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<cstdio>
#include<iostream>
#include<string>
using namespace std;

const int maxn=55,maxm=2505;
int n,m;
struct edge{
	int v,next;
}e[maxm];
int head[maxn],cnt;
int dfn[maxn],low[maxn],index;
int ans;

int read();
void readdata();
void add(int u,int v);
void tarjan(int u,int fa);

int main()
{
	readdata();
    return 0;
}

int read()
{
	int x=0,f=1;char c=getchar();
	while(!isdigit(c)){if(c=='-')f=-1;c=getchar();}
	while(isdigit(c)){x=x*10+c-'0';c=getchar();}
	return x*f;
}

void readdata()
{
	n=read(),m=read();
    for(int i=1;i<=m;i++)
	{
		int a,b;
		a=read(),b=read();
		add(a,b);
		add(b,a);
    }
    for(int i=1;i<=n;i++)
    {
    	if(!dfn[i])
    	{
    		tarjan(i,i);
		}
	}
    printf("%d\n",ans);	
}

void add(int u,int v)
{
	e[++cnt].v=v;
	e[cnt].next=head[u];
	head[u]=cnt;
}

void tarjan(int u,int fa)
{
    dfn[u]=low[u]=++index;
    for(int i=head[u];i;i=e[i].next)
	{
        int v=e[i].v;
        if(!dfn[v])
		{
            tarjan(v,u);
            low[u]=min(low[u],low[v]);
            if(low[v]>dfn[u]) 
			ans++;
        }
		else if(v!=fa)
        low[u]=min(low[u],dfn[v]);
    }
}