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Commit 6e4118a

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feat: add solutions to lc problem: No.2327 (#4707)
1 parent 368460e commit 6e4118a

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6 files changed

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-115
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6 files changed

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-115
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‎solution/2300-2399/2327.Number of People Aware of a Secret/README.md

Lines changed: 80 additions & 39 deletions
Original file line numberDiff line numberDiff line change
@@ -69,11 +69,13 @@ tags:
6969

7070
### 方法一:差分数组
7171

72-
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。
72+
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。
7373

74-
最终 $sum(d[:n+1])$ 就是答案。
74+
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。
7575

76-
时间复杂度 $O(n^2)$。
76+
答案为 $\sum_{i=1}^{n} d[i]$。
77+
78+
时间复杂度 $O(n^2),ドル空间复杂度 $O(n)$。其中 $n$ 为题目给定的整数。
7779

7880
<!-- tabs:start -->
7981

@@ -102,27 +104,26 @@ class Solution:
102104

103105
```java
104106
class Solution {
105-
private static final int MOD = (int) 1e9 + 7;
106-
107107
public int peopleAwareOfSecret(int n, int delay, int forget) {
108+
final int mod = (int) 1e9 + 7;
108109
int m = (n << 1) + 10;
109110
long[] d = new long[m];
110111
long[] cnt = new long[m];
111112
cnt[1] = 1;
112113
for (int i = 1; i <= n; ++i) {
113114
if (cnt[i] > 0) {
114-
d[i] = (d[i] + cnt[i]) % MOD;
115-
d[i + forget] = (d[i + forget] - cnt[i] + MOD) % MOD;
115+
d[i] = (d[i] + cnt[i]) % mod;
116+
d[i + forget] = (d[i + forget] - cnt[i] + mod) % mod;
116117
int nxt = i + delay;
117118
while (nxt < i + forget) {
118-
cnt[nxt] = (cnt[nxt] + cnt[i]) % MOD;
119+
cnt[nxt] = (cnt[nxt] + cnt[i]) % mod;
119120
++nxt;
120121
}
121122
}
122123
}
123124
long ans = 0;
124125
for (int i = 1; i <= n; ++i) {
125-
ans = (ans + d[i]) % MOD;
126+
ans = (ans + d[i]) % mod;
126127
}
127128
return (int) ans;
128129
}
@@ -132,29 +133,29 @@ class Solution {
132133
#### C++
133134

134135
```cpp
135-
using ll = long long;
136-
const int mod = 1e9 + 7;
137-
138136
class Solution {
139137
public:
140138
int peopleAwareOfSecret(int n, int delay, int forget) {
139+
const int mod = 1e9 + 7;
141140
int m = (n << 1) + 10;
142-
vector<ll> d(m);
143-
vector<ll> cnt(m);
141+
vector<long long> d(m), cnt(m);
144142
cnt[1] = 1;
145-
for (int i = 1; i <= n; ++i) {
146-
if (!cnt[i]) continue;
147-
d[i] = (d[i] + cnt[i]) % mod;
148-
d[i + forget] = (d[i + forget] - cnt[i] + mod) % mod;
149-
int nxt = i + delay;
150-
while (nxt < i + forget) {
151-
cnt[nxt] = (cnt[nxt] + cnt[i]) % mod;
152-
++nxt;
143+
for (int i = 1; i <= n; i++) {
144+
if (cnt[i]) {
145+
d[i] = (d[i] + cnt[i]) % mod;
146+
d[i + forget] = (d[i + forget] - cnt[i] + mod) % mod;
147+
int nxt = i + delay;
148+
while (nxt < i + forget) {
149+
cnt[nxt] = (cnt[nxt] + cnt[i]) % mod;
150+
nxt++;
151+
}
153152
}
154153
}
155-
int ans = 0;
156-
for (int i = 1; i <= n; ++i) ans = (ans + d[i]) % mod;
157-
return ans;
154+
long long ans = 0;
155+
for (int i = 0; i <= n; i++) {
156+
ans += d[i];
157+
}
158+
return ans % mod;
158159
}
159160
};
160161
```
@@ -192,25 +193,65 @@ func peopleAwareOfSecret(n int, delay int, forget int) int {
192193

193194
```ts
194195
function peopleAwareOfSecret(n: number, delay: number, forget: number): number {
195-
let dp = new Array(n + 1).fill(0n);
196-
dp[1] = 1n;
197-
for (let i = 2; i <= n; i++) {
198-
let pre = 0n;
199-
for (let j = i - forget + 1; j <= i - delay; j++) {
