From 3004a69a07fa5583d66b34a38237b1d6bc899c14 Mon Sep 17 00:00:00 2001 From: Libin YANG Date: Wed, 8 Jul 2026 08:32:27 +0800 Subject: [PATCH] feat: add solutions to lc problem: No.3756 Co-authored-by: Cursor --- .../README.md | 191 +++++++++++++++++- .../README_EN.md | 191 +++++++++++++++++- .../Solution.cpp | 37 ++++ .../Solution.go | 42 ++++ .../Solution.java | 36 ++++ .../Solution.py | 25 +++ .../Solution.ts | 30 +++ 7 files changed, 544 insertions(+), 8 deletions(-) create mode 100644 solution/3700-3799/3756.Concatenate Non-Zero Digits and Multiply by Sum II/Solution.cpp create mode 100644 solution/3700-3799/3756.Concatenate Non-Zero Digits and Multiply by Sum II/Solution.go create mode 100644 solution/3700-3799/3756.Concatenate Non-Zero Digits and Multiply by Sum II/Solution.java create mode 100644 solution/3700-3799/3756.Concatenate Non-Zero Digits and Multiply by Sum II/Solution.py create mode 100644 solution/3700-3799/3756.Concatenate Non-Zero Digits and Multiply by Sum II/Solution.ts diff --git a/solution/3700-3799/3756.Concatenate Non-Zero Digits and Multiply by Sum II/README.md b/solution/3700-3799/3756.Concatenate Non-Zero Digits and Multiply by Sum II/README.md index 6024d62fa633e..e50b1846cab92 100644 --- a/solution/3700-3799/3756.Concatenate Non-Zero Digits and Multiply by Sum II/README.md +++ b/solution/3700-3799/3756.Concatenate Non-Zero Digits and Multiply by Sum II/README.md @@ -144,32 +144,215 @@ tags: -### 方法一 +### 方法一：前缀和 + +我们预处理三个前缀数组： + +- `sum_d[i]` 表示字符串前 $i$ 个字符的数字和； +- `cnt_n0[i]` 表示字符串前 $i$ 个字符中非零数字的个数； +- `p[i]` 表示将前 $i$ 个字符中的所有非零数字按顺序连接后得到的数，对 $10^9 + 7$ 取模。 + +对于查询 $[l, r]$，子串中非零数字个数为 $n_0 = cnt\_n0[r + 1] - cnt\_n0[l]$，数字和为 $sd = sum\_d[r + 1] - sum\_d[l]$。由于 $p[r + 1] = p[l] \cdot 10^{n_0} + x$，可得 $x = p[r + 1] - p[l] \cdot 10^{n_0}$，答案为 $x \cdot sd$。 + +预处理 $10$ 的幂次，对每个查询 $O(1)$ 回答。 + +时间复杂度 $O(n + q)$，空间复杂度 $O(n)$。其中 $n$ 为字符串长度，$q$ 为查询次数。 #### Python3 ```python - +mx = 10**5 + 1 +mod = 10**9 + 7 +pow10 = [1] * mx +for i in range(1, mx): + pow10[i] = pow10[i - 1] * 10 % mod + + +class Solution: + def sumAndMultiply(self, s: str, queries: List[List[int]]) -> List[int]: + n = len(s) + sum_d = [0] * (n + 1) + cnt_n0 = [0] * (n + 1) + p = [0] * (n + 1) + for i, d in enumerate(map(int, s), 1): + sum_d[i] = sum_d[i - 1] + d + cnt_n0[i] = cnt_n0[i - 1] + int(d > 0) + p[i] = (p[i - 1] * 10 + d) % mod if d else p[i - 1] + + ans = [] + for l, r in queries: + n0 = cnt_n0[r + 1] - cnt_n0[l] + sd = sum_d[r + 1] - sum_d[l] + x = p[r + 1] - p[l] * pow10[n0] % mod + ans.append(x * sd % mod) + return ans ``` #### Java ```java - +class Solution { + private static final int MX = 100001; + private static final int MOD = 1_000_000_007; + private static final long[] POW10 = new long[MX]; + + static { + POW10[0] = 1; + for (int i = 1; i < MX; i++) { + POW10[i] = POW10[i - 1] * 10 % MOD; + } + } + + public int[] sumAndMultiply(String s, int[][] queries) { + int n = s.length(); + int[] sumD = new int[n + 1]; + int[] cntN0 = new int[n + 1]; + long[] p = new long[n + 1]; + + for (int i = 1; i <= n; i++) { + int d = s.charAt(i - 1) - '0'; + sumD[i] = sumD[i - 1] + d; + cntN0[i] = cntN0[i - 1] + (d > 0 ? 