EASIEST PYTHON3 CODE!!!
Intuition\n Describe your first thoughts on how to solve this problem. \nThe operation Alice performs essentially flips the bits of nums[u] and nums[v] at corre
# Intuition\n<!-- Describe your first thoughts on how to solve this problem. -->\nThe operation Alice performs essentially flips the bits of nums[u] and nums[v] at corresponding positions using the XOR (^) operator. This operation has some key properties that help us find the maximum sum:\n\nXOR with itself is zero: a ^ a = 0 for any value a. This means performing the operation on a node twice brings its value back to the original.\nCommutative: a ^ b = b ^ a. The order of nodes chosen for the operation doesn\'t matter.\n\n# Approach\n<!-- Describe your approach to solving the problem. -->\nIdentify independent groups: Since the tree has no cycles, we can analyze each connected component (subtree) independently. Nodes within a subtree are connected by edges, and the operation can influence each other\'s values.\n\nMaximize value within a group: We want to maximize the sum within each subtree. This can be achieved by ensuring all nodes in a subtree have the same bit value at a specific position (either 0 or 1) through XOR operations.\n\nMultiple bits, independent decisions: Each position in the binary representation of k represents an independent decision. We can analyze each bit of k separately.\n\nCounting nodes with desired bit: For each bit position in k, we need to find the number of nodes in a subtree that would contribute the most to the sum if their bit at that position is set to 0 or 1.\n\nMaximize sum based on bit counts: By comparing the count of nodes with 0 or 1 at a specific bit position, we can determine which configuration (all 0s or all 1s) maximizes the sum within the subtree for that bit position.\n\nCombine maximums for all bits: Finally, we add the maximum contribution from each bit position in k to get the overall maximum sum achievable for the entire tree.\n\n# Complexity\n- Time complexity:\n<!-- Add your time complexity here, e.g. $$O(n)$$ -->\n**O(n)**\n- Space complexity:\n<!-- Add your space complexity here, e.g. $$O(n)$$ -->\n**O(1)**\n# Code\n```\nclass Solution:\n    def maximumValueSum(self, nums: List[int], k: int, edges: List[List[int]]) -> int:\n        maxSum = sum(max(num, num ^ k) for num in nums)\n        changedCount = sum((num ^ k) > num for num in nums)\n        if changedCount % 2 == 0:\n            return maxSum\n        minChangeDiff = min(abs(num - (num ^ k)) for num in nums)\n        return maxSum - minChangeDiff\n        \n```
['Python3']