2440. Create Components With Same Value ¶

Problem

There is an undirected tree with n nodes labeled from 0 to n - 1.

You are given a 0-indexed integer array nums of length n where nums[i] represents the value of the i^th node. You are also given a 2D integer array edges of length n - 1 where edges[i] = [a_i, b_i] indicates that there is an edge between nodes a_i and b_i in the tree.

You are allowed to delete some edges, splitting the tree into multiple connected components. Let the value of a component be the sum of all nums[i] for which node i is in the component.

Return the maximum number of edges you can delete, such that every connected component in the tree has the same value.

Example 1:

Input: nums = [6,2,2,2,6], edges = [[0,1],[1,2],[1,3],[3,4]] 
Output: 2 
Explanation: The above figure shows how we can delete the edges [0,1] and [3,4]. The created components are nodes [0], [1,2,3] and [4]. The sum of the values in each component equals 6. It can be proven that no better deletion exists, so the answer is 2.

Example 2:

Input: nums = [2], edges = []
Output: 0
Explanation: There are no edges to be deleted.

Constraints:

1 <= n <= 2 * 10⁴
nums.length == n
1 <= nums[i] <= 50
edges.length == n - 1
edges[i].length == 2
0 <= edges[i][0], edges[i][1] <= n - 1
edges represents a valid tree.