1 : 0); + p[i] = d > 0 ? (p[i - 1] * 10 + d) % MOD : p[i - 1]; + } + + int[] ans = new int[queries.length]; + for (int i = 0; i < queries.length; i++) { + int l = queries[i][0], r = queries[i][1]; + int n0 = cntN0[r + 1] - cntN0[l]; + int sd = sumD[r + 1] - sumD[l]; + long x = (p[r + 1] - p[l] * POW10[n0] % MOD + MOD) % MOD; + ans[i] = (int) (x * sd % MOD); + } + return ans; + } +} ``` #### C++ ```cpp - +class Solution { +public: + vector sumAndMultiply(string s, vector>& queries) { + static const int MX = 100001; + static const int MOD = 1000000007; + static vector pow10 = [] { + vector p(MX); + p[0] = 1; + for (int i = 1; i < MX; i++) { + p[i] = p[i - 1] * 10 % MOD; + } + return p; + }(); + + int n = s.size(); + vector sumD(n + 1), cntN0(n + 1); + vector p(n + 1); + + for (int i = 1; i <= n; i++) { + int d = s[i - 1] - '0'; + sumD[i] = sumD[i - 1] + d; + cntN0[i] = cntN0[i - 1] + (d > 0); + p[i] = d ? (p[i - 1] * 10 + d) % MOD : p[i - 1]; + } + + vector ans; + ans.reserve(queries.size()); + for (auto& q : queries) { + int l = q[0], r = q[1]; + int n0 = cntN0[r + 1] - cntN0[l]; + int sd = sumD[r + 1] - sumD[l]; + long long x = (p[r + 1] - p[l] * pow10[n0] % MOD + MOD) % MOD; + ans.push_back(x * sd % MOD); + } + return ans; + } +}; ``` #### Go ```go +const ( + mx = 100001 + mod int64 = 1000000007 +) + +var pow10 = func() []int64 { + p := make([]int64, mx) + p[0] = 1 + for i := 1; i < mx; i++ { + p[i] = p[i-1] * 10 % mod + } + return p +}() + +func sumAndMultiply(s string, queries [][]int) []int { + n := len(s) + sumD := make([]int, n+1) + cntN0 := make([]int, n+1) + p := make([]int64, n+1) + + for i := 1; i <= n; i++ { + d := int64(s[i-1] - '0') + sumD[i] = sumD[i-1] + int(d) + cntN0[i] = cntN0[i-1] + if d > 0 { + cntN0[i]++ + p[i] = (p[i-1]*10 + d) % mod + } else { + p[i] = p[i-1] + } + } + + ans := make([]int, len(queries)) + for i, q := range queries { + l, r := q[0], q[1] + n0 := cntN0[r+1] - cntN0[l] + sd := int64(sumD[r+1] - sumD[l]) + x := (p[r+1] - p[l]*pow10[n0]%mod + mod) % mod + ans[i] = int(x * sd % mod) + } + return ans +} +``` +#### TypeScript + +```ts +const MX = 100001; +const MOD = 1000000007n; + +const pow10: bigint[] = Array(MX).fill(1n); +for (let i = 1; i < MX; i++) { + pow10[i] = (pow10[i - 1] * 10n) % MOD; +} + +function sumAndMultiply(s: string, queries: number[][]): number[] { + const n = s.length; + const sumD = Array(n + 1).fill(0); + const cntN0 = Array(n + 1).fill(0); + const p: bigint[] = Array(n + 1).fill(0n); + + for (let i = 1; i <= n; i++) { + const d = s.charCodeAt(i - 1) - 48; + sumD[i] = sumD[i - 1] + d; + cntN0[i] = cntN0[i - 1] + (d > 0 ? 