+ problem 2327

fruit-in · fruit-in · commit d4834354d4b3 · 2023-11-28T18:10:42.000+08:00
diff --git a/Problemset/2327-Number of People Aware of a Secret/README.md b/Problemset/2327-Number of People Aware of a Secret/README.md
@@ -0,0 +1,55 @@
+# 2327. Number of People Aware of a Secret
+On day `1`, one person discovers a secret.
+
+You are given an integer `delay`, which means that each person will **share** the secret with a new person **every day**, starting from `delay` days after discovering the secret. You are also given an integer `forget`, which means that each person will **forget** the secret `forget` days after discovering it. A person **cannot** share the secret on the same day they forgot it, or on any day afterwards.
+
+Given an integer `n`, return *the number of people who know the secret at the end of day* `n`. Since the answer may be very large, return it **modulo** <code>10<sup>9</sup> + 7</code>.
+
+#### Example 1:
+<pre>
+<strong>Input:</strong> n = 6, delay = 2, forget = 4
+<strong>Output:</strong> 5
+<strong>Explanation:</strong>
+Day 1: Suppose the first person is named A. (1 person)
+Day 2: A is the only person who knows the secret. (1 person)
+Day 3: A shares the secret with a new person, B. (2 people)
+Day 4: A shares the secret with a new person, C. (3 people)
+Day 5: A forgets the secret, and B shares the secret with a new person, D. (3 people)
+Day 6: B shares the secret with E, and C shares the secret with F. (5 people)
+</pre>
+
+#### Example 2:
+<pre>
+<strong>Input:</strong> n = 4, delay = 1, forget = 3
+<strong>Output:</strong> 6
+<strong>Explanation:</strong>
+Day 1: The first person is named A. (1 person)
+Day 2: A shares the secret with B. (2 people)
+Day 3: A and B share the secret with 2 new people, C and D. (4 people)
+Day 4: A forgets the secret. B, C, and D share the secret with 3 new people. (6 people)
+</pre>
+
+#### Constraints:
+* `2 <= n <= 1000`
+* `1 <= delay < forget <= n`
+
+## Solutions (Python)
+
+### 1. Solution
+```Python
+class Solution:
+    def peopleAwareOfSecret(self, n: int, delay: int, forget: int) -> int:
+        dp = [[0, 0, 0] for _ in range(n + 2)]
+        dp[1 + forget][0] = 1
+        dp[1 + delay][1] = 1
+        dp[1][2] = 1
+
+        for i in range(2, n + 1):
+            if i > 1 + forget:
+                dp[i][0] = dp[i - forget][1]
+            if i > 1 + delay:
+                dp[i][1] = dp[i - 1][1] - dp[i][0] + dp[i - delay][1]
+            dp[i][2] = dp[i - 1][2] - dp[i][0] + dp[i][1]
+
+        return dp[n][2] % 1000000007
+```
diff --git a/Problemset/2327-Number of People Aware of a Secret/README_CN.md b/Problemset/2327-Number of People Aware of a Secret/README_CN.md
@@ -0,0 +1,55 @@
+# 2327. 知道秘密的人数
+在第 `1` 天，有一个人发现了一个秘密。
+
+给你一个整数 `delay` ，表示每个人会在发现秘密后的 `delay` 天之后，**每天** 给一个新的人 **分享** 秘密。同时给你一个整数 `forget` ，表示每个人在发现秘密 `forget` 天之后会 **忘记** 这个秘密。一个人 **不能** 在忘记秘密那一天及之后的日子里分享秘密。
+
