Package g3001_3100.s3068_find_the_maximum_sum_of_node_values

Class Solution

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public final class Solution

    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 <code>edgesi = u<sub>i</sub>, v<sub>i</sub></code> indicates that there is an edge between nodes <code>u<sub>i</sub></code> and <code>v<sub>i</sub></code> 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:

    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. nums0 and nums2 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. nums0 becomes: 2 XOR 7 = 5 and nums1 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:

    • <code>2 <= n == nums.length <= 2 * 10<sup>4</sup></code>

    • <code>1 <= k <= 10<sup>9</sup></code>

    • <code>0 <= numsi<= 10<sup>9</sup></code>

    • edges.length == n - 1

    • edges[i].length == 2

    • 0 &lt;= edges[i][0], edges[i][1] &lt;= n - 1

    • The input is generated such that edges represent a valid tree.

    • Nested Class Summary

      Nested Classes 
      Modifier and Type Class Description

    • Field Summary

      Fields 
      Modifier and Type Field Description

    • Constructor Summary

      Constructors 
      Constructor Description
      Solution()

    • Enum Constant Summary

      Enum Constants 
      Enum Constant Description

    • Method Summary

      Modifier and Type Method Description
      final Long maximumValueSum(IntArray nums, Integer k, Array<IntArray> edges)

      • Methods inherited from class java.lang.Object

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