1 : 0); + p[i] = d > 0 ? (p[i - 1] * 10n + BigInt(d)) % MOD : p[i - 1]; + } + + const ans: number[] = []; + for (const [l, r] of queries) { + const n0 = cntN0[r + 1] - cntN0[l]; + const sd = BigInt(sumD[r + 1] - sumD[l]); + const x = (p[r + 1] - ((p[l] * pow10[n0]) % MOD) + MOD) % MOD; + ans.push(Number((x * sd) % MOD)); + } + return ans; +} ``` diff --git a/solution/3700-3799/3756.Concatenate Non-Zero Digits and Multiply by Sum II/README_EN.md b/solution/3700-3799/3756.Concatenate Non-Zero Digits and Multiply by Sum II/README_EN.md index 316a3d505dc71..cc889d41639fd 100644 --- a/solution/3700-3799/3756.Concatenate Non-Zero Digits and Multiply by Sum II/README_EN.md +++ b/solution/3700-3799/3756.Concatenate Non-Zero Digits and Multiply by Sum II/README_EN.md @@ -139,32 +139,215 @@ tags: -### Solution 1 +### Solution 1: Prefix Sum + +We preprocess three prefix arrays: + +- `sumD[i]` is the sum of digits in the first $i$ characters of the string; +- `cntN0[i]` is the count of non-zero digits in the first $i$ characters; +- `p[i]` is the number formed by concatenating all non-zero digits in the first $i$ characters, modulo $10^9 + 7$. + +For a query $[l, r]$, the number of non-zero digits in the substring is $n_0 = cntN0[r + 1] - cntN0[l]$, and the digit sum is $sd = sumD[r + 1] - sumD[l]$. Since $p[r + 1] = p[l] \cdot 10^{n_0} + x$, we have $x = p[r + 1] - p[l] \cdot 10^{n_0}$, and the answer is $x \cdot sd$. + +We precompute powers of $10$ and answer each query in $O(1)$. + +The time complexity is $O(n + q)$ and the space complexity is $O(n)$, where $n$ is the string length and $q$ is the number of queries. #### Python3 ```python - +mx = 10**5 + 1 +mod = 10**9 + 7 +pow10 = [1] * mx +for i in range(1, mx): + pow10[i] = pow10[i - 1] * 10 % mod + + +class Solution: + def sumAndMultiply(self, s: str, queries: List[List[int]]) -> List[int]: + n = len(s) + sum_d = [0] * (n + 1) + cnt_n0 = [0] * (n + 1) + p = [0] * (n + 1) + for i, d in enumerate(map(int, s), 1): + sum_d[i] = sum_d[i - 1] + d + cnt_n0[i] = cnt_n0[i - 1] + int(d > 0) + p[i] = (p[i - 1] * 10 + d) % mod if d else p[i - 1] + + ans = [] + for l, r in queries: + n0 = cnt_n0[r + 1] - cnt_n0[l] + sd = sum_d[r + 1] - sum_d[l] + x = p[r + 1] - p[l] * pow10[n0] % mod + ans.append(x * sd % mod) + return ans ``` #### Java ```java - +class Solution { + private static final int MX = 100001; + private static final int MOD = 1_000_000_007; + private static final long[] POW10 = new long[MX]; + + static { + POW10[0] = 1; + for (int i = 1; i < MX; i++) { + POW10[i] = POW10[i - 1] * 10 % MOD; + } + } + + public int[] sumAndMultiply(String s, int[][] queries) { + int n = s.length(); + int[] sumD = new int[n + 1]; + int[] cntN0 = new int[n + 1]; + long[] p = new long[n + 1]; + + for (int i = 1; i <= n; i++) { + int d = s.charAt(i - 1) - '0'; + sumD[i] = sumD[i - 1] + d; + cntN0[i] = cntN0[i - 1] + (d > 0 ? 