feat: Add Prefix Sum guide with interactive visualizations and examples

.agents/skills/guides-update/SKILL.md

@@ -0,0 +1,35 @@
+---
+name: Guides Update
+description: Skill for adding or updating educational algorithm guides, ensuring consistent patterns and simple explanations suitable for an 8-year-old.
+---
+
+# Guides Update Skill
+
+This skill is invoked when adding a new concept guide (like "prefix sum", "recursion", etc.) to the pattern guides section.
+
+## Workflow Process
+
+### 1. Identify and Structure
+- When asked to add a new guide pattern, first check existing guides (e.g., `src/data/guides/recursion.ts`) to understand the layout and format.
+- Ensure the guide data file is created in `src/data/guides/` and exposes a `content` markdown string.
+- Create a corresponding page in `src/app/guides/patterns/<slug>/page.tsx`.
+- Register the new guide in `src/data/guidesData.ts` under the appropriate category or as a new category, ensuring the new category matches the `id` and structure of existing categories.
+- **CRITICAL:** Add the new guide's `id` to the `PATTERN_IDS` array in `src/config/sidebarNav.ts` so it appears in the sidebar navigation!
+
+### 2. Implementation Rules & Standards
+
+When writing the content for the guide, rigidly follow these rules:
+
+1. **Simple Analogy First:** Always start with a relatable, real-world analogy. The explanation MUST be simple enough for an 8-year-old to understand (e.g., using piggy banks, Russian nesting dolls, lines at a movie theater).
+2. **Engaging Formatting:** Use emojis, bold text for key terms, and clear headings to make the guide visually appealing and easy to read.
+3. **Core Formula/Concept:** Clearly outline the core formula, rules, or strategy of the pattern after the analogy.
+4. **Interactive Visualization Link:** Always include a markdown link to the interactive simulator visualization for the pattern. Format: `[Visualize <Topic> in the Interactive Simulator](viz:<slug>)`.
+5. **Multi-Language Code Examples:** Provide complete, working code implementations in Python, Java, C++, and TypeScript. Use clear, educational variable names. **Crucially, all code blocks (the solution viewer codes) must be well-commented at a moderate rate so the user can easily understand what each line or block does.**
+6. **Problem Walkthroughs:** Include at least one common problem walkthrough (e.g., Range Sum Query, Climbing Stairs) showing how to apply the pattern.
+7. **Common Mistakes:** Add a section explicitly listing common pitfalls or errors to watch out for (e.g., infinite loops, off-by-one errors).
+8. **Practice Links:** End the guide with a list of related practice problems linked to the platform.
+
+### 3. Verification
+- Verify that `guidesData.ts` has been correctly updated and has no syntax errors.
+- Verify that the guide page route (`page.tsx`) correctly mounts `GuidesClient` with the metadata setup.
+- Verify that the language uses plain English and avoids overly dense academic jargon.

next-env.d.ts

@@ -1,7 +1,7 @@
 /// <reference types="next" />
 /// <reference types="next/image-types/global" />
 /// <reference types="next/navigation-types/compat/navigation" />
-import "./.next/dev/types/routes.d.ts";
+import "./.next/types/routes.d.ts";
 
 // NOTE: This file should not be edited
 // see https://nextjs.org/docs/app/api-reference/config/typescript for more information.