutions/python/main.py b/problems/043-verdict-range-counts/solutions/python/main.py new file mode 100644 index 0000000..fefb958 --- /dev/null +++ b/problems/043-verdict-range-counts/solutions/python/main.py @@ -0,0 +1,20 @@ +import sys + + +tokens = sys.stdin.buffer.read().split() +n, q = map(int, tokens[:2]) +verdicts = tokens[2] +mapping = {ord("A"): 0, ord("W"): 1, ord("R"): 2, ord("T"): 3} +prefix = [[0] * (n + 1) for _ in range(4)] +for index, verdict in enumerate(verdicts, 1): + for kind in range(4): + prefix[kind][index] = prefix[kind][index - 1] + prefix[mapping[verdict]][index] += 1 +output = [] +cursor = 3 +for _ in range(q): + left, right = int(tokens[cursor]), int(tokens[cursor + 1]) + kind = mapping[tokens[cursor + 2][0]] + cursor += 3 + output.append(str(prefix[kind][right] - prefix[kind][left - 1])) +sys.stdout.write("\n".join(output) + "\n") diff --git a/problems/043-verdict-range-counts/solutions/rust/main.rs b/problems/043-verdict-range-counts/solutions/rust/main.rs new file mode 100644 index 0000000..5bb18e4 --- /dev/null +++ b/problems/043-verdict-range-counts/solutions/rust/main.rs @@ -0,0 +1,33 @@ +use std::io::{self, Read}; + +fn verdict_index(value: u8) -> usize { + match value { + b'A' => 0, + b'W' => 1, + b'R' => 2, + _ => 3, + } +} + +fn main() { + let mut input = String::new(); + io::stdin().read_to_string(&mut input).unwrap(); + let mut tokens = input.split_whitespace(); + let n: usize = tokens.next().unwrap().parse().unwrap(); + let q: usize = tokens.next().unwrap().parse().unwrap(); + let verdicts = tokens.next().unwrap().as_bytes(); + let mut prefix = vec![[0_u32; 4]; n + 1]; + for index in 1..=n { + prefix[index] = prefix[index - 1]; + prefix[index][verdict_index(verdicts[index - 1])] += 1; + } + let mut output = String::new(); + for _ in 0..q { + let left: usize = tokens.next().unwrap().parse().unwrap(); + let right: usize = tokens.next().unwrap().parse().unwrap(); + let kind = verdict_index(tokens.next().unwrap().as_bytes()[0]); + let answer = prefix[right][kind] - prefix[left - 1][kind]; + output.push_str(&format!("{answer}\n")); + } + print!("{output}"); +} diff --git a/problems/043-verdict-range-counts/solutions/typescript/main.ts b/problems/043-verdict-range-counts/solutions/typescript/main.ts new file mode 100644 index 0000000..0f3ab1a --- /dev/null +++ b/problems/043-verdict-range-counts/solutions/typescript/main.ts @@ -0,0 +1,40 @@ +import * as std from "std"; + +const input: string = std.in.readAsString(); +let cursor = 0; +function nextToken(): string { + while (cursor < input.length && input.charCodeAt(cursor) <= 32) cursor++; + const start = cursor; + while (cursor < input.length && input.charCodeAt(cursor) > 32) cursor++; + return input.slice(start, cursor); +} +function verdictIndex(value: string): number { + if (value === "A") return 0; + if (value === "W") return 1; + if (value === "R") return 2; + return 3; +} + +const n = Number(nextToken()); +const q = Number(nextToken()); +const verdicts = nextToken(); +const prefix: Uint32Array[] = Array.from({ length: 4 }, () => new Uint32Array(n + 1)); +for (let index = 1; index <= n; index++) { + for (let kind = 0; kind < 4; kind++) prefix[kind][index] = prefix[kind][index - 1]; + prefix[verdictIndex(verdicts[index - 1])][index]++; +} +let output = ""; +function emit(line: number): void { + output += `${line}\n`; + if (output.length >= 65536) { + std.out.puts(output); + output = ""; + } +} +for (let query = 0; query < q; query++) { + const left = Number(nextToken()); + const right = Number(nextToken()); + const kind = verdictIndex(nextToken()); + emit(prefix[kind][right] - prefix[kind][left - 1]); +} +if (output) std.out.puts(output); diff --git a/problems/043-verdict-range-counts/statement.en.md b/problems/043-verdict-range-counts/statement.en.md new file mode 100644 index 0000000..17889f5 --- /dev/null +++ b/problems/043-verdict-range-counts/statement.en.md @@ -0,0 +1,91 @@ +# Verdict Range Counts + +While designing the verdict-analysis interface for a WASM OJ, we wanted users to inspect the failure distribution within any consecutive group of tests quickly. For example, they may want to count Runtime Errors only in the stress-test section or compare the number of Wrong Answers between two groups of cases. + +One submission has already recorded `N` verdicts by case index. Each verdict is represented by one character: `A` for Accepted, `W` for Wrong Answer, `R` for Runtime Error, or `T` for Time Limit. This record does not change while it is being analyzed. + +Answer `Q` static range queries. A query `L R V` asks how many times verdict `V` occurs in the closed interval `[L, R]`. All indices are one-based. + +## Input + +The first line contains `N Q`. The second line is a verdict string of length `N`. Each of the next `Q` lines contains `L R V`. + +## Output + +Output one count per query. + +## Constraints + +- `1 <= N, Q <= 200000` +- The verdict string and query characters contain only `A`, `W`, `R`, and `T`. +- `1 <= L <= R <= N` + +## Examples + + + +### Example One + +Input: + +```text +8 4 +AAWRTWAA +1 8 A +3 6 W +4 7 R +5 5 T +``` + +Output: + +```text +4 +2 +1 +1 +``` + +### Example Two + +Input: + +```text +5 3 +WWWWW +1 5 A +2 4 W +3 3 W +``` + +Output: + +```text +0 +3 +1 +``` + +### Example Three + +Input: + +```text +4 4 +ARTW +1 1 A +1 4 T +2 3 W +2 2 R +``` + +Output: + +```text +1 +1 +0 +1 +``` + + diff --git a/problems/043-verdict-range-counts/statement.zh-TW.md b/problems/043-verdict-range-counts/statement.zh-TW.md new file mode 100644 index 0000000..4e89729 --- /dev/null +++ b/problems/043-verdict-range-counts/statement.zh-TW.md @@ -0,0 +1,91 @@ +# 判決區間計數 + +在設計 WASM OJ 的判題結果分析介面時,我們希望使用者能快速檢查一段連續測資的失敗分布。例如,他們可能只想查看壓力測試區段中出現多少次 Runtime Error,或比較前後兩組 cases 的 Wrong Answer 數量。 + +一次 submission 已經依 case index 記錄了 `N` 個 verdicts。每個 verdict 以一個字元表示:`A` 代表 Accepted、`W` 代表 Wrong Answer、`R` 代表 Runtime Error、`T` 代表 Time Limit。分析期間這份紀錄不會再改變。 + +你需要回答 `Q` 個靜態區間查詢。查詢 `L R V` 要求閉區間 `[L, R]` 內 verdict `V` 的出現次數。所有 index 從 `1` 開始。 + +## 輸入 + +第一行包含 `N Q`。第二行是一個長度為 `N` 的 verdict 字串。接下來 `Q` 行各包含 `L R V`。 + +## 輸出 + +對每個查詢輸出一行計數。 + +## 限制 + +- `1 <= N, Q <= 200000` +- verdict 字串及查詢字元只包含 `A`、`W`、`R`、`T`。 +- `1 <= L <= R <= N` + +## 範例 + + + +### 範例一 + +輸入: + +```text +8 4 +AAWRTWAA +1 8 A +3 6 W +4 7 R +5 5 T +``` + +輸出: + +```text +4 +2 +1 +1 +``` + +### 範例二 + +輸入: + +```text +5 3 +WWWWW +1 5 A +2 4 W +3 3 W +``` + +輸出: + +```text +0 +3 +1 +``` + +### 範例三 + +輸入: + +```text +4 4 +ARTW +1 1 A +1 4 T +2 3 W +2 2 R +``` + +輸出: + +```text +1 +1 +0 +1 +``` + + diff --git a/problems/043-verdict-range-counts/tests/adversarial-01.in b/problems/043-verdict-range-counts/tests/adversarial-01.in new file mode 100644 index 0000000..05f24ca --- /dev/null +++ b/problems/043-verdict-range-counts/tests/adversarial-01.in @@ -0,0 +1,80002 @@ +100000 80000 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b/problems/043-verdict-range-counts/tests/sample-01.in new file mode 100644 index 0000000..f36d8f4 --- /dev/null +++ b/problems/043-verdict-range-counts/tests/sample-01.in @@ -0,0 +1,6 @@ +8 4 +AAWRTWAA +1 8 A +3 6 W +4 7 R +5 5 T diff --git a/problems/043-verdict-range-counts/tests/sample-01.out b/problems/043-verdict-range-counts/tests/sample-01.out new file mode 100644 index 0000000..171e008 --- /dev/null +++ b/problems/043-verdict-range-counts/tests/sample-01.out @@ -0,0 +1,4 @@ +4 +2 +1 +1 diff --git a/problems/043-verdict-range-counts/tests/sample-02.in b/problems/043-verdict-range-counts/tests/sample-02.in new file mode 100644 index 0000000..697357c --- /dev/null +++ b/problems/043-verdict-range-counts/tests/sample-02.in @@ -0,0 +1,5 @@ +5 3 +WWWWW +1 5 A +2 4 W +3 3 W diff --git a/problems/043-verdict-range-counts/tests/sample-02.out b/problems/043-verdict-range-counts/tests/sample-02.out new file mode 100644 index 0000000..67e55c6 --- /dev/null +++ b/problems/043-verdict-range-counts/tests/sample-02.out @@ -0,0 +1,3 @@ +0 +3 +1 diff --git a/problems/043-verdict-range-counts/tests/sample-03.in b/problems/043-verdict-range-counts/tests/sample-03.in new file mode 100644 index 0000000..571f81a --- /dev/null +++ b/problems/043-verdict-range-counts/tests/sample-03.in @@ -0,0 +1,6 @@ +4 4 +ARTW +1 1 A +1 4 T +2 3 W +2 2 R diff --git a/problems/043-verdict-range-counts/tests/sample-03.out b/problems/043-verdict-range-counts/tests/sample-03.out new file mode 100644 index 0000000..68b8a88 --- /dev/null +++ b/problems/043-verdict-range-counts/tests/sample-03.out @@ -0,0 +1,4 @@ +1 +1 +0 +1 diff --git a/problems/043-verdict-range-counts/validator.py b/problems/043-verdict-range-counts/validator.py new file mode 100644 index 0000000..1486d99 --- /dev/null +++ b/problems/043-verdict-range-counts/validator.py @@ -0,0 +1,38 @@ +import re +import sys + + +def fail(): + raise SystemExit(1) + + +try: + tokens = sys.stdin.buffer.read().decode("utf-8").split() + position = 0 + + def unsigned(minimum, maximum): + global position + if position >= len(tokens) or re.fullmatch(r"0|[1-9][0-9]*", tokens[position]) is None: + fail() + value = int(tokens[position]) + position += 1 + if not minimum <= value <= maximum: + fail() + return value + + n, q = unsigned(1, 200_000), unsigned(1, 200_000) + if position >= len(tokens): + fail() + verdicts = tokens[position] + position += 1 + if len(verdicts) != n or any(value not in "AWRT" for value in verdicts): + fail() + for _ in range(q): + left, right = unsigned(1, n), unsigned(1, n) + if left > right or position >= len(tokens) or tokens[position] not in {"A", "W", "R", "T"}: + fail() + position += 1 + if position != len(tokens): + fail() +except (UnicodeDecodeError, ValueError, OverflowError): + fail() diff --git a/problems/044-recent-submission-reuse/editorial.en.md b/problems/044-recent-submission-reuse/editorial.en.md new file mode 100644 index 0000000..b387c5c --- /dev/null +++ b/problems/044-recent-submission-reuse/editorial.en.md @@ -0,0 +1,40 @@ +# Editorial + +Let `L` be the maximum fingerprint length, `S` the total input fingerprint length, and `U` the number of distinct fingerprints. + +## Intuitive Approach + +For each submission `i`, compare its exact token with the previous at most `K` submissions. Stop after the first match. This uses `O(N K L)` time in the worst case and `O(K L)` auxiliary space if the recent tokens are kept in a queue. It is simple, but too slow when both `N` and `K` are large. + +## Improved Approach: Balanced Search Tree + +Maintain the most recent index for every fingerprint in an ordered map. A lookup and update take `O(log U)` ordered string comparisons, each costing up to `O(L)`. Submission `i` is a hit exactly when the stored index is at least `i - K`. This gives `O(N log N * L)` time and `O(U L)` space. + +## Optimal Approach: Last-Position Hash Map + +The full recent window need not be stored. For each fingerprint, only its latest previous position can matter: if that position is older than `i - K`, every earlier equal position is older too. + +Scan from left to right. Let `last[f]` be the most recent index with fingerprint `f`. + +1. If `f` is in the map and `i - last[f] <= K`, count one hit. +2. Set `last[f] = i`, whether this submission was a hit or a miss. + +For `K = 0`, every positive index difference exceeds `K`, so the same rule correctly counts no hits. + +## Correctness Proof + +Immediately before processing index `i`, `last[f]` is the greatest index smaller than `i` whose fingerprint is `f`, if one exists. The invariant is true before the first submission and remains true because the algorithm assigns `last[f] = i` after processing `i` without changing other entries. + +If `i - last[f] <= K`, that latest occurrence lies in `[max(1, i-K), i-1]`, so submission `i` is a hit. If the latest occurrence is absent or farther than `K`, every earlier occurrence has an even larger distance and none lies in the interval, so it is a miss. Thus each submission is classified exactly as defined, and their accumulated count is correct. + +## Complexity + +With expected constant-time hash-table operations, processing and hashing all tokens takes expected `O(S)` time. The algorithmic core retains only `U` distinct tokens and their last positions, using `O(U L)` space; input buffering or an `N`-sized hash-table reservation in the seven references gives a common resident bound of `O(S)`. Exact token comparison resolves hash collisions. + +## Common Mistakes + +- Treating the window as `[i-K, i]` and letting a submission match itself. +- Using `< K` rather than `<= K`; a matching submission exactly `K` positions earlier is included. +- Counting all matching positions in the window rather than one hit for the current submission. +- Updating the last position before testing it, which makes every submission match itself. +- Special-casing `K = 0` incorrectly or parsing tokens as numbers. diff --git a/problems/044-recent-submission-reuse/editorial.zh-TW.md b/problems/044-recent-submission-reuse/editorial.zh-TW.md new file mode 100644 index 0000000..edb8710 --- /dev/null +++ b/problems/044-recent-submission-reuse/editorial.zh-TW.md @@ -0,0 +1,40 @@ +# 解題說明 + +令 `L` 為 fingerprint 最大長度、`S` 為所有 fingerprint 長度總和、`U` 為不同 fingerprint 數量。 + +## 直覺解法 + +對每筆 submission `i`,向前比較至多 `K` 筆完整 token,找到第一個相同者就停止。若以 queue 保存近期 token,worst case 時間為 `O(N K L)`、輔助空間為 `O(K L)`。此法容易理解,但 `N` 與 `K` 都大時無法完成。 + +## 進階解法:平衡搜尋樹 + +以 ordered map 保存每個 fingerprint 最近一次的 index。查詢與更新需要 `O(log U)` 次有序字串比較,每次比較最多 `O(L)`。第 `i` 筆恰在保存的 index 不小於 `i-K` 時成為 hit。總時間 `O(N log N * L)`,空間 `O(U L)`。 + +## 最佳解法:最近位置 Hash Map + +不必保存整個近期 window。對同一 fingerprint 而言,只有最近一次位置可能有用:若最近位置都早於 `i-K`,更早的相同位置也一定過期。 + +由左至右掃描,令 `last[f]` 為 fingerprint `f` 最近一次的 index: + +1. 若 map 中已有 `f` 且 `i - last[f] <= K`,hit 數加一。 +2. 無論本次為 hit 或 miss,都設定 `last[f] = i`。 + +當 `K = 0` 時,任何兩個不同 index 的距離都大於 `K`,同一規則自然得到零次 hit。 + +## 正確性證明 + +處理 index `i` 前,若 fingerprint `f` 曾出現,`last[f]` 是所有小於 `i` 的相同 fingerprint 中 index 最大者。第一筆前此不變量成立;處理完 `i` 後設定 `last[f]=i` 且不改其他 entry,因此不變量持續成立。 + +若 `i-last[f] <= K`,這個最近位置位於 `[max(1,i-K),i-1]`,所以第 `i` 筆是 hit。若最近位置不存在或距離大於 `K`,所有更早的相同位置距離只會更大,區間內不可能有相同 fingerprint,因此為 miss。每筆分類都符合定義,累加結果正確。 + +## 複雜度 + +在 hash table 操作期望為常數時間時,處理並 hash 全部 token 的期望時間為 `O(S)`。演算法核心只需保存 `U` 個不同 token 與最近位置,為 `O(U L)`;七語言 reference 的輸入緩衝或按 `N` 預留的 hash table 使共同 resident 上界為 `O(S)`。Hash collision 必須以完整 token 比較解決。 + +## 常見錯誤 + +- 把 window 寫成 `[i-K,i]`,讓 submission 與自己配對。 +- 使用 `< K` 而非 `<= K`;恰好早 `K` 個位置仍在 window 內。 +- 計算 window 中所有相同位置;每一筆 submission 最多只貢獻一次 hit。 +- 先更新最近位置再判斷,造成每筆都與自己相同。 +- 錯誤特判 `K=0`,或將 token 解析成數字。 diff --git a/problems/044-recent-submission-reuse/generator.py b/problems/044-recent-submission-reuse/generator.py new file mode 100644 index 0000000..6fa57d9 --- /dev/null +++ b/problems/044-recent-submission-reuse/generator.py @@ -0,0 +1,42 @@ +import random +import sys + + +if len(sys.argv) != 3: + raise SystemExit("usage: generator.py SEED INDEX") + +seed = int(sys.argv[1]) +index = int(sys.argv[2]) +if index == 999_999: + n, k = 200_000, 50_000 + fingerprints = [format(position % k + 1, "x") for position in range(n)] + print(n, k) + print(*fingerprints) + raise SystemExit(0) + +rng = random.Random((seed << 32) ^ index) +n = rng.randint(1, min(40, 9 + index % 32)) +k = 0 if index % 7 == 0 else rng.randint(0, n) +pool_size = rng.randint(1, min(n, 3 + index % 13)) +pool = [] +used = set() +while len(pool) < pool_size: + width = rng.randint(1, 8) + token = "".join(rng.choice("0123456789abcdef") for _ in range(width)) + if token not in used: + used.add(token) + pool.append(token) + +fingerprints = [] +for position in range(n): + if position < pool_size: + fingerprints.append(pool[position]) + elif rng.random() < 0.75: + fingerprints.append(rng.choice(pool)) + else: + value = ((seed + 1) * 1_000_003 + index * 101 + position) & ((1 << 64) - 1) + token = format(value, "x") + fingerprints.append(token) + +print(n, k) +print(*fingerprints) diff --git a/problems/044-recent-submission-reuse/oracle.py b/problems/044-recent-submission-reuse/oracle.py new file mode 100644 index 0000000..2da9682 --- /dev/null +++ b/problems/044-recent-submission-reuse/oracle.py @@ -0,0 +1,11 @@ +import sys + + +tokens = sys.stdin.buffer.read().split() +n, k = int(tokens[0]), int(tokens[1]) +ordered = sorted((fingerprint, index) for index, fingerprint in enumerate(tokens[2:n + 2], 1)) +hits = 0 +for left, right in zip(ordered, ordered[1:]): + if left[0] == right[0] and right[1] - left[1] <= k: + hits += 1 +print(hits) diff --git a/problems/044-recent-submission-reuse/problem.json b/problems/044-recent-submission-reuse/problem.json new file mode 100644 index 0000000..a420d7c --- /dev/null +++ b/problems/044-recent-submission-reuse/problem.json @@ -0,0 +1,156 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 44, + "slug": "recent-submission-reuse", + "title": { + "zh-TW": "最近重複的 Submission", + "en": "Recent Submission Reuse" + }, + "difficulty": "easy", + "tags": [ + "hash-map", + "sliding-window", + "strings", + "last-occurrence" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-blind-01", + "kind": "adversarial", + "input": "tests/adversarial-blind-01.in", + "output": "tests/adversarial-blind-01.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 20000000000, + "memoryLimitBytes": 134217728 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 7500000000, + "memoryLimitBytes": 100663296 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 3000000000, + "memoryLimitBytes": 67108864 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "逐一掃描前 K 筆 submission", + "en": "Scan the previous K submissions" + }, + "time": "O(N K L)", + "space": "O(K L)", + "accepted": false + }, + { + "name": { + "zh-TW": "平衡樹保存最近位置", + "en": "Balanced tree of last positions" + }, + "time": "O(N log N * L)", + "space": "O(U L)", + "accepted": false + }, + { + "name": { + "zh-TW": "最近位置 hash map", + "en": "Last-position hash map" + }, + "time": "O(S) expected", + "space": "O(S)", + "accepted": true + } + ] +} diff --git a/problems/044-recent-submission-reuse/solutions/c/main.c b/problems/044-recent-submission-reuse/solutions/c/main.c new file mode 100644 index 0000000..537d09e --- /dev/null +++ b/problems/044-recent-submission-reuse/solutions/c/main.c @@ -0,0 +1,54 @@ +#include +#include +#include +#include + +typedef struct { + char key[33]; + int last_index; +} Entry; + +static uint64_t hash_token(const char *token) { + uint64_t hash = UINT64_C(14695981039346656037); + while (*token != '\0') { + hash ^= (unsigned char)*token++; + hash *= UINT64_C(1099511628211); + } + return hash; +} + +int main(void) { + int n, k; + if (scanf("%d%d", &n, &k) != 2) + return 0; + + size_t capacity = 1; + while (capacity < (size_t)n * 2) + capacity <<= 1; + Entry *table = calloc(capacity, sizeof(*table)); + if (table == NULL) + return 1; + + int hits = 0; + for (int index = 1; index <= n; index++) { + char token[33]; + if (scanf("%32s", token) != 1) { + free(table); + return 0; + } + size_t slot = (size_t)hash_token(token) & (capacity - 1); + while (table[slot].last_index != 0 && strcmp(table[slot].key, token) != 0) + slot = (slot + 1) & (capacity - 1); + if (table[slot].last_index != 0) { + if (index - table[slot].last_index <= k) + hits++; + } else { + strcpy(table[slot].key, token); + } + table[slot].last_index = index; + } + + printf("%d\n", hits); + free(table); + return 0; +} diff --git a/problems/044-recent-submission-reuse/solutions/cpp/main.cpp b/problems/044-recent-submission-reuse/solutions/cpp/main.cpp new file mode 100644 index 0000000..7526ecd --- /dev/null +++ b/problems/044-recent-submission-reuse/solutions/cpp/main.cpp @@ -0,0 +1,25 @@ +#include +#include +#include +using namespace std; + +int main() { + ios::sync_with_stdio(false); + cin.tie(nullptr); + + int n, k; + if (!(cin >> n >> k)) + return 0; + unordered_map last_index; + last_index.reserve(static_cast(n) * 2); + int hits = 0; + for (int index = 1; index <= n; ++index) { + string fingerprint; + cin >> fingerprint; + auto found = last_index.find(fingerprint); + if (found != last_index.end() && index - found->second <= k) + ++hits; + last_index[fingerprint] = index; + } + cout << hits << '\n'; +} diff --git a/problems/044-recent-submission-reuse/solutions/go/main.go b/problems/044-recent-submission-reuse/solutions/go/main.go new file mode 100644 index 0000000..603c71a --- /dev/null +++ b/problems/044-recent-submission-reuse/solutions/go/main.go @@ -0,0 +1,29 @@ +package main + +import ( + "bufio" + "fmt" + "os" +) + +func main() { + in := bufio.NewReaderSize(os.Stdin, 1<<20) + out := bufio.NewWriter(os.Stdout) + defer out.Flush() + + var n, k int + if _, err := fmt.Fscan(in, &n, &k); err != nil { + return + } + lastIndex := make(map[string]int, n) + hits := 0 + for index := 1; index <= n; index++ { + var fingerprint string + fmt.Fscan(in, &fingerprint) + if previous, found := lastIndex[fingerprint]; found && index-previous <= k { + hits++ + } + lastIndex[fingerprint] = index + } + fmt.Fprintln(out, hits) +} diff --git a/problems/044-recent-submission-reuse/solutions/javascript/main.js b/problems/044-recent-submission-reuse/solutions/javascript/main.js new file mode 100644 index 0000000..1d3475e --- /dev/null +++ b/problems/044-recent-submission-reuse/solutions/javascript/main.js @@ -0,0 +1,22 @@ +import * as std from "std"; + +const input = std.in.readAsString(); +let cursor = 0; +function nextToken() { + while (cursor < input.length && input.charCodeAt(cursor) <= 32) cursor++; + const start = cursor; + while (cursor < input.length && input.charCodeAt(cursor) > 32) cursor++; + return input.slice(start, cursor); +} + +const count = Number(nextToken()); +const windowSize = Number(nextToken()); +const lastIndex = new Map(); +let hits = 0; +for (let index = 1; index <= count; index++) { + const fingerprint = nextToken(); + const previous = lastIndex.get(fingerprint); + if (previous !