+给你一个整数 `n` ，请你返回在第 `n` 天结束时，知道秘密的人数。由于答案可能会很大，请你将结果对 <code>10<sup>9</sup> + 7</code> **取余** 后返回。
+
+#### 示例 1:
+<pre>
+<strong>输入:</strong> n = 6, delay = 2, forget = 4
+<strong>输出:</strong> 5
+<strong>解释:</strong>
+第 1 天：假设第一个人叫 A 。（一个人知道秘密）
+第 2 天：A 是唯一一个知道秘密的人。（一个人知道秘密）
+第 3 天：A 把秘密分享给 B 。（两个人知道秘密）
+第 4 天：A 把秘密分享给一个新的人 C 。（三个人知道秘密）
+第 5 天：A 忘记了秘密，B 把秘密分享给一个新的人 D 。（三个人知道秘密）
+第 6 天：B 把秘密分享给 E，C 把秘密分享给 F 。（五个人知道秘密）
+</pre>
+
+#### 示例 2:
+<pre>
+<strong>输入:</strong> n = 4, delay = 1, forget = 3
+<strong>输出:</strong> 6
+<strong>解释:</strong>
+第 1 天：第一个知道秘密的人为 A 。（一个人知道秘密）
+第 2 天：A 把秘密分享给 B 。（两个人知道秘密）
+第 3 天：A 和 B 把秘密分享给 2 个新的人 C 和 D 。（四个人知道秘密）
+第 4 天：A 忘记了秘密，B、C、D 分别分享给 3 个新的人。（六个人知道秘密）
+</pre>
+
+#### 提示:
+* `2 <= n <= 1000`
+* `1 <= delay < forget <= n`
+
+## 题解 (Python)
+
+### 1. 题解
+```Python
+class Solution:
+    def peopleAwareOfSecret(self, n: int, delay: int, forget: int) -> int:
+        dp = [[0, 0, 0] for _ in range(n + 2)]
+        dp[1 + forget][0] = 1
+        dp[1 + delay][1] = 1
+        dp[1][2] = 1
+
+        for i in range(2, n + 1):
+            if i > 1 + forget:
+                dp[i][0] = dp[i - forget][1]
+            if i > 1 + delay:
+                dp[i][1] = dp[i - 1][1] - dp[i][0] + dp[i - delay][1]
+            dp[i][2] = dp[i - 1][2] - dp[i][0] + dp[i][1]
+
+        return dp[n][2] % 1000000007
+```
diff --git a/Problemset/2327-Number of People Aware of a Secret/Solution.py b/Problemset/2327-Number of People Aware of a Secret/Solution.py
@@ -0,0 +1,15 @@
+class Solution:
+    def peopleAwareOfSecret(self, n: int, delay: int, forget: int) -> int:
+        dp = [[0, 0, 0] for _ in range(n + 2)]
+        dp[1 + forget][0] = 1
+        dp[1 + delay][1] = 1
+        dp[1][2] = 1
+
+        for i in range(2, n + 1):
+            if i > 1 + forget:
+                dp[i][0] = dp[i - forget][1]
+            if i > 1 + delay:
+                dp[i][1] = dp[i - 1][1] - dp[i][0] + dp[i - delay][1]
+            dp[i][2] = dp[i - 1][2] - dp[i][0] + dp[i][1]
+
+        return dp[n][2] % 1000000007
diff --git a/README.md b/README.md
@@ -1173,6 +1173,7 @@
 [2320][2320l]|[Count Number of Ways to Place Houses][2320]                                          |![rs]
 [2325][2325l]|[Decode the Message][2325]                                                            |![py]
 [2326][2326l]|[Spiral Matrix IV][2326]                                                              |![py]
+[2327][2327l]|[Number of People Aware of a Secret][2327]                                            |![py]
 [2331][2331l]|[Evaluate Boolean Binary Tree][2331]                                                  |![py]
 [2335][2335l]|[Minimum Amount of Time to Fill Cups][2335]                                           |![rs]
 [2336][2336l]|[Smallest Number in Infinite Set][2336]                                               |![rs]
@@ -2466,6 +2467,7 @@
