3544 - Subtree Inversion Sum.

Hard

You are given an undirected tree rooted at node 0, with n nodes numbered from 0 to n - 1. The tree is represented by a 2D integer array edges of length n - 1, where <code>edgesi = u_i, v_i</code> indicates an edge between nodes <code>u_i</code> and <code>v_i</code>.

You are also given an integer array nums of length n, where nums[i] represents the value at node i, and an integer k.

You may perform inversion operations on a subset of nodes subject to the following rules:

• Subtree Inversion Operation:

• Distance Constraint on Inversions:

Return the maximum possible sum of the tree's node values after applying inversion operations.

Example 1:

Input: edges = [0,1,0,2,1,3,1,4,2,5,2,6], nums = 4,-8,-6,3,7,-2,5, k = 2

Output: 27

Explanation:

• Apply inversion operations at nodes 0, 3, 4 and 6.

• The final nums array is [-4, 8, 6, 3, 7, 2, 5], and the total sum is 27.

Example 2:

Input: edges = [0,1,1,2,2,3,3,4], nums = -1,3,-2,4,-5, k = 2

Output: 9

Explanation:

• Apply the inversion operation at node 4.

• The final nums array becomes [-1, 3, -2, 4, 5], and the total sum is 9.

Example 3:

Input: edges = [0,1,0,2], nums = 0,-1,-2, k = 3

Output: 3

Explanation:

Apply inversion operations at nodes 1 and 2.

Constraints:

• <code>2 <= n <= 5 * 10⁴</code>

• edges.length == n - 1

• <code>edgesi = u_i, v_i</code>

• <code>0 <= u_i, v_i< n</code>

• nums.length == n

• <code>-5 * 10⁴<= numsi<= 5 * 10⁴</code>

• 1 <= k <= 50

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