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This approach involves checking all possible operations on each edge and calculating the resulting sum by applying the XOR operation. We must continuously update and evaluate for every operation on each pair of nodes linked by an edge to see if the resulting sum after the operation is beneficial.
This naive strategy will consider 2^n operations (since each edge can have 2 XOR states per pair), making it inefficient for larger datasets. Ideal for understanding XOR effects but not recommended for large n.
Time Complexity: O(n), where n is the number of nodes. Each iteration is constant time.
Space Complexity: O(1), since additional space used is constant.
1import java.util.List;
2
3public class Solution {
4 public static int getMaxSum(int[] nums, int k, int[][] edges) {
5 int sum = 0;
6 for (int num : nums) {
7 sum += num;
8 }
9 int maxSum = sum;
10 for (int[] edge : edges) {
11 int u = edge[0], v = edge[1];
12 int newSum = sum - (nums[u] + nums[v]) + ((nums[u] ^ k) + (nums[v] ^ k));
13 maxSum = Math.max(maxSum, newSum);
14 }
15 return maxSum;
16 }
17
18 public static void main(String[] args) {
19 int[] nums = {1, 2, 1};
20 int k = 3;
21 int[][] edges = {{0, 1}, {0, 2}};
22 System.out.println(getMaxSum(nums, k, edges));
23 }
24}This Java solution iterates over the edges array, calculates the potential sum after XOR operation on each edge, and updates the maximum recorded sum accordingly.
Instead of brute checking each edge operation individually, observe that XOR operation symmetry allows flipping of node values to be optimal only when advantageous. Analyze and preprocess which nodes when XOR'd with k will increase their value and prioritize these changes globally without redundant individual edge checks.
This idea is crucially about observing which nodes independently contribute more value when toggled and using the tree structure to apply XOR operations optimally.
Time Complexity: O(n), as it processes each node individually once.
Space Complexity: O(1), using a fixed amount of extra space.
This Java procedure iterates over the nums array, calculates the potential XOR sum for all, and returns the highest possible sum post their processing inclusively and globally.