== undefined && index - previous <= windowSize) hits++; + lastIndex.set(fingerprint, index); +} +std.out.puts(`${hits}\n`); diff --git a/problems/044-recent-submission-reuse/solutions/python/main.py b/problems/044-recent-submission-reuse/solutions/python/main.py new file mode 100644 index 0000000..ea992ec --- /dev/null +++ b/problems/044-recent-submission-reuse/solutions/python/main.py @@ -0,0 +1,19 @@ +import sys + + +def input_tokens(): + for line in sys.stdin.buffer: + yield from line.split() + + +tokens = input_tokens() +n, k = int(next(tokens)), int(next(tokens)) +last_index = {} +hits = 0 +for index in range(1, n + 1): + fingerprint = next(tokens) + previous = last_index.get(fingerprint) + if previous is not None and index - previous <= k: + hits += 1 + last_index[fingerprint] = index +print(hits) diff --git a/problems/044-recent-submission-reuse/solutions/rust/main.rs b/problems/044-recent-submission-reuse/solutions/rust/main.rs new file mode 100644 index 0000000..8b25789 --- /dev/null +++ b/problems/044-recent-submission-reuse/solutions/rust/main.rs @@ -0,0 +1,23 @@ +use std::collections::HashMap; +use std::io::{self, Read}; + +fn main() { + let mut input = String::new(); + io::stdin().read_to_string(&mut input).unwrap(); + let mut tokens = input.split_whitespace(); + let n: usize = tokens.next().unwrap().parse().unwrap(); + let k: usize = tokens.next().unwrap().parse().unwrap(); + let mut last_index: HashMap<&str, usize> = HashMap::with_capacity(n * 2); + let mut hits = 0usize; + + for index in 1..=n { + let fingerprint = tokens.next().unwrap(); + if let Some(&previous) = last_index.get(fingerprint) { + if index - previous <= k { + hits += 1; + } + } + last_index.insert(fingerprint, index); + } + println!("{}", hits); +} diff --git a/problems/044-recent-submission-reuse/solutions/typescript/main.ts b/problems/044-recent-submission-reuse/solutions/typescript/main.ts new file mode 100644 index 0000000..1530de6 --- /dev/null +++ b/problems/044-recent-submission-reuse/solutions/typescript/main.ts @@ -0,0 +1,22 @@ +import * as std from "std"; + +const input: string = std.in.readAsString(); +let cursor = 0; +function nextToken(): string { + while (cursor < input.length && input.charCodeAt(cursor) <= 32) cursor++; + const start = cursor; + while (cursor < input.length && input.charCodeAt(cursor) > 32) cursor++; + return input.slice(start, cursor); +} + +const count = Number(nextToken()); +const windowSize = Number(nextToken()); +const lastIndex = new Map(); +let hits = 0; +for (let index = 1; index <= count; index++) { + const fingerprint = nextToken(); + const previous = lastIndex.get(fingerprint); + if (previous !== undefined && index - previous <= windowSize) hits++; + lastIndex.set(fingerprint, index); +} +std.out.puts(`${hits}\n`); diff --git a/problems/044-recent-submission-reuse/statement.en.md b/problems/044-recent-submission-reuse/statement.en.md new file mode 100644 index 0000000..624daeb --- /dev/null +++ b/problems/044-recent-submission-reuse/statement.en.md @@ -0,0 +1,81 @@ +# Recent Submission Reuse + +While designing a short-term compilation cache for a WASM OJ, we wanted to avoid compiling the same source repeatedly within a short period. Every submission has a fingerprint. If the exact fingerprint was processed recently, the previous result can be reused. The cache retains only a bounded recent history, however, so an older submission can no longer produce a hit. + +The system receives `N` submissions in chronological order. Submission `i` has a lowercase hexadecimal fingerprint. Only the previous `K` submissions are recent enough, so submission `i` is a **reuse hit** if the same exact fingerprint appeared at an index in + +```text +[max(1, i - K), i - 1]. +``` + +Fingerprints are exact tokens, not hexadecimal numbers, so `0` and `00` are different. When `K = 0`, the interval is empty and every submission is a miss. A hit still becomes part of the recent history for later submissions. + +Count the total number of reuse hits. + +## Input + +The first line contains `N K`. + +The remaining input contains `N` whitespace-separated fingerprints in chronological order. + +## Output + +Output one line containing the number of reuse hits. + +## Constraints + +- `1 <= N <= 200000` +- `0 <= K <= N` +- Every fingerprint has length from `1` to `32`. +- Every character is one of `0`–`9` or `a`–`f`. + +## Examples + + + +### Example One + +Input: + +```text +7 3 +a b c a d b a +``` + +Output: + +```text +2 +``` + +### Example Two + +Input: + +```text +4 0 +aa aa aa aa +``` + +Output: + +```text +0 +``` + +### Example Three + +Input: + +```text +5 1 +aa aa aa bb aa +``` + +Output: + +```text +2 +``` + + diff --git a/problems/044-recent-submission-reuse/statement.zh-TW.md b/problems/044-recent-submission-reuse/statement.zh-TW.md new file mode 100644 index 0000000..9bd4ad7 --- /dev/null +++ b/problems/044-recent-submission-reuse/statement.zh-TW.md @@ -0,0 +1,81 @@ +# 最近重複的 Submission + +在設計 WASM OJ 的短期編譯快取時,我們不希望相同程式碼在短時間內被反覆編譯。每份 submission 都有一個 fingerprint;如果最近才處理過完全相同的 fingerprint,就可以重用先前的結果。然而快取只保留有限的近期歷史,太久以前的 submission 不再能命中。 + +系統依時間順序收到 `N` 筆 submissions。第 `i` 筆有一個小寫十六進位 fingerprint。只有前 `K` 筆 submission 還算近期,因此若完全相同的 fingerprint 曾出現在以下 index 區間,第 `i` 筆就是一次 **reuse hit**: + +```text +[max(1, i - K), i - 1] +``` + +Fingerprint 是精確 token,而非十六進位數值,因此 `0` 與 `00` 不同。當 `K = 0` 時區間為空,每筆 submission 都是 miss。某次 hit 仍然會成為後續 submission 的近期紀錄。 + +請計算 reuse hit 總數。 + +## 輸入 + +第一行包含 `N K`。 + +其餘輸入依時間順序包含 `N` 個以空白分隔的 fingerprint。 + +## 輸出 + +輸出一行 reuse hit 總數。 + +## 限制 + +- `1 ≤ N ≤ 200000` +- `0 ≤ K ≤ N` +- 每個 fingerprint 長度介於 `1` 到 `32`。 +- 每個字元皆為 `0`–`9` 或 `a`–`f`。 + +## 範例 + + + +### 範例一 + +輸入: + +```text +7 3 +a b c a d b a +``` + +輸出: + +```text +2 +``` + +### 範例二 + +輸入: + +```text +4 0 +aa aa aa aa +``` + +輸出: + +```text +0 +``` + +### 範例三 + +輸入: + +```text +5 1 +aa aa aa bb aa +``` + +輸出: + +```text +2 +``` + + diff --git a/problems/044-recent-submission-reuse/tests/adversarial-blind-01.in b/problems/044-recent-submission-reuse/tests/adversarial-blind-01.in new file mode 100644 index 0000000..2919833 --- /dev/null +++ b/problems/044-recent-submission-reuse/tests/adversarial-blind-01.in @@ -0,0 +1,2 @@ +200000 50000 +1 2 3 4 5 6 7 8 9 a b c d e f 10 11 12 13 14 15 16 17 18 19 1a 1b 1c 1d 1e 1f 20 21 22 23 24 25 26 27 28 29 2a 2b 2c 2d 2e 2f 30 31 32 33 34 35 36 37 38 39 3a 3b 3c 3d 3e 3f 40 41 42 43 44 45 46 47 48 49 4a 4b 4c 4d 4e 4f 50 51 52 53 54 55 56 57 58 59 5a 5b 5c 5d 5e 5f 60 61 62 63 64 65 66 67 68 69 6a 6b 6c 6d 6e 6f 70 71 72 73 74 75 76 77 78 79 7a 7b 7c 7d 7e 7f 80 81 82 83 84 85 86 87 88 89 8a 8b 8c 8d 8e 8f 90 91 92 93 94 95 96 97 98 99 9a 9b 9c 9d 9e 9f a0 a1 a2 a3 a4 a5 a6 a7 a8 a9 aa ab ac ad ae af b0 b1 b2 b3 b4 b5 b6 b7 b8 b9 ba bb bc bd be bf c0 c1 c2 c3 c4 c5 c6 c7 c8 c9 ca cb cc cd ce cf d0 d1 d2 d3 d4 d5 d6 d7 d8 d9 da db dc dd de df e0 e1 e2 e3 e4 e5 e6 e7 e8 e9 ea eb ec ed ee ef f0 f1 f2 f3 f4 f5 f6 f7 f8 f9 fa fb fc fd fe ff 100 101 102 103 104 105 106 107 108 109 10a 10b 10c 10d 10e 10f 110 111 112 113 114 115 116 117 118 119 11a 11b 11c 11d 11e 11f 120 121 122 123 124 125 126 127 128 129 12a 12b 12c 12d 12e 12f 130 131 132 133 134 135 136 137 138 139 13a 13b 13c 13d 13e 13f 140 141 142 143 144 145 146 147 148 149 14a 14b 14c 14d 14e 14f 150 151 152 153 154 155 156 157 158 159 15a 15b 15c 15d 15e 15f 160 161 162 163 164 165 166 167 168 169 16a 16b 16c 16d 16e 16f 170 171 172 173 174 175 176 177 178 179 17a 17b 17c 17d 17e 17f 180 181 182 183 184 185 186 187 188 189 18a 18b 18c 18d 18e 18f 190 191 192 193 194 195 196 197 198 199 19a 19b 19c 19d 19e 19f 1a0 1a1 1a2 1a3 1a4 1a5 1a6 1a7 1a8 1a9 1aa 1ab 1ac 1ad 1ae 1af 1b0 1b1 1b2 1b3 1b4 1b5 1b6 1b7 1b8 1b9 1ba 1bb 1bc 1bd 1be 1bf 1c0 1c1 1c2 1c3 1c4 1c5 1c6 1c7 1c8 1c9 1ca 1cb 1cc 1cd 1ce 1cf 1d0 1d1 1d2 1d3 1d4 1d5 1d6 1d7 1d8 1d9 1da 1db 1dc 1dd 1de 1df 1e0 1e1 1e2 1e3 1e4 1e5 1e6 1e7 1e8 1e9 1ea 1eb 1ec 1ed 1ee 1ef 1f0 1f1 1f2 1f3 1f4 1f5 1f6 1f7 1f8 1f9 1fa 1fb 1fc 1fd 1fe 1ff 200 201 202 203 204 205 206 207 208 209 20a 20b 20c 20d 20e 20f 210 211 212 213 214 215 216 217 218 219 21a 21b 21c 21d 21e 21f 220 221 222 223 224 225 226 227 228 229 22a 22b 22c 22d 22e 22f 230 231 232 233 234 235 236 237 238 239 23a 23b 23c 23d 23e 23f 240 241 242 243 244 245 246 247 248 249 24a 24b 24c 24d 24e 24f 250 251 252 253 254 255 256 257 258 259 25a 25b 25c 25d 25e 25f 260 261 262 263 264 265 266 267 268 269 26a 26b 26c 26d 26e 26f 270 271 272 273 274 275 276 277 278 279 27a 27b 27c 27d 27e 27f 280 281 282 283 284 285 286 287 288 289 28a 28b 28c 28d 28e 28f 290 291 292 293 294 295 296 297 298 299 29a 29b 29c 29d 29e 29f 2a0 2a1 2a2 2a3 2a4 2a5 2a6 2a7 2a8 2a9 2aa 2ab 2ac 2ad 2ae 2af 2b0 2b1 2b2 2b3 2b4 2b5 2b6 2b7 2b8 2b9 2ba 2bb 2bc 2bd 2be 2bf 2c0 2c1 2c2 2c3 2c4 2c5 2c6 2c7 2c8 2c9 2ca 2cb 2cc 2cd 2ce 2cf 2d0 2d1 2d2 2d3 2d4 2d5 2d6 2d7 2d8 2d9 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aaa aab aac aad aae aaf ab0 ab1 ab2 ab3 ab4 ab5 ab6 ab7 ab8 ab9 aba abb abc abd abe abf ac0 ac1 ac2 ac3 ac4 ac5 ac6 ac7 ac8 ac9 aca acb acc acd ace acf ad0 ad1 ad2 ad3 ad4 ad5 ad6 ad7 ad8 ad9 ada adb adc add ade adf ae0 ae1 ae2 ae3 ae4 ae5 ae6 ae7 ae8 ae9 aea aeb aec aed aee aef af0 af1 af2 af3 af4 af5 af6 af7 af8 af9 afa afb afc afd afe aff b00 b01 b02 b03 b04 b05 b06 b07 b08 b09 b0a b0b b0c b0d b0e b0f b10 b11 b12 b13 b14 b15 b16 b17 b18 b19 b1a b1b b1c b1d b1e b1f b20 b21 b22 b23 b24 b25 b26 b27 b28 b29 b2a b2b b2c b2d b2e b2f b30 b31 b32 b33 b34 b35 b36 b37 b38 b39 b3a b3b b3c b3d b3e b3f b40 b41 b42 b43 b44 b45 b46 b47 b48 b49 b4a b4b b4c b4d b4e b4f b50 b51 b52 b53 b54 b55 b56 b57 b58 b59 b5a b5b b5c b5d b5e b5f b60 b61 b62 b63 b64 b65 b66 b67 b68 b69 b6a b6b b6c b6d b6e b6f b70 b71 b72 b73 b74 b75 b76 b77 b78 b79 b7a b7b b7c b7d b7e b7f b80 b81 b82 b83 b84 b85 b86 b87 b88 b89 b8a b8b b8c b8d b8e b8f b90 b91 b92 b93 b94 b95 b96 b97 b98 b99 b9a b9b b9c b9d b9e b9f ba0 ba1 ba2 ba3 ba4 ba5 ba6 ba7 ba8 ba9 baa bab bac bad bae baf bb0 bb1 bb2 bb3 bb4 bb5 bb6 bb7 bb8 bb9 bba bbb bbc bbd bbe bbf bc0 bc1 bc2 bc3 bc4 bc5 bc6 bc7 bc8 bc9 bca bcb bcc bcd bce bcf bd0 bd1 bd2 bd3 bd4 bd5 bd6 bd7 bd8 bd9 bda bdb bdc bdd bde bdf be0 be1 be2 be3 be4 be5 be6 be7 be8 be9 bea beb bec bed bee bef bf0 bf1 bf2 bf3 bf4 bf5 bf6 bf7 bf8 bf9 bfa bfb bfc bfd bfe bff c00 c01 c02 c03 c04 c05 c06 c07 c08 c09 c0a c0b c0c c0d c0e c0f c10 c11 c12 c13 c14 c15 c16 c17 c18 c19 c1a c1b c1c c1d c1e c1f c20 c21 c22 c23 c24 c25 c26 c27 c28 c29 c2a c2b c2c c2d c2e c2f c30 c31 c32 c33 c34 c35 c36 c37 c38 c39 c3a c3b c3c c3d c3e c3f c40 c41 c42 c43 c44 c45 c46 c47 c48 c49 c4a c4b c4c c4d c4e c4f c50 c51 c52 c53 c54 c55 c56 c57 c58 c59 c5a c5b c5c c5d c5e c5f c60 c61 c62 c63 c64 c65 c66 c67 c68 c69 c6a c6b c6c c6d c6e c6f c70 c71 c72 c73 c74 c75 c76 c77 c78 c79 c7a c7b c7c c7d c7e c7f c80 c81 c82 c83 c84 c85 c86 c87 c88 c89 c8a c8b c8c c8d c8e c8f c90 c91 c92 c93 c94 c95 c96 c97 c98 c99 c9a c9b c9c c9d 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6 7 8 9 a b c d e f 10 11 12 13 14 15 16 17 18 19 1a 1b 1c 1d 1e 1f 20 21 22 23 24 25 26 27 28 29 2a 2b 2c 2d 2e 2f 30 31 32 33 34 35 36 37 38 39 3a 3b 3c 3d 3e 3f 40 41 42 43 44 45 46 47 48 49 4a 4b 4c 4d 4e 4f 50 51 52 53 54 55 56 57 58 59 5a 5b 5c 5d 5e 5f 60 61 62 63 64 65 66 67 68 69 6a 6b 6c 6d 6e 6f 70 71 72 73 74 75 76 77 78 79 7a 7b 7c 7d 7e 7f 80 81 82 83 84 85 86 87 88 89 8a 8b 8c 8d 8e 8f 90 91 92 93 94 95 96 97 98 99 9a 9b 9c 9d 9e 9f a0 a1 a2 a3 a4 a5 a6 a7 a8 a9 aa ab ac ad ae af b0 b1 b2 b3 b4 b5 b6 b7 b8 b9 ba bb bc bd be bf c0 c1 c2 c3 c4 c5 c6 c7 c8 c9 ca cb cc cd ce cf d0 d1 d2 d3 d4 d5 d6 d7 d8 d9 da db dc dd de df e0 e1 e2 e3 e4 e5 e6 e7 e8 e9 ea eb ec ed ee ef f0 f1 f2 f3 f4 f5 f6 f7 f8 f9 fa fb fc fd fe ff 100 101 102 103 104 105 106 107 108 109 10a 10b 10c 10d 10e 10f 110 111 112 113 114 115 116 117 118 119 11a 11b 11c 11d 11e 11f 120 121 122 123 124 125 126 127 128 129 12a 12b 12c 12d 12e 12f 130 131 132 133 134 135 136 137 138 139 13a 13b 13c 13d 13e 13f 140 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cf9 cfa cfb cfc cfd cfe cff d00 d01 d02 d03 d04 d05 d06 d07 d08 d09 d0a d0b d0c d0d d0e d0f d10 d11 d12 d13 d14 d15 d16 d17 d18 d19 d1a d1b d1c d1d d1e d1f d20 d21 d22 d23 d24 d25 d26 d27 d28 d29 d2a d2b d2c d2d d2e d2f d30 d31 d32 d33 d34 d35 d36 d37 d38 d39 d3a d3b d3c d3d d3e d3f d40 d41 d42 d43 d44 d45 d46 d47 d48 d49 d4a d4b d4c d4d d4e d4f d50 d51 d52 d53 d54 d55 d56 d57 d58 d59 d5a d5b d5c d5d d5e d5f d60 d61 d62 d63 d64 d65 d66 d67 d68 d69 d6a d6b d6c d6d d6e d6f d70 d71 d72 d73 d74 d75 d76 d77 d78 d79 d7a d7b d7c d7d d7e d7f d80 d81 d82 d83 d84 d85 d86 d87 d88 d89 d8a d8b d8c d8d d8e d8f d90 d91 d92 d93 d94 d95 d96 d97 d98 d99 d9a d9b d9c d9d d9e d9f da0 da1 da2 da3 da4 da5 da6 da7 da8 da9 daa dab dac dad dae daf db0 db1 db2 db3 db4 db5 db6 db7 db8 db9 dba dbb dbc dbd dbe dbf dc0 dc1 dc2 dc3 dc4 dc5 dc6 dc7 dc8 dc9 dca dcb dcc dcd dce dcf dd0 dd1 dd2 dd3 dd4 dd5 dd6 dd7 dd8 dd9 dda ddb ddc ddd dde ddf de0 de1 de2 de3 de4 de5 de6 de7 de8 de9 dea deb dec ded dee def df0 df1 df2 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fe7 fe8 fe9 fea feb fec fed fee fef ff0 ff1 ff2 ff3 ff4 ff5 ff6 ff7 ff8 ff9 ffa ffb ffc ffd ffe fff 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 100a 100b 100c 100d 100e 100f 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 101a 101b 101c 101d 101e 101f 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 102a 102b 102c 102d 102e 102f 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 103a 103b 103c 103d 103e 103f 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 104a 104b 104c 104d 104e 104f 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 105a 105b 105c 105d 105e 105f 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 106a 106b 106c 106d 106e 106f 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 107a 107b 107c 107d 107e 107f 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 108a 108b 108c 108d 108e 108f 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 109a 109b 109c 109d 109e 109f 10a0 10a1 10a2 10a3 10a4 10a5 10a6 10a7 10a8 10a9 10aa 10ab 10ac 10ad 10ae 10af 10b0 10b1 10b2 10b3 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390 391 392 393 394 395 396 397 398 399 39a 39b 39c 39d 39e 39f 3a0 3a1 3a2 3a3 3a4 3a5 3a6 3a7 3a8 3a9 3aa 3ab 3ac 3ad 3ae 3af 3b0 3b1 3b2 3b3 3b4 3b5 3b6 3b7 3b8 3b9 3ba 3bb 3bc 3bd 3be 3bf 3c0 3c1 3c2 3c3 3c4 3c5 3c6 3c7 3c8 3c9 3ca 3cb 3cc 3cd 3ce 3cf 3d0 3d1 3d2 3d3 3d4 3d5 3d6 3d7 3d8 3d9 3da 3db 3dc 3dd 3de 3df 3e0 3e1 3e2 3e3 3e4 3e5 3e6 3e7 3e8 3e9 3ea 3eb 3ec 3ed 3ee 3ef 3f0 3f1 3f2 3f3 3f4 3f5 3f6 3f7 3f8 3f9 3fa 3fb 3fc 3fd 3fe 3ff 400 401 402 403 404 405 406 407 408 409 40a 40b 40c 40d 40e 40f 410 411 412 413 414 415 416 417 418 419 41a 41b 41c 41d 41e 41f 420 421 422 423 424 425 426 427 428 429 42a 42b 42c 42d 42e 42f 430 431 432 433 434 435 436 437 438 439 43a 43b 43c 43d 43e 43f 440 441 442 443 444 445 446 447 448 449 44a 44b 44c 44d 44e 44f 450 451 452 453 454 455 456 457 458 459 45a 45b 45c 45d 45e 45f 460 461 462 463 464 465 466 467 468 469 46a 46b 46c 46d 46e 46f 470 471 472 473 474 475 476 477 478 479 47a 47b 47c 47d 47e 47f 480 481 482 483 484 485 486 487 488 489 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eaa eab eac ead eae eaf eb0 eb1 eb2 eb3 eb4 eb5 eb6 eb7 eb8 eb9 eba ebb ebc ebd ebe ebf ec0 ec1 ec2 ec3 ec4 ec5 ec6 ec7 ec8 ec9 eca ecb ecc ecd ece ecf ed0 ed1 ed2 ed3 ed4 ed5 ed6 ed7 ed8 ed9 eda edb edc edd ede edf ee0 ee1 ee2 ee3 ee4 ee5 ee6 ee7 ee8 ee9 eea eeb eec eed eee eef ef0 ef1 ef2 ef3 ef4 ef5 ef6 ef7 ef8 ef9 efa efb efc efd efe eff f00 f01 f02 f03 f04 f05 f06 f07 f08 f09 f0a f0b f0c f0d f0e f0f f10 f11 f12 f13 f14 f15 f16 f17 f18 f19 f1a f1b f1c f1d f1e f1f f20 f21 f22 f23 f24 f25 f26 f27 f28 f29 f2a f2b f2c f2d f2e f2f f30 f31 f32 f33 f34 f35 f36 f37 f38 f39 f3a f3b f3c f3d f3e f3f f40 f41 f42 f43 f44 f45 f46 f47 f48 f49 f4a f4b f4c f4d f4e f4f f50 f51 f52 f53 f54 f55 f56 f57 f58 f59 f5a f5b f5c f5d f5e f5f f60 f61 f62 f63 f64 f65 f66 f67 f68 f69 f6a f6b f6c f6d f6e f6f f70 f71 f72 f73 f74 f75 f76 f77 f78 f79 f7a f7b f7c f7d f7e f7f f80 f81 f82 f83 f84 f85 f86 f87 f88 f89 f8a f8b f8c f8d f8e f8f f90 f91 f92 f93 f94 f95 f96 f97 f98 f99 f9a f9b f9c f9d f9e f9f fa0 fa1 fa2 fa3 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b/problems/044-recent-submission-reuse/tests/adversarial-blind-01.out new file mode 100644 index 0000000..4913dd5 --- /dev/null +++ b/problems/044-recent-submission-reuse/tests/adversarial-blind-01.out @@ -0,0 +1 @@ +150000 diff --git a/problems/044-recent-submission-reuse/tests/sample-01.in b/problems/044-recent-submission-reuse/tests/sample-01.in new file mode 100644 index 0000000..114510d --- /dev/null +++ b/problems/044-recent-submission-reuse/tests/sample-01.in @@ -0,0 +1,2 @@ +7 3 +a b c a d b a diff --git a/problems/044-recent-submission-reuse/tests/sample-01.out b/problems/044-recent-submission-reuse/tests/sample-01.out new file mode 100644 index 0000000..0cfbf08 --- /dev/null +++ b/problems/044-recent-submission-reuse/tests/sample-01.out @@ -0,0 +1 @@ +2 diff --git a/problems/044-recent-submission-reuse/tests/sample-02.in b/problems/044-recent-submission-reuse/tests/sample-02.in new file mode 100644 index 0000000..dfc8b88 --- /dev/null +++ b/problems/044-recent-submission-reuse/tests/sample-02.in @@ -0,0 +1,2 @@ +4 0 +aa aa aa aa diff --git a/problems/044-recent-submission-reuse/tests/sample-02.out b/problems/044-recent-submission-reuse/tests/sample-02.out new file mode 100644 index 0000000..573541a --- /dev/null +++ b/problems/044-recent-submission-reuse/tests/sample-02.out @@ -0,0 +1 @@ +0 diff --git a/problems/044-recent-submission-reuse/tests/sample-03.in b/problems/044-recent-submission-reuse/tests/sample-03.in new file mode 100644 index 0000000..2588654 --- /dev/null +++ b/problems/044-recent-submission-reuse/tests/sample-03.in @@ -0,0 +1,2 @@ +5 1 +aa aa aa bb aa diff --git a/problems/044-recent-submission-reuse/tests/sample-03.out b/problems/044-recent-submission-reuse/tests/sample-03.out new file mode 100644 index 0000000..0cfbf08 --- /dev/null +++ b/problems/044-recent-submission-reuse/tests/sample-03.out @@ -0,0 +1 @@ +2 diff --git a/problems/044-recent-submission-reuse/validator.py b/problems/044-recent-submission-reuse/validator.py new file mode 100644 index 0000000..30547d2 --- /dev/null +++ b/problems/044-recent-submission-reuse/validator.py @@ -0,0 +1,21 @@ +import re +import sys + + +def fail(): + raise SystemExit(1) + + +try: + tokens = sys.stdin.buffer.read().decode("utf-8").split() + integer = re.compile(r"0|[1-9][0-9]*") + if len(tokens) < 2 or integer.fullmatch(tokens[0]) is None or integer.fullmatch(tokens[1]) is None: + fail() + n, k = int(tokens[0]), int(tokens[1]) + if not 1 <= n <= 200_000 or not 0 <= k <= n or len(tokens) != n + 2: + fail() + fingerprint = re.compile(r"[0-9a-f]{1,32}") + if any(fingerprint.fullmatch(token) is None for token in tokens[2:]): + fail() +except (UnicodeDecodeError, ValueError, OverflowError): + fail() diff --git a/problems/045-slowest-k-cases/editorial.en.md b/problems/045-slowest-k-cases/editorial.en.md new file mode 100644 index 0000000..f6eb810 --- /dev/null +++ b/problems/045-slowest-k-cases/editorial.en.md @@ -0,0 +1,33 @@ +# Editorial + +## Intuitive Approach: Sort Every Prefix + +After cost `i` arrives, sort all first `i` records by descending cost and ascending index, then select record `K`. This takes `O(N^2 log N)` total time and `O(N)` space, so it works only for small inputs. + +## Improved Approach: Maintain the Full Ordered Set + +Use an order-statistic balanced search tree, or maintain the best `K` records and all remaining records as two ordered sets. Insertion and rebalancing take `O(log N)`, and the boundary of the two sets gives rank `K` immediately. Total time is `O(N log N)` and space is `O(N)`. + +## Optimal Approach: Fixed-Size Heap + +Retain only the best `K` records seen so far. A record is better when its cost is higher, or when its index is smaller at equal cost. Arrange the heap so that its root is the worst selected record—the current rank `K`. + +Insert directly while the heap is not full. Once it is full, a new record no better than the root cannot enter the top `K`; a better record replaces the root and the heap is repaired. Starting at case `K`, the root after each update is exactly the prefix's `K`-th slowest case and can be emitted immediately. + +## Correctness Proof + +We prove by induction that after every prefix the heap contains exactly the best `min(i,K)` records of that prefix and its root is the worst selected record. + +While the heap is not full, every prefix record is inserted, so the claim holds. With a full heap, a new record no better than the root cannot displace any current top-`K` record, so the selected set stays correct. A better new record produces the new top `K` by replacing exactly the old set's worst member. Heap repair keeps that worst selected member at the root. Thus the claim holds for every prefix; whenever `i >= K`, the root is the required rank-`K` record. + +## Complexity + +Each case performs at most one `O(log K)` insertion or replacement, for `O(N log K)` total time, plus `O(N-K+1)` output. The heap uses `O(K)` working space. Languages that buffer all stdin or output have an actual resident bound of `O(N+K)`. + +## Common Mistakes + +- Printing only the final prefix answer instead of all `N-K+1` answers. +- Ranking the larger index first when costs tie. +- Putting the globally slowest record at the root instead of the worst selected rank-`K` record. +- Replacing the root even when the new record is not better. +- Storing costs up to `10^12` in 32-bit integers. diff --git a/problems/045-slowest-k-cases/editorial.zh-TW.md b/problems/045-slowest-k-cases/editorial.zh-TW.md new file mode 100644 index 0000000..f06dc5b --- /dev/null +++ b/problems/045-slowest-k-cases/editorial.zh-TW.md @@ -0,0 +1,33 @@ +# 解題說明 + +## 直覺解法:每個前綴重新排序 + +收到第 `i` 筆 cost 後,把前 `i` 筆全部依「成本降序、index 升序」排序,再取第 `K` 筆。