From e0aa2ce28737c3ea933d14ddff28193c0c88863e Mon Sep 17 00:00:00 2001 From: Libin YANG Date: Tue, 9 Sep 2025 07:27:46 +0800 Subject: [PATCH] feat: add solutions to lc problem: No.2327 --- .../README.md | 119 +++++++++++------ .../README_EN.md | 121 ++++++++++++------ .../Solution.cpp | 34 ++--- .../Solution.java | 13 +- .../Solution.rs | 31 +++++ .../Solution.ts | 34 ++--- 6 files changed, 237 insertions(+), 115 deletions(-) create mode 100644 solution/2300-2399/2327.Number of People Aware of a Secret/Solution.rs diff --git a/solution/2300-2399/2327.Number of People Aware of a Secret/README.md b/solution/2300-2399/2327.Number of People Aware of a Secret/README.md index 2ce1e427c180c..58d0ef4ce2d35 100644 --- a/solution/2300-2399/2327.Number of People Aware of a Secret/README.md +++ b/solution/2300-2399/2327.Number of People Aware of a Secret/README.md @@ -69,11 +69,13 @@ tags: ### 方法一：差分数组 -差分数组 $d[i]$ 记录每天知道秘密的人数变化情况，$cnt[i]$ 记录第 $i$ 天新得知秘密的人数。那么从 $[i+delay,i+forget)$ 的这段时间内，$cnt[i]$ 个人每天都能分享给另外 $cnt[i]$ 个人。 +我们用一个差分数组 $d[i]$ 来记录第 $i$ 天知道秘密的人数变化情况，用一个数组 $cnt[i]$ 来记录第 $i$ 天新得知秘密的人数。 -最终 $sum(d[:n+1])$ 就是答案。 +那么，对于第 $i$ 天新得知秘密的 $cnt[i]$ 个人来说，他们会在 $[i+\text{delay}, i+\text{forget})$ 这段时间内每天都能分享给另外 $cnt[i]$ 个人。 -时间复杂度 $O(n^2)$。 +答案为 $\sum_{i=1}^{n} d[i]$。 + +时间复杂度 $O(n^2)$，空间复杂度 $O(n)$。其中 $n$ 为题目给定的整数。 @@ -102,27 +104,26 @@ class Solution: ```java class Solution { - private static final int MOD = (int) 1e9 + 7; - public int peopleAwareOfSecret(int n, int delay, int forget) { + final int mod = (int) 1e9 + 7; int m = (n << 1) + 10; long[] d = new long[m]; long[] cnt = new long[m]; cnt[1] = 1; for (int i = 1; i <= n; ++i) { if (cnt[i] > 0) { - d[i] = (d[i] + cnt[i]) % MOD; - d[i + forget] = (d[i + forget] - cnt[i] + MOD) % MOD; + d[i] = (d[i] + cnt[i]) % mod; + d[i + forget] = (d[i + forget] - cnt[i] + mod) % mod; int nxt = i + delay; while (nxt < i + forget) { - cnt[nxt] = (cnt[nxt] + cnt[i]) % MOD; + cnt[nxt] = (cnt[nxt] + cnt[i]) % mod; ++nxt; } } } long ans = 0; for (int i = 1; i <= n; ++i) { - ans = (ans + d[i]) % MOD; + ans = (ans + d[i]) % mod; } return (int) ans; } @@ -132,29 +133,29 @@ class Solution { #### C++ ```cpp -using ll = long long; -const int mod = 1e9 + 7; - class Solution { public: int peopleAwareOfSecret(int n, int delay, int forget) { + const int mod = 1e9 + 7; int m = (n << 1) + 10; - vector d(m); - vector cnt(m); + vector d(m), cnt(m); cnt[1] = 1; - for (int i = 1; i <= n; ++i) { - if (!cnt[i]) continue; - d[i] = (d[i] + cnt[i]) % mod; - d[i + forget] = (d[i + forget] - cnt[i] + mod) % mod; - int nxt = i + delay; - while (nxt < i + forget) { - cnt[nxt] = (cnt[nxt] + cnt[i]) % mod; - ++nxt; + for (int i = 1; i <= n; i++) { + if (cnt[i]) { + d[i] = (d[i] + cnt[i]) % mod; + d[i + forget] = (d[i + forget] - cnt[i] + mod) % mod; + int nxt = i + delay; + while (nxt < i + forget) { + cnt[nxt] = (cnt[nxt] + cnt[i]) % mod; + nxt++; + } } } - int ans = 0; - for (int i = 1; i <= n; ++i) ans = (ans + d[i]) % mod; - return ans; + long long ans = 0; + for (int i = 0; i <= n; i++) { + ans += d[i]; + } + return ans % mod; } }; ``` @@ -192,25 +193,65 @@ func peopleAwareOfSecret(n int, delay int, forget int) int { ```ts function peopleAwareOfSecret(n: number, delay: number, forget: number): number { - let dp = new Array(n + 1).fill(0n); - dp[1] = 1n; - for (let i = 2; i <= n; i++) { - let pre = 0n; - for (let j = i - forget + 1; j <= i - delay; j++) { - if (j > 0) { - pre += dp[j]; + const mod = 1e9 + 7; + const m = (n << 1) + 10; + const d: number[] = Array(m).fill(0); + const cnt: number[] = Array(m).fill(0); + + cnt[1] = 1; + for (let i = 1; i <= n; ++i) { + if (cnt[i] > 0) { + d[i] = (d[i] + cnt[i]) % mod; + d[i + forget] = (d[i + forget] - cnt[i] + mod) % mod; + let nxt = i + delay; + while (nxt < i + forget) { + cnt[nxt] = (cnt[nxt] + cnt[i]) % mod; + ++nxt; } } - dp[i] = pre; } - let pre = 0n; - let i = n + 1; - for (let j = i - forget; j < i; j++) { - if (j > 0) { - pre += dp[j]; + + let ans = 0; + for (let i = 1; i <= n; ++i) { + ans = (ans + d[i]) % mod; + } + return ans; +} +``` + +#### Rust + +```rust +impl Solution { + pub fn people_aware_of_secret(n: i32, delay: i32, forget: i32) -> i32 { + let n = n as usize; + let delay = delay as usize; + let forget = forget as usize; + let m = (n << 1) + 10; + let modulo: i64 = 1_000_000_007; + + let mut d = vec![0i64; m]; + let mut cnt = vec![0i64; m]; + + cnt[1] = 1; + for i in 1..=n { + if cnt[i] > 0 { + d[i] = (d[i] + cnt[i]) % modulo; + d[i + forget] = (d[i + forget] - cnt[i] + modulo) % modulo; + let mut nxt = i + delay; + while nxt < i + forget { + cnt[nxt] = (cnt[nxt] + cnt[i]) % modulo; + nxt += 1; + } + } + } + + let mut ans: i64 = 0; + for i in 1..=n { + ans = (ans + d[i]) % modulo; } + ans as i32 } - return Number(pre % BigInt(10 ** 9 + 7)); } ``` diff --git a/solution/2300-2399/2327.Number of People Aware of a Secret/README_EN.md b/solution/2300-2399/2327.Number of People Aware of a Secret/README_EN.md index 0872e1acdb5cc..6d5759fa94ced 100644 --- a/solution/2300-2399/2327.Number of People Aware of a Secret/README_EN.md +++ b/solution/2300-2399/2327.Number of People Aware of a Secret/README_EN.md @@ -67,7 +67,15 @@ Day 4: A forgets the secret. B, C, and D share the secret with 3 new people. (6 -### Solution 1 +### Solution 1: Difference Array + +We use a difference array $d[i]$ to record the change in the number of people who know the secret on day $i$, and an array $cnt[i]$ to record the number of people who newly learn the secret on day $i$. + +For the $cnt[i]$ people who newly learn the secret on day $i$, they can share the secret with another $cnt[i]$ people each