Minimum Degree of a Connected Trio in a Graph

graph theoryenumeration

Problem Statement

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] = [u _i , v _i ] indicates that there is an undirected edge between u _i and v _i .

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.

Examples

Example 1

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

2 <= n <= 400

edges[i].length == 2

1 <= edges.length <= n * (n-1) / 2

1 <= u _i , v _i <= n

u _i != v _i

There are no repeated edges.

😤

Hard

Difficulty

Topic Info

ModuleDSA

CategoryGraph Theory

Sub-topicEnumeration