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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
 
const int MAXN = 55;
const int MAXM = 500;
 
struct Edge
{
    int to,next;
}edge[MAXM];
int head[MAXN],tot;
int Dfn[MAXN],Low[MAXN];
int Index,res;
 
void addedge(int u, int v)
{
    edge[tot].to = v;
    edge[tot].next = head[u];
    head[u] = tot++;
}
 
void Tarjan(int u, int fa)
{
    Dfn[u] = Low[u] = ++Index;
    for(int i = head[u]; i != -1; i = edge[i].next)
    {
        int v = edge[i].to;
        if(!Dfn[v])
        {
            Tarjan(v,u);
            Low[u] = min(Low[u],Low[v]);
            if(Low[v] > Dfn[u])
                ++res;
        }
        else if(v != fa)
            Low[u] = min(Low[u],Dfn[v]);
    }
}
 
void solve(int n)
{
    Index = res = 0;
    memset(Dfn,0,sizeof(Dfn));
    memset(Low,0,sizeof(Low));
    Tarjan(1,-1);
    printf("%d\n",res);
}
 
int main()
{
    int n,m,u,v;
    memset(head,-1,sizeof(head));
    tot = 0;
    scanf("%d %d",&n,&m);
    for(int i = 0; i < m; ++i)
    {
        scanf("%d %d",&u,&v);
        addedge(u,v);
        addedge(v,u);
    }
    solve(n);
    return 0;
}