leetcode-problemset/leetcode-cn/originData/count-number-of-possible-root-nodes.json

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        "question": {
            "questionId": "2652",
            "questionFrontendId": "2581",
            "categoryTitle": "Algorithms",
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            "title": "Count Number of Possible Root Nodes",
            "titleSlug": "count-number-of-possible-root-nodes",
            "content": "<p>Alice has an undirected tree with <code>n</code> nodes labeled from <code>0</code> to <code>n - 1</code>. The tree is represented as a 2D integer array <code>edges</code> of length <code>n - 1</code> where <code>edges[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> indicates that there is an edge between nodes <code>a<sub>i</sub></code> and <code>b<sub>i</sub></code> in the tree.</p>\n\n<p>Alice wants Bob to find the root of the tree. She allows Bob to make several <strong>guesses</strong> about her tree. In one guess, he does the following:</p>\n\n<ul>\n\t<li>Chooses two <strong>distinct</strong> integers <code>u</code> and <code>v</code> such that there exists an edge <code>[u, v]</code> in the tree.</li>\n\t<li>He tells Alice that <code>u</code> is the <strong>parent</strong> of <code>v</code> in the tree.</li>\n</ul>\n\n<p>Bob&#39;s guesses are represented by a 2D integer array <code>guesses</code> where <code>guesses[j] = [u<sub>j</sub>, v<sub>j</sub>]</code> indicates Bob guessed <code>u<sub>j</sub></code> to be the parent of <code>v<sub>j</sub></code>.</p>\n\n<p>Alice being lazy, does not reply to each of Bob&#39;s guesses, but just says that <strong>at least</strong> <code>k</code> of his guesses are <code>true</code>.</p>\n\n<p>Given the 2D integer arrays <code>edges</code>, <code>guesses</code> and the integer <code>k</code>, return <em>the <strong>number of possible nodes</strong> that can be the root of Alice&#39;s tree</em>. If there is no such tree, return <code>0</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/12/19/ex-1.png\" style=\"width: 727px; height: 250px;\" /></p>\n\n<pre>\n<strong>Input:</strong> edges = [[0,1],[1,2],[1,3],[4,2]], guesses = [[1,3],[0,1],[1,0],[2,4]], k = 3\n<strong>Output:</strong> 3\n<strong>Explanation:</strong> \nRoot = 0, correct guesses = [1,3], [0,1], [2,4]\nRoot = 1, correct guesses = [1,3], [1,0], [2,4]\nRoot = 2, correct guesses = [1,3], [1,0], [2,4]\nRoot = 3, correct guesses = [1,0], [2,4]\nRoot = 4, correct guesses = [1,3], [1,0]\nConsidering 0, 1, or 2 as root node leads to 3 correct guesses.\n\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/12/19/ex-2.png\" style=\"width: 600px; height: 303px;\" /></p>\n\n<pre>\n<strong>Input:</strong> edges = [[0,1],[1,2],[2,3],[3,4]], guesses = [[1,0],[3,4],[2,1],[3,2]], k = 1\n<strong>Output:</strong> 5\n<strong>Explanation:</strong> \nRoot = 0, correct guesses = [3,4]\nRoot = 1, correct guesses = [1,0], [3,4]\nRoot = 2, correct guesses = [1,0], [2,1], [3,4]\nRoot = 3, correct guesses = [1,0], [2,1], [3,2], [3,4]\nRoot = 4, correct guesses = [1,0], [2,1], [3,2]\nConsidering any node as root will give at least 1 correct guess. \n\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>edges.length == n - 1</code></li>\n\t<li><code>2 &lt;= n &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= guesses.