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 <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <utility>
using namespace std;
typedef long long ll;
#define rep(i,n) for (int i=0;i < (int)(n);i++)
vector<bool> seen;

class union_find {
public:
vector<int> par,rank;
union_find(int n): par(n),rank(n){
   for (int i=0;i < n;i++){
      par[i]=i;
      rank[i]=0;
   }
}

int find(int x){
   if (par[x]==x){
      return x;
   }
   else{
      return par[x] = find(par[x]); 
   }
}

void unite(int x ,int y){
   x=find(x);
   y=find(y);
   if (x==y) return;
   if (rank[x] < rank[y]){
      par[x] = y;
   }else{
      par[y]=x;
      if (rank[x]==rank[y]) rank[x]++;
   }
}

bool same(int x, int y){
   return find(x) == find(y);
}
};

int main(){
    int n,m;
    cin >> n >> m;
    vector<pair<int,int>> w(m);    
    for (int i=0;i < m;i++){
        int x,y;
        cin >> x >> y;
        x--;y--;
        pair<int,int> p=make_pair(x,y);
        w[i]=p;
    }
    int count=0;
    int ans=0;
    for (int j=0;j <m;j++){
        union_find g(n);
        for (int k=0;k < m;k++){
            if (j==k) continue;
            pair<int,int> p=w[k];
            g.unite(p.first,p.second);
        }
        count=0;
        for (int i=0;i < n;i++){
            if (g.par[i]==i) count++;
        }
        if (count!=1) ans++;
    }
    cout << ans << endl;
    return 0;
}