Package g3001_3100.s3068_find_the_maximum_sum_of_node_values

Class Solution

java.lang.Object
g3001_3100.s3068_find_the_maximum_sum_of_node_values.Solution
public class Solution extends java.lang.Object
3068 - Find the Maximum Sum of Node Values.

Hard

There exists an undirected tree with n nodes numbered 0 to n - 1. You are given a 0-indexed 2D integer array edges of length n - 1, where edges[i] = [ui, vi] indicates that there is an edge between nodes ui and vi in the tree. You are also given a positive integer k, and a 0-indexed array of non-negative 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 nodes u and v, 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 * 104
  • 1 <= k <= 109
  • 0 <= nums[i] <= 109
  • 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.

  • Constructor Summary

    Constructors
    Constructor
    Description
    Solution()
     

  • Method Summary

    Modifier and Type
    Method
    Description
    long
    maximumValueSum(int[] nums, int k, int[][] edges)
     

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Constructor Details

    • Solution

      public Solution()

  • Method Details

    • maximumValueSum

      public long maximumValueSum(int[] nums, int k, int[][] edges)