Shortest Cycle in a Graph — LeetCode 2608 Python Solution

The problem

There is a bi-directional graph with n vertices, where each vertex is labeled from 0 to n - 1. The edges in the graph are represented by a given 2D integer array edges, where edges[i] = [ui, vi] denotes an edge between vertex ui and vertex vi.

Example

Input

n = 7, edges = [[0,1],[1,2],[2,0],[3,4],[4,5],[5,6],[6,3]]

Output

3

Explanation

The cycle with the smallest length is : 0 -> 1 -> 2 -> 0

Python solution

class Solution:
    def findShortestCycle(self, n: int, edges: List[List[int]]) -> int:
        def bfs(u: int, v: int) -> int:
            dist = [inf] * n
            dist[u] = 0
            q = deque([u])
            while q:
                i = q.popleft()
                for j in g[i]:
                    if (i, j) != (u, v) and (j, i) != (u, v) and dist[j] == inf:
                        dist[j] = dist[i] + 1
                        q.append(j)
            return dist[v] + 1

        g = defaultdict(set)
        for u, v in edges:
            g[u].add(v)
            g[v].add(u)
        ans = min(bfs(u, v) for u, v in edges)
        return ans if ans < inf else -1

Complexity

Pattern: Breadth-First Search

Expand outward level by level, so the first time you arrive is the shortest way. LeetCode 2608. Shortest Cycle in a Graph is filed here because LeetCode tags it Breadth-First Search, which is the vocabulary this hub collects.

The breadth-first search guide has the Python template for the pattern and the 233 LeetCode problems that use it.

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