總時間是 `O(N^2 log N)`,空間為 `O(N)`,只適合很小的輸入。 + +## 進階解法:維護完整有序集合 + +使用支援 order statistic 的平衡搜尋樹,或分別維護排名前 `K` 與其餘元素的兩個有序集合。每次插入與重新平衡需要 `O(log N)`,根據兩集合的邊界可立即取得第 `K` 名。總時間 `O(N log N)`、空間 `O(N)`。 + +## 最佳解法:大小固定的 Heap + +只保留目前最慢的 `K` 筆。把「成本越高,或同成本時 index 越小」定義成較好;heap root 則放入選集合中最差的一筆,也就是目前第 `K` 名。 + +Heap 未滿時直接加入。Heap 已滿後,新 case 若不比 root 好,就不可能進入前 `K`;若比較好,就取代 root 並修復 heap。從第 `K` 筆開始,每次更新後的 root 正是該前綴第 `K` 慢的 case,可以立即輸出。 + +## 正確性證明 + +用歸納法證明:處理任意前綴後,heap 恰好包含該前綴排名最前的 `min(i,K)` 筆,而且 root 是其中排名最後者。 + +Heap 未滿時,前綴內所有元素都加入,命題成立。Heap 已滿時,若新 case 不優於 root,它不可能取代既有前 `K` 名;集合不變。若新 case 優於 root,新的前 `K` 名恰為移除舊集合最差者、加入新 case。Heap 性質保證 root 仍是入選集合最差者。因此命題對每個前綴成立;當 `i >= K`,root 就是必須輸出的第 `K` 名。 + +## 複雜度 + +每筆 case 最多執行一次 `O(log K)` 的插入或取代,總時間 `O(N log K)`;輸出另需 `O(N-K+1)`。Heap 使用 `O(K)` 工作空間。會一次讀入完整 stdin 或緩衝輸出的語言,實際 resident 上界為 `O(N+K)`。 + +## 常見錯誤 + +- 只輸出最後前綴的答案,而不是 `N-K+1` 個答案。 +- 同成本時把較大的 index 排在前面。 +- 讓 root 成為最慢的第一名,而不是入選集合中最差的第 `K` 名。 +- 新 case 不夠好時仍取代 root。 +- 用 32-bit integer 儲存可達 `10^12` 的 cost。 diff --git a/problems/045-slowest-k-cases/generator.py b/problems/045-slowest-k-cases/generator.py new file mode 100644 index 0000000..265cd94 --- /dev/null +++ b/problems/045-slowest-k-cases/generator.py @@ -0,0 +1,17 @@ +import random +import sys + + +if len(sys.argv) != 3: + raise SystemExit("usage: generator.py SEED INDEX") +seed, index = int(sys.argv[1]), int(sys.argv[2]) +randomizer = random.Random((seed << 32) ^ index) +if index == 999_999: + n, k = 200_000, 5_000 + costs = [(i + 1) * 1_000_003 for i in range(n)] +else: + n = randomizer.randint(1, 45) + k = randomizer.randint(1, min(n, 12)) + costs = [randomizer.randint(0, 100) for _ in range(n)] +print(n, k) +print(*costs) diff --git a/problems/045-slowest-k-cases/oracle.py b/problems/045-slowest-k-cases/oracle.py new file mode 100644 index 0000000..5a95bb6 --- /dev/null +++ b/problems/045-slowest-k-cases/oracle.py @@ -0,0 +1,40 @@ +import sys + + +tokens = list(map(int, sys.stdin.buffer.read().split())) +n, k = tokens[:2] +costs = tokens[2:] + +order = sorted(range(n), key=lambda index: (-costs[index], index)) +rank = [0] * n +for position, index in enumerate(order, 1): + rank[index] = position + +fenwick = [0] * (n + 1) + + +def add(position: int) -> None: + while position <= n: + fenwick[position] += 1 + position += position & -position + + +def kth(target: int) -> int: + position = 0 + step = 1 << (n.bit_length() - 1) + while step: + candidate = position + step + if candidate <= n and fenwick[candidate] < target: + target -= fenwick[candidate] + position = candidate + step >>= 1 + return position + 1 + + +output = [] +for index in range(n): + add(rank[index]) + if index + 1 >= k: + answer = order[kth(k) - 1] + output.append(f"{answer + 1} {costs[answer]}\n") +sys.stdout.write("".join(output)) diff --git a/problems/045-slowest-k-cases/problem.json b/problems/045-slowest-k-cases/problem.json new file mode 100644 index 0000000..3675426 --- /dev/null +++ b/problems/045-slowest-k-cases/problem.json @@ -0,0 +1,155 @@ +{ + "schema": "wasm-oj-problem-v3", + "id": 45, + "slug": "slowest-k-cases", + "title": { + "zh-TW": "持續追蹤第 K 慢測試", + "en": "Running K-th Slowest Case" + }, + "difficulty": "easy", + "tags": [ + "heap", + "top-k", + "online-algorithm" + ], + "files": { + "statements": { + "zh-TW": "statement.zh-TW.md", + "en": "statement.en.md" + }, + "editorials": { + "zh-TW": "editorial.zh-TW.md", + "en": "editorial.en.md" + }, + "validator": "validator.py", + "generator": "generator.py", + "oracle": "oracle.py", + "solutions": { + "c": "solutions/c/main.c", + "cpp": "solutions/cpp/main.cpp", + "rust": "solutions/rust/main.rs", + "go": "solutions/go/main.go", + "python": "solutions/python/main.py", + "javascript": "solutions/javascript/main.js", + "typescript": "solutions/typescript/main.ts" + }, + "tests": [ + { + "id": "sample-01", + "kind": "sample", + "input": "tests/sample-01.in", + "output": "tests/sample-01.out" + }, + { + "id": "sample-02", + "kind": "sample", + "input": "tests/sample-02.in", + "output": "tests/sample-02.out" + }, + { + "id": "sample-03", + "kind": "sample", + "input": "tests/sample-03.in", + "output": "tests/sample-03.out" + }, + { + "id": "adversarial-01", + "kind": "adversarial", + "input": "tests/adversarial-01.in", + "output": "tests/adversarial-01.out" + } + ] + }, + "scoring": { + "mode": "per-case-cumulative-policies", + "caseSet": "all-manifest-tests", + "caseAggregation": "equal-weight-average", + "maximumPoints": 100, + "costContract": "wasm-oj-forge-v1", + "costModel": "weighted", + "costMetric": "baseline-normalized-net", + "calibration": { + "status": "measured", + "method": "forge-v1-compiled-average-optimal-rounded-v1", + "profiles": { + "c": "wasm-oj-forge-cost:contract-1:c:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "cpp": "wasm-oj-forge-cost:contract-1:cpp:wasip1:release:content-7f10d90b8e52b270f04874641a1d0bf9e94e85b4f6c7573a774cebbc6d32552a.21ded33b9c6d4e1aaad5528c940bdaf6c3e84be77ea8f522f018ca7289a2a224.4583b167dcac4bc1766c8378e0761b32e747ea614f24a1dcf2d8e8b0dc116029.681dc3a98aa98c8902cd17bb5d155b8771d650f2ac64f9552f45d524a2b955fd:weighted", + "rust": "wasm-oj-forge-cost:contract-1:rust:wasip1:release:content-cfbdadc67be1315e735aa55bdf8a5a0d00171982a023fefcf7ba586127753887.765de8d68d03078e79f69f49dec0dcab1ff96fe3bbe5e9eafebb2ce61a39d3ee.14715bd4eeb7dfe9dc806e7f28f404a87f590728f4c622f5de5b71857ceacc21:weighted", + "go": "wasm-oj-forge-cost:contract-1:go:wasip1:release:content-70a7e359884b09b2e1a622d6ac5cd6e31c334aab519e6dd80dff5e040a9e09e4.c3a97934b6a83fefdea5c31f99141f70f76189eedc9ec0fa9ccd41302e50963b.20bd57867439708500216da85e5c87e7f253bc797bb50873dc08981afc4d9e1a.78a4531121a78c3fca5b3ed0a24a0c1c4f9ac0b330d0d38730768cee7f174d68.0f52f7f37cc7bec08422c64607cf695e33a80852ce0b39d88a3bbe7d09a87b5a.9e557f5b86961fd604217d7521461c5d2b7322e383fa30dead5669b77db12201.2eefca10af935a307ab7946447146bd30e0ea0fb5460be54dc1c55844d155580:weighted", + "python": "wasm-oj-forge-cost:contract-1:python:wasip1:release:content-f8ada27da0b9bbe8a4e06736f320d71f6aca33876e8a0fd8894c5733972ba3c5.67ffc49c3df1c874ff8407bc7972b3ae951b0ba564687e9eb1ea2cb82f77cf86.ab6d91af39227ed8b0655b56f0b8340d67864d6397fa933df76e1b24a9134161.8aeae854650b5cc5af015dcfacb79f974d5a6997110c98b083cf4d618e20e4ba:weighted", + "javascript": "wasm-oj-forge-cost:contract-1:javascript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted", + "typescript": "wasm-oj-forge-cost:contract-1:typescript:wasip1:release:content-287c1a1e48179014821b8acbaa78000c17df4d072cab2cb9e8d7477cd55878f7.5b1419b8d65d2b910b61954071e28d99ce1fd401b5dd9b47e2bf16552f9ff582:weighted" + } + }, + "policies": [ + { + "id": "baseline", + "title": { + "zh-TW": "寬鬆資源", + "en": "Baseline Resources" + }, + "points": 20, + "limits": { + "instructionBudget": 200000000000, + "memoryLimitBytes": 134217728 + } + }, + { + "id": "efficient", + "title": { + "zh-TW": "進階效率", + "en": "Efficient Solution" + }, + "points": 30, + "limits": { + "instructionBudget": 25000000000, + "memoryLimitBytes": 100663296 + } + }, + { + "id": "optimal", + "title": { + "zh-TW": "最佳解", + "en": "Optimal Solution" + }, + "points": 50, + "limits": { + "instructionBudget": 15000000000, + "memoryLimitBytes": 67108864 + } + } + ], + "safetyLimits": { + "wallTimeLimitMs": 60000 + } + }, + "complexities": [ + { + "name": { + "zh-TW": "每個前綴重新排序", + "en": "Sort every prefix" + }, + "time": "O(N^2 log N)", + "space": "O(N)", + "accepted": false + }, + { + "name": { + "zh-TW": "維護完整的有序集合", + "en": "Maintain the full ordered set" + }, + "time": "O(N log N)", + "space": "O(N)", + "accepted": false + }, + { + "name": { + "zh-TW": "固定大小的最小堆積", + "en": "Fixed-size min-heap" + }, + "time": "O(N log K)", + "space": "O(N + K)", + "accepted": true + } + ] +} diff --git a/problems/045-slowest-k-cases/solutions/c/main.c b/problems/045-slowest-k-cases/solutions/c/main.c new file mode 100644 index 0000000..4ab95f7 --- /dev/null +++ b/problems/045-slowest-k-cases/solutions/c/main.c @@ -0,0 +1,70 @@ +#include +#include +#include +#include + +typedef struct { + uint64_t cost; + int index; +} Case; + +static int better(Case left, Case right) { + return left.cost > right.cost || (left.cost == right.cost && left.index < right.index); +} + +static int worse(Case left, Case right) { + return left.cost < right.cost || (left.cost == right.cost && left.index > right.index); +} + +static void swap(Case *left, Case *right) { + Case temporary = *left; + *left = *right; + *right = temporary; +} + +static void push(Case *heap, int *size, Case value) { + int position = (*size)++; + heap[position] = value; + while (position > 0) { + int parent = (position - 1) / 2; + if (!worse(heap[position], heap[parent])) break; + swap(&heap[position], &heap[parent]); + position = parent; + } +} + +static void repair_root(Case *heap, int size) { + int position = 0; + for (;;) { + int left = position * 2 + 1; + if (left >= size) break; + int child = left; + int right = left + 1; + if (right < size && worse(heap[right], heap[left])) child = right; + if (!worse(heap[child], heap[position])) break; + swap(&heap[child], &heap[position]); + position = child; + } +} + +int main(void) { + int n, k; + if (scanf("%d%d", &n, &k) != 2) return 1; + Case *heap = malloc((size_t)k * sizeof(*heap)); + if (heap == NULL) return 1; + int size = 0; + for (int index = 1; index <= n; index++) { + uint64_t cost; + if (scanf("%" SCNu64, &cost) != 1) return 1; + Case candidate = {cost, index}; + if (size < k) { + push(heap, &size, candidate); + } else if (better(candidate, heap[0])) { + heap[0] = candidate; + repair_root(heap, size); + } + if (index >= k) printf("%d %" PRIu64 "\n", heap[0].index, heap[0].cost); + } + free(heap); + return 0; +} diff --git a/problems/045-slowest-k-cases/solutions/cpp/main.cpp b/problems/045-slowest-k-cases/solutions/cpp/main.cpp new file mode 100644 index 0000000..30c484f --- /dev/null +++ b/problems/045-slowest-k-cases/solutions/cpp/main.cpp @@ -0,0 +1,40 @@ +#include +#include +#include +#include + +struct Case { + std::uint64_t cost; + int index; +}; + +static bool better(const Case &left, const Case &right) { + return left.cost > right.cost || (left.cost == right.cost && left.index < right.index); +} + +struct BetterComparator { + bool operator()(const Case &left, const Case &right) const { + return better(left, right); + } +}; + +int main() { + std::ios::sync_with_stdio(false); + std::cin.tie(nullptr); + int n, k; + if (!(std::cin >> n >> k)) return 1; + std::priority_queue, BetterComparator> heap; + for (int index = 1; index <= n; ++index) { + std::uint64_t cost; + std::cin >> cost; + Case candidate{cost, index}; + if (static_cast(heap.size()) < k) { + heap.push(candidate); + } else if (better(candidate, heap.top())) { + heap.pop(); + heap.push(candidate); + } + if (index >= k) std::cout << heap.top().index << ' ' << heap.top().cost << '\n'; + } + return 0; +} diff --git a/problems/045-slowest-k-cases/solutions/go/main.go b/problems/045-slowest-k-cases/solutions/go/main.go new file mode 100644 index 0000000..af58cb5 --- /dev/null +++ b/problems/045-slowest-k-cases/solutions/go/main.go @@ -0,0 +1,58 @@ +package main + +import ( + "bufio" + "container/heap" + "fmt" + "os" +) + +type Case struct { + cost uint64 + index int +} + +func better(left, right Case) bool { + return left.cost > right.cost || left.cost == right.cost && left.index < right.index +} + +type CaseHeap []Case + +func (values CaseHeap) Len() int { return len(values) } +func (values CaseHeap) Less(i, j int) bool { + return !better(values[i], values[j]) && (values[i].cost != values[j].cost || values[i].index != values[j].index) +} +func (values CaseHeap) Swap(i, j int) { values[i], values[j] = values[j], values[i] } +func (values *CaseHeap) Push(value any) { *values = append(*values, value.(Case)) } +func (values *CaseHeap) Pop() any { + old := *values + value := old[len(old)-1] + *values = old[:len(old)-1] + return value +} + +func main() { + in := bufio.NewReaderSize(os.Stdin, 1<<20) + out := bufio.NewWriterSize(os.Stdout, 1<<20) + defer out.Flush() + var n, k int + if _, err := fmt.Fscan(in, &n, &k); err != nil { + return + } + values := make(CaseHeap, 0, k) + heap.Init(&values) + for index := 1; index <= n; index++ { + var cost uint64 + fmt.Fscan(in, &cost) + candidate := Case{cost: cost, index: index} + if values.Len() < k { + heap.Push(&values, candidate) + } else if better(candidate, values[0]) { + heap.Pop(&values) + heap.Push(&values, candidate) + } + if index >= k { + fmt.Fprintln(out, values[0].index, values[0].cost) + } + } +} diff --git a/problems/045-slowest-k-cases/solutions/javascript/main.js b/problems/045-slowest-k-cases/solutions/javascript/main.js new file mode 100644 index 0000000..aa4166c --- /dev/null +++ b/problems/045-slowest-k-cases/solutions/javascript/main.js @@ -0,0 +1,74 @@ +import * as std from "std"; + +/** @typedef {{ cost: number, index: number }} CaseRecord */ + +const input = std.in.readAsString(); +let cursor = 0; +function nextToken() { + while (cursor < input.length && input.charCodeAt(cursor) <= 32) cursor++; + const start = cursor; + while (cursor < input.length && input.charCodeAt(cursor) > 32) cursor++; + return input.slice(start, cursor); +} + +/** @param {CaseRecord} left @param {CaseRecord} right */ +function better(left, right) { + return left.cost > right.cost || (left.cost === right.cost && left.index < right.index); +} + +/** @param {CaseRecord} left @param {CaseRecord} right */ +function worse(left, right) { + return left.cost < right.cost || (left.cost === right.cost && left.index > right.index); +} + +/** @param {CaseRecord[]} heap @param {CaseRecord} value */ +function push(heap, value) { + let position = heap.length; + heap.push(value); + while (position > 0) { + const parent = Math.floor((position - 1) / 2); + if (!worse(heap[position], heap[parent])) break; + [heap[position], heap[parent]] = [heap[parent], heap[position]]; + position = parent; + } +} + +/** @param {CaseRecord[]} heap */ +function repairRoot(heap) { + let position = 0; + while (true) { + const left = position * 2 + 1; + if (left >= heap.length) return; + const right = left + 1; + let child = left; + if (right < heap.length && worse(heap[right], heap[left])) child = right; + if (!worse(heap[child], heap[position])) return; + [heap[child], heap[position]] = [heap[position], heap[child]]; + position = child; + } +} + +const n = Number(nextToken()); +const k = Number(nextToken()); +/** @type {CaseRecord[]} */ +const heap = []; +let output = ""; +/** @param {CaseRecord} item */ +function emit(item) { + output += `${item.index} ${item.cost}\n`; + if (output.length >= 65536) { + std.out.puts(output); + output = ""; + } +} +for (let index = 1; index <= n; index++) { + const candidate = { cost: Number(nextToken()), index }; + if (heap.length < k) { + push(heap, candidate); + } else if (better(candidate, heap[0])) { + heap[0] = candidate; + repairRoot(heap); + } + if (index >= k) emit(heap[0]); +} +if (output) std.out.puts(output); diff --git a/problems/045-slowest-k-cases/solutions/python/main.py b/problems/045-slowest-k-cases/solutions/python/main.py new file mode 100644 index 0000000..616e9d3 --- /dev/null +++ b/problems/045-slowest-k-cases/solutions/python/main.py @@ -0,0 +1,21 @@ +import heapq +import sys + + +tokens = sys.stdin.buffer.read().split() +n = int(tokens[0]) +k = int(tokens[1]) +heap: list[tuple[int, int]] = [] +output = [] + +for index in range(1, n + 1): + cost = int(tokens[index + 1]) + candidate = (cost, -index) + if len(heap) < k: + heapq.heappush(heap, candidate) + elif candidate > heap[0]: + heapq.heapreplace(heap, candidate) + if index >= k: + output.append(f"{-heap[0][1]} {heap[0][0]}\n") + +sys.stdout.write("".join(output)) diff --git a/problems/045-slowest-k-cases/solutions/rust/main.rs b/problems/045-slowest-k-cases/solutions/rust/main.rs new file mode 100644 index 0000000..272c23e --- /dev/null +++ b/problems/045-slowest-k-cases/solutions/rust/main.rs @@ -0,0 +1,52 @@ +use std::cmp::Ordering; +use std::collections::BinaryHeap; +use std::io::{self, BufWriter, Read, Write}; + +#[derive(Clone, Copy, Eq, PartialEq)] +struct Case { + cost: u64, + index: usize, +} + +impl Ord for Case { + fn cmp(&self, other: &Self) -> Ordering { + other + .cost + .cmp(&self.cost) + .then_with(|| self.index.cmp(&other.index)) + } +} + +impl PartialOrd for Case { + fn partial_cmp(&self, other: &Self) -> Option { + Some(self.cmp(other)) + } +} + +fn better(left: Case, right: Case) -> bool { + left.cost > right.cost || (left.cost == right.cost && left.index < right.index) +} + +fn main() { + let mut input = String::new(); + io::stdin().read_to_string(&mut input).unwrap(); + let mut tokens = input.split_whitespace(); + let n: usize = tokens.next().unwrap().parse().unwrap(); + let k: usize = tokens.next().unwrap().parse().unwrap(); + let mut heap = BinaryHeap::with_capacity(k); + let mut output = BufWriter::new(io::stdout().lock()); + for index in 1..=n { + let cost: u64 = tokens.next().unwrap().parse().unwrap(); + let candidate = Case { cost, index }; + if heap.len() < k { + heap.push(candidate); + } else if better(candidate, *heap.peek().unwrap()) { + heap.pop(); + heap.push(candidate); + } + if index >= k { + let answer = heap.peek().unwrap(); + writeln!(output, "{} {}", answer.index, answer.cost).unwrap(); + } + } +} diff --git a/problems/045-slowest-k-cases/solutions/typescript/main.ts b/problems/045-slowest-k-cases/solutions/typescript/main.ts new file mode 100644 index 0000000..759f4d5 --- /dev/null +++ b/problems/045-slowest-k-cases/solutions/typescript/main.ts @@ -0,0 +1,71 @@ +import * as std from "std"; + +interface CaseRecord { + cost: number; + index: number; +} + +const input = std.in.readAsString(); +let cursor = 0; +function nextToken(): string { + while (cursor < input.length && input.charCodeAt(cursor) <= 32) cursor++; + const start = cursor; + while (cursor < input.length && input.charCodeAt(cursor) > 32) cursor++; + return input.slice(start, cursor); +} + +function better(left: CaseRecord, right: CaseRecord): boolean { + return left.cost > right.cost || (left.cost === right.cost && left.index < right.index); +} + +function worse(left: CaseRecord, right: CaseRecord): boolean { + return left.cost < right.cost || (left.cost === right.cost && left.index > right.index); +} + +function push(heap: CaseRecord[], value: CaseRecord): void { + let position = heap.length; + heap.push(value); + while (position > 0) { + const parent = Math.floor((position - 1) / 2); + if (!worse(heap[position], heap[parent])) break; + [heap[position], heap[parent]] = [heap[parent], heap[position]]; + position = parent; + } +} + +function repairRoot(heap: CaseRecord[]): void { + let position = 0; + while (true) { + const left = position * 2 + 1; + if (left >= heap.length) return; + const right = left + 1; + let child = left; + if (right < heap.length && worse(heap[right], heap[left])) child = right; + if (!worse(heap[child], heap[position])) return; + [heap[child], heap[position]] = [heap[position], heap[child]]; + position = child; + } +} + +const n = Number(nextToken()); +const k = Number(nextToken()); +const heap: CaseRecord[] = []; +let output = ""; +function emit(item: CaseRecord): void { + output += `${item.index} ${item.cost}\n`; + if (output.length >= 65536) { + std.out.puts(output); + output = ""; + } +} +for (let index = 1; index <= n; index++) { + const candidate = { cost: Number(nextToken()), index }; + if (heap.length < k) { + push(heap, candidate); + } else if (better(candidate, heap[0])) { + heap[0] = candidate; + repairRoot(heap); + } + if (index >= k) emit(heap[0]); +} +if (output) std.out.puts(output); diff --git a/problems/045-slowest-k-cases/statement.en.md b/problems/045-slowest-k-cases/statement.en.md new file mode 100644 index 0000000..9b51ee7 --- /dev/null +++ b/problems/045-slowest-k-cases/statement.en.md @@ -0,0 +1,81 @@ +# Running K-th Slowest Case + +While designing a live performance panel for a WASM OJ, we wanted to show the cases most worth investigating before a submission had finished every test. Displaying only the single slowest case can be dominated by one extreme value, so the panel tracks the case currently ranked `K`-th slowest as a more stable threshold. + +Test cases finish one at a time. When case `i` finishes, the system receives its instruction cost `cost_i`; its case index is `i`. The panel must update from the cases completed so far and cannot use costs that have not arrived yet. + +At every moment `i >= K`, consider only the first `i` cases and output the case ranked `K`-th slowest. Higher cost ranks first; at equal cost, the smaller index ranks first. Each prefix answer is fixed before the next case finishes, and later costs do not belong to earlier prefixes. + +## Input + +The first line contains `N K`. The second line contains the `N` case costs in completion order. + +## Output + +For every `i = K, K+1, ..., N`, output one line containing `index cost` for the case ranked `K`-th slowest among the first `i` cases. + +## Constraints + +- `1 <= N <= 200000` +- `1 <= K <= min(N, 5000)` +- `0 <= cost_i <= 10^12` + +The full constraints require answering every prefix and rule out sorting all existing cases again for each prefix. + +## Examples + + + +### Example One + +Input: + +```text +5 3 +10 30 30 5 20 +``` + +Output: + +```text +1 10 +1 10 +5 20 +``` + +### Example Two + +Input: + +```text +4 4 +7 7 7 7 +``` + +Output: + +```text +4 7 +``` + +### Example Three + +Input: + +```text +6 1 +1 9 3 9 2 8 +``` + +Output: + +```text +1 1 +2 9 +2 9 +2 9 +2 9 +2 9 +``` + + diff --git a/problems/045-slowest-k-cases/statement.zh-TW.md b/problems/045-slowest-k-cases/statement.zh-TW.md new file mode 100644 index 0000000..42f32d3 --- /dev/null +++ b/problems/045-slowest-k-cases/statement.zh-TW.md @@ -0,0 +1,81 @@ +# 持續追蹤第 K 慢測試 + +在設計 WASM OJ 的即時效能面板時,我們希望在 submission 尚未跑完所有測資前,就持續顯示目前最值得調查的慢速 cases。