1761. Minimum Degree of a Connected Trio in a Graph

Description

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:

• 2 <= n <= 400
• edges[i].length == 2
• 1 <= edges.length <= n * (n-1) / 2
• 1 <= ui, vi <= n
• ui != vi
• There are no repeated edges.

 

Solutions

Solution: Brute Force

• Time complexity: O(n³)
• Space complexity: O(n²)

 

JavaScript

/**
 * @param {number} n
 * @param {number[][]} edges
 * @return {number}
 */
const minTrioDegree = function (n, edges) {
  const indegree = Array.from({ length: n + 1 }, () => 0);
  const connected = Array.from({ length: n + 1 }, () => new Array(n + 1).fill(false));
  let result = Number.MAX_SAFE_INTEGER;

  for (const [u, v] of edges) {
    indegree[u] += 1;
    indegree[v] += 1;
    connected[u][v] = true;
    connected[v][u] = true;
  }

  for (let u = 1; u <= n - 2; u++) {
    for (let v = u + 1; v <= n - 1; v++) {
      if (!connected[u][v]) continue;

      for (let k = v + 1; k <= n; k++) {
        if (!connected[v][k] || !connected[u][k]) continue;
        const degree = indegree[u] + indegree[v] + indegree[k] - 6;

        result = Math.min(degree, result);
      }
    }
  }

  return result === Number.MAX_SAFE_INTEGER ? -1 : result;
};