200-
if (j > 0) {
201-
pre += dp[j];
196+
const mod = 1e9 + 7;
197+
const m = (n << 1) + 10;
198+
const d: number[] = Array(m).fill(0);
199+
const cnt: number[] = Array(m).fill(0);
200+
201+
cnt[1] = 1;
202+
for (let i = 1; i <= n; ++i) {
203+
if (cnt[i] > 0) {
204+
d[i] = (d[i] + cnt[i]) % mod;
205+
d[i + forget] = (d[i + forget] - cnt[i] + mod) % mod;
206+
let nxt = i + delay;
207+
while (nxt < i + forget) {
208+
cnt[nxt] = (cnt[nxt] + cnt[i]) % mod;
209+
++nxt;
202210
}
203211
}
204-
dp[i] = pre;
205212
}
206-
let pre = 0n;
207-
let i = n + 1;
208-
for (let j = i - forget; j < i; j++) {
209-
if (j > 0) {
210-
pre += dp[j];
213+
214+
let ans = 0;
215+
for (let i = 1; i <= n; ++i) {
216+
ans = (ans + d[i]) % mod;
217+
}
218+
return ans;
219+
}
220+
```
221+
222+
#### Rust
223+
224+
```rust
225+
impl Solution {
226+
pub fn people_aware_of_secret(n: i32, delay: i32, forget: i32) -> i32 {
227+
let n = n as usize;
228+
let delay = delay as usize;
229+
let forget = forget as usize;
230+
let m = (n << 1) + 10;
231+
let modulo: i64 = 1_000_000_007;
232+
233+
let mut d = vec![0i64; m];
234+
let mut cnt = vec![0i64; m];
235+
236+
cnt[1] = 1;
237+
for i in 1..=n {
238+
if cnt[i] > 0 {
239+
d[i] = (d[i] + cnt[i]) % modulo;
240+
d[i + forget] = (d[i + forget] - cnt[i] + modulo) % modulo;
241+
let mut nxt = i + delay;
242+
while nxt < i + forget {
243+
cnt[nxt] = (cnt[nxt] + cnt[i]) % modulo;
244+
nxt += 1;
245+
}
246+
}
247+
}
248+
249+
let mut ans: i64 = 0;
250+
for i in 1..=n {
251+
ans = (ans + d[i]) % modulo;
211252
}
253+
ans as i32
212254
}
213-
return Number(pre % BigInt(10 ** 9 + 7));
214255
}
215256
```
216257

‎solution/2300-2399/2327.Number of People Aware of a Secret/README_EN.md

Lines changed: 84 additions & 37 deletions
Original file line numberDiff line numberDiff line change
@@ -67,7 +67,15 @@ Day 4: A forgets the secret. B, C, and D share the secret with 3 new people. (6
6767

6868
<!-- solution:start -->
6969

70-
### Solution 1
70+
### Solution 1: Difference Array
71+
72+
We use a difference array $d[i]$ to record the change in the number of people who know the secret on day $i,ドル and an array $cnt[i]$ to record the number of people who newly learn the secret on day $i$.
73+
74+
For the $cnt[i]$ people who newly learn the secret on day $i,ドル they can share the secret with another $cnt[i]$ people each day during the interval $[i+\text{delay}, i+\text{forget})$.
75+
76+
The answer is $\sum_{i=1}^{n} d[i]$.
77+
78+
The time complexity is $O(n^2),ドル and the space complexity is $O(n),ドル where $n$ is the given integer.
7179

7280
<!-- tabs:start -->
7381

@@ -96,27 +104,26 @@ class Solution:
96104

97105
```java
98106
class Solution {
99-
private static final int MOD = (int) 1e9 + 7;
100-
101107
public int peopleAwareOfSecret(int n, int delay, int forget) {
108+
final int mod = (int) 1e9 + 7;
102109
int m = (n << 1) + 10;
103110
long[] d = new long[m];
104111
long[] cnt = new long[m];
105112
cnt[1] = 1;
106113
for (int i = 1; i <= n; ++i) {
107114
if (cnt[i] > 0) {
108-
d[i] = (d[i] + cnt[i]) % MOD;
109-
d[i + forget] = (d[i + forget] - cnt[i] + MOD) % MOD;
115+
d[i] = (d[i] + cnt[i]) % mod;
116+
d[i + forget] = (d[i + forget] - cnt[i] + mod) % mod;
110117
int nxt = i + delay;
111118
while (nxt < i + forget) {
112-
cnt[nxt] = (cnt[nxt] + cnt[i]) % MOD;
119+
cnt[nxt] = (cnt[nxt] + cnt[i]) % mod;
113120
++nxt;
114121
}
115122
}
116123
}
117124
long ans = 0;
118125
for (int i = 1; i <= n; ++i) {
119-
ans = (ans + d[i]) % MOD;
126+
ans = (ans + d[i]) % mod;
120127
}
121128
return (int) ans;
122129
}
@@ -126,29 +133,29 @@ class Solution {
126133
#### C++
127134