1 : 0); + p[i] = d > 0 ? (p[i - 1] * 10 + d) % MOD : p[i - 1]; + } + + int[] ans = new int[queries.length]; + for (int i = 0; i < queries.length; i++) { + int l = queries[i][0], r = queries[i][1]; + int n0 = cntN0[r + 1] - cntN0[l]; + int sd = sumD[r + 1] - sumD[l]; + long x = (p[r + 1] - p[l] * POW10[n0] % MOD + MOD) % MOD; + ans[i] = (int) (x * sd % MOD); + } + return ans; + } +} ``` #### C++ ```cpp - +class Solution { +public: + vector sumAndMultiply(string s, vector>& queries) { + static const int MX = 100001; + static const int MOD = 1000000007; + static vector pow10 = [] { + vector p(MX); + p[0] = 1; + for (int i = 1; i < MX; i++) { + p[i] = p[i - 1] * 10 % MOD; + } + return p; + }(); + + int n = s.size(); + vector sumD(n + 1), cntN0(n + 1); + vector p(n + 1); + + for (int i = 1; i <= n; i++) { + int d = s[i - 1] - '0'; + sumD[i] = sumD[i - 1] + d; + cntN0[i] = cntN0[i - 1] + (d > 0); + p[i] = d ? (p[i - 1] * 10 + d) % MOD : p[i - 1]; + } + + vector ans; + ans.reserve(queries.size()); + for (auto& q : queries) { + int l = q[0], r = q[1]; + int n0 = cntN0[r + 1] - cntN0[l]; + int sd = sumD[r + 1] - sumD[l]; + long long x = (p[r + 1] - p[l] * pow10[n0] % MOD + MOD) % MOD; + ans.push_back(x * sd % MOD); + } + return ans; + } +}; ``` #### Go ```go +const ( + mx = 100001 + mod int64 = 1000000007 +) + +var pow10 = func() []int64 { + p := make([]int64, mx) + p[0] = 1 + for i := 1; i < mx; i++ { + p[i] = p[i-1] * 10 % mod + } + return p +}() + +func sumAndMultiply(s string, queries [][]int) []int { + n := len(s) + sumD := make([]int, n+1) + cntN0 := make([]int, n+1) + p := make([]int64, n+1) + + for i := 1; i <= n; i++ { + d := int64(s[i-1] - '0') + sumD[i] = sumD[i-1] + int(d) + cntN0[i] = cntN0[i-1] + if d > 0 { + cntN0[i]++ + p[i] = (p[i-1]*10 + d) % mod + } else { + p[i] = p[i-1] + } + } + + ans := make([]int, len(queries)) + for i, q := range queries { + l, r := q[0], q[1] + n0 := cntN0[r+1] - cntN0[l] + sd := int64(sumD[r+1] - sumD[l]) + x := (p[r+1] - p[l]*pow10[n0]%mod + mod) % mod + ans[i] = int(x * sd % mod) + } + return ans +} +``` +#### TypeScript + +```ts +const MX = 100001; +const MOD = 1000000007n; + +const pow10: bigint[] = Array(MX).fill(1n); +for (let i = 1; i < MX; i++) { + pow10[i] = (pow10[i - 1] * 10n) % MOD; +} + +function sumAndMultiply(s: string, queries: number[][]): number[] { + const n = s.length; + const sumD = Array(n + 1).fill(0); + const cntN0 = Array(n + 1).fill(0); + const p: bigint[] = Array(n + 1).fill(0n); + + for (let i = 1; i <= n; i++) { + const d = s.charCodeAt(i - 1) - 48; + sumD[i] = sumD[i - 1] + d; + cntN0[i] = cntN0[i - 1] + (d > 0 ? 1 : 0); + p[i] = d > 0 ? (p[i - 1] * 10n + BigInt(d)) % MOD : p[i - 1]; + } + + const ans: number[] = []; + for (const [l, r] of queries) { + const n0 = cntN0[r + 1] - cntN0[l]; + const sd = BigInt(sumD[r + 1] - sumD[l]); + const x = (p[r + 1] - ((p[l] * pow10[n0]) % MOD) + MOD) % MOD; + ans.push(Number((x * sd) % MOD)); + } + return ans; +} ``` diff --git a/solution/3700-3799/3756.Concatenate Non-Zero Digits and Multiply by Sum II/Solution.cpp b/solution/3700-3799/3756.Concatenate