Graph Cycle Detection

Given an undirected graph, determine whether it contains a cycle. The graph is represented by \( n \) vertices (numbered from 0 to \( n-1 \)) and \( m \) edges. An edge connecting a vertex to itself (a self-loop) is also considered a cycle. A cycle exists if there is a path that starts and ends at the same vertex and involves at least one edge. You can use Depth-First Search (DFS) or any other method of your choice.

If a cycle exists, output Cycle detected; otherwise, output No cycle.

inputFormat

The input is given from standard input (stdin) in the following format:

1. The first line contains two integers \( n \) and \( m \) separated by a space, where \( n \) is the number of vertices and \( m \) is the number of edges.
2. Each of the next \( m \) lines contains two integers \( u \) and \( v \), representing an undirected edge between vertex \( u \) and vertex \( v \).

outputFormat

Output a single line to standard output (stdout):

• If the graph contains a cycle, print Cycle detected.
• If the graph does not contain a cycle, print No cycle.

5 5
0 1
1 2
2 3
3 1
3 4

Cycle detected