day during the interval $[i+\text{delay}, i+\text{forget})$. + +The answer is $\sum_{i=1}^{n} d[i]$. + +The time complexity is $O(n^2)$, and the space complexity is $O(n)$, where $n$ is the given integer. @@ -96,27 +104,26 @@ class Solution: ```java class Solution { - private static final int MOD = (int) 1e9 + 7; - public int peopleAwareOfSecret(int n, int delay, int forget) { + final int mod = (int) 1e9 + 7; int m = (n << 1) + 10; long[] d = new long[m]; long[] cnt = new long[m]; cnt[1] = 1; for (int i = 1; i <= n; ++i) { if (cnt[i] > 0) { - d[i] = (d[i] + cnt[i]) % MOD; - d[i + forget] = (d[i + forget] - cnt[i] + MOD) % MOD; + d[i] = (d[i] + cnt[i]) % mod; + d[i + forget] = (d[i + forget] - cnt[i] + mod) % mod; int nxt = i + delay; while (nxt < i + forget) { - cnt[nxt] = (cnt[nxt] + cnt[i]) % MOD; + cnt[nxt] = (cnt[nxt] + cnt[i]) % mod; ++nxt; } } } long ans = 0; for (int i = 1; i <= n; ++i) { - ans = (ans + d[i]) % MOD; + ans = (ans + d[i]) % mod; } return (int) ans; } @@ -126,29 +133,29 @@ class Solution { #### C++ ```cpp -using ll = long long; -const int mod = 1e9 + 7; - class Solution { public: int peopleAwareOfSecret(int n, int delay, int forget) { + const int mod = 1e9 + 7; int m = (n << 1) + 10; - vector d(m); - vector cnt(m); + vector d(m), cnt(m); cnt[1] = 1; - for (int i = 1; i <= n; ++i) { - if (!cnt[i]) continue; - d[i] = (d[i] + cnt[i]) % mod; - d[i + forget] = (d[i + forget] - cnt[i] + mod) % mod; - int nxt = i + delay; - while (nxt < i + forget) { - cnt[nxt] = (cnt[nxt] + cnt[i]) % mod; - ++nxt; + for (int i = 1; i <= n; i++) { + if (cnt[i]) { + d[i] = (d[i] + cnt[i]) % mod; + d[i + forget] = (d[i + forget] - cnt[i] + mod) % mod; + int nxt = i + delay; + while (nxt < i + forget) { + cnt[nxt] = (cnt[nxt] + cnt[i]) % mod; + nxt++; + } } } - int ans = 0; - for (int i = 1; i <= n; ++i) ans = (ans + d[i]) % mod; - return ans; + long long ans = 0; + for (int i = 0; i <= n; i++) { + ans += d[i]; + } + return ans % mod; } }; ``` @@ -186,25 +193,65 @@ func peopleAwareOfSecret(n int, delay int, forget int) int { ```ts function peopleAwareOfSecret(n: number, delay: number, forget: number): number { - let dp = new Array(n + 1).fill(0n); - dp[1] = 1n; - for (let i = 2; i <= n; i++) { - let pre = 0n; - for (let j = i - forget + 1; j <= i - delay; j++) { - if (j > 0) { - pre += dp[j]; + const mod = 1e9 + 7; + const m = (n << 1) + 10; + const d: number[] = Array(m).fill(0); + const cnt: number[] = Array(m).fill(0); + + cnt[1] = 1; + for (let i = 1; i <= n; ++i) { + if (cnt[i] > 0) { + d[i] = (d[i] + cnt[i]) % mod; + d[i + forget] = (d[i + forget] - cnt[i] + mod) % mod; + let nxt = i + delay; + while (nxt < i + forget) { + cnt[nxt] = (cnt[nxt] + cnt[i]) % mod; + ++nxt; } } - dp[i] = pre; } - let pre = 0n; - let i = n + 1; - for (let j = i - forget; j < i; j++) { - if (j > 0) { - pre += dp[j]; + + let ans = 0; + for (let i = 1; i <= n; ++i) { + ans = (ans + d[i]) % mod; + } + return ans; +} +``` + +#### Rust + +```rust +impl Solution { + pub fn people_aware_of_secret(n: i32, delay: i32, forget: i32) -> i32 { + let n = n as usize; + let delay = delay as usize; + let forget = forget as usize; + let m = (n << 1) + 10; + let modulo: i64 = 1_000_000_007; + + let mut d = vec![0i64; m]; + let mut cnt = vec![0i64; m]; + + cnt[1] = 1; + for i in 1..=n { + if cnt[i] > 0 { + d[i] = (d[i] + cnt[i]) % modulo; + d[i + forget] = (d[i + forget] - cnt[i] + modulo) % modulo; + let mut nxt = i + delay; + while nxt < i + forget { + cnt[nxt] = (cnt[nxt] + cnt[i]) % modulo; + nxt += 1; + } + } + } + + let mut ans: i64 = 0; + for i in 1..=n { + ans = (ans + d[i]) % modulo; } + ans as i32 } - return Number(pre % BigInt(10 ** 9 + 7)); } ``` diff --git a/solution/2300-2399/2327.Number of People Aware of a Secret/Solution.cpp b/solution/2300-2399/2327.Number of People Aware of a Secret/Solution.cpp index 57e77afa5b2b6..73634e304f296 100644 --- a/solution/2300-2399/2327.Number of People Aware of a Secret/Solution.cpp +++ b/solution/2300-2399/2327.Number of People Aware of a Secret/Solution.cpp @@ -1,25 +1,25 @@ -using ll = long long; -const int mod = 1e9 + 7; - class Solution { public: int peopleAwareOfSecret(int n, int delay, int forget) { + const int mod = 1e9 + 7; int m = (n << 1) + 10; - vector d(m); - vector cnt(m); + vector d(m), cnt(m); cnt[1] = 1; - for (int i = 1; i <= n; ++i) { - if (!cnt[i]) continue; - d[i] = (d[i] + cnt[i]) % mod; - d[i + forget] = (d[i + forget] - cnt[i] + mod) % mod; - int nxt = i + delay; - while (nxt < i + forget) { - cnt[nxt] = (cnt[nxt] + cnt[i]) % mod; - ++nxt; + for (int i = 1; i <= n; i++) { + if (cnt[i]) { + d[i] = (d[i] + cnt[i]) % mod; + d[i + forget] = (d[i + forget] - cnt[i] + mod) % mod; + int nxt = i + delay; + while (nxt < i + forget) { + cnt[nxt] = (cnt[nxt] + cnt[i]) % mod; + nxt++; + } } } - int ans = 0; - for (int i = 1; i <= n; ++i) ans = (ans + d[i]) % mod; - return ans; + long long ans = 0; + for (int i = 0; i <= n; i++) { + ans += d[i]; + } + return ans % mod; } -}; \ No newline at end of file +}; diff --git a/solution/2300-2399/2327.Number of People Aware of a Secret/Solution.java b/solution/2300-2399/2327.Number of People Aware of a Secret/Solution.java index e9dbe1f831e9b..2852e41d5b479 100644 --- a/solution/2300-2399/2327.Number of People Aware of a Secret/Solution.java +++ b/solution/2300-2399/2327.Number of People Aware of a Secret/Solution.java @@ -1,26 +1,25 @@ class Solution { - private static final int MOD = (int) 1e9 + 7; - public int peopleAwareOfSecret(int n, int delay, int forget) { + final int mod = (int) 1e9 + 7; int m = (n << 1) + 10; long[] d = new long[m]; long[] cnt = new long[m]; cnt[1] = 