{ "data": { "question": { "questionId": "3307", "questionFrontendId": "3068", "categoryTitle": "Algorithms", "boundTopicId": 2659028, "title": "Find the Maximum Sum of Node Values", "titleSlug": "find-the-maximum-sum-of-node-values", "content": "

There exists an undirected tree with n nodes numbered 0 to n - 1. You are given a 0-indexed 2D integer array edges of length n - 1, where edges[i] = [ui, vi] indicates that there is an edge between nodes ui and vi in the tree. You are also given a positive integer k, and a 0-indexed array of non-negative integers nums of length n, where nums[i] represents the value of the node numbered i.

\n\n

Alice wants the sum of values of tree nodes to be maximum, for which Alice can perform the following operation any number of times (including zero) on the tree:

\n\n\n\n

Return the maximum possible sum of the values Alice can achieve by performing the operation any number of times.

\n\n

 

\n

Example 1:

\n\"\"\n
\nInput: nums = [1,2,1], k = 3, edges = [[0,1],[0,2]]\nOutput: 6\nExplanation: Alice can achieve the maximum sum of 6 using a single operation:\n- Choose the edge [0,2]. nums[0] and nums[2] become: 1 XOR 3 = 2, and the array nums becomes: [1,2,1] -> [2,2,2].\nThe total sum of values is 2 + 2 + 2 = 6.\nIt can be shown that 6 is the maximum achievable sum of values.\n
\n\n

Example 2:

\n\"\"\n
\nInput: nums = [2,3], k = 7, edges = [[0,1]]\nOutput: 9\nExplanation: Alice can achieve the maximum sum of 9 using a single operation:\n- Choose the edge [0,1]. nums[0] becomes: 2 XOR 7 = 5 and nums[1] become: 3 XOR 7 = 4, and the array nums becomes: [2,3] -> [5,4].\nThe total sum of values is 5 + 4 = 9.\nIt can be shown that 9 is the maximum achievable sum of values.\n
\n\n

Example 3:

\n\"\"\n
\nInput: nums = [7,7,7,7,7,7], k = 3, edges = [[0,1],[0,2],[0,3],[0,4],[0,5]]\nOutput: 42\nExplanation: The maximum achievable sum is 42 which can be achieved by Alice performing no operations.\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "最大节点价值之和", "translatedContent": "

给你一棵 n 个节点的 无向 树，节点从 0 到 n - 1 编号。树以长度为 n - 1 下标从 0 开始的二维整数数组 edges 的形式给你，其中 edges[i] = [ui, vi] 表示树中节点 ui 和 vi 之间有一条边。同时给你一个 正 整数 k 和一个长度为 n 下标从 0 开始的 非负 整数数组 nums ，其中 nums[i] 表示节点 i 的 价值 。

\n\n

Alice 想 最大化 树中所有节点价值之和。为了实现这一目标，Alice 可以执行以下操作 任意 次（包括 0 次）：

\n\n\n\n

请你返回 Alice 通过执行以上操作 任意次 后，可以得到所有节点 价值之和 的 最大值 。

\n\n

 

\n\n

示例 1：

\n\n

\"\"

\n\n
\n输入：nums = [1,2,1], k = 3, edges = [[0,1],[0,2]]\n输出：6\n解释：Alice 可以通过一次操作得到最大价值和 6 ：\n- 选择边 [0,2] 。nums[0] 和 nums[2] 都变为：1 XOR 3 = 2 ，数组 nums 变为：[1,2,1] -> [2,2,2] 。\n所有节点价值之和为 2 + 2 + 2 = 6 。\n6 是可以得到最大的价值之和。\n
\n\n

示例 2：

\n\n

\"\"

\n\n
\n输入：nums = [2,3], k = 7, edges = [[0,1]]\n输出：9\n解释：Alice 可以通过一次操作得到最大和 9 ：\n- 选择边 [0,1] 。nums[0] 变为：2 XOR 7 = 5 ，nums[1] 变为：3 XOR 7 = 4 ，数组 nums 变为：[2,3] -> [5,4] 。\n所有节点价值之和为 5 + 4 = 9 。\n9 是可以得到最大的价值之和。\n
\n\n

示例 3：

\n\n

\"\"

\n\n
\n输入：nums = [7,7,7,7,7,7], k = 3, edges = [[0,1],[0,2],[0,3],[0,4],[0,5]]\n输出：42\n解释：Alice 不需要执行任何操作，就可以得到最大价值之和 42 。\n
\n\n

 

\n\n

提示：

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edgesColSize) {\n \n}", "__typename": "CodeSnippetNode" }, { "lang": "C#", "langSlug": "csharp", "code": "public class Solution {\n public long MaximumValueSum(int[] nums, int k, int[][] edges) {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "JavaScript", "langSlug": "javascript", "code": "/**\n * @param {number[]} nums\n * @param {number} k\n * @param {number[][]} edges\n * @return {number}\n */\nvar maximumValueSum = function(nums, k, edges) {\n \n};", "__typename": "CodeSnippetNode" }, { "lang": "TypeScript", "langSlug": "typescript", "code": "function maximumValueSum(nums: number[], k: number, edges: number[][]): number {\n \n};", "__typename": "CodeSnippetNode" }, { "lang": "PHP", "langSlug": "php", "code": "class Solution {\n\n /**\n * @param Integer[] $nums\n * @param Integer $k\n * @param Integer[][] $edges\n * @return Integer\n */\n function maximumValueSum($nums, $k, $edges) {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Swift", "langSlug": "swift", 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