{ "data": { "question": { "questionId": "3058", "questionFrontendId": "2872", "categoryTitle": "Algorithms", "boundTopicId": 2463079, "title": "Maximum Number of K-Divisible Components", "titleSlug": "maximum-number-of-k-divisible-components", "content": "

There is an undirected tree with n nodes labeled from 0 to n - 1. You are given the integer n and a 2D integer array edges of length n - 1, where edges[i] = [ai, bi] indicates that there is an edge between nodes ai and bi in the tree.

\n\n

You are also given a 0-indexed integer array values of length n, where values[i] is the value associated with the ith node, and an integer k.

\n\n

A valid split 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 k, where the value of a connected component is the sum of the values of its nodes.

\n\n

Return the maximum number of components in any valid split.

\n\n

 

\n

Example 1:

\n\"\"\n
\nInput: n = 5, edges = [[0,2],[1,2],[1,3],[2,4]], values = [1,8,1,4,4], k = 6\nOutput: 2\nExplanation: 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.
\n\n

Example 2:

\n\"\"\n
\nInput: 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\nOutput: 3\nExplanation: 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
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "可以被 K 整除连通块的最大数目", "translatedContent": "

给你一棵 n 个节点的无向树，节点编号为 0 到 n - 1 。给你整数 n 和一个长度为 n - 1 的二维整数数组 edges ，其中 edges[i] = [ai, bi] 表示树中节点 ai 和 bi 有一条边。

\n\n

同时给你一个下标从 0 开始长度为 n 的整数数组 values ，其中 values[i] 是第 i 个节点的 值 。再给你一个整数 k 。

\n\n

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 连通块的值 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 k 整除，那么我们说这是一个 合法分割 。

\n\n

请你返回所有合法分割中，连通块数目的最大值 。

\n\n

 

\n\n

示例 1：

\n\n

\"\"

\n\n
\n输入：n = 5, edges = [[0,2],[1,2],[1,3],[2,4]], values = [1,8,1,4,4], k = 6\n输出：2\n解释：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。
\n\n

示例 2：

\n\n

\"\"

\n\n
\n输入：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输出：3\n解释：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
\n\n

 

\n\n

提示：

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            "book": null,
            "isSubscribed": false,
            "isDailyQuestion": false,
            "dailyRecordStatus": null,
            "editorType": "CKEDITOR",
            "ugcQuestionId": null,
            "style": "LEETCODE",
            "exampleTestcases": "5\n[[0,2],[1,2],[1,3],[2,4]]\n[1,8,1,4,4]\n6\n7\n[[0,1],[0,2],[1,3],[1,4],[2,5],[2,6]]\n[3,0,6,1,5,2,1]\n3",
            "__typename": "QuestionNode"
        }
    }
}