Maximum Number of K-Divisible Components
There is an undirected tree with n nodes labeled from 0 to n - 1. You are given the integer n and a 2D integer array edges of length n - 1, where edges[i] = [ai, bi] indicates that there is an edge between nodes ai and bi in the tree.
You are also given a 0-indexed integer array values of length n, where values[i] is the value associated with the i^th node, and an integer k.
A valid split of the tree is obtained by removing any set of edges, possibly empty, from the tree such that the resulting components all have values that are divisible by k, where the value of a connected component is the sum of the values of its nodes.
Return the maximum number of components in any valid split.
Example 1
Input
n = 5, edges = [[0,2],[1,2],[1,3],[2,4]], values = [1,8,1,4,4], k = 6Output
2Removing the edge between nodes 1 and 2 creates components with sums 12 and 6, both divisible by 6, and no valid split has more than 2 components.
Example 2
Input
n = 7, edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[2,6]], values = [3,0,6,1,5,2,1], k = 3Output
3Removing the edges between nodes 0 and 2 and between nodes 0 and 1 creates components with sums 3, 9, and 6, all divisible by 3, and no valid split has more than 3 components.
Constraints
- 1 <= n <= 3 * 10^4
- edges.length == n - 1
- edges[i].length == 2
- 0 <= ai, bi < n
- values.length == n
- 0 <= values[i] <= 10^9
- 1 <= k <= 10^9
- Sum of values is divisible by k.
- The input is generated such that edges represents a valid tree.