Package g2401_2500.s2493_divide_nodes_into_the_maximum_number_of_groups

Class Solution

  • public class Solution
extends 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 Detail

      • Solution

        public Solution()

    • Method Detail

      • magnificentSets

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