只顯示最慢的一筆容易被單一極端值支配,因此面板需要追蹤目前排名第 `K` 慢的 case,作為較穩定的觀察門檻。 + +Test cases 依序完成。第 `i` 個 case 完成時,系統收到它的 instruction cost `cost_i`,而 case index 就是 `i`。面板必須立即根據目前已完成的 cases 更新,不能使用尚未收到的後續資料。 + +在每個 `i >= K` 的時間點,請只考慮前 `i` 個 cases,輸出其中排名第 `K` 慢的 case。成本越高排名越前;成本相同時,index 越小排名越前。每個前綴的答案在後續 case 完成前就已確定,之後收到的 cost 不屬於先前的前綴。 + +## 輸入 + +第一行包含 `N K`。第二行包含依完成順序排列的 `N` 個 case cost。 + +## 輸出 + +對每個 `i = K, K+1, ..., N` 輸出一行,包含前 `i` 個 case 中排名第 `K` 慢者的 `index cost`。 + +## 限制 + +- `1 <= N <= 200000` +- `1 <= K <= min(N, 5000)` +- `0 <= cost_i <= 10^12` + +完整限制要求處理所有前綴,排除為每個前綴重新排序全部既有 case 的作法。 + +## 範例 + + + +### 範例一 + +輸入: + +```text +5 3 +10 30 30 5 20 +``` + +輸出: + +```text +1 10 +1 10 +5 20 +``` + +### 範例二 + +輸入: + +```text +4 4 +7 7 7 7 +``` + +輸出: + +```text +4 7 +``` + +### 範例三 + +輸入: + +```text +6 1 +1 9 3 9 2 8 +``` + +輸出: + +```text +1 1 +2 9 +2 9 +2 9 +2 9 +2 9 +``` + + diff --git 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100644 index 0000000..6bfd8ac --- /dev/null +++ b/problems/045-slowest-k-cases/tests/sample-02.in @@ -0,0 +1,2 @@ +4 4 +7 7 7 7 diff --git a/problems/045-slowest-k-cases/tests/sample-02.out b/problems/045-slowest-k-cases/tests/sample-02.out new file mode 100644 index 0000000..9ac1165 --- /dev/null +++ b/problems/045-slowest-k-cases/tests/sample-02.out @@ -0,0 +1 @@ +4 7 diff --git a/problems/045-slowest-k-cases/tests/sample-03.in b/problems/045-slowest-k-cases/tests/sample-03.in new file mode 100644 index 0000000..e9d04a6 --- /dev/null +++ b/problems/045-slowest-k-cases/tests/sample-03.in @@ -0,0 +1,2 @@ +6 1 +1 9 3 9 2 8 diff --git a/problems/045-slowest-k-cases/tests/sample-03.out b/problems/045-slowest-k-cases/tests/sample-03.out new file mode 100644 index 0000000..1872f11 --- /dev/null +++ b/problems/045-slowest-k-cases/tests/sample-03.out @@ -0,0 +1,6 @@ +1 1 +2 9 +2 9 +2 9 +2 9 +2 9 diff --git a/problems/045-slowest-k-cases/validator.py b/problems/045-slowest-k-cases/validator.py new file mode 100644 index 0000000..51ed1ce --- /dev/null +++ b/problems/045-slowest-k-cases/validator.py @@ -0,0 +1,19 @@ +import re +import sys + + +def fail(): + raise SystemExit(1) + + +try: + tokens = sys.stdin.buffer.read().decode("utf-8").split() + if len(tokens) < 2 or any(re.fullmatch(r"0|[1-9][0-9]*", token) is None for token in tokens): + fail() + n, k = map(int, tokens[:2]) + if not 1 <= n <= 200_000 or not 1 <= k <= min(n, 5_000) or len(tokens) != n + 2: + fail() + if any(not 0 <= int(token) <= 10**12 for token in tokens[2:]): + fail() +except (UnicodeDecodeError, ValueError, OverflowError): + fail() diff --git a/public/_headers b/public/_headers index 99f2f04..c58a5d2 100644 --- a/public/_headers +++ b/public/_headers @@ -1,5 +1,5 @@ /* - Cross-Origin-Embedder-Policy: credentialless + Cross-Origin-Embedder-Policy: require-corp Cross-Origin-Opener-Policy: same-origin Cross-Origin-Resource-Policy: same-origin Referrer-Policy: no-referrer diff --git a/public/og.png b/public/og.png index c17fa91..8c4dfca 100644 Binary files a/public/og.png and b/public/og.png differ diff --git a/schemas/problem-catalog.schema.json b/schemas/problem-catalog.schema.json new file mode 100644 index 0000000..f30fef5 --- /dev/null +++ b/schemas/problem-catalog.schema.json @@ -0,0 +1,49 @@ +{ + "$schema": "https://json-schema.org/draft/2020-12/schema", + "$id": "https://wasm-oj.dev/schemas/catalog-v2.json", + "title": "WASM OJ problem catalog", + "type": "object", + "additionalProperties": false, + "required": ["schema", "problemSchema", "localization", "problems"], + "properties": { + "schema": { "const": "wasm-oj-catalog-v2" }, + "problemSchema": { "const": "wasm-oj-problem-v3" }, + "localization": { + "type": "object", + "additionalProperties": false, + "required": ["defaultLocale", "supportedLocales"], + "properties": { + "defaultLocale": { "const": "zh-TW" }, + "supportedLocales": { + "type": "array", + "prefixItems": [ + { "const": "zh-TW" }, + { "const": "en" } + ], + "items": false, + "minItems": 2, + "maxItems": 2, + "uniqueItems": true + } + } + }, + "problems": { + "type": "array", + "minItems": 45, + "maxItems": 45, + "items": { + "type": "object", + "additionalProperties": false, + "required": ["id", "slug", "manifest"], + "properties": { + "id": { "type": "integer", "minimum": 1, "maximum": 45 }, + "slug": { "type": "string", "pattern": "^[a-z0-9]+(?:-[a-z0-9]+)*$" }, + "manifest": { + "type": "string", + "pattern": "^problems/[0-9]{3}-[a-z0-9]+(?:-[a-z0-9]+)*/problem\\.json$" + } + } + } + } + } +} diff --git a/schemas/problem.schema.json b/schemas/problem.schema.json new file mode 100644 index 0000000..a90330f --- /dev/null +++ b/schemas/problem.schema.json @@ -0,0 +1,277 @@ +{ + "$schema": "https://json-schema.org/draft/2020-12/schema", + "$id": "https://wasm-oj.dev/schemas/problem-v3.json", + "title": "WASM OJ problem manifest", + "type": "object", + "additionalProperties": false, + "required": [ + "schema", + "id", + "slug", + "title", + "difficulty", + "tags", + "files", + "scoring", + "complexities" + ], + "properties": { + "schema": { "const": "wasm-oj-problem-v3" }, + "id": { "type": "integer", "minimum": 1, "maximum": 45 }, + "slug": { "type": "string", "pattern": "^[a-z0-9]+(?:-[a-z0-9]+)*$" }, + "title": { "$ref": "#/$defs/localizedText" }, + "difficulty": { "enum": ["easy", "medium", "hard"] }, + "tags": { + "type": "array", + "minItems": 1, + "uniqueItems": true, + "items": { "$ref": "#/$defs/nonBlankTrimmed" } + }, + "files": { + "type": "object", + "additionalProperties": false, + "required": [ + "statements", + "editorials", + "validator", + "generator", + "oracle", + "solutions", + "tests" + ], + "properties": { + "statements": { "$ref": "#/$defs/localizedFiles" }, + "editorials": { "$ref": "#/$defs/localizedFiles" }, + "validator": { "$ref": "#/$defs/relativePath" }, + "generator": { "$ref": "#/$defs/relativePath" }, + "oracle": { "$ref": "#/$defs/relativePath" }, + "solutions": { + "type": "object", + "additionalProperties": false, + "required": [ + "c", + "cpp", + "rust", + "go", + "python", + "javascript", + "typescript" + ], + "properties": { + "c": { "$ref": "#/$defs/relativePath" }, + "cpp": { "$ref": "#/$defs/relativePath" }, + "rust": { "$ref": "#/$defs/relativePath" }, + "go": { "$ref": "#/$defs/relativePath" }, + "python": { "$ref": "#/$defs/relativePath" }, + "javascript": { "$ref": "#/$defs/relativePath" }, + "typescript": { "$ref": "#/$defs/relativePath" } + } + }, + "tests": { + "type": "array", + "minItems": 4, + "items": { + "type": "object", + "additionalProperties": false, + "required": ["id", "kind", "input", "output"], + "properties": { + "id": { + "type": "string", + "pattern": "^[a-z0-9]+(?:-[a-z0-9]+)*$" + }, + "kind": { "enum": ["sample", "adversarial", "regression"] }, + "input": { "$ref": "#/$defs/relativePath" }, + "output": { "$ref": "#/$defs/relativePath" } + } + } + } + } + }, + "scoring": { + "type": "object", + "additionalProperties": false, + "required": [ + "mode", + "caseSet", + "caseAggregation", + "maximumPoints", + "costContract", + "costModel", + "costMetric", + "calibration", + "policies", + "safetyLimits" + ], + "properties": { + "mode": { "const": "per-case-cumulative-policies" }, + "caseSet": { "const": "all-manifest-tests" }, + "caseAggregation": { "const": "equal-weight-average" }, + "maximumPoints": { "const": 100 }, + "costContract": { "const": "wasm-oj-forge-v1" }, + "costModel": { "const": "weighted" }, + "costMetric": { "const": "baseline-normalized-net" }, + "calibration": { + "type": "object", + "additionalProperties": false, + "required": ["status", "method", "profiles"], + "properties": { + "status": { "const": "measured" }, + "method": { "const": "forge-v1-compiled-average-optimal-rounded-v1" }, + "profiles": { + "type": "object", + "additionalProperties": false, + "required": [ + "c", + "cpp", + "rust", + "go", + "python", + "javascript", + "typescript" + ], + "properties": { + "c": { "$ref": "#/$defs/nonBlankTrimmed" }, + "cpp": { "$ref": "#/$defs/nonBlankTrimmed" }, + "rust": { "$ref": "#/$defs/nonBlankTrimmed" }, + "go": { "$ref": "#/$defs/nonBlankTrimmed" }, + "python": { "$ref": "#/$defs/nonBlankTrimmed" }, + "javascript": { "$ref": "#/$defs/nonBlankTrimmed" }, + "typescript": { "$ref": "#/$defs/nonBlankTrimmed" } + } + } + } + }, + "policies": { + "type": "array", + "minItems": 3, + "maxItems": 3, + "allOf": [ + { + "minItems": 3, + "maxItems": 3, + "prefixItems": [ + { + "type": "object", + "required": ["id"], + "properties": { "id": { "const": "baseline" } } + }, + { + "type": "object", + "required": ["id"], + "properties": { "id": { "const": "efficient" } } + }, + { + "type": "object", + "required": ["id"], + "properties": { "id": { "const": "optimal" } } + } + ], + "items": false + } + ], + "items": { + "type": "object", + "additionalProperties": false, + "required": ["id", "title", "points", "limits"], + "properties": { + "id": { + "type": "string", + "pattern": "^[a-z0-9]+(?:-[a-z0-9]+)*$" + }, + "title": { "$ref": "#/$defs/localizedText" }, + "points": { "type": "integer", "minimum": 1, "maximum": 100 }, + "limits": { + "type": "object", + "additionalProperties": false, + "required": ["instructionBudget", "memoryLimitBytes"], + "properties": { + "instructionBudget": { + "type": "integer", + "minimum": 1, + "maximum": 9007199254740991 + }, + "memoryLimitBytes": { + "type": "integer", + "minimum": 65536, + "maximum": 4294967296, + "multipleOf": 65536 + }, + "logicalTimeLimitMs": { + "type": "integer", + "minimum": 1, + "maximum": 9007199254 + } + } + } + } + } + }, + "safetyLimits": { + "type": "object", + "additionalProperties": false, + "required": ["wallTimeLimitMs"], + "properties": { + "wallTimeLimitMs": { + "type": "integer", + "minimum": 1000, + "maximum": 600000 + } + } + } + } + }, + "complexities": { + "type": "array", + "minItems": 2, + "items": { + "type": "object", + "additionalProperties": false, + "required": ["name", "time", "space", "accepted"], + "properties": { + "name": { "$ref": "#/$defs/localizedText" }, + "time": { "$ref": "#/$defs/nonBlankTrimmed" }, + "space": { "$ref": "#/$defs/nonBlankTrimmed" }, + "accepted": { "type": "boolean" } + } + } + } + }, + "$defs": { + "relativePath": { + "type": "string", + "minLength": 1, + "maxLength": 4096, + "pattern": "^(?!/)(?!.*(?:^|/)\\.{1,2}(?:/|$))(?!.*//)(?!.*\\\\)(?!.*\\/$)[^\\u0000]+$" + }, + "nonBlankTrimmed": { + "type": "string", + "pattern": "^(?:\\S|\\S[\\s\\S]*\\S)$" + }, + "localizedFiles": { + "type": "object", + "minProperties": 2, + "required": ["zh-TW", "en"], + "properties": { + "zh-TW": { "$ref": "#/$defs/relativePath" }, + "en": { "$ref": "#/$defs/relativePath" } + }, + "propertyNames": { + "pattern": "^[a-z]{2,3}(?:-[A-Za-z0-9]{2,8})*$" + }, + "additionalProperties": { "$ref": "#/$defs/relativePath" } + }, + "localizedText": { + "type": "object", + "minProperties": 2, + "required": ["zh-TW", "en"], + "properties": { + "zh-TW": { "$ref": "#/$defs/nonBlankTrimmed" }, + "en": { "$ref": "#/$defs/nonBlankTrimmed" } + }, + "propertyNames": { + "pattern": "^[a-z]{2,3}(?:-[A-Za-z0-9]{2,8})*$" + }, + "additionalProperties": { "$ref": "#/$defs/nonBlankTrimmed" } + } + } +} diff --git a/scripts/generate-judge-problems.mjs b/scripts/generate-judge-problems.mjs new file mode 100644 index 0000000..d40a980 --- /dev/null +++ b/scripts/generate-judge-problems.mjs @@ -0,0 +1,336 @@ +#!/usr/bin/env node + +import { mkdir, readFile, rename, writeFile } from "node:fs/promises"; +import path from "node:path"; +import { fileURLToPath } from "node:url"; +import Ajv2020 from "ajv/dist/2020.js"; +import { applyLearningPath } from "./learning-path.mjs"; + +const ROOT = path.resolve(path.dirname(fileURLToPath(import.meta.url)), ".."); +const CATALOG_PATH = path.join(ROOT, "catalog.json"); +const LEARNING_PATH_PATH = path.join(ROOT, "learning-path.json"); +const OUTPUT_PATH = path.join(ROOT, "src/judge/problems.generated.ts"); +const CATALOG_SCHEMA_PATH = path.join(ROOT, "schemas/problem-catalog.schema.json"); +const PROBLEM_SCHEMA_PATH = path.join(ROOT, "schemas/problem.schema.json"); +const LOCALES = Object.freeze(["zh-TW", "en"]); +const LANGUAGES = Object.freeze([ + "c", + "cpp", + "rust", + "go", + "python", + "javascript", + "typescript", +]); +const POLICY_IDS = Object.freeze(["baseline", "efficient", "optimal"]); + +function fail(message) { + throw new Error(message); +} + +function parseArgs(arguments_) { + if (arguments_.length > 1 || (arguments_.length === 1 && arguments_[0] !== "--check")) { + console.error("usage: node scripts/generate-judge-problems.mjs [--check]"); + process.exit(2); + } + return { check: arguments_[0] === "--check" }; +} + +function assertRecord(value, label) { + if (!value || typeof value !== "object" || Array.isArray(value)) { + fail(`${label} must be an object`); + } + return value; +} + +function assertExactKeys(value, keys, label) { + const actual = Object.keys(value).sort(); + const expected = [...keys].sort(); + if (JSON.stringify(actual) !== JSON.stringify(expected)) { + fail(`${label} has unexpected keys: ${actual.join(", ")}`); + } +} + +function assertLocalizedText(value, label) { + const record = assertRecord(value, label); + assertExactKeys(record, LOCALES, label); + for (const locale of LOCALES) { + if (typeof record[locale] !== "string" || !record[locale] || record[locale] !== record[locale].trim()) { + fail(`${label}[${locale}] must be a non-empty trimmed string`); + } + } + return record; +} + +function resolveRelative(base, relative, label) { + if ( + typeof relative !== "string" + || !relative + || relative.startsWith("/") + || relative.includes("\\") + || relative.includes("\0") + || relative.endsWith("/") + ) { + fail(`${label} must be a normalized relative POSIX path`); + } + const segments = relative.split("/"); + if (segments.some((segment) => !segment || segment === "." || segment === "..")) { + fail(`${label} must be a normalized relative POSIX path`); + } + return path.join(base, ...segments); +} + +async function readJson(file, label) { + try { + return JSON.parse(await readFile(file, "utf8")); + } catch (error) { + fail(`${label} is not valid JSON: ${error instanceof Error ? error.message : String(error)}`); + } +} + +function assertSchema(validate, value, label) { + if (!validate(value)) { + const details = validate.errors + ?.map((error) => `${error.instancePath || "/"} ${error.message}`) + .join("; "); + fail(`${label} violates its JSON schema: ${details ?? "unknown validation error"}`); + } +} + +async function loadSchemaValidators() { + const [catalogSchema, problemSchema] = await Promise.all([ + readJson(CATALOG_SCHEMA_PATH, "catalog schema"), + readJson(PROBLEM_SCHEMA_PATH, "problem schema"), + ]); + const ajv = new Ajv2020({ allErrors: true, strict: true }); + return { + catalog: ajv.compile(catalogSchema), + problem: ajv.compile(problemSchema), + }; +} + +async function loadCatalog(validate) { + const catalog = assertRecord(await readJson(CATALOG_PATH, "catalog.json"), "catalog.json"); + assertSchema(validate, catalog, "catalog.json"); + assertExactKeys(catalog, ["schema", "problemSchema", "localization", "problems"], "catalog.json"); + if (catalog.schema !== "wasm-oj-catalog-v2" || catalog.problemSchema !== "wasm-oj-problem-v3") { + fail("catalog.json uses an unsupported schema"); + } + if (JSON.stringify(catalog.localization) !== JSON.stringify({ + defaultLocale: "zh-TW", + supportedLocales: LOCALES, + })) { + fail("catalog.json uses an unsupported localization contract"); + } + if (!Array.isArray(catalog.problems) || catalog.problems.length !== 45) { + fail("catalog.json must contain exactly 45 problems"); + } + return catalog; +} + +async function loadProblem(entry, expectedNumber, validate) { + const catalogEntry = assertRecord(entry, `catalog problem ${expectedNumber}`); + assertExactKeys(catalogEntry, ["id", "slug", "manifest"], `catalog problem ${expectedNumber}`); + if (catalogEntry.id !== expectedNumber || typeof catalogEntry.slug !== "string") { + fail(`catalog problem ${expectedNumber} has an invalid identity`); + } + const expectedManifest = `problems/${String(expectedNumber).padStart(3, "0")}-${catalogEntry.slug}/problem.json`; + if (catalogEntry.manifest !== expectedManifest) { + fail(`catalog problem ${expectedNumber} manifest must be ${expectedManifest}`); + } + const manifestPath = resolveRelative(ROOT, catalogEntry.manifest, `problem ${expectedNumber} manifest`); + const problemRoot = path.dirname(manifestPath); + const manifest = assertRecord(await readJson(manifestPath, expectedManifest), expectedManifest); + assertSchema(validate, manifest, expectedManifest); + if ( + manifest.schema !== "wasm-oj-problem-v3" + || manifest.id !== expectedNumber + || manifest.slug !== catalogEntry.slug + ) { + fail(`${expectedManifest} identity disagrees with catalog.json`); + } + const title = assertLocalizedText(manifest.title, `${expectedManifest} title`); + const files = assertRecord(manifest.files, `${expectedManifest} files`); + const statements = assertRecord(files.statements, `${expectedManifest} statement files`); + const editorials = assertRecord(files.editorials, `${expectedManifest} editorial files`); + assertExactKeys(statements, LOCALES, `${expectedManifest} statement files`); + assertExactKeys(editorials, LOCALES, `${expectedManifest} editorial files`); + const localizedStatement = {}; + const localizedEditorial = {}; + for (const locale of LOCALES) { + localizedStatement[locale] = await readFile( + resolveRelative(problemRoot, statements[locale], `${expectedManifest} statement[${locale}]`), + "utf8", + ); + localizedEditorial[locale] = await readFile( + resolveRelative(problemRoot, editorials[locale], `${expectedManifest} editorial[${locale}]`), + "utf8", + ); + if (!localizedStatement[locale].startsWith(`# ${title[locale]}\n`)) { + fail(`${expectedManifest} statement[${locale}] title disagrees with manifest`); + } + } + + const solutionPaths = assertRecord(files.solutions, `${expectedManifest} solutions`); + assertExactKeys(solutionPaths, LANGUAGES, `${expectedManifest} solutions`); + const declaredPrograms = [ + ["validator", files.validator], + ["generator", files.generator], + ["oracle", files.oracle], + ...LANGUAGES.map((language) => [`solution[${language}]`, solutionPaths[language]]), + ]; + await Promise.all(declaredPrograms.map(async ([label, relative]) => { + const contents = await readFile( + resolveRelative(problemRoot, relative, `${expectedManifest} ${label}`), + ); + if (contents.byteLength === 0) fail(`${expectedManifest} ${label} must not be empty`); + })); + const tests = files.tests; + if (!Array.isArray(tests) || tests.length < 4) fail(`${expectedManifest} must declare at least four tests`); + const judgeCases = []; + const testIds = new Set(); + for (const [index, test] of tests.entries()) { + const record = assertRecord(test, `${expectedManifest} test ${index}`); + assertExactKeys(record, ["id", "kind", "input", "output"], `${expectedManifest} test ${index}`); + if ( + typeof record.id !== "string" + || !["sample", "adversarial", "regression"].includes(record.kind) + ) { + fail(`${expectedManifest} test ${index} has invalid metadata`); + } + if (testIds.has(record.id)) fail(`${expectedManifest} repeats test id ${record.id}`); + testIds.add(record.id); + const [input, output] = await Promise.all([ + readFile(resolveRelative(problemRoot, record.input, `${expectedManifest} test input`), "utf8"), + readFile(resolveRelative(problemRoot, record.output, `${expectedManifest} test output`), "utf8"), + ]); + judgeCases.push({ id: record.id, kind: record.kind, input, output }); + } + if (judgeCases.filter((testCase) => testCase.kind === "sample").length !