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub>, u<sub>j</sub>, v<sub>j</sub> &lt;= n - 1</code></li>\n\t<li><code>a<sub>i</sub> != b<sub>i</sub></code></li>\n\t<li><code>u<sub>j</sub> != v<sub>j</sub></code></li>\n\t<li><code>edges</code> represents a valid tree.</li>\n\t<li><code>guesses[j]</code> is an edge of the tree.</li>\n\t<li><code>guesses</code> is unique.</li>\n\t<li><code>0 &lt;= k &lt;= guesses.length</code></li>\n</ul>\n",
            "translatedTitle": "统计可能的树根数目",
            "translatedContent": "<p>Alice 有一棵 <code>n</code> 个节点的树，节点编号为 <code>0</code> 到 <code>n - 1</code> 。树用一个长度为 <code>n - 1</code> 的二维整数数组 <code>edges</code> 表示，其中 <code>edges[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> ，表示树中节点 <code>a<sub>i</sub></code> 和 <code>b<sub>i</sub></code> 之间有一条边。</p>\n\n<p>Alice 想要 Bob 找到这棵树的根。她允许 Bob 对这棵树进行若干次 <strong>猜测</strong> 。每一次猜测，Bob 做如下事情：</p>\n\n<ul>\n\t<li>选择两个 <strong>不相等</strong>&nbsp;的整数&nbsp;<code>u</code> 和&nbsp;<code>v</code>&nbsp;，且树中必须存在边&nbsp;<code>[u, v]</code>&nbsp;。</li>\n\t<li>Bob 猜测树中&nbsp;<code>u</code>&nbsp;是&nbsp;<code>v</code>&nbsp;的 <strong>父节点</strong>&nbsp;。</li>\n</ul>\n\n<p>Bob 的猜测用二维整数数组&nbsp;<code>guesses</code> 表示，其中&nbsp;<code>guesses[j] = [u<sub>j</sub>, v<sub>j</sub>]</code>&nbsp;表示 Bob 猜&nbsp;<code>u<sub>j</sub></code> 是&nbsp;<code>v<sub>j</sub></code>&nbsp;的父节点。</p>\n\n<p>Alice 非常懒，她不想逐个回答&nbsp;Bob 的猜测，只告诉 Bob 这些猜测里面 <strong>至少</strong>&nbsp;有&nbsp;<code>k</code>&nbsp;个猜测的结果为&nbsp;<code>true</code>&nbsp;。</p>\n\n<p>给你二维整数数组 <code>edges</code>&nbsp;，Bob 的所有猜测和整数&nbsp;<code>k</code>&nbsp;，请你返回可能成为树根的&nbsp;<strong>节点数目</strong>&nbsp;。如果没有这样的树，则返回 <code>0</code>。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/12/19/ex-1.png\" style=\"width: 727px; height: 250px;\" /></p>\n\n<pre>\n<b>输入：</b>edges = [[0,1],[1,2],[1,3],[4,2]], guesses = [[1,3],[0,1],[1,0],[2,4]], k = 3\n<b>输出：</b>3\n<b>解释：</b>\n根为节点 0 ，正确的猜测为 [1,3], [0,1], [2,4]\n根为节点 1 ，正确的猜测为 [1,3], [1,0], [2,4]\n根为节点 2 ，正确的猜测为 [1,3], [1,0], [2,4]\n根为节点 3 ，正确的猜测为 [1,0], [2,4]\n根为节点 4 ，正确的猜测为 [1,3], [1,0]\n节点 0 ，1 或 2 为根时，可以得到 3 个正确的猜测。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/12/19/ex-2.png\" style=\"width: 600px; height: 303px;\" /></p>\n\n<pre>\n<b>输入：</b>edges = [[0,1],[1,2],[2,3],[3,4]], guesses = [[1,0],[3,4],[2,1],[3,2]], k = 1\n<b>输出：</b>5\n<b>解释：</b>\n根为节点 0 ，正确的猜测为 [3,4]\n根为节点 1 ，正确的猜测为 [1,0], [3,4]\n根为节点 2 ，正确的猜测为 [1,0], [2,1], [3,4]\n根为节点 3 ，正确的猜测为 [1,0], [2,1], [3,2], [3,4]\n根为节点 4 ，正确的猜测为 [1,0], [2,1], [3,2]\n任何节点为根，都至少有 1 个正确的猜测。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>edges.length == n - 1</code></li>\n\t<li><code>2 &lt;= n &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= guesses.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub>, u<sub>j</sub>, v<sub>j</sub> &lt;= n - 1</code></li>\n\t<li><code>a<sub>i</sub> != b<sub>i</sub></code></li>\n\t<li><code>u<sub>j</sub> != v<sub>j</sub></code></li>\n\t<li><code>edges</code>&nbsp;表示一棵有效的树。</li>\n\t<li><code>guesses[j]</code>&nbsp;是树中的一条边。</li>\n\t<li><code>guesses</code>&nbsp;是唯一的。</li>\n\t<li><code>0 &lt;= k &lt;= guesses.length</code></li>\n</ul>\n",
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