Problem:
Score : 300 points

Problem Statement

You are given an undirected connected graph with N vertices and M edges that does not contain self-loops and double edges.

The i-th edge (1 \leq i \leq M) connects Vertex a_i and Vertex b_i.

An edge whose removal disconnects the graph is called a bridge.

Find the number of the edges that are bridges among the M edges.

Notes

A self-loop is an edge i such that a_i=b_i (1 \leq i \leq M).

Double edges are a pair of edges i,j such that a_i=a_j and b_i=b_j (1 \leq i<j \leq M).

An undirected graph is said to be connected when there exists a path between every pair of vertices.

Constraints

2 \leq N \leq 50

N-1 \leq M \leq min(N(N−1)⁄2,50)

1 \leq a_i<b_i \leq N

The given graph does not contain self-loops and double edges.

The given graph is connected.

Input

Input is given from Standard Input in the following format:

N M
a_1 b_1
a_2 b_2
:
a_M b_M

Output

Print the number of the edges that are bridges among the M edges.

Sample Input 1

7 7
1 3
2 7
3 4
4 5
4 6
5 6
6 7

Sample Output 1

4

The figure below shows the given graph:

The edges shown in red are bridges. There are four of them.

Sample Input 2

3 3
1 2
1 3
2 3

Sample Output 2

0

It is possible that there is no bridge.

Sample Input 3

6 5
1 2
2 3
3 4
4 5
5 6

Sample Output 3

5

It is possible that every edge is a bridge.

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
     
using namespace std;

vector <pair<int,int>> edge;
bool adj[51][51];
bool visited[51];
int n,m,a,b;

void dfs(int now)
{
    visited[now] = true;
    for(int next=1;next<=n;next++)
    {
        if(adj[now][next] && visited[next]==false)
        {
            dfs(next);
        }
    }
}

int main(void)
{
    cin.tie(0);
    ios::sync_with_stdio(false);

    cin >> n >> m;

    for(int i=0;i<m;i++)
    {
        cin >> a >> b;
        adj[a][b] = true;
        adj[b][a] = true;
        edge.push_back(make_pair(a,b));
    }

    int res = 0;
    int count = 0;
    int cnt = 0;

    memset(visited,false,sizeof(visited));
    for(int i=1;i<=n;i++)
    {
        if(visited[i]==false)
        {
            count++;
            dfs(i);
        }
    }

    for(int i=0;i<m;i++)
    {
        memset(visited,false,sizeof(visited));
        adj[edge[i].first][edge[i].second] = false;
        adj[edge[i].second][edge[i].first] = false;
        cnt = 0;
        for(int j=1;j<=n;j++)
        {
            if(visited[j]==false)
            {
                cnt++;
                dfs(j);
            }
        }
        if(cnt > count)
        {
            res++;
        }
        adj[edge[i].first][edge[i].second] = true;
        adj[edge[i].second][edge[i].first] = true;        
    }

    cout << res << '\n';
    
    return 0;
}