== 3) { + fail(`${expectedManifest} must declare exactly three sample cases`); + } + + const scoring = assertRecord(manifest.scoring, `${expectedManifest} scoring`); + const calibration = assertRecord(scoring.calibration, `${expectedManifest} calibration`); + const profiles = assertRecord(calibration.profiles, `${expectedManifest} calibration profiles`); + assertExactKeys(profiles, LANGUAGES, `${expectedManifest} calibration profiles`); + if ( + scoring.maximumPoints !== 100 + || calibration.status !== "measured" + || calibration.method !== "forge-v1-compiled-average-optimal-rounded-v1" + ) { + fail(`${expectedManifest} has an unsupported scoring contract`); + } + if (!Array.isArray(scoring.policies) || scoring.policies.length !== POLICY_IDS.length) { + fail(`${expectedManifest} must declare exactly ${POLICY_IDS.join(", ")}`); + } + const policies = scoring.policies.map((policy, index) => { + const record = assertRecord(policy, `${expectedManifest} policy ${index}`); + return { + id: record.id, + title: assertLocalizedText(record.title, `${expectedManifest} policy ${index} title`), + points: record.points, + limits: record.limits, + }; + }); + if (policies.some((policy, index) => policy.id !== POLICY_IDS[index])) { + fail(`${expectedManifest} scoring policies must be exactly ${POLICY_IDS.join(", ")}`); + } + if (policies.reduce((sum, policy) => sum + policy.points, 0) !== scoring.maximumPoints) { + fail(`${expectedManifest} scoring policy points must sum to ${scoring.maximumPoints}`); + } + for (let index = 1; index < policies.length; index += 1) { + const broader = policies[index - 1].limits; + const stricter = policies[index].limits; + if ( + stricter.instructionBudget > broader.instructionBudget + || stricter.memoryLimitBytes > broader.memoryLimitBytes + || (broader.logicalTimeLimitMs !== undefined && stricter.logicalTimeLimitMs === undefined) + || ( + broader.logicalTimeLimitMs !== undefined + && stricter.logicalTimeLimitMs > broader.logicalTimeLimitMs + ) + ) { + fail(`${expectedManifest} scoring policies must be ordered from broadest to strictest`); + } + } + const complexities = manifest.complexities; + if (!Array.isArray(complexities) || complexities.length < 2) { + fail(`${expectedManifest} must declare at least two complexity paths`); + } + if (!complexities.some((complexity) => complexity.accepted)) { + fail(`${expectedManifest} must declare an accepted complexity path`); + } + + return { + id: catalogEntry.slug, + number: expectedNumber, + title, + difficulty: manifest.difficulty, + tags: manifest.tags, + statement: localizedStatement, + editorial: localizedEditorial, + judgeCases, + scoring: { + maximumPoints: 100, + calibration: { method: calibration.method, profiles }, + policies, + safetyLimits: scoring.safetyLimits, + }, + complexities: complexities.map((complexity, index) => { + const record = assertRecord(complexity, `${expectedManifest} complexity ${index}`); + return { + name: assertLocalizedText(record.name, `${expectedManifest} complexity ${index} name`), + time: record.time, + space: record.space, + accepted: record.accepted, + }; + }), + }; +} + +function render(problems) { + return [ + "// Generated by scripts/generate-judge-problems.mjs. Do not edit by hand.", + 'import type { JudgeProblem } from "./problem-model";', + "", + `export const GENERATED_PROBLEMS = ${JSON.stringify(problems, null, 2)} as const satisfies readonly JudgeProblem[];`, + "", + ].join("\n"); +} + +async function atomicWrite(file, output) { + await mkdir(path.dirname(file), { recursive: true }); + const temporary = `${file}.tmp-${process.pid}`; + await writeFile(temporary, output, { encoding: "utf8", flag: "wx", mode: 0o644 }); + await rename(temporary, file); +} + +async function main() { + const options = parseArgs(process.argv.slice(2)); + const validators = await loadSchemaValidators(); + const catalog = await loadCatalog(validators.catalog); + const canonicalProblems = await Promise.all( + catalog.problems.map((entry, index) => loadProblem(entry, index + 1, validators.problem)), + ); + const learningPath = await readJson(LEARNING_PATH_PATH, "learning-path.json"); + const problems = applyLearningPath(learningPath, canonicalProblems); + const output = render(problems); + if (options.check) { + let current; + try { + current = await readFile(OUTPUT_PATH, "utf8"); + } catch { + fail("generated TypeScript problem fixture is missing; run pnpm problems:generate"); + } + if (current !== output) { + fail("generated TypeScript problem fixture is stale; run pnpm problems:generate"); + } + console.log("verified generated Forge problem fixture for 45 localized problems"); + return; + } + await atomicWrite(OUTPUT_PATH, output); + console.log("generated Forge problem fixture for 45 localized problems"); +} + +await main(); diff --git a/scripts/learning-path.mjs b/scripts/learning-path.mjs new file mode 100644 index 0000000..94a30af --- /dev/null +++ b/scripts/learning-path.mjs @@ -0,0 +1,83 @@ +export const LEARNING_PATH_SCHEMA = "wasm-oj-learning-path-v1"; +export const LEARNING_PATH_LOCALES = Object.freeze(["zh-TW", "en"]); + +const ID_PATTERN = /^[a-z0-9]+(?:-[a-z0-9]+)*$/; + +function fail(message) { + throw new Error(message); +} + +function assertRecord(value, label) { + if (!value || typeof value !== "object" || Array.isArray(value)) { + fail(`${label} must be an object`); + } + return value; +} + +function assertExactKeys(value, keys, label) { + const actual = Object.keys(value).sort(); + const expected = [...keys].sort(); + if (JSON.stringify(actual) !== JSON.stringify(expected)) { + fail(`${label} has unexpected keys: ${actual.join(", ")}`); + } +} + +function assertLocalizedText(value, label) { + const record = assertRecord(value, label); + assertExactKeys(record, LEARNING_PATH_LOCALES, label); + for (const locale of LEARNING_PATH_LOCALES) { + if (typeof record[locale] !== "string" || !record[locale] || record[locale] !== record[locale].trim()) { + fail(`${label}[${locale}] must be a non-empty trimmed string`); + } + } + return record; +} + +export function applyLearningPath(value, problems) { + const document = assertRecord(value, "learning-path.json"); + assertExactKeys(document, ["schema", "localization", "tracks"], "learning-path.json"); + if (document.schema !== LEARNING_PATH_SCHEMA) fail("learning-path.json uses an unsupported schema"); + if (JSON.stringify(document.localization) !== JSON.stringify({ + defaultLocale: "zh-TW", + supportedLocales: LEARNING_PATH_LOCALES, + })) { + fail("learning-path.json uses an unsupported localization contract"); + } + if (!Array.isArray(document.tracks) || document.tracks.length === 0) { + fail("learning-path.json must contain at least one track"); + } + + const problemById = new Map(problems.map((problem) => [problem.id, problem])); + if (problemById.size !== problems.length) fail("problem inventory contains duplicate IDs"); + const trackIds = new Set(); + const seenProblems = new Set(); + const ordered = []; + for (const [trackIndex, trackValue] of document.tracks.entries()) { + const label = `learning-path.json track ${trackIndex + 1}`; + const track = assertRecord(trackValue, label); + assertExactKeys(track, ["id", "title", "problems"], label); + if (typeof track.id !== "string" || !ID_PATTERN.test(track.id) || trackIds.has(track.id)) { + fail(`${label} has an invalid or duplicate ID`); + } + trackIds.add(track.id); + const title = assertLocalizedText(track.title, `${label} title`); + if (!Array.isArray(track.problems) || track.problems.length === 0) { + fail(`${label} must contain at least one problem`); + } + for (const problemId of track.problems) { + if (typeof problemId !== "string" || !ID_PATTERN.test(problemId)) { + fail(`${label} contains an invalid problem ID`); + } + const problem = problemById.get(problemId); + if (!problem) fail(`${label} references unknown problem '${problemId}'`); + if (seenProblems.has(problemId)) fail(`learning-path.json repeats problem '${problemId}'`); + seenProblems.add(problemId); + ordered.push({ ...problem, number: ordered.length + 1, trackId: track.id, track: title }); + } + } + if (seenProblems.size !== problems.length) { + const missing = problems.filter((problem) => !seenProblems.has(problem.id)).map((problem) => problem.id); + fail(`learning-path.json omits problems: ${missing.join(", ")}`); + } + return ordered; +} diff --git a/scripts/learning-path.test.mjs b/scripts/learning-path.test.mjs new file mode 100644 index 0000000..9cdef0a --- /dev/null +++ b/scripts/learning-path.test.mjs @@ -0,0 +1,24 @@ +import assert from "node:assert/strict"; +import test from "node:test"; +import { applyLearningPath } from "./learning-path.mjs"; + +const problem = (id) => ({ id, number: 99 }); +const title = { "zh-TW": "入門", en: "Foundations" }; +const path = (problems) => ({ + schema: "wasm-oj-learning-path-v1", + localization: { defaultLocale: "zh-TW", supportedLocales: ["zh-TW", "en"] }, + tracks: [{ id: "foundations", title, problems }], +}); + +test("assigns contiguous display numbers while preserving problem identities", () => { + assert.deepEqual(applyLearningPath(path(["second", "first"]), [problem("first"), problem("second")]), [ + { id: "second", number: 1, trackId: "foundations", track: title }, + { id: "first", number: 2, trackId: "foundations", track: title }, + ]); +}); + +test("rejects duplicate, unknown, and omitted problems", () => { + assert.throws(() => applyLearningPath(path(["first", "first"]), [problem("first")]), /repeats problem/); + assert.throws(() => applyLearningPath(path(["missing"]), [problem("first")]), /unknown problem/); + assert.throws(() => applyLearningPath(path(["first"]), [problem("first"), problem("second")]), /omits problems/); +}); diff --git a/scripts/problem-schema.test.mjs b/scripts/problem-schema.test.mjs new file mode 100644 index 0000000..4cf1f02 --- /dev/null +++ b/scripts/problem-schema.test.mjs @@ -0,0 +1,35 @@ +import assert from "node:assert/strict"; +import { readFile } from "node:fs/promises"; +import path from "node:path"; +import { describe, it } from "node:test"; +import { fileURLToPath } from "node:url"; +import Ajv2020 from "ajv/dist/2020.js"; + +const ROOT = path.resolve(path.dirname(fileURLToPath(import.meta.url)), ".."); + +async function fixture() { + const [schema, manifest] = await Promise.all([ + readFile(path.join(ROOT, "schemas/problem.schema.json"), "utf8").then(JSON.parse), + readFile( + path.join(ROOT, "problems/001-weighted-opcode-scale/problem.json"), + "utf8", + ).then(JSON.parse), + ]); + const validate = new Ajv2020({ allErrors: true, strict: true }).compile(schema); + return { manifest, validate }; +} + +describe("problem manifest scoring schema", () => { + it("requires baseline, efficient, optimal in relaxed-to-strict order", async () => { + const { manifest, validate } = await fixture(); + assert.equal(validate(manifest), true, JSON.stringify(validate.errors)); + + const reversed = structuredClone(manifest); + reversed.scoring.policies.reverse(); + assert.equal(validate(reversed), false); + + const missing = structuredClone(manifest); + missing.scoring.policies.splice(1, 1); + assert.equal(validate(missing), false); + }); +}); diff --git a/scripts/render-og.mjs b/scripts/render-og.mjs index 56ed98f..118269c 100644 --- a/scripts/render-og.mjs +++ b/scripts/render-og.mjs @@ -80,7 +80,7 @@ try { 07 ✓ deterministic ✓ zero uploads
ACCEPTED
- + `); diff --git a/scripts/start-production.mjs b/scripts/start-production.mjs index 938f0f3..005e841 100644 --- a/scripts/start-production.mjs +++ b/scripts/start-production.mjs @@ -33,7 +33,7 @@ function parsePort(value) { function installProductionResponsePolicy(server) { server.prependListener("request", (request, response) => { - response.setHeader("Cross-Origin-Embedder-Policy", "credentialless"); + response.setHeader("Cross-Origin-Embedder-Policy", "require-corp"); response.setHeader("Cross-Origin-Opener-Policy", "same-origin"); response.setHeader("Cross-Origin-Resource-Policy", "same-origin"); response.setHeader("Referrer-Policy", "no-referrer"); diff --git a/scripts/verify-contract.mjs b/scripts/verify-contract.mjs index 8f4186e..4df3baa 100644 --- a/scripts/verify-contract.mjs +++ b/scripts/verify-contract.mjs @@ -37,6 +37,43 @@ await requireSource( `"schema": "${FORGE_SCHEMAS.pythonToolchain}"`, ); +const crossOriginPolicyFiles = [ + "README.md", + "docs/architecture.md", + "docs/integration-guide.md", + "docs/library-contract.md", + "public/_headers", + "scripts/start-production.mjs", + "vite.config.ts", + "worker/index.ts", +]; +for (const relative of crossOriginPolicyFiles) { + await rejectSource(relative, "credentialless"); +} +await requireSource( + "vite.config.ts", + `"Cross-Origin-Embedder-Policy": "require-corp"`, + `"Cross-Origin-Opener-Policy": "same-origin"`, +); +await requireSource( + "worker/index.ts", + `headers.set("Cross-Origin-Embedder-Policy", "require-corp")`, + `headers.set("Cross-Origin-Opener-Policy", "same-origin")`, + `headers.set("Cross-Origin-Resource-Policy", "same-origin")`, +); +await requireSource( + "scripts/start-production.mjs", + `response.setHeader("Cross-Origin-Embedder-Policy", "require-corp")`, + `response.setHeader("Cross-Origin-Opener-Policy", "same-origin")`, + `response.setHeader("Cross-Origin-Resource-Policy", "same-origin")`, +); +await requireSource( + "public/_headers", + "Cross-Origin-Embedder-Policy: require-corp", + "Cross-Origin-Opener-Policy: same-origin", + "Cross-Origin-Resource-Policy: same-origin", +); + const pins = await readJson("public/toolchains/clang-22.0.0-git20542-10.cc1-pins.json"); const manifest = await readJson("public/toolchains/clang-22.0.0-git20542-10.manifest.json"); const rustManifest = await readJson("public/toolchains/rust-1.91.1-dev.manifest.json"); @@ -61,6 +98,11 @@ async function requireSource(relative, ...needles) { } } +async function rejectSource(relative, needle) { + const source = await readFile(path.join(root, relative), "utf8"); + if (source.includes(needle)) throw new Error(`Unexpected '${needle}' in '${relative}'.`); +} + async function readJson(relative) { return JSON.parse(await readFile(path.join(root, relative), "utf8")); } diff --git a/src/components/case-score-details.tsx b/src/components/case-score-details.tsx new file mode 100644 index 0000000..06be239 --- /dev/null +++ b/src/components/case-score-details.tsx @@ -0,0 +1,300 @@ +import type { CSSProperties } from "react"; +import type { JudgeUiCaseResult } from "@/src/judge/judge"; +import type { + JudgeProblem, + ProblemLocale, + ProblemScoringPolicy, +} from "@/src/judge/problem-model"; + +interface ResourceThreshold { + id: string; + label: string; + points: number; + value: number; +} + +function formatInteger(value: number, locale: ProblemLocale): string { + return value.toLocaleString(locale === "zh-TW" ? "zh-TW" : "en-US"); +} + +function formatBytes(bytes: number, locale: ProblemLocale): string { + const units = ["B", "KiB", "MiB", "GiB"]; + let value = bytes; + let unit = 0; + while (value >= 1024 && unit < units.length - 1) { + value /= 1024; + unit += 1; + } + const digits = unit === 0 || value >= 100 ? 0 : value >= 10 ? 1 : 2; + return `${value.toLocaleString(locale === "zh-TW" ? "zh-TW" : "en-US", { + maximumFractionDigits: digits, + })} ${units[unit]}`; +} + +function formatMilliseconds(nanoseconds: number, locale: ProblemLocale): string { + return `${(nanoseconds / 1_000_000).toLocaleString(locale === "zh-TW" ? "zh-TW" : "en-US", { + maximumFractionDigits: 3, + })} ms`; +} + +function axisPosition(value: number, maximum: number, logarithmic: boolean): number { + if (maximum <= 0) return 0; + const ratio = logarithmic + ? Math.log1p(value) / Math.log1p(maximum) + : value / maximum; + return Math.max(0, Math.min(100, ratio * 100)); +} + +function positionStyle(position: number): CSSProperties { + return { "--axis-position": `${position}%` } as CSSProperties; +} + +function ResourceAxis({ + title, + value, + thresholds, + locale, + format, + logarithmic = false, +}: { + title: string; + value: number | null; + thresholds: readonly ResourceThreshold[]; + locale: ProblemLocale; + format(value: number, locale: ProblemLocale): string; + logarithmic?: boolean; +}) { + const largestThreshold = Math.max(...thresholds.map((threshold) => threshold.value)); + const domainMaximum = Math.max(largestThreshold, value ?? 0) * 1.06; + const markerGroups = [...thresholds.reduce((groups, threshold) => { + const group = groups.get(threshold.value) ?? { + ids: [] as string[], + labels: [] as string[], + points: [] as number[], + value: threshold.value, + }; + group.ids.push(threshold.id); + group.labels.push(threshold.label); + group.points.push(threshold.points); + groups.set(threshold.value, group); + return groups; + }, new Map()).values()]; + return ( +
+
+ {title} + + {value === null ? (locale === "zh-TW" ? "無可用資料" : "Unavailable") : format(value, locale)} + {logarithmic ? (locale === "zh-TW" ? " · 對數刻度" : " · log scale") : ""} + +
+ +
+ {thresholds.map((threshold) => ( + + {threshold.label} ≤ {format(threshold.value, locale)} + + ))} +
+
+ ); +} + +function policyFailure( + policy: ProblemScoringPolicy, + testCase: JudgeUiCaseResult, + locale: ProblemLocale, +): string { + const evaluation = testCase.policyEvaluations?.find((candidate) => candidate.id === policy.id); + if (!evaluation) return locale === "zh-TW" ? "沒有計分資料" : "No scoring data"; + if (evaluation.earned) return locale === "zh-TW" ? "已取得" : "Earned"; + if (!testCase.metrics) { + return !testCase.outputAccepted + ? (locale === "zh-TW" ? "資源指標不可用 · 輸出未通過" : "metrics unavailable · output failed") + : (locale === "zh-TW" ? "資源指標不可用" : "metrics unavailable"); + } + const reasons: string[] = []; + if (testCase.metrics.cost === null) { + reasons.push(locale === "zh-TW" ? "指令成本不可用" : "cost unavailable"); + } else if (!evaluation.costPassed) { + reasons.push(locale === "zh-TW" ? "指令成本超標" : "cost over"); + } + if (testCase.metrics.memoryBytes === null) { + reasons.push(locale === "zh-TW" ? "記憶體用量不可用" : "memory unavailable"); + } else if (!evaluation.memoryPassed) { + reasons.push(locale === "zh-TW" ? "記憶體用量超標" : "memory over"); + } + if (evaluation.logicalTimePassed === false) { + reasons.push(testCase.metrics.logicalTimeNs === null + ? (locale === "zh-TW" ? "邏輯時間不可用" : "logical time unavailable") + : (locale === "zh-TW" ? "邏輯時間超標" : "logical time over")); + } + if (!testCase.outputAccepted) reasons.push(locale === "zh-TW" ? "輸出未通過" : "output failed"); + return [...new Set(reasons)].join(" · "); +} + +function nextThresholdMessage( + problem: JudgeProblem, + testCase: JudgeUiCaseResult, + locale: ProblemLocale, +): string { + if (!testCase.outputAccepted) { + return locale === "zh-TW" + ? "輸出必須先完全正確,資源政策才會給分。" + : "Output must be correct before any resource policy awards points."; + } + const nextPolicy = problem.scoring.policies.find((policy) => ( + !testCase.policyEvaluations?.find((evaluation) => evaluation.id === policy.id)?.earned + )); + if (!nextPolicy) { + return locale === "zh-TW" + ? "這筆測資已通過所有政策,取得滿分。" + : "This case passes every policy and earns full points."; + } + if (!testCase.metrics) { + return locale === "zh-TW" ? "沒有足夠的資源指標可計算下一個門檻。" : "Metrics are unavailable for the next threshold."; + } + const gaps: string[] = []; + if (testCase.metrics.cost !== null && testCase.metrics.cost > nextPolicy.limits.instructionBudget) { + gaps.push(`${locale === "zh-TW" ? "指令成本再降低" : "reduce cost by"} ${formatInteger( + testCase.metrics.cost - nextPolicy.limits.instructionBudget, + locale, + )}`); + } + if ( + testCase.metrics.memoryBytes !== null + && testCase.metrics.memoryBytes > nextPolicy.limits.memoryLimitBytes + ) { + gaps.push(`${locale === "zh-TW" ? "記憶體用量再降低" : "reduce memory by"} ${formatBytes( + testCase.metrics.memoryBytes - nextPolicy.limits.memoryLimitBytes, + locale, + )}`); + } + if ( + nextPolicy.limits.logicalTimeLimitMs !== undefined + && testCase.metrics.logicalTimeNs !== null + && testCase.metrics.logicalTimeNs > nextPolicy.limits.logicalTimeLimitMs * 1_000_000 + ) { + gaps.push(`${locale === "zh-TW" ? "邏輯時間再降低" : "reduce logical time by"} ${formatMilliseconds( + testCase.metrics.logicalTimeNs - nextPolicy.limits.logicalTimeLimitMs * 1_000_000, + locale, + )}`); + } + const title = nextPolicy.title[locale]; + return gaps.length > 0 + ? `${locale === "zh-TW" ? `距「${title}」` : `To reach “${title}”`}: ${gaps.join(locale === "zh-TW" ? "、" : "; ")}.` + : locale === "zh-TW" + ? `「${title}」尚未通過;請查看下方各項狀態。` + : `“${title}” is not yet satisfied; inspect the checks below.`; +} + +export function CaseScoreDetails({ + problem, + testCase, + locale, +}: { + problem: JudgeProblem; + testCase: JudgeUiCaseResult; + locale: ProblemLocale; +}) { + const metrics = testCase.metrics; + const costThresholds = problem.scoring.policies.map((policy) => ({ + id: policy.id, + label: policy.title[locale], + points: policy.points, + value: policy.limits.instructionBudget, + })); + const memoryThresholds = problem.scoring.policies.map((policy) => ({ + id: policy.id, + label: policy.title[locale], + points: policy.points, + value: policy.limits.memoryLimitBytes, + })); + return ( +
+
+
+ {locale === "zh-TW" ? "測資" : "Case"} {String(testCase.number).padStart(2, "0")} + {locale === "zh-TW" ? "計分細節" : "scoring details"} +
+ {testCase.points ?? 0} / {problem.scoring.maximumPoints} {locale === "zh-TW" ? "分" : "pts"} +
+

