Introduction

In this blog post, we will explore how to solve the LeetCode problem "1761" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

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] = [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.

Explanation

Here's a breakdown of the solution:

• Adjacency Matrix: Use an adjacency matrix to efficiently check for the existence of edges between nodes.
• Trio Iteration: Iterate through all possible combinations of three nodes to identify connected trios.

• Degree Calculation: For each connected trio, calculate its degree by counting edges connected to the trio's nodes but not part of the trio itself. Keep track of the minimum degree encountered.

• Runtime Complexity: O(n^3), Storage Complexity: O(n^2)

Code

    def minTrioDegree(n: int, edges: list[list[int]]) -> int:
    """
    Finds the minimum degree of a connected trio in a graph.

    Args:
        n: The number of nodes in the graph.
        edges: A list of edges, where each edge is a list of two node indices.

    Returns:
        The minimum degree of a connected trio, or -1 if no trios exist.
    """

    adj_matrix = [[False] * (n + 1) for _ in range(n + 1)]
    degrees = [0] * (n + 1)

    for u, v in edges:
        adj_matrix[u][v] = True
        adj_matrix[v][u] = True
        degrees[u] += 1
        degrees[v] += 1

    min_degree = float('inf')
    trio_found = False

    for i in range(1, n + 1):
        for j in range(i + 1, n + 1):
            if adj_matrix[i][j]:
                for k in range(j + 1, n + 1):
                    if adj_matrix[i][k] and adj_matrix[j][k]:
                        trio_found = True
                        degree = degrees[i] + degrees[j] + degrees[k] - 6  # Subtract 6 for the 3 edges within the trio.
                        min_degree = min(min_degree, degree)

    if not trio_found:
        return -1
    else:
        return min_degree