Non-Zero Digits and Multiply by Sum II/Solution.cpp new file mode 100644 index 0000000000000..7fe091e0a555d --- /dev/null +++ b/solution/3700-3799/3756.Concatenate Non-Zero Digits and Multiply by Sum II/Solution.cpp @@ -0,0 +1,37 @@ +class Solution { +public: + vector sumAndMultiply(string s, vector>& queries) { + static const int MX = 100001; + static const int MOD = 1000000007; + static vector pow10 = [] { + vector p(MX); + p[0] = 1; + for (int i = 1; i < MX; i++) { + p[i] = p[i - 1] * 10 % MOD; + } + return p; + }(); + + int n = s.size(); + vector sumD(n + 1), cntN0(n + 1); + vector p(n + 1); + + for (int i = 1; i <= n; i++) { + int d = s[i - 1] - '0'; + sumD[i] = sumD[i - 1] + d; + cntN0[i] = cntN0[i - 1] + (d > 0); + p[i] = d ? (p[i - 1] * 10 + d) % MOD : p[i - 1]; + } + + vector ans; + ans.reserve(queries.size()); + for (auto& q : queries) { + int l = q[0], r = q[1]; + int n0 = cntN0[r + 1] - cntN0[l]; + int sd = sumD[r + 1] - sumD[l]; + long long x = (p[r + 1] - p[l] * pow10[n0] % MOD + MOD) % MOD; + ans.push_back(x * sd % MOD); + } + return ans; + } +}; \ No newline at end of file diff --git a/solution/3700-3799/3756.Concatenate Non-Zero Digits and Multiply by Sum II/Solution.go b/solution/3700-3799/3756.Concatenate Non-Zero Digits and Multiply by Sum II/Solution.go new file mode 100644 index 0000000000000..c1bbacc1b56f6 --- /dev/null +++ b/solution/3700-3799/3756.Concatenate Non-Zero Digits and Multiply by Sum II/Solution.go @@ -0,0 +1,42 @@ +const ( + mx = 100001 + mod int64 = 1000000007 +) + +var pow10 = func() []int64 { + p := make([]int64, mx) + p[0] = 1 + for i := 1; i < mx; i++ { + p[i] = p[i-1] * 10 % mod + } + return p +}() + +func sumAndMultiply(s string, queries [][]int) []int { + n := len(s) + sumD := make([]int, n+1) + cntN0 := make([]int, n+1) + p := make([]int64, n+1) + + for i := 1; i <= n; i++ { + d := int64(s[i-1] - '0') + sumD[i] = sumD[i-1] + int(d) + cntN0[i] = cntN0[i-1] + if d > 0 { + cntN0[i]++ + p[i] = (p[i-1]*10 + d) % mod + } else { + p[i] = p[i-1] + } + } + + ans := make([]int, len(queries)) + for i, q := range queries { + l, r := q[0], q[1] + n0 := cntN0[r+1] - cntN0[l] + sd := int64(sumD[r+1] - sumD[l]) + x := (p[r+1] - p[l]*pow10[n0]%mod + mod) % mod + ans[i] = int(x * sd % mod) + } + return ans +} diff --git a/solution/3700-3799/3756.Concatenate Non-Zero Digits and Multiply by Sum II/Solution.java b/solution/3700-3799/3756.Concatenate Non-Zero Digits and Multiply by Sum II/Solution.java new file mode 100644 index 0000000000000..4a8ac4a5948c6 --- /dev/null +++ b/solution/3700-3799/3756.Concatenate Non-Zero Digits and Multiply by Sum II/Solution.java @@ -0,0 +1,36 @@ +class Solution { + private static final int MX = 100001; + private static final int MOD = 1_000_000_007; + private static final long[] POW10 = new long[MX]; + + static { + POW10[0] = 1; + for (int i = 1; i < MX; i++) { + POW10[i] = POW10[i - 1] * 10 % MOD; + } + } + + public int[] sumAndMultiply(String s, int[][] queries) { + int n = s.length(); + int[] sumD = new int[n + 1]; + int[] cntN0 = new int[n + 1]; + long[] p = new long[n + 1]; + + for (int i = 1; i <= n; i++) { + int d = s.charAt(i - 1) - '0'; + sumD[i] = sumD[i - 1] + d; + cntN0[i] = cntN0[i - 1] + (d > 0 ? 