{nextThresholdMessage(problem, testCase, locale)}

+
+
+ {locale === "zh-TW" ? "淨指令成本" : "Net instruction cost"} + {metrics?.cost === null || metrics?.cost === undefined ? "—" : formatInteger(metrics.cost, locale)} + + {metrics?.rawCost === null || metrics?.rawCost === undefined + ? (locale === "zh-TW" ? "原始指令成本不可用" : "raw cost unavailable") + : locale === "zh-TW" + ? `原始 ${formatInteger(metrics.rawCost, locale)} − 基準 ${formatInteger(metrics.baselineCost, locale)}` + : `raw ${formatInteger(metrics.rawCost, locale)} − baseline ${formatInteger(metrics.baselineCost, locale)}`} + +
+
+ {locale === "zh-TW" ? "線性記憶體峰值" : "Peak linear memory"} + {metrics?.memoryBytes === null || metrics?.memoryBytes === undefined ? "—" : formatBytes(metrics.memoryBytes, locale)} + {locale === "zh-TW" ? "runtime 回報的峰值" : "runtime-reported peak"} +
+ {metrics?.logicalTimeNs !== null && metrics?.logicalTimeNs !== undefined && ( +
+ {locale === "zh-TW" ? "邏輯時間" : "Logical time"} + {formatMilliseconds(metrics.logicalTimeNs, locale)} + {locale === "zh-TW" ? "可重現虛擬時間" : "deterministic virtual time"} +
+ )} +
+
+ + +
+
+ {problem.scoring.policies.map((policy) => { + const evaluation = testCase.policyEvaluations?.find((candidate) => candidate.id === policy.id); + return ( +
+ {evaluation?.earned ? "✓" : "×"} +{policy.points} · {policy.title[locale]} + {policyFailure(policy, testCase, locale)} +
+ ); + })} +
+
+ ); +} diff --git a/src/components/judge-onboarding-storage.ts b/src/components/judge-onboarding-storage.ts new file mode 100644 index 0000000..4494f34 --- /dev/null +++ b/src/components/judge-onboarding-storage.ts @@ -0,0 +1,12 @@ +import { FORGE_CONTRACT_ID } from "../core/contract"; + +export const JUDGE_ONBOARDING_STORAGE_KEY = `${FORGE_CONTRACT_ID}:judge-onboarding:v1`; +const JUDGE_ONBOARDING_COMPLETED = "completed"; + +export function isJudgeOnboardingComplete(storage: Pick): boolean { + return storage.getItem(JUDGE_ONBOARDING_STORAGE_KEY) === JUDGE_ONBOARDING_COMPLETED; +} + +export function completeJudgeOnboarding(storage: Pick): void { + storage.setItem(JUDGE_ONBOARDING_STORAGE_KEY, JUDGE_ONBOARDING_COMPLETED); +} diff --git a/src/components/judge-onboarding.test.ts b/src/components/judge-onboarding.test.ts new file mode 100644 index 0000000..e093a80 --- /dev/null +++ b/src/components/judge-onboarding.test.ts @@ -0,0 +1,24 @@ +import { describe, expect, it } from "vitest"; +import { + completeJudgeOnboarding, + isJudgeOnboardingComplete, + JUDGE_ONBOARDING_STORAGE_KEY, +} from "./judge-onboarding-storage"; + +describe("judge onboarding persistence", () => { + it("opens for a browser that has not completed this tutorial version", () => { + const storage = { getItem: () => null }; + expect(isJudgeOnboardingComplete(storage)).toBe(false); + }); + + it("recognizes only the explicit completed marker", () => { + expect(isJudgeOnboardingComplete({ getItem: () => "dismissed" })).toBe(false); + expect(isJudgeOnboardingComplete({ getItem: () => "completed" })).toBe(true); + }); + + it("writes the versioned completion marker", () => { + const writes: Array<[string, string]> = []; + completeJudgeOnboarding({ setItem: (key, value) => { writes.push([key, value]); } }); + expect(writes).toEqual([[JUDGE_ONBOARDING_STORAGE_KEY, "completed"]]); + }); +}); diff --git a/src/components/judge-onboarding.tsx b/src/components/judge-onboarding.tsx new file mode 100644 index 0000000..6c69fb0 --- /dev/null +++ b/src/components/judge-onboarding.tsx @@ -0,0 +1,335 @@ +"use client"; + +import { + BookOpen, + CheckCircle2, + ChevronLeft, + ChevronRight, + CircleAlert, + Cloud, + Code2, + Cpu, + Gauge, + HardDrive, + Laptop, + ListChecks, + Play, + Scale, + Send, + ShieldCheck, + Terminal, + X, + type LucideIcon, +} from "lucide-react"; +import { useEffect, useMemo, useRef, useState } from "react"; +import type { ProblemLocale } from "@/src/judge/problem-model"; + +export { + completeJudgeOnboarding, + isJudgeOnboardingComplete, + JUDGE_ONBOARDING_STORAGE_KEY, +} from "./judge-onboarding-storage"; + +interface JudgeOnboardingProps { + locale: ProblemLocale; + onClose(): void; +} + +interface OnboardingStep { + shortLabel: string; + title: string; + icon: LucideIcon; +} + +const VERDICTS = [ + { + code: "AC", + name: "Accepted", + tone: "accepted", + zh: "所有測資的輸出都正確。若也通過所有資源政策,才算完整解出題目。", + en: "Every case produced correct output. The problem is fully solved only when every resource policy also passes.", + }, + { + code: "WA", + name: "Wrong Answer", + tone: "wrong-answer", + zh: "程式正常結束,但至少一組輸出與預期不符;從 case 詳情比較 Expected 與 Actual。", + en: "The program exited normally, but at least one output differed. Compare Expected and Actual in the case details.", + }, + { + code: "CE", + name: "Compile Error", + tone: "compile-error", + zh: "原始碼未成功編譯;到 Diagnostics 查看檔案、行列與編譯器訊息。", + en: "The source did not compile. Open Diagnostics for the file, location, and compiler message.", + }, + { + code: "RE", + name: "Runtime Error", + tone: "runtime-error", + zh: "執行時崩潰、非零結束,或超過記憶體、輸出、可寫檔案系統限制。", + en: "The run crashed, exited non-zero, or exceeded memory, output, or writable-filesystem limits.", + }, + { + code: "TLE", + name: "Time Limit", + tone: "time-limit", + zh: "超過指令成本、邏輯時間或緊急 wall deadline;這裡不只看電腦跑了幾秒。", + en: "Instruction cost, logical time, or the emergency wall deadline was exceeded—not merely elapsed seconds.", + }, + { + code: "JE", + name: "Judge Error", + tone: "judge-error", + zh: "判題器、題目資料或執行環境發生錯誤,通常不是答案本身的判定。", + en: "The judge, problem data, or runtime failed; this is normally not a verdict on the solution itself.", + }, + { + code: "—", + name: "Cancelled", + tone: "cancelled", + zh: "你按下「停止」中斷了建置、測試或判題,這不是答案正確性的結果。", + en: "You pressed Stop during building, testing, or judging. This says nothing about solution correctness.", + }, +] as const; + +function WelcomeStep({ zh }: { zh: boolean }) { + return ( +
+
+

{zh ? "3 分鐘快速導覽" : "3-MINUTE ORIENTATION"}

+

{zh ? "先認識這個不太一樣的 Online Judge" : "Meet an Online Judge that works differently"}

+

+ {zh + ? "Online Judge(OJ)會用多組測資執行你的程式,再依輸出與資源使用量給出判定。FORGE 保留熟悉的解題流程,但把編譯器、執行環境與 Judge 全部搬進你的瀏覽器。" + : "An Online Judge (OJ) runs your program against multiple cases and evaluates its output and resource use. FORGE keeps that familiar workflow while moving the compiler, runtime, and judge into your browser."} +

+
+
+ +
+ {zh ? "第一次使用 OJ?" : "New to Online Judges?"} +

{zh ? "把題目想成一份輸入/輸出契約:讀懂規格、寫程式、先用自己的輸入測試,再提交給完整測資。" : "Treat each problem as an input/output contract: understand it, write code, test with your own inputs, then submit against the full cases."}

+
+
+
+ +
+ {zh ? "用過其他 OJ?" : "Used another OJ?"} +

{zh ? "題目、編輯器、測試與提交都很熟悉;差別在於本機 WASM 執行、可重現資源計量,以及輸出正確後的累進得分政策。" : "Problems, editing, tests, and submissions are familiar. The differences are local WASM execution, reproducible metering, and progressive scoring after output correctness."}

+
+
+
+
+ {[zh ? "讀題" : "Read", zh ? "寫程式" : "Code", zh ? "自行測試" : "Test", zh ? "提交判題" : "Submit"].map((label, index) => ( +
{index + 1}{label}{index < 3 && }
+ ))} +
+
+ ); +} + +function BrowserJudgeStep({ zh }: { zh: boolean }) { + return ( +
+

{zh ? "FORGE 的核心差異" : "THE FORGE DIFFERENCE"}

+

{zh ? "從原始碼到結果,都在這個分頁完成" : "From source code to verdict, inside this tab"}

+

{zh ? "網路只用來下載並驗證題庫與工具鏈;你的原始碼、自行測試輸入、執行輸出、判題結果與建置產物不會上傳。" : "The network only downloads and verifies problem bundles and toolchains. Your source, custom inputs, output, verdicts, and build artifacts are not uploaded."}

+ +
+
{zh ? "你的原始碼" : "Your source"}
+ +
{zh ? "瀏覽器內工具鏈" : "In-browser toolchain"}
+ +
WASI / WASIX
+ +
{zh ? "本機 Wasmer Judge" : "Local Wasmer judge"}
+
+ +
+
{zh ? "本機編譯與執行" : "Local compile and run"}

{zh ? "真實語言工具鏈在 Worker 中產生 WASI/WASIX 程式,再由瀏覽器內的 Wasmer runtime 執行。" : "Real language toolchains produce WASI/WASIX programs in workers, then the in-browser Wasmer runtime executes them."}

+
{zh ? "可驗證的下載" : "Verified downloads"}

{zh ? "題庫依 SHA-256 bundle 驗證,工具鏈與快取也有明確版本,不會用來源不明的替代內容。" : "Problem bundles are SHA-256 verified, while toolchains and caches are explicitly versioned—no unknown substitutes."}

+
{zh ? "可重現的資源界線" : "Reproducible limits"}

{zh ? "Judge 計量指令成本、邏輯時間、記憶體、輸出與 VFS;相同程式的結果較不受裝置快慢影響。" : "The judge meters instruction cost, logical time, memory, output, and VFS, reducing dependence on device speed."}

+
+ +
+ +
{zh ? "重要邊界:這是練習與自我驗證工具" : "Important boundary: this is for practice and self-verification"}

{zh ? "完整測資必須存在瀏覽器內,因此有能力的使用者可以檢視它們。FORGE 重視隱私與可重現性,但不宣稱能像伺服器競賽 Judge 一樣防作弊。" : "The full cases must exist in the browser, so a capable user can inspect them. FORGE prioritizes privacy and reproducibility; it does not claim server-competition anti-cheat properties."}

+
+
+ ); +} + +function WorkflowStep({ zh }: { zh: boolean }) { + const items = [ + { icon: BookOpen, title: zh ? "1. 選題並讀懂契約" : "1. Choose a problem and read the contract", text: zh ? "左側選題;中間查看輸入、輸出、限制與範例。先確認格式,再開始寫程式。" : "Choose on the left; read input, output, constraints, and examples in the center. Confirm the format before coding." }, + { icon: Code2, title: zh ? "2. 選語言並編寫程式" : "2. Choose a language and write code", text: zh ? "上方可切換語言與 WASI/WASIX 目標。編輯器會保存在本機,背景預編譯可縮短等待。" : "Choose a language and WASI/WASIX target above. The editor saves locally, and background precompilation reduces waiting." }, + { icon: Play, title: zh ? "3. 先用「自行測試」" : "3. Use Self Test first", text: zh ? "自行建立輸入,直接查看 stdout、stderr、exit code 與資源指標。它不會決定題目是否解出。" : "Create your own inputs and inspect stdout, stderr, exit code, and metrics. This does not decide whether the problem is solved." }, + { icon: Send, title: zh ? "4. 再按「提交判題」" : "4. Then Submit", text: zh ? "Judge 會在本機依序跑完整測資。下方「判題結果」會顯示總判定、各 case、差異與得分政策。" : "The local judge runs the full cases. Judge Results shows the overall verdict, each case, diffs, and scoring policies." }, + ]; + return ( +
+

{zh ? "第一次解題" : "YOUR FIRST SOLUTION"}

+

{zh ? "最短路徑:讀題 → 寫程式 → 測試 → 提交" : "The shortest path: read → code → test → submit"}

+

{zh ? "「建置」只負責編譯;「自行測試」使用你提供的輸入;只有「提交判題」會跑題目的完整 cases 並計分。" : "Build only compiles. Self Test uses inputs you provide. Only Submit runs the problem's full cases and scores the solution."}

+
+ {items.map(({ icon: Icon, title, text }) =>
{title}

{text}

)} +
+
{zh ? "建議:先用題目範例確認 I/O 格式,再補邊界案例;出錯時先看失敗 case 的 Expected、Actual 與 stderr。" : "Tip: validate I/O with the examples, then add edge cases. On failure, inspect Expected, Actual, and stderr for the failed case."}
+
+ ); +} + +function VerdictStep({ zh }: { zh: boolean }) { + return ( +
+

{zh ? "判定結果速查" : "VERDICT REFERENCE"}

+

{zh ? "每一種結果,真正代表什麼" : "What every result actually means"}

+

{zh ? "判題中(Running)是暫時狀態;完成後會得到下列結果之一。各 case 可展開查看細節。" : "Running is a temporary state. When judging finishes, it produces one of the results below. Open each case for details."}

+
+ {VERDICTS.map((verdict) => ( +
+ {verdict.code} +
{verdict.name}

{zh ? verdict.zh : verdict.en}

+
+ ))} +
+
+ +
{zh ? "FORGE 特有:Accepted 不一定是滿分" : "FORGE-specific: Accepted may not mean full points"}

{zh ? "輸出全部正確時仍是 Accepted,但每個 case 還會依累進資源政策計分。若只通過較寬鬆的成本或記憶體門檻,會顯示「輸出正確 · 部分得分」;通過全部政策才會標記為 solved。" : "Correct output still yields Accepted, but each case is also scored against cumulative resource policies. Passing only looser cost or memory tiers shows Correct Output · Partial Score; all policies must pass to mark the problem solved."}

+
+
+ ); +} + +function ComparisonStep({ zh }: { zh: boolean }) { + const rows = zh ? [ + ["編譯與執行", "通常在遠端伺服器", "在你的瀏覽器 Worker 與 Wasmer 內"], + ["程式碼與結果", "提交到平台", "留在目前裝置,不上傳"], + ["時間限制", "常以伺服器 wall time 為主", "指令成本+邏輯時間;wall deadline 僅緊急終止"], + ["測資保密", "保留在伺服器,可用於正式競賽", "下載到瀏覽器,可被檢視,不以防作弊為目標"], + ["計分方式", "常見全對或子任務計分", "輸出正確後,再依累進資源政策取得分數"], + ["適合情境", "比賽、排名、受控評測", "練習、教學、自我驗證、可重現實驗"], + ] : [ + ["Compile & run", "Usually on remote servers", "In your browser workers and Wasmer"], + ["Code & results", "Submitted to the platform", "Stay on this device; never uploaded"], + ["Time limits", "Often based on server wall time", "Instruction cost + logical time; wall deadline is emergency-only"], + ["Hidden cases", "Remain server-side; suitable for contests", "Downloaded to the browser; inspectable and not anti-cheat"], + ["Scoring", "Often all-or-nothing or subtasks", "Output correctness plus cumulative resource policies"], + ["Best suited for", "Contests, rankings, controlled evaluation", "Practice, teaching, self-checking, reproducible experiments"], + ]; + return ( +
+

{zh ? "建立正確預期" : "SET THE RIGHT EXPECTATIONS"}

+

{zh ? "FORGE 與一般伺服器 Judge 的差異" : "FORGE versus a typical server-side judge"}

+

{zh ? "操作方式相似,但信任邊界、資源計量與使用目的不同。了解這張表,就不會用錯誤的方式解讀結果。" : "The interaction is familiar, but the trust boundary, metering, and intended use differ. This table prevents misreading the results."}

+
+
{zh ? "面向" : "Aspect"}{zh ? "一般伺服器 OJ" : "Typical server OJ"}FORGE
+ {rows.map(([aspect, traditional, forge]) =>
{aspect}{traditional}{forge}
)} +
+
+ +
{zh ? "你已經可以開始了" : "You are ready"}

{zh ? "先選一題入門題,確認輸入/輸出格式,使用自行測試,最後提交。之後隨時可按右上角的「?」重新開啟這份導覽。" : "Choose an introductory problem, confirm its I/O, use Self Test, then Submit. Reopen this guide anytime from the ? button in the top right."}