 [2320]:Problemset/2320-Count%20Number%20of%20Ways%20to%20Place%20Houses/README.md#2320-count-number-of-ways-to-place-houses
 [2325]:Problemset/2325-Decode%20the%20Message/README.md#2325-decode-the-message
 [2326]:Problemset/2326-Spiral%20Matrix%20IV/README.md#2326-spiral-matrix-iv
+[2327]:Problemset/2327-Number%20of%20People%20Aware%20of%20a%20Secret/README.md#2327-number-of-people-aware-of-a-secret
 [2331]:Problemset/2331-Evaluate%20Boolean%20Binary%20Tree/README.md#2331-evaluate-boolean-binary-tree
 [2335]:Problemset/2335-Minimum%20Amount%20of%20Time%20to%20Fill%20Cups/README.md#2335-minimum-amount-of-time-to-fill-cups
 [2336]:Problemset/2336-Smallest%20Number%20in%20Infinite%20Set/README.md#2336-smallest-number-in-infinite-set
@@ -3762,6 +3764,7 @@
 [2320l]:https://leetcode.com/problems/count-number-of-ways-to-place-houses/
 [2325l]:https://leetcode.com/problems/decode-the-message/
 [2326l]:https://leetcode.com/problems/spiral-matrix-iv/
+[2327l]:https://leetcode.com/problems/number-of-people-aware-of-a-secret/
 [2331l]:https://leetcode.com/problems/evaluate-boolean-binary-tree/
 [2335l]:https://leetcode.com/problems/minimum-amount-of-time-to-fill-cups/
 [2336l]:https://leetcode.com/problems/smallest-number-in-infinite-set/
diff --git a/README_CN.md b/README_CN.md
@@ -1173,6 +1173,7 @@
 [2320][2320l]|[统计放置房子的方式数][2320]                              |![rs]
 [2325][2325l]|[解密消息][2325]                                          |![py]
 [2326][2326l]|[螺旋矩阵 IV][2326]                                       |![py]
+[2327][2327l]|[知道秘密的人数][2327]                                    |![py]
 [2331][2331l]|[计算布尔二叉树的值][2331]                                |![py]
 [2335][2335l]|[装满杯子需要的最短总时长][2335]                          |![rs]
 [2336][2336l]|[无限集中的最小数字][2336]                                |![rs]
@@ -2466,6 +2467,7 @@
 [2320]:Problemset/2320-Count%20Number%20of%20Ways%20to%20Place%20Houses/README_CN.md#2320-统计放置房子的方式数
 [2325]:Problemset/2325-Decode%20the%20Message/README_CN.md#2325-解密消息
 [2326]:Problemset/2326-Spiral%20Matrix%20IV/README_CN.md#2326-螺旋矩阵-iv
+[2327]:Problemset/2327-Number%20of%20People%20Aware%20of%20a%20Secret/README_CN.md#2327-知道秘密的人数
 [2331]:Problemset/2331-Evaluate%20Boolean%20Binary%20Tree/README_CN.md#2331-计算布尔二叉树的值
 [2335]:Problemset/2335-Minimum%20Amount%20of%20Time%20to%20Fill%20Cups/README_CN.md#2335-装满杯子需要的最短总时长
 [2336]:Problemset/2336-Smallest%20Number%20in%20Infinite%20Set/README_CN.md#2336-无限集中的最小数字
@@ -3762,6 +3764,7 @@
 [2320l]:https://leetcode.cn/problems/count-number-of-ways-to-place-houses/
 [2325l]:https://leetcode.cn/problems/decode-the-message/
 [2326l]:https://leetcode.cn/problems/spiral-matrix-iv/
+[2327l]:https://leetcode.cn/problems/number-of-people-aware-of-a-secret/
 [2331l]:https://leetcode.cn/problems/evaluate-boolean-binary-tree/
 [2335l]:https://leetcode.cn/problems/minimum-amount-of-time-to-fill-cups/
 [2336l]:https://leetcode.cn/problems/smallest-number-in-infinite-set/
