Package g2401_2500.s2493_divide_nodes_into_the_maximum_number_of_groups

Class Solution

java.lang.Object
g2401_2500.s2493_divide_nodes_into_the_maximum_number_of_groups.Solution
public class Solution extends java.lang.Object
2493 - Divide Nodes Into the Maximum Number of Groups.

Hard

You are given a positive integer n representing the number of nodes in an undirected graph. The nodes are labeled from 1 to n.

You are also given a 2D integer array edges, where edges[i] = [ai, bi] indicates that there is a bidirectional edge between nodes ai and bi. Notice that the given graph may be disconnected.

Divide the nodes of the graph into m groups ( 1-indexed ) such that:

  • Each node in the graph belongs to exactly one group.
  • For every pair of nodes in the graph that are connected by an edge [ai, bi], if ai belongs to the group with index x, and bi belongs to the group with index y, then |y - x| = 1.

Return the maximum number of groups (i.e., maximum m) into which you can divide the nodes. Return -1 if it is impossible to group the nodes with the given conditions.

Example 1:

Input: n = 6, edges = [[1,2],[1,4],[1,5],[2,6],[2,3],[4,6]]

Output: 4

Explanation: As shown in the image we:

  • Add node 5 to the first group.
  • Add node 1 to the second group.
  • Add nodes 2 and 4 to the third group.
  • Add nodes 3 and 6 to the fourth group.

We can see that every edge is satisfied. It can be shown that that if we create a fifth group and move any node from the third or fourth group to it, at least on of the edges will not be satisfied.

Example 2:

Input: n = 3, edges = [[1,2],[2,3],[3,1]]

Output: -1

Explanation: If we add node 1 to the first group, node 2 to the second group, and node 3 to the third group to satisfy the first two edges, we can see that the third edge will not be satisfied. It can be shown that no grouping is possible.

Constraints:

  • 1 <= n <= 500
  • 1 <= edges.length <= 104
  • edges[i].length == 2
  • 1 <= ai, bi <= n
  • ai != bi
  • There is at most one edge between any pair of vertices.

  • Constructor Summary

    Constructors
    Constructor
    Description
    Solution()
     

  • Method Summary

    Modifier and Type
    Method
    Description
    int
    magnificentSets(int n, int[][] edges)
     

    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

    • magnificentSets

      public int magnificentSets(int n, int[][] edges)