1; for (int i = 1; i <= n; ++i) { if (cnt[i] > 0) { - d[i] = (d[i] + cnt[i]) % MOD; - d[i + forget] = (d[i + forget] - cnt[i] + MOD) % MOD; + d[i] = (d[i] + cnt[i]) % mod; + d[i + forget] = (d[i + forget] - cnt[i] + mod) % mod; int nxt = i + delay; while (nxt < i + forget) { - cnt[nxt] = (cnt[nxt] + cnt[i]) % MOD; + cnt[nxt] = (cnt[nxt] + cnt[i]) % mod; ++nxt; } } } long ans = 0; for (int i = 1; i <= n; ++i) { - ans = (ans + d[i]) % MOD; + ans = (ans + d[i]) % mod; } return (int) ans; } -} \ No newline at end of file +} diff --git a/solution/2300-2399/2327.Number of People Aware of a Secret/Solution.rs b/solution/2300-2399/2327.Number of People Aware of a Secret/Solution.rs new file mode 100644 index 0000000000000..1f2e7e105d059 --- /dev/null +++ b/solution/2300-2399/2327.Number of People Aware of a Secret/Solution.rs @@ -0,0 +1,31 @@ +impl Solution { + pub fn people_aware_of_secret(n: i32, delay: i32, forget: i32) -> i32 { + let n = n as usize; + let delay = delay as usize; + let forget = forget as usize; + let m = (n << 1) + 10; + let modulo: i64 = 1_000_000_007; + + let mut d = vec![0i64; m]; + let mut cnt = vec![0i64; m]; + + cnt[1] = 1; + for i in 1..=n { + if cnt[i] > 0 { + d[i] = (d[i] + cnt[i]) % modulo; + d[i + forget] = (d[i + forget] - cnt[i] + modulo) % modulo; + let mut nxt = i + delay; + while nxt < i + forget { + cnt[nxt] = (cnt[nxt] + cnt[i]) % modulo; + nxt += 1; + } + } + } + + let mut ans: i64 = 0; + for i in 1..=n { + ans = (ans + d[i]) % modulo; + } + ans as i32 + } +} diff --git a/solution/2300-2399/2327.Number of People Aware of a Secret/Solution.ts b/solution/2300-2399/2327.Number of People Aware of a Secret/Solution.ts index ba8d348026526..2fd608b0ff759 100644 --- a/solution/2300-2399/2327.Number of People Aware of a Secret/Solution.ts +++ b/solution/2300-2399/2327.Number of People Aware of a Secret/Solution.ts @@ -1,21 +1,25 @@ function peopleAwareOfSecret(n: number, delay: number, forget: number): number { - let dp = new Array(n + 1).fill(0n); - dp[1] = 1n; - for (let i = 2; i <= n; i++) { - let pre = 0n; - for (let j = i - forget + 1; j <= i - delay; j++) { - if (j > 0) { - pre += dp[j]; + const mod = 1e9 + 7; + const m = (n << 1) + 10; + const d: number[] = Array(m).fill(0); + const cnt: number[] = Array(m).fill(0); + + cnt[1] = 1; + for (let i = 1; i <= n; ++i) { + if (cnt[i] > 0) { + d[i] = (d[i] + cnt[i]) % mod; + d[i + forget] = (d[i + forget] - cnt[i] + mod) % mod; + let nxt = i + delay; + while (nxt < i + forget) { + cnt[nxt] = (cnt[nxt] + cnt[i]) % mod; + ++nxt; } } - dp[i] = pre; } - let pre = 0n; - let i = n + 1; - for (let j = i - forget; j < i; j++) { - if (j > 0) { - pre += dp[j]; - } + + let ans = 0; + for (let i = 1; i <= n; ++i) { + ans = (ans + d[i]) % mod; } - return Number(pre % BigInt(10 ** 9 + 7)); + return ans; }