leetcode-problemset/leetcode-cn/originData/number-of-good-paths.json

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        "question": {
            "questionId": "2505",
            "questionFrontendId": "2421",
            "categoryTitle": "Algorithms",
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            "title": "Number of Good Paths",
            "titleSlug": "number-of-good-paths",
            "content": "<p>There is a tree (i.e. a connected, undirected graph with no cycles) consisting of <code>n</code> nodes numbered from <code>0</code> to <code>n - 1</code> and exactly <code>n - 1</code> edges.</p>\n\n<p>You are given a <strong>0-indexed</strong> integer array <code>vals</code> of length <code>n</code> where <code>vals[i]</code> denotes the value of the <code>i<sup>th</sup></code> node. You are also given a 2D integer array <code>edges</code> where <code>edges[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> denotes that there exists an <strong>undirected</strong> edge connecting nodes <code>a<sub>i</sub></code> and <code>b<sub>i</sub></code>.</p>\n\n<p>A <strong>good path</strong> is a simple path that satisfies the following conditions:</p>\n\n<ol>\n\t<li>The starting node and the ending node have the <strong>same</strong> value.</li>\n\t<li>All nodes between the starting node and the ending node have values <strong>less than or equal to</strong> the starting node (i.e. the starting node&#39;s value should be the maximum value along the path).</li>\n</ol>\n\n<p>Return <em>the number of distinct good paths</em>.</p>\n\n<p>Note that a path and its reverse are counted as the <strong>same</strong> path. For example, <code>0 -&gt; 1</code> is considered to be the same as <code>1 -&gt; 0</code>. A single node is also considered as a valid path.</p>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/08/04/f9caaac15b383af9115c5586779dec5.png\" style=\"width: 400px; height: 333px;\" />\n<pre>\n<strong>Input:</strong> vals = [1,3,2,1,3], edges = [[0,1],[0,2],[2,3],[2,4]]\n<strong>Output:</strong> 6\n<strong>Explanation:</strong> There are 5 good paths consisting of a single node.\nThere is 1 additional good path: 1 -&gt; 0 -&gt; 2 -&gt; 4.\n(The reverse path 4 -&gt; 2 -&gt; 0 -&gt; 1 is treated as the same as 1 -&gt; 0 -&gt; 2 -&gt; 4.)\nNote that 0 -&gt; 2 -&gt; 3 is not a good path because vals[2] &gt; vals[0].\n</pre>\n\n<p><strong>Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/08/04/149d3065ec165a71a1b9aec890776ff.png\" style=\"width: 273px; height: 350px;\" />\n<pre>\n<strong>Input:</strong> vals = [1,1,2,2,3], edges = [[0,1],[1,2],[2,3],[2,4]]\n<strong>Output:</strong> 7\n<strong>Explanation:</strong> There are 5 good paths consisting of a single node.\nThere are 2 additional good paths: 0 -&gt; 1 and 2 -&gt; 3.\n</pre>\n\n<p><strong>Example 3:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/08/04/31705e22af3d9c0a557459bc7d1b62d.png\" style=\"width: 100px; height: 88px;\" />\n<pre>\n<strong>Input:</strong> vals = [1], edges = []\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> The tree consists of only one node, so there is one good path.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>n == vals.length</code></li>\n\t<li><code>1 &lt;= n &lt;= 3 * 10<sup>4</sup></code></li>\n\t<li><code>0 &lt;= vals[i] &lt;= 10<sup>5</sup></code></li>\n\t<li><code>edges.length == n - 1</code></li>\n\t<li><code>edges[i].length == 2</code></li>\n\t<li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt; n</code></li>\n\t<li><code>a<sub>i</sub> != b<sub>i</sub></code></li>\n\t<li><code>edges</code> represents a valid tree.</li>\n</ul>\n",
