{ "data": { "question": { "questionId": "3307", "questionFrontendId": "3068", "boundTopicId": null, "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.

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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:

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

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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
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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
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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
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Constraints:

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