1 : 0); + p[i] = d > 0 ? (p[i - 1] * 10 + d) % MOD : p[i - 1]; + } + + int[] ans = new int[queries.length]; + for (int i = 0; i < queries.length; i++) { + int l = queries[i][0], r = queries[i][1]; + int n0 = cntN0[r + 1] - cntN0[l]; + int sd = sumD[r + 1] - sumD[l]; + long x = (p[r + 1] - p[l] * POW10[n0] % MOD + MOD) % MOD; + ans[i] = (int) (x * sd % MOD); + } + return ans; + } +} \ No newline at end of file diff --git a/solution/3700-3799/3756.Concatenate Non-Zero Digits and Multiply by Sum II/Solution.py b/solution/3700-3799/3756.Concatenate Non-Zero Digits and Multiply by Sum II/Solution.py new file mode 100644 index 0000000000000..71a854600dbe6 --- /dev/null +++ b/solution/3700-3799/3756.Concatenate Non-Zero Digits and Multiply by Sum II/Solution.py @@ -0,0 +1,25 @@ +mx = 10**5 + 1 +mod = 10**9 + 7 +pow10 = [1] * mx +for i in range(1, mx): + pow10[i] = pow10[i - 1] * 10 % mod + + +class Solution: + def sumAndMultiply(self, s: str, queries: List[List[int]]) -> List[int]: + n = len(s) + sum_d = [0] * (n + 1) + cnt_n0 = [0] * (n + 1) + p = [0] * (n + 1) + for i, d in enumerate(map(int, s), 1): + sum_d[i] = sum_d[i - 1] + d + cnt_n0[i] = cnt_n0[i - 1] + int(d > 0) + p[i] = (p[i - 1] * 10 + d) % mod if d else p[i - 1] + + ans = [] + for l, r in queries: + n0 = cnt_n0[r + 1] - cnt_n0[l] + sd = sum_d[r + 1] - sum_d[l] + x = p[r + 1] - p[l] * pow10[n0] % mod + ans.append(x * sd % mod) + return ans diff --git a/solution/3700-3799/3756.Concatenate Non-Zero Digits and Multiply by Sum II/Solution.ts b/solution/3700-3799/3756.Concatenate Non-Zero Digits and Multiply by Sum II/Solution.ts new file mode 100644 index 0000000000000..795429132ce78 --- /dev/null +++ b/solution/3700-3799/3756.Concatenate Non-Zero Digits and Multiply by Sum II/Solution.ts @@ -0,0 +1,30 @@ +const MX = 100001; +const MOD = 1000000007n; + +const pow10: bigint[] = Array(MX).fill(1n); +for (let i = 1; i < MX; i++) { + pow10[i] = (pow10[i - 1] * 10n) % MOD; +} + +function sumAndMultiply(s: string, queries: number[][]): number[] { + const n = s.length; + const sumD = Array(n + 1).fill(0); + const cntN0 = Array(n + 1).fill(0); + const p: bigint[] = Array(n + 1).fill(0n); + + for (let i = 1; i <= n; i++) { + const d = s.charCodeAt(i - 1) - 48; + sumD[i] = sumD[i - 1] + d; + cntN0[i] = cntN0[i - 1] + (d > 0 ? 1 : 0); + p[i] = d > 0 ? (p[i - 1] * 10n + BigInt(d)) % MOD : p[i - 1]; + } + + const ans: number[] = []; + for (const [l, r] of queries) { + const n0 = cntN0[r + 1] - cntN0[l]; + const sd = BigInt(sumD[r + 1] - sumD[l]); + const x = (p[r + 1] - ((p[l] * pow10[n0]) % MOD) + MOD) % MOD; + ans.push(Number((x * sd) % MOD)); + } + return ans; +}