            "translatedTitle": "好路径的数目",
            "translatedContent": "<p>给你一棵 <code>n</code>&nbsp;个节点的树（连通无向无环的图），节点编号从&nbsp;<code>0</code>&nbsp;到&nbsp;<code>n - 1</code>&nbsp;且恰好有&nbsp;<code>n - 1</code>&nbsp;条边。</p>\n\n<p>给你一个长度为 <code>n</code>&nbsp;下标从 <strong>0</strong>&nbsp;开始的整数数组&nbsp;<code>vals</code>&nbsp;，分别表示每个节点的值。同时给你一个二维整数数组&nbsp;<code>edges</code>&nbsp;，其中&nbsp;<code>edges[i] = [a<sub>i</sub>, b<sub>i</sub>]</code>&nbsp;表示节点&nbsp;<code>a<sub>i</sub></code> 和&nbsp;<code>b<sub>i</sub></code><sub>&nbsp;</sub>之间有一条&nbsp;<strong>无向</strong>&nbsp;边。</p>\n\n<p>一条 <strong>好路径</strong>&nbsp;需要满足以下条件：</p>\n\n<ol>\n\t<li>开始节点和结束节点的值 <strong>相同</strong>&nbsp;。</li>\n\t<li>开始节点和结束节点中间的所有节点值都 <strong>小于等于</strong>&nbsp;开始节点的值（也就是说开始节点的值应该是路径上所有节点的最大值）。</li>\n</ol>\n\n<p>请你返回不同好路径的数目。</p>\n\n<p>注意，一条路径和它反向的路径算作 <strong>同一</strong>&nbsp;路径。比方说，&nbsp;<code>0 -&gt; 1</code>&nbsp;与&nbsp;<code>1 -&gt; 0</code>&nbsp;视为同一条路径。单个节点也视为一条合法路径。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例&nbsp;1：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/08/04/f9caaac15b383af9115c5586779dec5.png\" style=\"width: 400px; height: 333px;\"></p>\n\n<pre><b>输入：</b>vals = [1,3,2,1,3], edges = [[0,1],[0,2],[2,3],[2,4]]\n<b>输出：</b>6\n<b>解释：</b>总共有 5 条单个节点的好路径。\n还有 1 条好路径：1 -&gt; 0 -&gt; 2 -&gt; 4 。\n（反方向的路径 4 -&gt; 2 -&gt; 0 -&gt; 1 视为跟 1 -&gt; 0 -&gt; 2 -&gt; 4 一样的路径）\n注意 0 -&gt; 2 -&gt; 3 不是一条好路径，因为 vals[2] &gt; vals[0] 。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/08/04/149d3065ec165a71a1b9aec890776ff.png\" style=\"width: 273px; height: 350px;\"></p>\n\n<pre><b>输入：</b>vals = [1,1,2,2,3], edges = [[0,1],[1,2],[2,3],[2,4]]\n<b>输出：</b>7\n<strong>解释：</strong>总共有 5 条单个节点的好路径。\n还有 2 条好路径：0 -&gt; 1 和 2 -&gt; 3 。\n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/08/04/31705e22af3d9c0a557459bc7d1b62d.png\" style=\"width: 100px; height: 88px;\"></p>\n\n<pre><b>输入：</b>vals = [1], edges = []\n<b>输出：</b>1\n<b>解释：</b>这棵树只有一个节点，所以只有一条好路径。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>n == vals.length</code></li>\n\t<li><code>1 &lt;= n &lt;= 3 * 10<sup>4</sup></code></li>\n\t<li><code>0 &lt;= vals[i] &lt;= 10<sup>5</sup></code></li>\n\t<li><code>edges.length == n - 1</code></li>\n\t<li><code>edges[i].length == 2</code></li>\n\t<li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt; n</code></li>\n\t<li><code>a<sub>i</sub> != b<sub>i</sub></code></li>\n\t<li><code>edges</code>&nbsp;表示一棵合法的树。</li>\n</ul>\n",
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href=\\\"https:\\/\\/godoc.org\\/github.com\\/emirpasic\\/gods\\\" target=\\\"_blank\\\">https:\\/\\/godoc.org\\/github.com\\/emirpasic\\/gods<\\/a> \\u7b2c\\u4e09\\u65b9\\u5e93\\u3002<\\/p>\"],\"python3\":[\"Python3\",\"<p>\\u7248\\u672c\\uff1a<code>Python 3.10<\\/code><\\/p>\\r\\n\\r\\n<p>\\u4e3a\\u4e86\\u65b9\\u4fbf\\u8d77\\u89c1\\uff0c\\u5927\\u90e8\\u5206\\u5e38\\u7528\\u5e93\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8 \\u5bfc\\u5165\\uff0c\\u5982<a href=\\\"https:\\/\\/docs.python.org\\/3\\/library\\/array.html\\\" target=\\\"_blank\\\">array<\\/a>, <a href=\\\"https:\\/\\/docs.python.org\\/3\\/library\\/bisect.html\\\" target=\\\"_blank\\\">bisect<\\/a>, <a href=\\\"https:\\/\\/docs.python.org\\/3\\/library\\/collections.html\\\" target=\\\"_blank\\\">collections<\\/a>\\u3002 \\u5982\\u679c\\u60a8\\u9700\\u8981\\u4f7f\\u7528\\u5176\\u4ed6\\u5e93\\u51fd\\u6570\\uff0c\\u8bf7\\u81ea\\u884c\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n<p>\\u5982\\u9700\\u4f7f\\u7528 Map\\/TreeMap 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