Python3 || O(n) and O(1) TIME AND SPACE || May 19 2024 Daily
Intuition\nTo maximize the sum of the values of tree nodes, we need to carefully apply the XOR operation using the given integer \nk. The XOR operation can pote
# Intuition\nTo maximize the sum of the values of tree nodes, we need to carefully apply the XOR operation using the given integer \nk. The XOR operation can potentially increase the value of a node, but we must consider how to maximize the overall sum by selectively applying this operation to the tree\'s edges. The goal is to determine when performing the XOR operation yields a higher sum and handle the parity (odd or even nature) of the total number of value changes optimally.\n\n# Approach\nInitial Calculation: For each node, calculate the maximum value it can achieve by comparing its current value with its value after applying the XOR operation. This can be expressed as max(num, num ^ k).\nCount Changes: Count how many nodes would change if the XOR operation was applied to all nodes.\nHandle Even and Odd Changes:\nIf the number of changes is even, simply return the maximum sum because we can always pair changes to maintain an optimal sum.\nIf the number of changes is odd, find the smallest possible change difference to make the total sum of changes even, thereby maximizing the sum.\nCompute the Result: Return the computed maximum possible sum with the necessary adjustments based on the parity of changes.\n\n# Complexity\n- Time complexity:\n$$O(n)$$ because we iterate through the list of nodes to compute the sums and determine the minimal change difference.\n\n- Space complexity:\n$$O(1)$$ as we use a fixed amount of extra space regardless of the input size.\n\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```
['Array', 'Dynamic Programming', 'Greedy', 'Bit Manipulation', 'Tree', 'Sorting', 'Python3']