leetcode-problemset/leetcode-cn/originData/count-pairs-of-connectable-servers-in-a-weighted-tree-network.json

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            "questionId": "3326",
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            "categoryTitle": "Algorithms",
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            "title": "Count Pairs of Connectable Servers in a Weighted Tree Network",
            "titleSlug": "count-pairs-of-connectable-servers-in-a-weighted-tree-network",
            "content": "<p>You are given an unrooted weighted tree with <code>n</code> vertices representing servers numbered from <code>0</code> to <code>n - 1</code>, an array <code>edges</code> where <code>edges[i] = [a<sub>i</sub>, b<sub>i</sub>, weight<sub>i</sub>]</code> represents a bidirectional edge between vertices <code>a<sub>i</sub></code> and <code>b<sub>i</sub></code> of weight <code>weight<sub>i</sub></code>. You are also given an integer <code>signalSpeed</code>.</p>\n\n<p>Two servers <code>a</code> and <code>b</code> are <strong>connectable</strong> through a server <code>c</code> if:</p>\n\n<ul>\n\t<li><code>a &lt; b</code>, <code>a != c</code> and <code>b != c</code>.</li>\n\t<li>The distance from <code>c</code> to <code>a</code> is divisible by <code>signalSpeed</code>.</li>\n\t<li>The distance from <code>c</code> to <code>b</code> is divisible by <code>signalSpeed</code>.</li>\n\t<li>The path from <code>c</code> to <code>b</code> and the path from <code>c</code> to <code>a</code> do not share any edges.</li>\n</ul>\n\n<p>Return <em>an integer array</em> <code>count</code> <em>of length</em> <code>n</code> <em>where</em> <code>count[i]</code> <em>is the <strong>number</strong> of server pairs that are <strong>connectable</strong> through</em> <em>the server</em> <code>i</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/01/21/example22.png\" style=\"width: 438px; height: 243px; padding: 10px; background: #fff; border-radius: .5rem;\" />\n<pre>\n<strong>Input:</strong> edges = [[0,1,1],[1,2,5],[2,3,13],[3,4,9],[4,5,2]], signalSpeed = 1\n<strong>Output:</strong> [0,4,6,6,4,0]\n<strong>Explanation:</strong> Since signalSpeed is 1, count[c] is equal to the number of pairs of paths that start at c and do not share any edges.\nIn the case of the given path graph, count[c] is equal to the number of servers to the left of c multiplied by the servers to the right of c.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/01/21/example11.png\" style=\"width: 495px; height: 484px; padding: 10px; background: #fff; border-radius: .5rem;\" />\n<pre>\n<strong>Input:</strong> edges = [[0,6,3],[6,5,3],[0,3,1],[3,2,7],[3,1,6],[3,4,2]], signalSpeed = 3\n<strong>Output:</strong> [2,0,0,0,0,0,2]\n<strong>Explanation:</strong> Through server 0, there are 2 pairs of connectable servers: (4, 5) and (4, 6).\nThrough server 6, there are 2 pairs of connectable servers: (4, 5) and (0, 5).\nIt can be shown that no two servers are connectable through servers other than 0 and 6.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= n &lt;= 1000</code></li>\n\t<li><code>edges.length == n - 1</code></li>\n\t<li><code>edges[i].length == 3</code></li>\n\t<li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt; n</code></li>\n\t<li><code>edges[i] = [a<sub>i</sub>, b<sub>i</sub>, weight<sub>i</sub>]</code><!-- notionvc: a2623897-1bb1-4c07-84b6-917ffdcd83ec --></li>\n\t<li><code>1 &lt;= weight<sub>i</sub> &lt;= 10<sup>6</sup></code></li>\n\t<li><code>1 &lt;= signalSpeed &lt;= 10<sup>6</sup></code></li>\n\t<li>The input is generated such that <code>edges</code> represents a valid tree.</li>\n</ul>\n",
