leetcode-problemset/leetcode-cn/originData/count-paths-that-can-form-a-palindrome-in-a-tree.json

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            "categoryTitle": "Algorithms",
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            "title": "Count Paths That Can Form a Palindrome in a Tree",
            "titleSlug": "count-paths-that-can-form-a-palindrome-in-a-tree",
            "content": "<p>You are given a <strong>tree</strong> (i.e. a connected, undirected graph that has no cycles) <strong>rooted</strong> at node <code>0</code> consisting of <code>n</code> nodes numbered from <code>0</code> to <code>n - 1</code>. The tree is represented by a <strong>0-indexed</strong> array <code>parent</code> of size <code>n</code>, where <code>parent[i]</code> is the parent of node <code>i</code>. Since node <code>0</code> is the root, <code>parent[0] == -1</code>.</p>\n\n<p>You are also given a string <code>s</code> of length <code>n</code>, where <code>s[i]</code> is the character assigned to the edge between <code>i</code> and <code>parent[i]</code>. <code>s[0]</code> can be ignored.</p>\n\n<p>Return <em>the number of pairs of nodes </em><code>(u, v)</code><em> such that </em><code>u &lt; v</code><em> and the characters assigned to edges on the path from </em><code>u</code><em> to </em><code>v</code><em> can be <strong>rearranged</strong> to form a <strong>palindrome</strong></em>.</p>\n\n<p>A string is a <strong>palindrome</strong> when it reads the same backwards as forwards.</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/2023/07/15/treedrawio-8drawio.png\" style=\"width: 281px; height: 181px;\" /></p>\n\n<pre>\n<strong>Input:</strong> parent = [-1,0,0,1,1,2], s = &quot;acaabc&quot;\n<strong>Output:</strong> 8\n<strong>Explanation:</strong> The valid pairs are:\n- All the pairs (0,1), (0,2), (1,3), (1,4) and (2,5) result in one character which is always a palindrome.\n- The pair (2,3) result in the string &quot;aca&quot; which is a palindrome.\n- The pair (1,5) result in the string &quot;cac&quot; which is a palindrome.\n- The pair (3,5) result in the string &quot;acac&quot; which can be rearranged into the palindrome &quot;acca&quot;.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> parent = [-1,0,0,0,0], s = &quot;aaaaa&quot;\n<strong>Output:</strong> 10\n<strong>Explanation:</strong> Any pair of nodes (u,v) where u &lt; v is valid.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>n == parent.length == s.length</code></li>\n\t<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>\n\t<li><code>0 &lt;= parent[i] &lt;= n - 1</code> for all <code>i &gt;= 1</code></li>\n\t<li><code>parent[0] == -1</code></li>\n\t<li><code>parent</code> represents a valid tree.</li>\n\t<li><code>s</code> consists of only lowercase English letters.</li>\n</ul>\n",
            "translatedTitle": "树中可以形成回文的路径数",
            "translatedContent": "<p>给你一棵 <strong>树</strong>（即，一个连通、无向且无环的图），<strong>根</strong> 节点为 <code>0</code> ，由编号从 <code>0</code> 到 <code>n - 1</code> 的 <code>n</code> 个节点组成。这棵树用一个长度为 <code>n</code> 、下标从 <strong>0</strong> 开始的数组 <code>parent</code> 表示，其中 <code>parent[i]</code> 为节点 <code>i</code> 的父节点，由于节点 <code>0</code> 为根节点，所以 <code>parent[0] == -1</code> 。</p>\n\n<p>另给你一个长度为 <code>n</code> 的字符串 <code>s</code> ，其中 <code>s[i]</code> 是分配给 <code>i</code> 和 <code>parent[i]</code> 之间的边的字符。<code>s[0]</code> 可以忽略。</p>\n\n<p>找出满足 <code>u &lt; v</code> ，且从 <code>u</code> 到 <code>v</code> 的路径上分配的字符可以 <strong>重新排列</strong> 形成 <strong>回文</strong> 的所有节点对&nbsp;<code>(u, v)</code> ，并返回节点对的数目。</p>\n\n<p>如果一个字符串正着读和反着读都相同，那么这个字符串就是一个 <strong>回文</strong> 。</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/2023/07/15/treedrawio-8drawio.png\" style=\"width: 281px; height: 181px;\" /></p>\n\n<pre>\n<strong>输入：</strong>parent = [-1,0,0,1,1,2], s = \"acaabc\"\n<strong>输出：</strong>8\n<strong>解释：</strong>符合题目要求的节点对分别是：\n- (0,1)、(0,2)、(1,3)、(1,4) 和 (2,5) ，路径上只有一个字符，满足回文定义。\n- (2,3)，路径上字符形成的字符串是 \"aca\" ，满足回文定义。\n- (1,5)，路径上字符形成的字符串是 \"cac\" ，满足回文定义。\n- (3,5)，路径上字符形成的字符串是 \"acac\" ，可以重排形成回文 \"acca\" 。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<strong>输入：</strong>parent = [-1,0,0,0,0], s = \"aaaaa\"\n<strong>输出：</strong>10\n<strong>解释：</strong>任何满足 u &lt; v 的节点对 (u,v) 都符合题目要求。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>n == parent.length == s.length</code></li>\n\t<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>\n\t<li>对于所有 <code>i &gt;= 1</code> ，<code>0 &lt;= parent[i] &lt;= n - 1</code> 均成立</li>\n\t<li><code>parent[0] == -1</code></li>\n\t<li><code>parent</code> 表示一棵有效的树</li>\n\t<li><code>s</code> 仅由小写英文字母组成</li>\n</ul>\n",
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