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3068. Find the Maximum Sum of Node Values
Description
There exists an undirected tree with n
nodes numbered 0
to n  1
. You are given a 0indexed 2D integer array edges
of length n  1
, where edges[i] = [u_{i}, v_{i}]
indicates that there is an edge between nodes u_{i}
and v_{i}
in the tree. You are also given a positive integer k
, and a 0indexed array of nonnegative integers nums
of length n
, where nums[i]
represents the value of the node numbered i
.
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:
 Choose any edge
[u, v]
connecting the nodesu
andv
, and update their values as follows:nums[u] = nums[u] XOR k
nums[v] = nums[v] XOR k
Return the maximum possible sum of the values Alice can achieve by performing the operation any number of times.
Example 1:
Input: nums = [1,2,1], k = 3, edges = [[0,1],[0,2]] Output: 6 Explanation: Alice can achieve the maximum sum of 6 using a single operation:  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]. The total sum of values is 2 + 2 + 2 = 6. It can be shown that 6 is the maximum achievable sum of values.
Example 2:
Input: nums = [2,3], k = 7, edges = [[0,1]] Output: 9 Explanation: Alice can achieve the maximum sum of 9 using a single operation:  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]. The total sum of values is 5 + 4 = 9. It can be shown that 9 is the maximum achievable sum of values.
Example 3:
Input: nums = [7,7,7,7,7,7], k = 3, edges = [[0,1],[0,2],[0,3],[0,4],[0,5]] Output: 42 Explanation: The maximum achievable sum is 42 which can be achieved by Alice performing no operations.
Constraints:
2 <= n == nums.length <= 2 * 10^{4}
1 <= k <= 10^{9}
0 <= nums[i] <= 10^{9}
edges.length == n  1
edges[i].length == 2
0 <= edges[i][0], edges[i][1] <= n  1
 The input is generated such that
edges
represent a valid tree.
Solutions
Solution 1

class Solution { public: long long maximumValueSum(vector<int>& nums, int k, vector<vector<int>>& edges) { long long totalSum = 0; int count = 0; int positiveMin = INT_MAX; int negativeMax = INT_MIN; for (int nodeValue : nums) { int nodeValAfterOperation = nodeValue ^ k; totalSum += nodeValue; int netChange = nodeValAfterOperation  nodeValue; if (netChange > 0) { positiveMin = min(positiveMin, netChange); totalSum += netChange; count += 1; } else { negativeMax = max(negativeMax, netChange); } } if (count % 2 == 0) { return totalSum; } return max(totalSum  positiveMin, totalSum + negativeMax); } };