from collections import deque

def add_edge(adj: list, u, v):
    adj[u].append(v)
    adj[v].append(u)

def detect_cycle(adj: list, s, V, visited: list):
    parent = [-1] * V
    q = deque()
    visited[s] = True
    q.append(s)

    while q != []:
        u = q.pop()
        for v in adj[u]:
            if not visited[v]:
                visited[v] = True
                q.append(v)
                parent[v] = u
            elif parent[u] != v:
                return True
    return False

def cycle_disconnected(adj: list, V):
    visited = [False] * V
    for i in range(V):
        if not visited[i] and detect_cycle(adj, i, V, visited):
            return True
    return False

if __name__ == "__main__":
    V = 5
    adj = [[] for i in range(V)]
    add_edge(adj, 0, 1)
    add_edge(adj, 1, 2)
    add_edge(adj, 2, 0)
    add_edge(adj, 2, 3)
    add_edge(adj, 2, 1)

    if cycle_disconnected(adj, V):
        print("有5个顶点在图中")
        print("0-->1")
        print("1-->2")
        print("2-->0")
        print("2-->3")
        print("2-->1")
        print("是否有一个循环?")
        print("Yes")
    else:
        print("有5个顶点在图中")
        print("0-->1")
        print("1-->2")
        print("2-->0")
        print("2-->3")
        print("2-->1")
        print("是否有一个循环?")
        print("Yes")
        print("没有")

有5个顶点在图中
0-->1
1-->2
2-->0
2-->3
2-->1
是否有一个循环?
Yes