128135
```cpp
129-
using ll = long long;
130-
const int mod = 1e9 + 7;
131-
132136
class Solution {
133137
public:
134138
int peopleAwareOfSecret(int n, int delay, int forget) {
139+
const int mod = 1e9 + 7;
135140
int m = (n << 1) + 10;
136-
vector<ll> d(m);
137-
vector<ll> cnt(m);
141+
vector<long long> d(m), cnt(m);
138142
cnt[1] = 1;
139-
for (int i = 1; i <= n; ++i) {
140-
if (!cnt[i]) continue;
141-
d[i] = (d[i] + cnt[i]) % mod;
142-
d[i + forget] = (d[i + forget] - cnt[i] + mod) % mod;
143-
int nxt = i + delay;
144-
while (nxt < i + forget) {
145-
cnt[nxt] = (cnt[nxt] + cnt[i]) % mod;
146-
++nxt;
143+
for (int i = 1; i <= n; i++) {
144+
if (cnt[i]) {
145+
d[i] = (d[i] + cnt[i]) % mod;
146+
d[i + forget] = (d[i + forget] - cnt[i] + mod) % mod;
147+
int nxt = i + delay;
148+
while (nxt < i + forget) {
149+
cnt[nxt] = (cnt[nxt] + cnt[i]) % mod;
150+
nxt++;
151+
}
147152
}
148153
}
149-
int ans = 0;
150-
for (int i = 1; i <= n; ++i) ans = (ans + d[i]) % mod;
151-
return ans;
154+
long long ans = 0;
155+
for (int i = 0; i <= n; i++) {
156+
ans += d[i];
157+
}
158+
return ans % mod;
152159
}
153160
};
154161
```
@@ -186,25 +193,65 @@ func peopleAwareOfSecret(n int, delay int, forget int) int {
186193

