leetcode-problemset/leetcode-cn/originData/count-nodes-with-the-highest-score.json

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        "question": {
            "questionId": "2175",
            "questionFrontendId": "2049",
            "categoryTitle": "Algorithms",
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            "title": "Count Nodes With the Highest Score",
            "titleSlug": "count-nodes-with-the-highest-score",
            "content": "<p>There is a <strong>binary</strong> tree rooted at <code>0</code> consisting of <code>n</code> nodes. The nodes are labeled from <code>0</code> to <code>n - 1</code>. You are given a <strong>0-indexed</strong> integer array <code>parents</code> representing the tree, where <code>parents[i]</code> is the parent of node <code>i</code>. Since node <code>0</code> is the root, <code>parents[0] == -1</code>.</p>\n\n<p>Each node has a <strong>score</strong>. To find the score of a node, consider if the node and the edges connected to it were <strong>removed</strong>. The tree would become one or more <strong>non-empty</strong> subtrees. The <strong>size</strong> of a subtree is the number of the nodes in it. The <strong>score</strong> of the node is the <strong>product of the sizes</strong> of all those subtrees.</p>\n\n<p>Return <em>the <strong>number</strong> of nodes that have the <strong>highest score</strong></em>.</p>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n<img alt=\"example-1\" src=\"https://assets.leetcode.com/uploads/2021/10/03/example-1.png\" style=\"width: 604px; height: 266px;\" />\n<pre>\n<strong>Input:</strong> parents = [-1,2,0,2,0]\n<strong>Output:</strong> 3\n<strong>Explanation:</strong>\n- The score of node 0 is: 3 * 1 = 3\n- The score of node 1 is: 4 = 4\n- The score of node 2 is: 1 * 1 * 2 = 2\n- The score of node 3 is: 4 = 4\n- The score of node 4 is: 4 = 4\nThe highest score is 4, and three nodes (node 1, node 3, and node 4) have the highest score.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n<img alt=\"example-2\" src=\"https://assets.leetcode.com/uploads/2021/10/03/example-2.png\" style=\"width: 95px; height: 143px;\" />\n<pre>\n<strong>Input:</strong> parents = [-1,2,0]\n<strong>Output:</strong> 2\n<strong>Explanation:</strong>\n- The score of node 0 is: 2 = 2\n- The score of node 1 is: 2 = 2\n- The score of node 2 is: 1 * 1 = 1\nThe highest score is 2, and two nodes (node 0 and node 1) have the highest score.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>n == parents.length</code></li>\n\t<li><code>2 &lt;= n &lt;= 10<sup>5</sup></code></li>\n\t<li><code>parents[0] == -1</code></li>\n\t<li><code>0 &lt;= parents[i] &lt;= n - 1</code> for <code>i != 0</code></li>\n\t<li><code>parents</code> represents a valid binary tree.</li>\n</ul>\n",
            "translatedTitle": "统计最高分的节点数目",
            "translatedContent": "<p>给你一棵根节点为 <code>0</code> 的&nbsp;<strong>二叉树</strong>&nbsp;，它总共有 <code>n</code>&nbsp;个节点，节点编号为&nbsp;<code>0</code>&nbsp;到&nbsp;<code>n - 1</code>&nbsp;。同时给你一个下标从&nbsp;<strong>0</strong>&nbsp;开始的整数数组&nbsp;<code>parents</code>&nbsp;表示这棵树，其中&nbsp;<code>parents[i]</code>&nbsp;是节点 <code>i</code>&nbsp;的父节点。由于节点 <code>0</code>&nbsp;是根，所以&nbsp;<code>parents[0] == -1</code>&nbsp;。</p>\n\n<p>一个子树的 <strong>大小</strong>&nbsp;为这个子树内节点的数目。每个节点都有一个与之关联的&nbsp;<strong>分数</strong>&nbsp;。求出某个节点分数的方法是，将这个节点和与它相连的边全部 <strong>删除</strong>&nbsp;，剩余部分是若干个 <strong>非空</strong>&nbsp;子树，这个节点的 <strong>分数</strong>&nbsp;为所有这些子树 <strong>大小的乘积</strong>&nbsp;。</p>\n\n<p>请你返回有 <strong>最高得分</strong>&nbsp;节点的 <strong>数目</strong>&nbsp;。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例&nbsp;1:</strong></p>\n\n<p><img alt=\"example-1\" src=\"https://assets.leetcode.com/uploads/2021/10/03/example-1.png\" style=\"width: 604px; height: 266px;\"></p>\n\n<pre><b>输入：</b>parents = [-1,2,0,2,0]\n<b>输出：</b>3\n<strong>解释：</strong>\n- 节点 0 的分数为：3 * 1 = 3\n- 节点 1 的分数为：4 = 4\n- 节点 2 的分数为：1 * 1 * 2 = 2\n- 节点 3 的分数为：4 = 4\n- 节点 4 的分数为：4 = 4\n最高得分为 4 ，有三个节点得分为 4 （分别是节点 1，3 和 4 ）。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<p><img alt=\"example-2\" src=\"https://assets.leetcode.com/uploads/2021/10/03/example-2.png\" style=\"width: 95px; height: 143px;\"></p>\n\n<pre><b>输入：</b>parents = [-1,2,0]\n<b>输出：</b>2\n<strong>解释：</strong>\n- 节点 0 的分数为：2 = 2\n- 节点 1 的分数为：2 = 2\n- 节点 2 的分数为：1 * 1 = 1\n最高分数为 2 ，有两个节点分数为 2 （分别为节点 0 和 1 ）。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>n == parents.length</code></li>\n\t<li><code>2 &lt;= n &lt;= 10<sup>5</sup></code></li>\n\t<li><code>parents[0] == -1</code></li>\n\t<li>对于&nbsp;<code>i != 0</code>&nbsp;，有&nbsp;<code>0 &lt;= parents[i] &lt;= n - 1</code></li>\n\t<li><code>parents</code>&nbsp;表示一棵二叉树。</li>\n</ul>\n",
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            "hints": [
                "For each node, you need to find the sizes of the subtrees rooted in each of its children. Maybe DFS?",
                "How to determine the number of nodes in the rest of the tree? Can you subtract the size of the subtree rooted at the node from the total number of nodes of the tree?",
                "Use these values to compute the score of the node. Track the maximum score, and how many nodes achieve such score."
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