            "translatedTitle": "在带权树网络中统计可连接服务器对数目",
            "translatedContent": "<p>给你一棵无根带权树，树中总共有 <code>n</code>&nbsp;个节点，分别表示 <code>n</code>&nbsp;个服务器，服务器从 <code>0</code>&nbsp;到 <code>n - 1</code>&nbsp;编号。同时给你一个数组&nbsp;<code>edges</code>&nbsp;，其中&nbsp;<code>edges[i] = [a<sub>i</sub>, b<sub>i</sub>, weight<sub>i</sub>]</code>&nbsp;表示节点&nbsp;<code>a<sub>i</sub></code> 和&nbsp;<code>b<sub>i</sub></code>&nbsp;之间有一条双向边，边的权值为&nbsp;<code>weight<sub>i</sub></code>&nbsp;。再给你一个整数&nbsp;<code>signalSpeed</code>&nbsp;。</p>\n\n<p>如果两个服务器 <code>a</code>&nbsp;，<code>b</code>&nbsp;和 <code>c</code>&nbsp;满足以下条件，那么我们称服务器 <code>a</code>&nbsp;和 <code>b</code>&nbsp;是通过服务器 <code>c</code>&nbsp;<strong>可连接的</strong>&nbsp;：</p>\n\n<ul>\n\t<li><code>a &lt; b</code>&nbsp;，<code>a != c</code> 且&nbsp;<code>b != c</code>&nbsp;。</li>\n\t<li>从&nbsp;<code>c</code>&nbsp;到&nbsp;<code>a</code>&nbsp;的距离是可以被&nbsp;<code>signalSpeed</code>&nbsp;整除的。</li>\n\t<li>从&nbsp;<code>c</code>&nbsp;到&nbsp;<code>b</code>&nbsp;的距离是可以被&nbsp;<code>signalSpeed</code>&nbsp;整除的。</li>\n\t<li>从&nbsp;<code>c</code>&nbsp;到&nbsp;<code>b</code>&nbsp;的路径与从&nbsp;<code>c</code>&nbsp;到&nbsp;<code>a</code>&nbsp;的路径没有任何公共边。</li>\n</ul>\n\n<p>请你返回一个长度为 <code>n</code>&nbsp;的整数数组&nbsp;<code>count</code>&nbsp;，其中&nbsp;<code>count[i]</code> 表示通过服务器&nbsp;<code>i</code>&nbsp;<strong>可连接</strong>&nbsp;的服务器对的&nbsp;<strong>数目</strong>&nbsp;。</p>\n\n<p>&nbsp;</p>\n\n<p><b>示例 1：</b></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/01/21/example22.png\" style=\"width: 438px; height: 243px; padding: 10px; background: #fff; border-radius: .5rem;\" /></p>\n\n<pre>\n<b>输入：</b>edges = [[0,1,1],[1,2,5],[2,3,13],[3,4,9],[4,5,2]], signalSpeed = 1\n<b>输出：</b>[0,4,6,6,4,0]\n<b>解释：</b>由于 signalSpeed 等于 1 ，count[c] 等于所有从 c 开始且没有公共边的路径对数目。\n在输入图中，count[c] 等于服务器 c 左边服务器数目乘以右边服务器数目。\n</pre>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/01/21/example11.png\" style=\"width: 495px; height: 484px; padding: 10px; background: #fff; border-radius: .5rem;\" /></p>\n\n<pre>\n<b>输入：</b>edges = [[0,6,3],[6,5,3],[0,3,1],[3,2,7],[3,1,6],[3,4,2]], signalSpeed = 3\n<b>输出：</b>[2,0,0,0,0,0,2]\n<b>解释：</b>通过服务器 0 ，有 2 个可连接服务器对(4, 5) 和 (4, 6) 。\n通过服务器 6 ，有 2 个可连接服务器对 (4, 5) 和 (0, 5) 。\n所有服务器对都必须通过服务器 0 或 6 才可连接，所以其他服务器对应的可连接服务器对数目都为 0 。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= n &lt;= 1000</code></li>\n\t<li><code>edges.length == n - 1</code></li>\n\t<li><code>edges[i].length == 3</code></li>\n\t<li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt; n</code></li>\n\t<li><code>edges[i] = [a<sub>i</sub>, b<sub>i</sub>, weight<sub>i</sub>]</code><!-- notionvc: a2623897-1bb1-4c07-84b6-917ffdcd83ec --></li>\n\t<li><code>1 &lt;= weight<sub>i</sub> &lt;= 10<sup>6</sup></code></li>\n\t<li><code>1 &lt;= signalSpeed &lt;= 10<sup>6</sup></code></li>\n\t<li>输入保证&nbsp;<code>edges</code>&nbsp;构成一棵合法的树。</li>\n</ul>\n",
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