leetcode-problemset/leetcode-cn/originData/maximum-number-of-k-divisible-components.json

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        "question": {
            "questionId": "3058",
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            "title": "Maximum Number of K-Divisible Components",
            "titleSlug": "maximum-number-of-k-divisible-components",
            "content": "<p>There is an undirected tree with <code>n</code> nodes labeled from <code>0</code> to <code>n - 1</code>. You are given the integer <code>n</code> and 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>You are also given a <strong>0-indexed</strong> integer array <code>values</code> of length <code>n</code>, where <code>values[i]</code> is the <strong>value</strong> associated with the <code>i<sup>th</sup></code> node, and an integer <code>k</code>.</p>\n\n<p>A <strong>valid split</strong> of the tree is obtained by removing any set of edges, possibly empty, from the tree such that the resulting components all have values that are divisible by <code>k</code>, where the <strong>value of a connected component</strong> is the sum of the values of its nodes.</p>\n\n<p>Return <em>the <strong>maximum number of components</strong> in any valid split</em>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/08/07/example12-cropped2svg.jpg\" style=\"width: 1024px; height: 453px;\" />\n<pre>\n<strong>Input:</strong> n = 5, edges = [[0,2],[1,2],[1,3],[2,4]], values = [1,8,1,4,4], k = 6\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> We remove the edge connecting node 1 with 2. The resulting split is valid because:\n- The value of the component containing nodes 1 and 3 is values[1] + values[3] = 12.\n- The value of the component containing nodes 0, 2, and 4 is values[0] + values[2] + values[4] = 6.\nIt can be shown that no other valid split has more than 2 connected components.</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/08/07/example21svg-1.jpg\" style=\"width: 999px; height: 338px;\" />\n<pre>\n<strong>Input:</strong> n = 7, edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[2,6]], values = [3,0,6,1,5,2,1], k = 3\n<strong>Output:</strong> 3\n<strong>Explanation:</strong> We remove the edge connecting node 0 with 2, and the edge connecting node 0 with 1. The resulting split is valid because:\n- The value of the component containing node 0 is values[0] = 3.\n- The value of the component containing nodes 2, 5, and 6 is values[2] + values[5] + values[6] = 9.\n- The value of the component containing nodes 1, 3, and 4 is values[1] + values[3] + values[4] = 6.\nIt can be shown that no other valid split has more than 3 connected components.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n &lt;= 3 * 10<sup>4</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>values.length == n</code></li>\n\t<li><code>0 &lt;= values[i] &lt;= 10<sup>9</sup></code></li>\n\t<li><code>1 &lt;= k &lt;= 10<sup>9</sup></code></li>\n\t<li>Sum of <code>values</code> is divisible by <code>k</code>.</li>\n\t<li>The input is generated such that <code>edges</code> represents a valid tree.</li>\n</ul>\n",
            "translatedTitle": "可以被 K 整除连通块的最大数目",
            "translatedContent": "<p>给你一棵 <code>n</code>&nbsp;个节点的无向树，节点编号为&nbsp;<code>0</code>&nbsp;到&nbsp;<code>n - 1</code>&nbsp;。给你整数&nbsp;<code>n</code>&nbsp;和一个长度为 <code>n - 1</code>&nbsp;的二维整数数组&nbsp;<code>edges</code>&nbsp;，其中&nbsp;<code>edges[i] = [a<sub>i</sub>, b<sub>i</sub>]</code>&nbsp;表示树中节点&nbsp;<code>a<sub>i</sub></code> 和&nbsp;<code>b<sub>i</sub></code>&nbsp;有一条边。</p>\n\n<p>同时给你一个下标从 <strong>0</strong>&nbsp;开始长度为 <code>n</code>&nbsp;的整数数组&nbsp;<code>values</code>&nbsp;，其中&nbsp;<code>values[i]</code>&nbsp;是第 <code>i</code>&nbsp;个节点的 <strong>值</strong>&nbsp;。再给你一个整数&nbsp;<code>k</code>&nbsp;。</p>\n\n<p>你可以从树中删除一些边，也可以一条边也不删，得到若干连通块。一个 <strong>连通块的值</strong> 定义为连通块中所有节点值之和。如果所有连通块的值都可以被 <code>k</code>&nbsp;整除，那么我们说这是一个 <strong>合法分割</strong>&nbsp;。</p>\n\n<p>请你返回所有合法分割中，<b>连通块数目的最大值</b>&nbsp;。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/08/07/example12-cropped2svg.jpg\" style=\"width: 1024px; height: 453px;\" /></p>\n\n<pre>\n<b>输入：</b>n = 5, edges = [[0,2],[1,2],[1,3],[2,4]], values = [1,8,1,4,4], k = 6\n<b>输出：</b>2\n<b>解释：</b>我们删除节点 1 和 2 之间的边。这是一个合法分割，因为：\n- 节点 1 和 3 所在连通块的值为 values[1] + values[3] = 12 。\n- 节点 0 ，2 和 4 所在连通块的值为 values[0] + values[2] + values[4] = 6 。\n最多可以得到 2 个连通块的合法分割。</pre>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/08/07/example21svg-1.jpg\" style=\"width: 999px; height: 338px;\" /></p>\n\n<pre>\n<b>输入：</b>n = 7, edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[2,6]], values = [3,0,6,1,5,2,1], k = 3\n<b>输出：</b>3\n<b>解释：</b>我们删除节点 0 和 2 ，以及节点 0 和 1 之间的边。这是一个合法分割，因为：\n- 节点 0 的连通块的值为 values[0] = 3 。\n- 节点 2 ，5 和 6 所在连通块的值为 values[2] + values[5] + values[6] = 9 。\n- 节点 1 ，3 和 4 的连通块的值为 values[1] + values[3] + values[4] = 6 。\n最多可以得到 3 个连通块的合法分割。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n &lt;= 3 * 10<sup>4</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>values.length == n</code></li>\n\t<li><code>0 &lt;= values[i] &lt;= 10<sup>9</sup></code></li>\n\t<li><code>1 &lt;= k &lt;= 10<sup>9</sup></code></li>\n\t<li><code>values</code>&nbsp;之和可以被 <code>k</code>&nbsp;整除。</li>\n\t<li>输入保证&nbsp;<code>edges</code>&nbsp;是一棵无向树。</li>\n</ul>\n",
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