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"question": {
"questionId": "2408",
"questionFrontendId": "2327",
"categoryTitle": "Algorithms",
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"title": "Number of People Aware of a Secret",
"titleSlug": "number-of-people-aware-of-a-secret",
"content": "<p>On day <code>1</code>, one person discovers a secret.</p>\n\n<p>You are given an integer <code>delay</code>, which means that each person will <strong>share</strong> the secret with a new person <strong>every day</strong>, starting from <code>delay</code> days after discovering the secret. You are also given an integer <code>forget</code>, which means that each person will <strong>forget</strong> the secret <code>forget</code> days after discovering it. A person <strong>cannot</strong> share the secret on the same day they forgot it, or on any day afterwards.</p>\n\n<p>Given an integer <code>n</code>, return<em> the number of people who know the secret at the end of day </em><code>n</code>. Since the answer may be very large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 6, delay = 2, forget = 4\n<strong>Output:</strong> 5\n<strong>Explanation:</strong>\nDay 1: Suppose the first person is named A. (1 person)\nDay 2: A is the only person who knows the secret. (1 person)\nDay 3: A shares the secret with a new person, B. (2 people)\nDay 4: A shares the secret with a new person, C. (3 people)\nDay 5: A forgets the secret, and B shares the secret with a new person, D. (3 people)\nDay 6: B shares the secret with E, and C shares the secret with F. (5 people)\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 4, delay = 1, forget = 3\n<strong>Output:</strong> 6\n<strong>Explanation:</strong>\nDay 1: The first person is named A. (1 person)\nDay 2: A shares the secret with B. (2 people)\nDay 3: A and B share the secret with 2 new people, C and D. (4 people)\nDay 4: A forgets the secret. B, C, and D share the secret with 3 new people. (6 people)\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= n &lt;= 1000</code></li>\n\t<li><code>1 &lt;= delay &lt; forget &lt;= n</code></li>\n</ul>\n",
"translatedTitle": "知道秘密的人数",
"translatedContent": "<p>在第 <code>1</code>&nbsp;天,有一个人发现了一个秘密。</p>\n\n<p>给你一个整数&nbsp;<code>delay</code>&nbsp;,表示每个人会在发现秘密后的 <code>delay</code>&nbsp;天之后,<strong>每天</strong>&nbsp;给一个新的人&nbsp;<strong>分享</strong>&nbsp;秘密。同时给你一个整数&nbsp;<code>forget</code>&nbsp;,表示每个人在发现秘密&nbsp;<code>forget</code>&nbsp;天之后会&nbsp;<strong>忘记</strong>&nbsp;这个秘密。一个人&nbsp;<strong>不能</strong>&nbsp;在忘记秘密那一天及之后的日子里分享秘密。</p>\n\n<p>给你一个整数&nbsp;<code>n</code>&nbsp;,请你返回在第 <code>n</code>&nbsp;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&nbsp;<code>10<sup>9</sup> + 7</code>&nbsp;<strong>取余</strong>&nbsp;后返回。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1</strong></p>\n\n<pre><b>输入:</b>n = 6, delay = 2, forget = 4\n<b>输出:</b>5\n<strong>解释:</strong>\n第 1 天:假设第一个人叫 A 。(一个人知道秘密)\n第 2 天A 是唯一一个知道秘密的人。(一个人知道秘密)\n第 3 天A 把秘密分享给 B 。(两个人知道秘密)\n第 4 天A 把秘密分享给一个新的人 C 。(三个人知道秘密)\n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)\n第 6 天B 把秘密分享给 EC 把秘密分享给 F 。(五个人知道秘密)\n</pre>\n\n<p><strong>示例 2</strong></p>\n\n<pre><b>输入:</b>n = 4, delay = 1, forget = 3\n<b>输出:</b>6\n<strong>解释:</strong>\n第 1 天:第一个知道秘密的人为 A 。(一个人知道秘密)\n第 2 天A 把秘密分享给 B 。(两个人知道秘密)\n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)\n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)\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示:</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= n &lt;= 1000</code></li>\n\t<li><code>1 &lt;= delay &lt; forget &lt;= n</code></li>\n</ul>\n",
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"Let dp[i][j] be the number of people who have known the secret for exactly j + 1 days, at day i.",
"If j > 0, dp[i][j] = dp[i 1][j 1].",
"dp[i][0] = sum(dp[i 1][j]) for j in [delay 1, forget 2]."
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