leetcode-problemset/leetcode-cn/originData/count-ways-to-build-rooms-in-an-ant-colony.json

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            "questionId": "1313",
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            "categoryTitle": "Algorithms",
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            "title": "Count Ways to Build Rooms in an Ant Colony",
            "titleSlug": "count-ways-to-build-rooms-in-an-ant-colony",
            "content": "<p>You are an ant tasked with adding <code>n</code> new rooms numbered <code>0</code> to <code>n-1</code> to your colony. You are given the expansion plan as a <strong>0-indexed</strong> integer array of length <code>n</code>, <code>prevRoom</code>, where <code>prevRoom[i]</code> indicates that you must build room <code>prevRoom[i]</code> before building room <code>i</code>, and these two rooms must be connected <strong>directly</strong>. Room <code>0</code> is already built, so <code>prevRoom[0] = -1</code>. The expansion&nbsp;plan is given such that once all the rooms are built, every room will be reachable from room <code>0</code>.</p>\r\n\r\n<p>You can only build <strong>one room</strong> at a time, and you can travel freely between rooms you have <strong>already built</strong> only if they are <strong>connected</strong>.&nbsp;You can choose to build <strong>any room</strong> as long as its <strong>previous room</strong>&nbsp;is already built.</p>\r\n\r\n<p>Return <em>the <strong>number of different orders</strong> you can build all the rooms in</em>. Since the answer may be large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>\r\n\r\n<p>&nbsp;</p>\r\n<p><strong class=\"example\">Example 1:</strong></p>\r\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/06/19/d1.JPG\" style=\"width: 200px; height: 212px;\" />\r\n<pre>\r\n<strong>Input:</strong> prevRoom = [-1,0,1]\r\n<strong>Output:</strong> 1\r\n<strong>Explanation:</strong>&nbsp;There is only one way to build the additional rooms: 0 &rarr; 1 &rarr; 2\r\n</pre>\r\n\r\n<p><strong class=\"example\">Example 2:</strong></p>\r\n<strong><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/06/19/d2.JPG\" style=\"width: 200px; height: 239px;\" /></strong>\r\n\r\n<pre>\r\n<strong>Input:</strong> prevRoom = [-1,0,0,1,2]\r\n<strong>Output:</strong> 6\r\n<strong>Explanation:\r\n</strong>The 6 ways are:\r\n0 &rarr; 1 &rarr; 3 &rarr; 2 &rarr; 4\r\n0 &rarr; 2 &rarr; 4 &rarr; 1 &rarr; 3\r\n0 &rarr; 1 &rarr; 2 &rarr; 3 &rarr; 4\r\n0 &rarr; 1 &rarr; 2 &rarr; 4 &rarr; 3\r\n0 &rarr; 2 &rarr; 1 &rarr; 3 &rarr; 4\r\n0 &rarr; 2 &rarr; 1 &rarr; 4 &rarr; 3\r\n</pre>\r\n\r\n<p>&nbsp;</p>\r\n<p><strong>Constraints:</strong></p>\r\n\r\n<ul>\r\n\t<li><code>n == prevRoom.length</code></li>\r\n\t<li><code>2 &lt;= n &lt;= 10<sup>5</sup></code></li>\r\n\t<li><code>prevRoom[0] == -1</code></li>\r\n\t<li><code>0 &lt;= prevRoom[i] &lt; n</code> for all <code>1 &lt;= i &lt; n</code></li>\r\n\t<li>Every room is reachable from room <code>0</code> once all the rooms are built.</li>\r\n</ul>",
            "translatedTitle": "统计为蚁群构筑房间的不同顺序",
            "translatedContent": "<p>你是一只蚂蚁，负责为蚁群构筑 <code>n</code> 间编号从 <code>0</code> 到 <code>n-1</code> 的新房间。给你一个 <strong>下标从 0 开始</strong> 且长度为 <code>n</code> 的整数数组&nbsp;<code>prevRoom</code> 作为扩建计划。其中，<code>prevRoom[i]</code> 表示在构筑房间 <code>i</code> 之前，你必须先构筑房间 <code>prevRoom[i]</code> ，并且这两个房间必须 <strong>直接</strong> 相连。房间 <code>0</code> 已经构筑完成，所以 <code>prevRoom[0] = -1</code> 。扩建计划中还有一条硬性要求，在完成所有房间的构筑之后，从房间 <code>0</code> 可以访问到每个房间。</p>\n\n<p>你一次只能构筑 <strong>一个</strong> 房间。你可以在 <strong>已经构筑好的</strong> 房间之间自由穿行，只要这些房间是 <strong>相连的</strong> 。如果房间&nbsp;<code>prevRoom[i]</code> 已经构筑完成，那么你就可以构筑房间 <code>i</code>。</p>\n\n<p>返回你构筑所有房间的 <strong>不同顺序的数目</strong> 。由于答案可能很大，请返回对 <code>10<sup>9</sup> + 7</code> <strong>取余</strong> 的结果。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/06/19/d1.JPG\" style=\"width: 200px; height: 212px;\" />\n<pre>\n<strong>输入：</strong><code>prevRoom</code> = [-1,0,1]\n<strong>输出：</strong>1\n<strong>解释：</strong>仅有一种方案可以完成所有房间的构筑：0 → 1 → 2\n</pre>\n\n<p><strong>示例 2：</strong></p>\n<strong><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/06/19/d2.JPG\" style=\"width: 200px; height: 239px;\" /></strong>\n\n<pre>\n<strong>输入：</strong><code>prevRoom</code> = [-1,0,0,1,2]\n<strong>输出：</strong>6\n<strong>解释：\n</strong>有 6 种不同顺序：\n0 → 1 → 3 → 2 → 4\n0 → 2 → 4 → 1 → 3\n0 → 1 → 2 → 3 → 4\n0 → 1 → 2 → 4 → 3\n0 → 2 → 1 → 3 → 4\n0 → 2 → 1 → 4 → 3\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>n == prevRoom.length</code></li>\n\t<li><code>2 &lt;= n &lt;= 10<sup>5</sup></code></li>\n\t<li><code>prevRoom[0] == -1</code></li>\n\t<li>对于所有的&nbsp;<code>1 &lt;= i &lt; n</code>&nbsp;，都有&nbsp;<code>0 &lt;= prevRoom[i] &lt; n</code></li>\n\t<li>题目保证所有房间都构筑完成后，从房间 <code>0</code> 可以访问到每个房间</li>\n</ul>\n",
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