Package g2801_2900.s2872_maximum_number_of_k_divisible_components

Class Solution

java.lang.Object
g2801_2900.s2872_maximum_number_of_k_divisible_components.Solution
public class Solution extends java.lang.Object
2872 - Maximum Number of K-Divisible Components.

Hard

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 ith 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 = 6

Output: 2

Explanation: We remove the edge connecting node 1 with 2. The resulting split is valid because:

  • The value of the component containing nodes 1 and 3 is values[1] + values[3] = 12.
  • The value of the component containing nodes 0, 2, and 4 is values[0] + values[2] + values[4] = 6.

It can be shown that no other valid split has more than 2 connected 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 = 3

Output: 3

Explanation: We remove the edge connecting node 0 with 2, and the edge connecting node 0 with 1. The resulting split is valid because:

  • The value of the component containing node 0 is values[0] = 3.
  • The value of the component containing nodes 2, 5, and 6 is values[2] + values[5] + values[6] = 9.
  • The value of the component containing nodes 1, 3, and 4 is values[1] + values[3] + values[4] = 6.

It can be shown that no other valid split has more than 3 connected components.

Constraints:

  • 1 <= n <= 3 * 104
  • edges.length == n - 1
  • edges[i].length == 2
  • 0 <= ai, bi < n
  • values.length == n
  • 0 <= values[i] <= 109
  • 1 <= k <= 109
  • Sum of values is divisible by k.
  • The input is generated such that edges represents a valid tree.

  • Constructor Summary

    Constructors
    Constructor
    Description
    Solution()
     

  • Method Summary

    Modifier and Type
    Method
    Description
    int
    maxKDivisibleComponents(int n, int[][] edges, int[] values, int k)
     

    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

    • maxKDivisibleComponents

      public int maxKDivisibleComponents(int n, int[][] edges, int[] values, int k)