Minimum Degree of a Connected Trio in a Graph

You are given an undirected graph. You are given an integer n which is the number of nodes in the graph and an array edges, where each edges[i] = [ui, vi] indicates that there is an undirected edge between ui and vi.

A connected trio is a set of three nodes where there is an edge between every pair of them.

The degree of a connected trio is the number of edges where one endpoint is in the trio, and the other is not.

Return the minimum degree of a connected trio in the graph, or -1 if the graph has no connected trios.

 

Example 1:

Input: n = 6, edges = [[1,2],[1,3],[3,2],[4,1],[5,2],[3,6]]
Output: 3
Explanation: There is exactly one trio, which is [1,2,3]. The edges that form its degree are bolded in the figure above.

Example 2:

Input: n = 7, edges = [[1,3],[4,1],[4,3],[2,5],[5,6],[6,7],[7,5],[2,6]]
Output: 0
Explanation: There are exactly three trios:
1) [1,4,3] with degree 0.
2) [2,5,6] with degree 2.
3) [5,6,7] with degree 2.

 

Constraints:


Solution:

class Solution {
    public int minTrioDegree(int n, int[][] edges) {
        Map<Integer, Integer> degree = new HashMap();
        boolean[][] matrix = new boolean[n + 1][n + 1];
        for (int[] edge : edges) {
            degree.put(edge[0], degree.getOrDefault(edge[0], 0) + 1);
            degree.put(edge[1], degree.getOrDefault(edge[1], 0) + 1);
            matrix[edge[0]][edge[1]] = true;
            matrix[edge[1]][edge[0]] = true;
        }
        
        int min = Integer.MAX_VALUE;
        for (int[] edge : edges) {
            int i = edge[0], j = edge[1];
            for (int k = 1; k <= n; k ++) {
                if (matrix[i][k] && matrix[j][k]) {
                    min = Math.min(min, degree.get(i) + degree.get(j) + degree.get(k) - 6);
                }
            }
        }                
        return min == Integer.MAX_VALUE ? -1 : min;
    }
}