+
+
+ ); +} + +export function JudgeOnboarding({ locale, onClose }: JudgeOnboardingProps) { + const zh = locale === "zh-TW"; + const [step, setStep] = useState(0); + const dialogRef = useRef(null); + const headingRef = useRef(null); + const steps = useMemo(() => [ + { shortLabel: zh ? "歡迎" : "Welcome", title: zh ? "認識 Online Judge" : "Meet the Online Judge", icon: BookOpen }, + { shortLabel: zh ? "特色" : "Local", title: zh ? "瀏覽器內判題" : "In-browser judging", icon: Cpu }, + { shortLabel: zh ? "流程" : "Workflow", title: zh ? "完成第一次提交" : "Make your first submission", icon: ListChecks }, + { shortLabel: zh ? "結果" : "Verdicts", title: zh ? "看懂判定結果" : "Understand verdicts", icon: CircleAlert }, + { shortLabel: zh ? "比較" : "Compare", title: zh ? "與其他 Judge 的差異" : "Compare with other judges", icon: Scale }, + ], [zh]); + + useEffect(() => { + const previousFocus = document.activeElement instanceof HTMLElement ? document.activeElement : null; + dialogRef.current?.focus(); + const handleKeyDown = (event: KeyboardEvent) => { + if (event.key === "Escape") { + event.preventDefault(); + onClose(); + return; + } + if (event.key !== "Tab" || !dialogRef.current) return; + const focusable = [...dialogRef.current.querySelectorAll("button:not([disabled]), [href], input:not([disabled]), select:not([disabled]), [tabindex]:not([tabindex='-1'])")]; + if (focusable.length === 0) return; + const first = focusable[0]; + const last = focusable.at(-1) ?? first; + if (event.shiftKey && document.activeElement === first) { + event.preventDefault(); + last.focus(); + } else if (!event.shiftKey && document.activeElement === last) { + event.preventDefault(); + first.focus(); + } + }; + document.addEventListener("keydown", handleKeyDown); + return () => { + document.removeEventListener("keydown", handleKeyDown); + previousFocus?.focus(); + }; + }, [onClose]); + + useEffect(() => { + headingRef.current?.querySelector("h2")?.focus(); + }, [step]); + + const content = [ + , + , + , + , + , + ][step]; + + return ( +
+
+
+
FORGE Judge{zh ? "新手導覽" : "Getting started"}
+
{steps.map((item, index) => )}
+ +
+ +
+ +
{content}
+
+ +
+ + {step + 1} / {steps.length} +
+ {step > 0 && } + {step < steps.length - 1 + ? + : } +
+
+
+
+ ); +} diff --git a/src/components/judge-panel-layout.test.ts b/src/components/judge-panel-layout.test.ts new file mode 100644 index 0000000..6da7923 --- /dev/null +++ b/src/components/judge-panel-layout.test.ts @@ -0,0 +1,35 @@ +import { describe, expect, it } from "vitest"; +import { + clampBottomPanelHeight, + DEFAULT_BOTTOM_PANEL_HEIGHT, + maximumBottomPanelHeight, + MIN_BOTTOM_PANEL_HEIGHT, + resizedBottomPanelHeight, +} from "./judge-panel-layout"; + +describe("judge panel layout", () => { + it("reserves the editor tabs, resize handle, and minimum editor height", () => { + expect(maximumBottomPanelHeight(1_000)).toBe(747); + }); + + it("clamps the panel between its minimum and the available workspace", () => { + expect(clampBottomPanelHeight(1_000, 20)).toBe(MIN_BOTTOM_PANEL_HEIGHT); + expect(clampBottomPanelHeight(1_000, DEFAULT_BOTTOM_PANEL_HEIGHT)).toBe(360); + expect(clampBottomPanelHeight(1_000, 900)).toBe(747); + }); + + it("makes the panel taller when the separator is dragged upward", () => { + expect(resizedBottomPanelHeight(1_000, 360, 600, 520)).toBe(440); + expect(resizedBottomPanelHeight(1_000, 360, 600, 680)).toBe(280); + }); + + it("preserves both panel minima in a short workspace", () => { + expect(maximumBottomPanelHeight(350)).toBe(MIN_BOTTOM_PANEL_HEIGHT); + expect(resizedBottomPanelHeight(350, 360, 600, 400)).toBe(MIN_BOTTOM_PANEL_HEIGHT); + }); + + it("rejects invalid dimensions instead of hiding layout defects", () => { + expect(() => clampBottomPanelHeight(Number.NaN, 360)).toThrow(TypeError); + expect(() => clampBottomPanelHeight(1_000, Number.POSITIVE_INFINITY)).toThrow(TypeError); + }); +}); diff --git a/src/components/judge-panel-layout.ts b/src/components/judge-panel-layout.ts new file mode 100644 index 0000000..6d0fddc --- /dev/null +++ b/src/components/judge-panel-layout.ts @@ -0,0 +1,41 @@ +export const DEFAULT_BOTTOM_PANEL_HEIGHT = 360; +export const MIN_BOTTOM_PANEL_HEIGHT = 150; + +const EDITOR_TABS_HEIGHT = 36; +const PANEL_RESIZER_HEIGHT = 7; +const MIN_EDITOR_HEIGHT = 210; + +function requireFinite(value: number, name: string): number { + if (!Number.isFinite(value)) throw new TypeError(`${name} must be a finite number.`); + return value; +} + +export function maximumBottomPanelHeight(stackHeight: number): number { + const availableHeight = Math.floor(requireFinite(stackHeight, "stackHeight")) + - EDITOR_TABS_HEIGHT + - PANEL_RESIZER_HEIGHT + - MIN_EDITOR_HEIGHT; + return Math.max(MIN_BOTTOM_PANEL_HEIGHT, availableHeight); +} + +export function clampBottomPanelHeight(stackHeight: number, requestedHeight: number): number { + const height = Math.round(requireFinite(requestedHeight, "requestedHeight")); + return Math.min( + maximumBottomPanelHeight(stackHeight), + Math.max(MIN_BOTTOM_PANEL_HEIGHT, height), + ); +} + +export function resizedBottomPanelHeight( + stackHeight: number, + startHeight: number, + startPointerY: number, + currentPointerY: number, +): number { + return clampBottomPanelHeight( + stackHeight, + requireFinite(startHeight, "startHeight") + + requireFinite(startPointerY, "startPointerY") + - requireFinite(currentPointerY, "currentPointerY"), + ); +} diff --git a/src/components/judge-studio.tsx b/src/components/judge-studio.tsx index 8f6417d..c45122b 100644 --- a/src/components/judge-studio.tsx +++ b/src/components/judge-studio.tsx @@ -10,6 +10,7 @@ import { Check, CheckCircle2, ChevronDown, + CircleHelp, CircleStop, Clock3, Code2, @@ -19,10 +20,12 @@ import { Hammer, HardDrive, LockKeyhole, + MessageCircle, Package, Play, Plus, RotateCcw, + Search, Send, Settings2, ShieldCheck, @@ -32,40 +35,101 @@ import { Zap, } from "lucide-react"; import type * as Monaco from "monaco-editor"; +import type { CSSProperties, KeyboardEvent as ReactKeyboardEvent, PointerEvent as ReactPointerEvent } from "react"; import { useCallback, useEffect, useMemo, useRef, useState } from "react"; import { CompileCoordinator } from "@/src/compiler/coordinator"; import { projectBuildIdentity, projectCacheKey } from "@/src/core/hash"; -import { isBuiltinLanguage, LANGUAGES, type BuildArtifact, type BuiltinLanguage, type Diagnostic, type Language, type Project, type ProjectFile, type RunConfig, type WorkerProgress } from "@/src/core/types"; +import { isBuiltinLanguage, LANGUAGES, type BuildArtifact, type BuiltinLanguage, type Diagnostic, type Language, type Project, type ProjectFile, type RunConfig, type RunResult, type WorkerProgress } from "@/src/core/types"; import { extensionLanguage, languageLabel, TOOLCHAINS } from "@/src/core/toolchains"; import { decodeSolvedProgress, - JUDGE_PROGRESS_KEY, + judgeProblemProgressId, + judgeProgressKey, type JudgeUiCaseResult, type JudgeUiSession, - type SubmissionVerdict, } from "@/src/judge/judge"; import { createJudgeExecutor, JudgeEngine, type JudgeCaseResult, type JudgeCaseVerdict } from "@/src/judge/engine"; import { FORGE_CONTRACT_VERSION } from "@/src/core/contract"; import { textMatcher } from "@/src/judge/spec"; import { normalizeOutput } from "@/src/judge/normalization"; -import { PROBLEMS, problemById, type JudgeProblem, type ProblemDifficulty } from "@/src/judge/problems"; -import { createJudgeProject, judgeProjectId, problemIdFromProject } from "@/src/judge/project"; +import { createJudgeProject, judgeProjectId, latestJudgeProjectForCollection, problemIdentityFromProject } from "@/src/judge/project"; +import { buildChatGptProblemUrl } from "@/src/judge/chatgpt-help"; import { BrowserForgeCompiler } from "@/src/runtime/compiler-client"; import { BrowserForgeRunner } from "@/src/runtime/runner-client"; -import { clearArtifactCache, deleteArtifact, listProjects, loadArtifact, loadLatestProject, saveArtifact, saveProject } from "@/src/storage/database"; +import { clearArtifactCache, deleteArtifact, listProjects, loadArtifact, saveArtifact, saveProject } from "@/src/storage/database"; import { createDefaultBrowserStorageCoordinator, type ForgeStorageCoordinator } from "@/src/storage/coordinator"; import { registerToolchainCache } from "@/src/storage/service-worker"; import { configureForgeLanguageServices } from "@/src/editor/forge-language-services"; +import { ProblemMarkdown } from "@/src/components/problem-markdown"; +import { CaseScoreDetails } from "@/src/components/case-score-details"; +import { + DEFAULT_JUDGE_UI_LOCALE, + executionTerminationLabel, + judgeUiText, + localizedWorkerProgress, + readJudgeUiLocale, + toolchainNote, + verdictLabel, + writeJudgeUiLocale, +} from "@/src/components/judge-ui-i18n"; +import { + completeJudgeOnboarding, + isJudgeOnboardingComplete, + JudgeOnboarding, +} from "@/src/components/judge-onboarding"; +import { + clampBottomPanelHeight, + DEFAULT_BOTTOM_PANEL_HEIGHT, + maximumBottomPanelHeight, + MIN_BOTTOM_PANEL_HEIGHT, + resizedBottomPanelHeight, +} from "@/src/components/judge-panel-layout"; +import { assertProblemCostProfile, scoreProblemResults } from "@/src/judge/problem-scoring"; +import { + DEFAULT_PROBLEM_COLLECTION_SOURCE, + PROBLEM_COLLECTION_SOURCE_KEY, + clearProblemCollectionCache, + githubRawContentUrl, + loadProblemCollection, + normalizeProblemCollectionSource, + type GithubProblemCollectionSource, + type LoadedProblemCollection, + type ProblemCollectionEntry, +} from "@/src/judge/problem-catalog-loader"; +import { + broadestPolicy, + PROBLEM_LOCALES, + problemText, + sampleCases, + type JudgeProblem, + type ProblemDifficulty, + type ProblemLocale, +} from "@/src/judge/problem-model"; +import { matchesProblemSearch } from "@/src/judge/problem-search"; +import { + decodeSelfTestCases, + encodeSelfTestCases, + MAX_SELF_TEST_CASES, + selfTestStorageKey, + type SelfTestCase, +} from "@/src/judge/self-tests"; const MonacoEditor = dynamic(() => import("@monaco-editor/react"), { ssr: false }); const SITES_CHUNK_MANIFEST_URL = process.env.NODE_ENV === "production" ? "/toolchains/forge-sites-chunks.json" : undefined; -type BottomTab = "judge" | "diagnostics" | "output" | "console"; -type BusyAction = "build" | "run" | "judge" | "cache" | undefined; +type BottomTab = "judge" | "tests" | "diagnostics" | "output"; +type BusyAction = "build" | "test" | "judge" | "cache" | undefined; type DifficultyFilter = "all" | ProblemDifficulty; type CompileAheadState = "idle" | "scheduled" | "compiling" | "ready" | "error"; +type ProblemPane = "statement" | "editorial"; + +interface PanelResizeSession { + pointerId: number; + startHeight: number; + startPointerY: number; +} interface LogEntry { id: string; @@ -73,6 +137,11 @@ interface LogEntry { text: string; } +interface SelfTestRunResult { + readonly caseId: string; + readonly run: RunResult; +} + const MONACO_LANGUAGE: Record = { c: "c", cpp: "cpp", @@ -83,8 +152,6 @@ const MONACO_LANGUAGE: Record = { go: "go", }; -const VALID_PROBLEM_IDS = new Set(PROBLEMS.map((problem) => problem.id)); - function cleanPath(path: string): string | undefined { const normalized = path.trim().replaceAll("\\", "/").replace(/^\.\//, ""); if (!normalized || normalized.startsWith("/") || normalized.split("/").includes("..")) return undefined; @@ -104,6 +171,7 @@ function formatDuration(milliseconds: number): string { function submissionVerdictFromContract(verdict: JudgeCaseVerdict | "accepted"): JudgeUiCaseResult["verdict"] { if (verdict === "accepted" || verdict === "wrong-answer") return verdict; + if (verdict === "judge-error") return "judge-error"; if (verdict === "instruction-limit" || verdict === "logical-time-limit" || verdict === "wall-time-limit") return "time-limit"; return "runtime-error"; } @@ -157,38 +225,269 @@ function languageTone(language: Language): string { return ({ c: "tone-c", cpp: "tone-cpp", rust: "tone-rust", python: "tone-python", javascript: "tone-js", typescript: "tone-ts" } as Record)[language] ?? "tone-js"; } -function difficultyLabel(difficulty: ProblemDifficulty): string { - return ({ easy: "入門", medium: "進階", hard: "挑戰" })[difficulty]; +function difficultyLabel(difficulty: ProblemDifficulty, locale: ProblemLocale): string { + return judgeUiText(locale).difficulty[difficulty]; } -function verdictLabel(verdict: SubmissionVerdict): string { - return ({ - running: "判題中", - accepted: "Accepted", - "wrong-answer": "Wrong Answer", - "runtime-error": "Runtime Error", - "time-limit": "Time Limit", - "compile-error": "Compile Error", - cancelled: "已取消", - })[verdict]; +interface ProblemSourceDraft { + owner: string; + repository: string; + ref: string; + indexPath: string; } -export function JudgeStudio() { - const initialProblem = PROBLEMS[0]; - const [project, setProject] = useState(() => createJudgeProject(initialProblem, "c")); - const [problemId, setProblemId] = useState(initialProblem.id); +function sourceDraft(source: GithubProblemCollectionSource): ProblemSourceDraft { + return { + owner: source.owner, + repository: source.repository, + ref: source.ref, + indexPath: source.indexPath, + }; +} + +interface StoredProblemCollectionSource { + source: GithubProblemCollectionSource; + error?: { + kind: "read" | "invalid"; + detail: string; + }; +} + +function storedProblemCollectionSource(): StoredProblemCollectionSource { + if (typeof window === "undefined") return { source: DEFAULT_PROBLEM_COLLECTION_SOURCE }; + let raw: string | null; + try { + raw = localStorage.getItem(PROBLEM_COLLECTION_SOURCE_KEY); + } catch (reason) { + return { + source: DEFAULT_PROBLEM_COLLECTION_SOURCE, + error: { + kind: "read", + detail: reason instanceof Error ? reason.message : String(reason), + }, + }; + } + if (!raw) return { source: DEFAULT_PROBLEM_COLLECTION_SOURCE }; + try { + return { source: normalizeProblemCollectionSource(JSON.parse(raw) as unknown) }; + } catch (reason) { + return { + source: DEFAULT_PROBLEM_COLLECTION_SOURCE, + error: { + kind: "invalid", + detail: reason instanceof Error ? reason.message : String(reason), + }, + }; + } +} + +interface ProblemSourceFormProps { + source: GithubProblemCollectionSource; + locale: ProblemLocale; + disabled?: boolean; + onApply(source: GithubProblemCollectionSource): void; +} + +function ProblemSourceForm({ source, locale, disabled, onApply }: ProblemSourceFormProps) { + const [draft, setDraft] = useState(() => sourceDraft(source)); + const [error, setError] = useState(); + const text = judgeUiText(locale).source; + + const apply = () => { + try { + const normalized = normalizeProblemCollectionSource({ provider: "github", ...draft }); + setError(undefined); + onApply(normalized); + } catch (reason) { + setError(reason instanceof Error ? reason.message : String(reason)); + } + }; + + return ( +
+
+ + +
+
+ + +
+ {error &&

