C# Solution for Find the Maximum Sum of Node Values Problem
Intuition\n Describe your first thoughts on how to solve this problem. \nThe key intuition behind this solution is to leverage dynamic programming to maximize t
# Intuition\n<!-- Describe your first thoughts on how to solve this problem. -->\nThe key intuition behind this solution is to leverage dynamic programming to maximize the sum of node values after potentially performing XOR operations on the tree edges. We use a 2D dynamic programming array (dp) to track the maximum sums for different states: whether the number of XOR operations performed so far is even or odd.\n\n# Approach\n<!-- Describe your approach to solving the problem. -->\n1.\tInitialization:\n\t\u2022\tCreate a dp array of size (n + 1) x 2, where n is the length of the nums array.\n\t\u2022\tInitialize the base cases: dp[n, 1] to 0 (no operations performed on an odd number of elements), and dp[n, 0] to long.MinValue.\n2.\tDynamic Programming Transition:\n\t\u2022\tIterate through the nums array in reverse order, from n-1 to 0.\n\t\u2022\tFor each index and each parity state (isEven), calculate the maximum value sum by considering:\n\t\u2022\tNo XOR Operation: The sum if no XOR operation is performed on the current element.\n\t\u2022\tXOR Operation: The sum if an XOR operation is performed on the current element.\n\t\u2022\tUpdate the dp array with the maximum of these two sums.\n3.\tResult Extraction:\n\t\u2022\tThe desired result is stored in dp[0, 1], representing the maximum possible sum when starting from the first element with an even number of XOR operations.\n\n# Complexity\n- Time complexity:\n<!-- Add your time complexity here, e.g. $$O(n)$$ -->\n\u2022\tTraversal: We iterate over each element in the nums array once.\n\u2022\tDP Transition: For each element, we consider two states (isEven being 0 or 1).\n\u2022\tThus, the time complexity is O(n), where n is the length of the nums array.\n\n- Space complexity:\n<!-- Add your space complexity here, e.g. $$O(n)$$ -->\n\u2022\tDP Array: We use a 2D array of size (n + 1) x 2.\n\u2022\tThus, the space complexity is O(n), which accounts for the dp array.\n\n# Code\n```\npublic class Solution {\n    public long MaximumValueSum(int[] nums, int k, int[][] edges) {\n        int n = nums.Length;\n        long[,] dp = new long[n + 1, 2];\n        \n        // Base case initialization\n        dp[n, 1] = 0;\n        dp[n, 0] = long.MinValue;\n        \n        // Iterate through the nums array in reverse order\n        for (int index = n - 1; index >= 0; index--) {\n            for (int isEven = 0; isEven <= 1; isEven++) {\n                long dontPerformOperation = dp[index + 1, isEven] + nums[index];\n                long performOperation = dp[index + 1, isEven ^ 1] + (nums[index] ^ k);\n                \n                dp[index, isEven] = Math.Max(dontPerformOperation, performOperation);\n            }\n        }\n        \n        // The result is the maximum sum starting with an even number of operations\n        return dp[0, 1];\n    }\n}\n```
['C#']