187194
```ts
188195
function peopleAwareOfSecret(n: number, delay: number, forget: number): number {
189-
let dp = new Array(n + 1).fill(0n);
190-
dp[1] = 1n;
191-
for (let i = 2; i <= n; i++) {
192-
let pre = 0n;
193-
for (let j = i - forget + 1; j <= i - delay; j++) {
194-
if (j > 0) {
195-
pre += dp[j];
196+
const mod = 1e9 + 7;
197+
const m = (n << 1) + 10;
198+
const d: number[] = Array(m).fill(0);
199+
const cnt: number[] = Array(m).fill(0);
200+
201+
cnt[1] = 1;
202+
for (let i = 1; i <= n; ++i) {
203+
if (cnt[i] > 0) {
204+
d[i] = (d[i] + cnt[i]) % mod;
205+
d[i + forget] = (d[i + forget] - cnt[i] + mod) % mod;
206+
let nxt = i + delay;
207+
while (nxt < i + forget) {
208+
cnt[nxt] = (cnt[nxt] + cnt[i]) % mod;
209+
++nxt;
196210
}
197211
}
198-
dp[i] = pre;
199212
}
200-
let pre = 0n;
201-
let i = n + 1;
202-
for (let j = i - forget; j < i; j++) {
203-
if (j > 0) {
204-
pre += dp[j];
213+
214+
let ans = 0;
215+
for (let i = 1; i <= n; ++i) {
216+
ans = (ans + d[i]) % mod;
217+
}
218+
return ans;
219+
}
220+
```
221+
222+
#### Rust
223+
224+
```rust
225+
impl Solution {
226+
pub fn people_aware_of_secret(n: i32, delay: i32, forget: i32) -> i32 {
227+
let n = n as usize;
228+
let delay = delay as usize;
229+
let forget = forget as usize;
230+
let m = (n << 1) + 10;
231+
let modulo: i64 = 1_000_000_007;
232+
233+
let mut d = vec![0i64; m];
234+
let mut cnt = vec![0i64; m];
235+
236+
cnt[1] = 1;
237+
for i in 1..=n {
238+
if cnt[i] > 0 {
239+
d[i] = (d[i] + cnt[i]) % modulo;
240+
d[i + forget] = (d[i + forget] - cnt[i] + modulo) % modulo;
241+
let mut nxt = i + delay;
242+
while nxt < i + forget {
243+
cnt[nxt] = (cnt[nxt] + cnt[i]) % modulo;
244+
nxt += 1;
245+
}
246+
}
247+
}
248+
249+
let mut ans: i64 = 0;
250+
for i in 1..=n {
251+
ans = (ans + d[i]) % modulo;
205252
}
253+
ans as i32
206254
}
207-
return Number(pre % BigInt(10 ** 9 + 7));
208255
}
209256
```
210257

Lines changed: 17 additions & 17 deletions
Original file line numberDiff line numberDiff line change
@@ -1,25 +1,25 @@
1-
using ll = long long;
2-
const int mod = 1e9 + 7;
3-
41
class Solution {
52
public:
63
int peopleAwareOfSecret(int n, int delay, int forget) {
4+
const int mod = 1e9 + 7;
75
int m = (n << 1) + 10;
8-
vector<ll> d(m);
9-
vector<ll> cnt(m);
6+
vector<long long> d(m), cnt(m);
107
cnt[1] = 1;
11-
for (int i = 1; i <= n; ++i) {
12-
if (!cnt[i]) continue;
13-
d[i] = (d[i] + cnt[i]) % mod;
14-
d[i + forget] = (d[i + forget] - cnt[i] + mod) % mod;
15-
int nxt = i + delay;
16-
while (nxt < i + forget) {
17-
cnt[nxt] = (cnt[nxt] + cnt[i]) % mod;
18-
++nxt;
8+
for (int i = 1; i <= n; i++) {
9+
if (cnt[i]) {
10+
d[i] = (d[i] + cnt[i]) % mod;
11+
d[i + forget] = (d[i + forget] - cnt[i] + mod) % mod;
12+
int nxt = i + delay;
13+
while (nxt < i + forget) {
14+
cnt[nxt] = (cnt[nxt] + cnt[i]) % mod;
15+
nxt++;
16+
}
1917
}
2018
}
21-
int ans = 0;
22-
for (int i = 1; i <= n; ++i) ans = (ans + d[i]) % mod;
23-
return ans;
19+
long long ans = 0;
20+
for (int i = 0; i <= n; i++) {
21+
ans += d[i];
22+
}
23+
return ans % mod;
2424
}
25-
};
25+
};

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