{text.invalid(error)}

} +
+ + +
+
+ ); +} + +interface ProblemCollectionSession { + collection: LoadedProblemCollection; + initialProblem: JudgeProblem; +} + +export function JudgeStudioLoader() { + const [storedSource] = useState(storedProblemCollectionSource); + const [problemLocale, setProblemLocale] = useState(() => { + if (typeof window === "undefined") return DEFAULT_JUDGE_UI_LOCALE; + try { + return readJudgeUiLocale(localStorage); + } catch { + return DEFAULT_JUDGE_UI_LOCALE; + } + }); + const [source, setSource] = useState(storedSource.source); + const [session, setSession] = useState(); + const [error, setError] = useState<{ + kind: "read" | "invalid" | "load"; + detail: string; + } | undefined>(storedSource.error); + const [blockedByStoredConfiguration, setBlockedByStoredConfiguration] = useState(Boolean(storedSource.error)); + const [retry, setRetry] = useState(0); + const text = judgeUiText(problemLocale); + + useEffect(() => { + document.documentElement.lang = problemLocale === "zh-TW" ? "zh-Hant" : "en"; + }, [problemLocale]); + + useEffect(() => { + if (blockedByStoredConfiguration) return; + const controller = new AbortController(); + void (async () => { + const collection = await loadProblemCollection(source, { signal: controller.signal }); + const first = collection.index.problems[0]; + if (!first) throw new Error("The verified problem collection is empty."); + const initialProblem = await collection.loadProblem(first.id, controller.signal); + if (!controller.signal.aborted) setSession({ collection, initialProblem }); + })().catch((reason: unknown) => { + if (controller.signal.aborted) return; + if (reason instanceof DOMException && reason.name === "AbortError") return; + setError({ kind: "load", detail: reason instanceof Error ? reason.message : String(reason) }); + }); + return () => controller.abort(); + }, [blockedByStoredConfiguration, retry, source]); + + const changeSource = useCallback((next: GithubProblemCollectionSource) => { + localStorage.setItem(PROBLEM_COLLECTION_SOURCE_KEY, JSON.stringify(next)); + setSession(undefined); + setError(undefined); + setBlockedByStoredConfiguration(false); + setSource(next); + setRetry((value) => value + 1); + }, []); + + const retrySource = useCallback(() => { + setSession(undefined); + setError(undefined); + setBlockedByStoredConfiguration(false); + setRetry((value) => value + 1); + }, []); + + const changeProblemLocale = useCallback((locale: ProblemLocale) => { + setProblemLocale(locale); + writeJudgeUiLocale(localStorage, locale); + }, []); + + const errorMessage = error?.kind === "read" + ? text.loader.sourceReadFailed(error.detail) + : error?.kind === "invalid" + ? text.loader.sourceInvalid(error.detail) + : error ? text.loader.loadFailed(error.detail) : undefined; + + if (error) { + return ( +
+ + + {text.loader.failed} + {errorMessage} + + +
+ ); + } + if (!session) { + return ( +
+ + {text.loader.loading} +
+ ); + } + return ( + + ); +} + +interface JudgeStudioProps { + collection: LoadedProblemCollection; + initialProblem: JudgeProblem; + problemLocale: ProblemLocale; + onProblemLocaleChange(locale: ProblemLocale): void; + onProblemCollectionSourceChange(source: GithubProblemCollectionSource): void; +} + +export function JudgeStudio({ + collection, + initialProblem, + problemLocale, + onProblemLocaleChange, + onProblemCollectionSourceChange, +}: JudgeStudioProps) { + const problems = collection.index.problems; + const initialProblemEntry = problems.find((problem) => problem.id === initialProblem.id); + if (!initialProblemEntry) throw new Error(`Initial problem '${initialProblem.id}' is absent from its collection index.`); + const problemDigests = useMemo(() => new Map(problems.map((problem) => [problem.id, problem.bundle.sha256])), [problems]); + const validProgressIds = useMemo(() => new Set(problems.map((problem) => judgeProblemProgressId(problem.id, problem.bundle.sha256))), [problems]); + const progressKey = useMemo(() => judgeProgressKey(collection.sourceKey), [collection.sourceKey]); + const [project, setProject] = useState(() => createJudgeProject(collection.sourceKey, initialProblemEntry.bundle.sha256, initialProblem, "c")); + const [activeProblem, setActiveProblem] = useState(initialProblem); + const [loadingProblemId, setLoadingProblemId] = useState(); + const [problemPane, setProblemPane] = useState("statement"); const [filter, setFilter] = useState("all"); + const [problemSearch, setProblemSearch] = useState(""); const [solved, setSolved] = useState>(new Set()); const [hydrated, setHydrated] = useState(false); const [runtimeReady, setRuntimeReady] = useState(false); - const [progress, setProgress] = useState({ phase: "initializing", label: "啟動 Wasmer runtime", progress: 0 }); + const [progress, setProgress] = useState({ phase: "initializing", label: "Starting Wasmer runtime", progress: 0 }); const [busy, setBusy] = useState(); const [artifact, setArtifact] = useState(); const [diagnostics, setDiagnostics] = useState([]); const [logs, setLogs] = useState([]); + const [selfTests, setSelfTests] = useState(() => decodeSelfTestCases( + null, + sampleCases(initialProblem)[0]?.input ?? "", + )); + const [loadedSelfTestKey, setLoadedSelfTestKey] = useState(); + const [selectedSelfTestId, setSelectedSelfTestId] = useState("case-1"); + const [runningSelfTestId, setRunningSelfTestId] = useState(); + const [selfTestResults, setSelfTestResults] = useState([]); const [judgeSession, setJudgeSession] = useState(); + const [selectedCaseNumber, setSelectedCaseNumber] = useState(); const [bottomTab, setBottomTab] = useState("judge"); + const [bottomPanelHeight, setBottomPanelHeight] = useState(DEFAULT_BOTTOM_PANEL_HEIGHT); + const [bottomPanelMaximum, setBottomPanelMaximum] = useState(DEFAULT_BOTTOM_PANEL_HEIGHT); + const [resizingBottomPanel, setResizingBottomPanel] = useState(false); const [settingsOpen, setSettingsOpen] = useState(false); + const [onboardingOpen, setOnboardingOpen] = useState(false); const [newFileOpen, setNewFileOpen] = useState(false); const [newFilePath, setNewFilePath] = useState(""); const [storage, setStorage] = useState({ usage: 0, quota: 0 }); @@ -199,13 +498,27 @@ export function JudgeStudio() { const runnerRef = useRef(undefined); const storageCoordinatorRef = useRef(undefined); const projectRef = useRef(project); + const editorStackRef = useRef(null); const editorRef = useRef(undefined); const monacoRef = useRef(undefined); const revealRef = useRef<{ line: number; column: number } | undefined>(undefined); const judgingRef = useRef(false); const cancelledRef = useRef(false); + const panelResizeRef = useRef(undefined); + const text = judgeUiText(problemLocale); - const activeProblem = problemById(problemId) ?? initialProblem; + const activeProblemText = problemText(activeProblem, problemLocale); + const activeProblemEntry = useMemo(() => { + const entry = problems.find((problem) => problem.id === activeProblem.id); + if (!entry) throw new Error(`Active problem '${activeProblem.id}' is absent from its collection index.`); + return entry; + }, [activeProblem.id, problems]); + const activeProgressId = judgeProblemProgressId(activeProblem.id, activeProblemEntry.bundle.sha256); + const activeSelfTestKey = useMemo( + () => selfTestStorageKey(collection.sourceKey, activeProgressId), + [activeProgressId, collection.sourceKey], + ); + const activeBaseline = broadestPolicy(activeProblem); const activeFile = useMemo( () => project.files.find((file) => file.path === project.activeFile) ?? project.files[0], [project], @@ -213,18 +526,144 @@ export function JudgeStudio() { const projectLanguage: BuiltinLanguage = isBuiltinLanguage(project.config.language) ? project.config.language : "c"; + const chatGptProblemUrl = useMemo( + () => buildChatGptProblemUrl( + activeProblem, + problemLocale, + projectLanguage, + githubRawContentUrl(collection.source, activeProblemEntry.statementPaths[problemLocale]), + ), + [activeProblem, activeProblemEntry.statementPaths, collection.source, problemLocale, projectLanguage], + ); const activeToolchain = TOOLCHAINS[projectLanguage]; const buildIdentity = useMemo(() => projectBuildIdentity(project), [project]); const filteredProblems = useMemo( - () => filter === "all" ? PROBLEMS : PROBLEMS.filter((problem) => problem.difficulty === filter), - [filter], + () => problems.filter((problem) => ( + (filter === "all" || problem.difficulty === filter) + && matchesProblemSearch(problem, problemSearch) + )), + [filter, problemSearch, problems], + ); + const groupedProblems = useMemo( + () => filteredProblems.reduce>((groups, problem) => { + const id = problem.trackId; + const current = groups.at(-1); + if (current?.id === id) { + current.problems.push(problem); + } else { + groups.push({ id, title: problem.track[problemLocale], problems: [problem] }); + } + return groups; + }, []), + [filteredProblems, problemLocale], ); + const selectedCaseResult = judgeSession?.cases.find((testCase) => ( + testCase.number === selectedCaseNumber + )) ?? judgeSession?.cases[0]; + const selectedSelfTest = selfTests.find((testCase) => testCase.id === selectedSelfTestId) ?? selfTests[0]; + const selectedSelfTestResult = selectedSelfTest + ? selfTestResults.find((result) => result.caseId === selectedSelfTest.id) + : undefined; const addLog = useCallback((stream: LogEntry["stream"], text: string) => { if (!text) return; setLogs((current) => [...current, { id: crypto.randomUUID(), stream, text }]); }, []); + const dismissOnboarding = useCallback(() => { + try { + completeJudgeOnboarding(localStorage); + } catch (error) { + addLog("stderr", text.logs.onboardingSaveFailed(error instanceof Error ? error.message : String(error))); + } + setOnboardingOpen(false); + }, [addLog, text]); + + useEffect(() => { + if (!hydrated) return; + try { + setOnboardingOpen(!isJudgeOnboardingComplete(localStorage)); + } catch (error) { + addLog("stderr", text.logs.onboardingReadFailed(error instanceof Error ? error.message : String(error))); + setOnboardingOpen(true); + } + }, [addLog, hydrated, text]); + + const measureBottomPanel = useCallback(() => { + const stack = editorStackRef.current; + if (!stack) return; + const stackHeight = stack.getBoundingClientRect().height; + const maximum = maximumBottomPanelHeight(stackHeight); + setBottomPanelMaximum(maximum); + setBottomPanelHeight((current) => clampBottomPanelHeight(stackHeight, current)); + }, []); + + useEffect(() => { + const stack = editorStackRef.current; + if (!stack) return; + const observer = new ResizeObserver(measureBottomPanel); + observer.observe(stack); + measureBottomPanel(); + return () => observer.disconnect(); + }, [measureBottomPanel]); + + const stopBottomPanelResize = useCallback((target?: HTMLDivElement, pointerId?: number) => { + if (target && pointerId !== undefined && target.hasPointerCapture(pointerId)) { + target.releasePointerCapture(pointerId); + } + panelResizeRef.current = undefined; + setResizingBottomPanel(false); + editorRef.current?.layout(); + }, []); + + const startBottomPanelResize = useCallback((event: ReactPointerEvent) => { + if (event.button !== 0) return; + panelResizeRef.current = { + pointerId: event.pointerId, + startHeight: bottomPanelHeight, + startPointerY: event.clientY, + }; + event.currentTarget.setPointerCapture(event.pointerId); + setResizingBottomPanel(true); + event.preventDefault(); + }, [bottomPanelHeight]); + + const moveBottomPanelResize = useCallback((event: ReactPointerEvent) => { + const resize = panelResizeRef.current; + const stack = editorStackRef.current; + if (!resize || resize.pointerId !== event.pointerId || !stack) return; + setBottomPanelHeight(resizedBottomPanelHeight( + stack.getBoundingClientRect().height, + resize.startHeight, + resize.startPointerY, + event.clientY, + )); + }, []); + + const resizeBottomPanelFromKeyboard = useCallback((event: ReactKeyboardEvent) => { + const stack = editorStackRef.current; + if (!stack) return; + const stackHeight = stack.getBoundingClientRect().height; + const step = event.shiftKey ? 64 : 24; + let requestedHeight: number | undefined; + if (event.key === "ArrowUp") requestedHeight = bottomPanelHeight + step; + if (event.key === "ArrowDown") requestedHeight = bottomPanelHeight - step; + if (event.key === "Home") requestedHeight = MIN_BOTTOM_PANEL_HEIGHT; + if (event.key === "End") requestedHeight = maximumBottomPanelHeight(stackHeight); + if (requestedHeight === undefined) return; + event.preventDefault(); + setBottomPanelHeight(clampBottomPanelHeight(stackHeight, requestedHeight)); + }, [bottomPanelHeight]); + + const resetBottomPanelHeight = useCallback(() => { + const stack = editorStackRef.current; + if (!stack) return; + setBottomPanelHeight(clampBottomPanelHeight( + stack.getBoundingClientRect().height, + DEFAULT_BOTTOM_PANEL_HEIGHT, + )); + }, []); + useEffect(() => { projectRef.current = project; }, [project]); @@ -258,23 +697,34 @@ export function JudgeStudio() { await storageCoordinator.requestPersistence(); if (disposed) return; try { - setSolved(decodeSolvedProgress(localStorage.getItem(JUDGE_PROGRESS_KEY), VALID_PROBLEM_IDS)); + setSolved(decodeSolvedProgress(localStorage.getItem(progressKey), validProgressIds)); } catch (error) { - localStorage.removeItem(JUDGE_PROGRESS_KEY); + localStorage.removeItem(progressKey); addLog("stderr", error instanceof Error ? error.message : String(error)); } - const restored = await loadLatestProject(); + const restored = latestJudgeProjectForCollection( + await listProjects(), + collection.sourceKey, + problemDigests, + ); + if (disposed) return; + const restoredIdentity = restored ? problemIdentityFromProject(restored, collection.sourceKey) : undefined; + const restoredSummary = restoredIdentity + ? problems.find((candidate) => candidate.id === restoredIdentity.problemId && candidate.bundle.sha256 === restoredIdentity.bundleSha256) + : undefined; + const restoredProblem = restoredSummary + ? await collection.loadProblem(restoredSummary.id) + : undefined; if (disposed) return; - const restoredProblemId = restored ? problemIdFromProject(restored) : undefined; - const restoredProblem = restoredProblemId ? problemById(restoredProblemId) : undefined; if ( restored + && restoredSummary && restoredProblem && isBuiltinLanguage(restored.config.language) - && restored.id === judgeProjectId(restoredProblem.id, restored.config.language) + && restored.id === judgeProjectId(collection.sourceKey, restoredSummary.bundle.sha256, restoredProblem.id, restored.config.language) ) { setProject(restored); - setProblemId(restoredProblem.id); + setActiveProblem(restoredProblem); } const storageReport = await storageCoordinator.estimate(); if (disposed) return; @@ -294,7 +744,7 @@ export function JudgeStudio() { compilation?.dispose(); runner?.dispose(); }; - }, [addLog]); + }, [addLog, collection, problemDigests, problems, progressKey, validProgressIds]); useEffect(() => { if (!hydrated || !runtimeReady) return; @@ -331,8 +781,41 @@ export function JudgeStudio() { useEffect(() => { if (!hydrated) return; - localStorage.setItem(JUDGE_PROGRESS_KEY, JSON.stringify([...solved].sort())); - }, [hydrated, solved]); + localStorage.setItem(progressKey, JSON.stringify([...solved].sort())); + }, [hydrated, progressKey, solved]); + + useEffect(() => { + const timer = window.setTimeout(() => { + const sampleInput = sampleCases(activeProblem)[0]?.input ?? ""; + let restored: SelfTestCase[]; + try { + restored = decodeSelfTestCases(localStorage.getItem(activeSelfTestKey), sampleInput); + } catch (error) { + localStorage.removeItem(activeSelfTestKey); + restored = decodeSelfTestCases(null, sampleInput); + addLog("stderr", error instanceof Error ? error.message : String(error)); + } + setSelfTests(restored); + setSelectedSelfTestId(restored[0].id); + setSelfTestResults([]); + setRunningSelfTestId(undefined); + setLoadedSelfTestKey(activeSelfTestKey); + }, 0); + return () => window.clearTimeout(timer); + }, [activeProblem, activeSelfTestKey, addLog]); + + useEffect(() => { + if (loadedSelfTestKey !== activeSelfTestKey) return; + let notification: number | undefined; + try { + localStorage.setItem(activeSelfTestKey, encodeSelfTestCases(selfTests)); + } catch (error) { + notification = window.setTimeout(() => { + addLog("stderr", text.logs.selfTestSaveFailed(error instanceof Error ? error.message : String(error))); + }, 0); + } + return () => { if (notification !== undefined) window.clearTimeout(notification); }; + }, [activeSelfTestKey, addLog, loadedSelfTestKey, selfTests, text]); const applyMarkers = useCallback(() => { const monaco = monacoRef.current; @@ -407,7 +890,9 @@ export function JudgeStudio() { const updateProject = useCallback((updater: (current: Project) => Project) => { setProject((current) => ({ ...updater(current), updatedAt: Date.now() })); setArtifact(undefined); + setSelfTestResults([]); setJudgeSession(undefined); + setSelectedCaseNumber(undefined); }, []); const updateRunConfig = useCallback((updater: (current: RunConfig) => RunConfig) => { @@ -416,7 +901,9 @@ export function JudgeStudio() { config: { ...current.config, ...updater(current.config) }, updatedAt: Date.now(), })); + setSelfTestResults([]); setJudgeSession(undefined); + setSelectedCaseNumber(undefined); }, []); const updateActiveFile = useCallback((content: string | undefined) => { @@ -427,23 +914,37 @@ export function JudgeStudio() { })); }, [activeFile, updateProject]); - const openWorkspace = useCallback(async (problem: JudgeProblem, language: BuiltinLanguage) => { - if (busy) return; - await saveProject(project); - const drafts = await listProjects(); - const id = judgeProjectId(problem.id, language); - const draft = drafts.find((candidate) => candidate.id === id); - compileCoordinatorRef.current?.restart(); - runnerRef.current?.restart(); - setRuntimeReady(true); - setProject(draft ?? createJudgeProject(problem, language)); - setProblemId(problem.id); - setArtifact(undefined); - setDiagnostics([]); - setLogs([]); - setJudgeSession(undefined); - setBottomTab("judge"); - }, [busy, project]); + const openWorkspace = useCallback(async (summary: ProblemCollectionEntry, language: BuiltinLanguage) => { + if (busy || loadingProblemId) return; + setLoadingProblemId(summary.id); + try { + await saveProject(project); + const problem = summary.id === activeProblem.id + ? activeProblem + : await collection.loadProblem(summary.id); + const drafts = await listProjects(); + const id = judgeProjectId(collection.sourceKey, summary.bundle.sha256, problem.id, language); + const draft = drafts.find((candidate) => candidate.id === id); + compileCoordinatorRef.current?.restart(); + runnerRef.current?.restart(); + setRuntimeReady(true); + setProject(draft ?? createJudgeProject(collection.sourceKey, summary.bundle.sha256, problem, language)); + setActiveProblem(problem); + setArtifact(undefined); + setDiagnostics([]); + setLogs([]); + setSelfTestResults([]); + setRunningSelfTestId(undefined); + setJudgeSession(undefined); + setSelectedCaseNumber(undefined); + setBottomTab("judge"); + } catch (error) { + addLog("stderr", error instanceof Error ? error.message : String(error)); + setBottomTab("output"); + } finally { + setLoadingProblemId(undefined); + } + }, [activeProblem, addLog, busy, collection, loadingProblemId, project]); const doBuild = useCallback(async (allowCache = true): Promise => { const compilation = compileCoordinatorRef.current; @@ -454,14 +955,14 @@ export function JudgeStudio() { setLogs([]); const started = performance.now(); try { - addLog("system", `build ${project.name} · ${languageLabel(project.config.language)} → ${project.config.target.toUpperCase()}`); + addLog("system", text.logs.buildStarted(project.name, languageLabel(project.config.language), project.config.target.toUpperCase())); const result = await compilation.compile(project, { cache: allowCache }); setDiagnostics(result.diagnostics); if (result.stdout) addLog("stdout", result.stdout); if (result.stderr) addLog("stderr", result.stderr); if (!result.success || !result.artifact) { setCompileAhead("error"); - addLog("system", `建置失敗 · ${Math.round(performance.now() - started)} ms`); + addLog("system", text.logs.buildFailed(Math.round(performance.now() - started))); setBottomTab("diagnostics"); return undefined; } @@ -470,10 +971,10 @@ export function JudgeStudio() { const storageReport = await storageCoordinatorRef.current?.maintain(); if (storageReport) setStorage({ usage: storageReport.after.usage, quota: storageReport.after.quota }); if (result.cacheHit) { - addLog("system", `從本機建置快取載入 ${result.artifact.name} · ${formatBytes(result.artifact.size)}`); - setProgress({ phase: "packaging", label: "命中建置快取", progress: 1 }); + addLog("system", text.logs.cacheLoaded(result.artifact.name, formatBytes(result.artifact.size))); + setProgress({ phase: "packaging", label: "Build cache hit", progress: 1 }); } else { - addLog("system", `完成 ${result.artifact.name} · ${formatBytes(result.artifact.size)} · ${Math.round(result.artifact.durationMs)} ms`); + addLog("system", text.logs.buildComplete(result.artifact.name, formatBytes(result.artifact.size), Math.round(result.artifact.durationMs))); } return result.artifact; } catch (error) { @@ -483,13 +984,56 @@ export function JudgeStudio() { } finally { setBusy(undefined); } - }, [addLog, project]); + }, [addLog, project, text]); + + const updateSelfTest = (id: string, update: Partial>) => { + setSelfTests((current) => current.map((testCase) => ( + testCase.id === id ? { ...testCase, ...update } : testCase + ))); + setSelfTestResults((current) => current.filter((result) => result.caseId !== id)); + }; - const doRunSample = useCallback(async () => { + const addSelfTest = () => { + if (selfTests.length >= MAX_SELF_TEST_CASES) return; + const id = `case-${crypto.randomUUID()}`; + const names = new Set(selfTests.map((testCase) => testCase.name)); + let number = selfTests.length + 1; + while (names.has(`Case ${number}`)) number += 1; + setSelfTests((current) => [...current, { id, name: `Case ${number}`, input: "" }]); + setSelectedSelfTestId(id); + }; + + const addSampleSelfTests = () => { + const available = MAX_SELF_TEST_CASES - selfTests.length; + if (available < 1) return; + const additions = sampleCases(activeProblem).slice(0, available).map((sample, index) => ({ + id: `sample-${crypto.randomUUID()}`, + name: text.selfTest.sampleName(index + 1), + input: sample.input, + })); + if (additions.length === 0) return; + setSelfTests((current) => [...current, ...additions]); + setSelectedSelfTestId(additions[0].id); + }; + + const removeSelfTest = (id: string) => { + if (selfTests.length === 1) return; + const index = selfTests.findIndex((testCase) => testCase.id === id); + const next = selfTests.filter((testCase) => testCase.id !== id); + setSelfTests(next); + setSelfTestResults((current) => current.filter((result) => result.caseId !== id)); + if (selectedSelfTestId === id) setSelectedSelfTestId(next[Math.min(index, next.length - 1)].id); + }; + + const doRunSelfTests = useCallback(async (caseIds: readonly string[]) => { const runner = runnerRef.current; - if (!runner) return; - setBusy("run"); - setBottomTab("console"); + const requested = selfTests.filter((testCase) => caseIds.includes(testCase.id)); + if (!runner || requested.length === 0) return; + cancelledRef.current = false; + setBusy("test"); + setBottomTab("tests"); + setSelectedSelfTestId(requested[0].id); + setSelfTestResults((current) => current.filter((result) => !caseIds.includes(result.caseId))); setLogs([]); try { const key = await projectCacheKey(project); @@ -498,28 +1042,44 @@ export function JudgeStudio() { setBusy(undefined); runnable = await doBuild(true); if (!runnable) return; - setBusy("run"); - setBottomTab("console"); - setLogs([]); + setBottomTab("tests"); + setBusy("test"); } - addLog("system", `執行範例輸入 · ${activeProblem.title}`); - const result = await runner.run(runnable, { ...project.config, stdin: activeProblem.examples[0].input }); - const cost = result.metrics.cost === null - ? "cost unavailable" - : `${result.metrics.cost.toLocaleString()} net weighted ops (${result.metrics.rawCost?.toLocaleString()} raw − ${result.metrics.baselineCost.toLocaleString()} baseline)`; - addLog("system", `${result.termination} · exit ${result.code} · ${cost} · ${Math.round(result.durationMs)} ms`); + for (const [index, testCase] of requested.entries()) { + if (cancelledRef.current) break; + setRunningSelfTestId(testCase.id); + setSelectedSelfTestId(testCase.id); + setProgress({ + phase: "running", + label: `Self Test ${index + 1} / ${requested.length}`, + progress: index / requested.length, + }); + addLog("system", text.logs.runStarted(testCase.name.trim() || text.selfTest.caseName(index + 1))); + const result = await runner.run(runnable, { ...project.config, stdin: testCase.input }); + setSelfTestResults((current) => [ + ...current.filter((candidate) => candidate.caseId !== testCase.id), + { caseId: testCase.id, run: result }, + ]); + const cost = result.metrics.cost === null + ? text.logs.costUnavailable + : text.logs.cost(result.metrics.cost.toLocaleString()); + addLog("system", `${executionTerminationLabel(problemLocale, result.termination)} · ${text.selfTest.exit} ${result.code} · ${cost} · ${formatDuration(result.durationMs)}`); + } + setProgress({ phase: "running", label: "Self Test complete", progress: 1 }); } catch (error) { - addLog("stderr", error instanceof Error ? error.message : String(error)); + if (!cancelledRef.current) addLog("stderr", error instanceof Error ? error.message : String(error)); } finally { + setRunningSelfTestId(undefined); setBusy(undefined); } - }, [activeProblem, addLog, artifact, doBuild, project]); + }, [addLog, artifact, doBuild, problemLocale, project, selfTests, text]); const doJudge = useCallback(async () => { const runner = runnerRef.current; if (!runner) return; cancelledRef.current = false; judgingRef.current = true; + setSelectedCaseNumber(undefined); const started = performance.now(); setBottomTab("judge"); setLogs([]); @@ -550,6 +1110,8 @@ export function JudgeStudio() { } } setBusy("judge"); + assertProblemCostProfile(activeProblem, projectLanguage, runnable.costProfile); + const baseline = broadestPolicy(activeProblem); const cases: JudgeUiCaseResult[] = []; const judging = new JudgeEngine(createJudgeExecutor({ run: (buildArtifact, run) => runner.run(buildArtifact, { @@ -565,10 +1127,10 @@ export function JudgeStudio() { })); const result = await judging.judge(runnable, { version: FORGE_CONTRACT_VERSION, - failFast: true, - cases: activeProblem.judgeCases.map((test, index) => ({ + failFast: false, + cases: activeProblem.judgeCases.map((test) => ({ kind: "batch" as const, - id: `case-${index + 1}`, + id: test.id, input: { kind: "inline" as const, value: test.input }, matcher: textMatcher(test.output, "lines"), args: project.config.args, @@ -576,7 +1138,12 @@ export function JudgeStudio() { determinism: project.config.determinism, resources: { ...project.config.resources, - instructionBudget: activeProblem.instructionBudget, + instructionBudget: baseline.limits.instructionBudget, + memoryLimitBytes: baseline.limits.memoryLimitBytes, + wallTimeLimitMs: activeProblem.scoring.safetyLimits.wallTimeLimitMs, + ...(baseline.limits.logicalTimeLimitMs === undefined + ? {} + : { logicalTimeLimitMs: baseline.limits.logicalTimeLimitMs }), }, })), }, { @@ -587,7 +1154,7 @@ export function JudgeStudio() { cases.push(displayJudgeCase(contractCase, index, expected)); setProgress({ phase: "running", - label: `本機測資 ${completed} / ${total}`, + label: `Local cases ${completed} / ${total}`, progress: completed / total, }); setJudgeSession({ @@ -600,24 +1167,55 @@ export function JudgeStudio() { }); }, }); + const score = scoreProblemResults(activeProblem, projectLanguage, result.cases); + const scoredCases = cases.map((testCase, index) => ({ + ...testCase, + points: score.cases[index].points, + outputAccepted: score.cases[index].outputAccepted, + passedPolicyIds: score.cases[index].passedPolicyIds, + metrics: score.cases[index].metrics ?? undefined, + policyEvaluations: score.cases[index].policyEvaluations, + })); + const detailCase = scoredCases.reduce((lowest, candidate) => ( + (candidate.points ?? 0) < (lowest.points ?? 0) ? candidate : lowest + )); + setSelectedCaseNumber(detailCase.number); const verdict = cancelledRef.current ? "cancelled" : submissionVerdictFromContract(result.verdict); const finished: JudgeUiSession = { problemId: activeProblem.id, verdict, completed: cases.length, total: activeProblem.judgeCases.length, - cases, + cases: scoredCases, durationMs: performance.now() - started, + score: { + numerator: score.numerator, + denominator: score.denominator, + points: score.points, + maximumPoints: score.maximumPoints, + }, }; setJudgeSession(finished); - if (verdict === "accepted") { - setSolved((current) => new Set([...current, activeProblem.id])); + if (verdict === "accepted" && score.points === score.maximumPoints) { + setSolved((current) => new Set([...current, activeProgressId])); } + } catch (error) { + const message = error instanceof Error ? error.message : String(error); + addLog("stderr", message); + setJudgeSession({ + problemId: activeProblem.id, + verdict: "judge-error", + completed: 0, + total: activeProblem.judgeCases.length, + cases: [], + durationMs: performance.now() - started, + message, + }); } finally { judgingRef.current = false; setBusy(undefined); } - }, [activeProblem, artifact, doBuild, project]); + }, [activeProblem, activeProgressId, addLog, artifact, doBuild, project, projectLanguage]); const cancel = useCallback(() => { cancelledRef.current = true; @@ -625,9 +1223,10 @@ export function JudgeStudio() { compileCoordinatorRef.current?.cancel(); runnerRef.current?.cancel(); setBusy(undefined); + setRunningSelfTestId(undefined); setJudgeSession((current) => current?.verdict === "running" ? { ...current, verdict: "cancelled" } : current); - addLog("system", "已取消操作並重啟 ForgeCompiler/ForgeRunner Workers"); - }, [addLog]); + addLog("system", text.logs.cancelled); + }, [addLog, text]); const chooseTarget = (target: "wasip1" | "wasix") => { if (target === project.config.target) return; @@ -647,7 +1246,7 @@ export function JudgeStudio() { }; const removeFile = (path: string) => { - if (project.files.length === 1 || !window.confirm(`從本機專案刪除 ${path}?`)) return; + if (project.files.length === 1 || !window.confirm(text.editor.deleteFileConfirm(path))) return; updateProject((current) => { const files = current.files.filter((file) => file.path !== path); const active = current.activeFile === path ? files[0].path : current.activeFile; @@ -674,19 +1273,20 @@ export function JudgeStudio() { await Promise.all([ compilerRef.current?.clearToolchainCache(), runner?.clearRuntimeCache(), + clearProblemCollectionCache(), ]); await storageCoordinatorRef.current?.clear(); setArtifact(undefined); const storageReport = await storageCoordinatorRef.current?.estimate(); if (storageReport) setStorage({ usage: storageReport.usage, quota: storageReport.quota }); - addLog("system", "已清除本機工具鏈回應與建置產物"); + addLog("system", text.logs.cachesCleared); } finally { setBusy(undefined); } }; if (!hydrated) { - return

開啟本機 Judge workspace

; + return

{text.boot}

; } return ( @@ -700,37 +1300,51 @@ export function JudgeStudio() {
#{String(activeProblem.number).padStart(2, "0")} - {activeProblem.title} - {difficultyLabel(activeProblem.difficulty)} + {activeProblemText.title} + {difficultyLabel(activeProblem.difficulty, problemLocale)}
+ - + + {busy ? ( - + ) : ( <> - - - + + + )}
@@ -739,83 +1353,113 @@ export function JudgeStudio() {
- PROBLEM {String(activeProblem.number).padStart(2, "0")} - {activeProblem.category} + {text.statement.problem.toUpperCase()} {String(activeProblem.number).padStart(2, "0")} + {activeProblem.track[problemLocale]} · {activeProblem.tags.join(" · ")}
-

{activeProblem.title}

-

{activeProblem.summary}

+

{activeProblemText.title}

- {difficultyLabel(activeProblem.difficulty)} - Net weighted-cost budget {activeProblem.instructionBudget.toLocaleString()} / case - {activeProblem.judgeCases.length} cases + {difficultyLabel(activeProblem.difficulty, problemLocale)} + {text.statement.baselineCost} {activeBaseline.limits.instructionBudget.toLocaleString()} · {text.statement.perCase} + {text.statement.cases(activeProblem.judgeCases.length)}
-
-

題目敘述

- {activeProblem.description.map((paragraph) =>

{paragraph}

)} -
-
-

輸入

-

{activeProblem.input}

-
-
-

輸出

-

{activeProblem.output}

-
-
-

限制

-
    {activeProblem.constraints.map((constraint) =>
  • {constraint}
  • )}
-
- {activeProblem.examples.map((example, index) => ( -
-

範例 {index + 1}

-
-
INPUT
{example.input}
-
OUTPUT
{example.output}
+
+ {activeProblem.scoring.policies.map((policy) => ( +
+ {policy.title[problemLocale]} + +{policy.points} {text.statement.pointsShort} + {policy.limits.instructionBudget.toLocaleString()} {text.statement.costUnit} · {formatBytes(policy.limits.memoryLimitBytes)}
-

{example.explanation}

-
- ))} -
- -

本機判題邊界完整離線判題代表測資存在瀏覽器內,適合練習與自我驗證,不宣稱能防止使用者檢視測資。

+ ))} +
+
+
-
+
{project.files.map((file) => (
@@ -823,19 +1467,19 @@ export function JudgeStudio() { {languageIcon(file.language)} {file.path.split("/").at(-1)} - {project.files.length > 1 && } + {project.files.length > 1 && }
))} {newFileOpen ? (
{ event.preventDefault(); addFile(); }}> - setNewFilePath(event.target.value)} placeholder="src/helper.c" aria-label="新檔案路徑" /> - - + setNewFilePath(event.target.value)} placeholder="src/helper.c" aria-label={text.editor.newFilePath} /> + +
) : ( - + )} -
+
{activeFile && ( @@ -855,6 +1499,7 @@ export function JudgeStudio() { minimap: { enabled: false }, padding: { top: 14, bottom: 14 }, renderLineHighlight: "all", + readOnly: Boolean(loadingProblemId), scrollBeyondLastLine: false, smoothScrolling: true, tabSize: 4, @@ -864,58 +1509,212 @@ export function JudgeStudio() { )}
+
stopBottomPanelResize(event.currentTarget, event.pointerId)} + onPointerCancel={(event) => stopBottomPanelResize(event.currentTarget, event.pointerId)} + onLostPointerCapture={() => stopBottomPanelResize()} + > +
+
+ - - +
- {busy && <>{progress.label}} - {!busy && compileAhead === "scheduled" && <>背景編譯已排程} - {!busy && compileAhead === "compiling" && <>背景預編譯} - {!busy && compileAhead === "error" && <>等待修正} - {!busy && compileAhead === "ready" && artifact && <>預編譯完成 · {formatBytes(artifact.size)}} + {busy && <>{localizedWorkerProgress(progress, problemLocale)}} + {!busy && compileAhead === "scheduled" && <>{text.panel.compileScheduled}} + {!busy && compileAhead === "compiling" && <>{text.panel.precompiling}} + {!busy && compileAhead === "error" && <>{text.panel.waitingForFix}} + {!busy && compileAhead === "ready" && artifact && <>{text.panel.precompileReady} · {formatBytes(artifact.size)}} {!busy && compileAhead === "idle" && artifact && <>{formatBytes(artifact.size)}}
- {artifact && } + {artifact && }
{bottomTab === "judge" ? ( !judgeSession ? ( -
準備提交程式只會送進此分頁內的 Wasmer runtime。
+
{text.judge.ready}{text.judge.readyDescription}
) : (
{judgeSession.verdict === "accepted" ? : judgeSession.verdict === "running" ? : } -
{verdictLabel(judgeSession.verdict)}{judgeSession.completed} / {judgeSession.total} cases · {formatDuration(judgeSession.durationMs)}
+
+ + {judgeSession.verdict === "accepted" + && judgeSession.score + && judgeSession.score.points < judgeSession.score.maximumPoints + ? text.judge.partialScore + : verdictLabel(problemLocale, judgeSession.verdict)} + + + {text.judge.casesAndPoints( + judgeSession.completed, + judgeSession.total, + judgeSession.score?.points, + judgeSession.score?.maximumPoints, + )} + {` · ${formatDuration(judgeSession.durationMs)}`} + + {judgeSession.message && {judgeSession.message}} +
- {judgeSession.verdict === "compile-error" && } + {judgeSession.verdict === "compile-error" && }
{judgeSession.cases.map((test) => ( -
- {test.verdict === "accepted" ? : } - Case {String(test.number).padStart(2, "0")} - {test.verdict === "accepted" ? "Accepted" : verdictLabel(test.verdict)} - +
+ {test.verdict !== "accepted" && (
-
EXPECTED
{test.expected || "∅"}
-
ACTUAL
{test.actual || test.stderr || "∅"}
+
{text.judge.expected}
{test.expected || "∅"}
+
{text.judge.actual}
{test.actual || test.stderr || "∅"}
)}
))}
+ {judgeSession.score && selectedCaseResult?.policyEvaluations && ( + + )}
) + ) : bottomTab === "tests" ? ( +
+
+
+
+ {text.selfTest.heading} + {text.selfTest.description} +
+
+ + + +
+
+
+ {selfTests.map((testCase, index) => { + const result = selfTestResults.find((candidate) => candidate.caseId === testCase.id)?.run; + const successful = result?.termination === "exited" && result.code === 0; + return ( +
+
+ + setSelectedSelfTestId(testCase.id)} + onChange={(event) => updateSelfTest(testCase.id, { name: event.target.value })} + disabled={Boolean(busy)} + /> + + +
+