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 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <math.h>
#include <stdlib.h>
#include <stdbool.h>
#define MOD 1000000007
#define END printf("\n");return 0;
#define QS09(how_data,data) qsort(data,how_data,sizeof(long),(int (*)(const void *,const void *))qsort_09);
#define QS90(how_data,data) qsort(data,how_data,sizeof(long),(int (*)(const void *,const void *))qsort_90);
#define In(a) long a;scanf("%ld",&a);
#define Out(a) printf("%ld\n",a);
void input_array(long how_data,long *data);
void output_array(long how_data,long *data);
void input_array2(long first , long second , long data[][2]);
void format_array(long how_data ,long *data,long what);
long get_random(long min, long max);
long factorial(long n);
long fibonacci(long n);
int qsort_09(const int *sys1 , const int *sys2);
int qsort_90(const int *sys1 , const int *sys2);
long sel_max(long a , long b);
long sel_min(long a , long b);
long array_max(long how_data,long *data);
long array_min(long how_data,long *data);
long can_DP(long how_data,long *data,long how_can,bool *can);
long array_sum(long how_data,long *data);
long Leven_dist(char *now , char *target);
void prime_fact(long target, long *data);
long get_digit(long target);
long ncr(long n , long r);
long npr(long n , long r);
long nhr(long n , long r);

void dfs(long vertex,long habuku);

long loop1,loop2,loop3,loop4,loop5,i_temp;
char c_temp;


typedef struct{
    long from;
    long to;
    long omomi;
} wdg; //WeightedDirectedGraph
long BellmanFord(long how_tyouten,long how_hen,long start_ten,long goal_ten,wdg hen_data[]);

//グローバル変数
long how_tyouten;
long how_hen;
long hen_data[100][2]={{0}};
bool flag[100]={0};


int main(void){
    //グラフが連結かどうかを、1本ずつ除いて見る
    scanf("%ld %ld\n",&how_tyouten,&how_hen);
    input_array2(how_hen,2,hen_data);
    //0-indexにする
    for(loop1=0;loop1<how_hen;loop1++){
        hen_data[loop1][0]--;
        hen_data[loop1][1]--;
    }
    
    //連結かを判定するにはどうすればいいか？
    //深さ優先探索とかいうのをやってみようかな
    //参考文献
    //http://www.hongo.wide.ad.jp/~jo2lxq/dm/lecture/07.pdf
    //http://wikiwiki.jp/kut-pg/?%A5%A2%A5%EB%A5%B4%A5%EA%A5%BA%A5%E0%CA%D9%B6%AF%B2%F1%2F%C3%B5%BA%F7
    
    long ans=0;
    
    for(loop1=0;loop1<how_hen;loop1++){
        for(loop2=0;loop2<100;loop2++){
            flag[loop2]=0;
        }
        dfs(0,loop1);
        for(loop2=0;loop2<how_tyouten;loop2++){
            if(flag[loop2]==0){
                ans++;
                //printf("%ld\n",loop2);
                break;
            }
        }
    }
    printf("%ld",ans);
    END;
    
    
}
 

 
void input_array(long how_data,long *data){
    long loop;
    for(loop=0;loop<how_data;loop++){
        scanf("%ld",&data[loop]);
    }
    return ;
}
void output_array(long how_data,long *data){
    long loop;
    for(loop=0;loop<how_data-1;loop++){
        printf("%ld ",data[loop]);
    }
    return ;
}
 
void input_array2(long first,long second,long data[][2]){
    long loopA,loopB;
    for(loopA=0;loopA<first;loopA++){
        for(loopB=0;loopB<second;loopB++){
            scanf("%ld",&data[loopA][loopB]);
        }
    }
    return ;
}
void format_array(long how_data ,long *data,long what){
    long loopA;
    for(loopA=0;loopA<how_data;loopA++){
        data[loopA]=what;
    }
    return ;
}
 
long get_random(long min, long max){   //指定の範囲から乱数を1つ返すやつ
    //srand((unsigned int)time(0));   //現在時刻で疑似乱数初期化
    rand();rand();rand();rand();    //乱数を空打ち
    return (rand()%(max+1-min))+min;
}
 
 
long factorial(long n){//n!のMOD10^9+7を返すやつ
    unsigned long long int ret=1;
    for(long i=1;i<=n;i++)ret=(ret*i)%1000000007;
    return (long)ret;
}
 
int qsort_09(const int *sys1 , const int *sys2){ //小さいのが上にくるやつ
    //qsort(data,how_data,sizeof(long),(int (*)(const void *,const void *))qsort_09);
    if(*sys1<*sys2){
        return -1;
    }else if(*sys1==*sys2){
        return 0;
    }else{
        return 1;
    }
}
 
int qsort_90(const int *sys1 , const int *sys2){ //大きいのが上にくるやつ
    //qsort(data,how_data,sizeof(long),(int (*)(const void *,const void *))qsort_90);
    if(*sys1<*sys2){
        return 1;
    }else if(*sys1==*sys2){
        return 0;
    }else{
        return -1;
    }
}
 
long fibonacci(long n){
    switch(n){
        case 0:return 0;
        case 1:return 1;
        default :return fibonacci(n-1)+fibonacci(n-2);
    }
}
 
long sel_max(long a,long b){
    if(a>b)return a;
    return b;
}
 
long sel_min(long a,long b){
    if(a>b)return b;
    return a;
}
 
long can_DP(long how_data,long *data,long how_can,bool *can){//Typical DP Contest A
    //data内で組み合わせられる和をcanに0 or 1で入れる
    //返り値はパターン数
    long loopA,loopB;
    long ret=0;
    for(loopA=0;loopA<how_can;loopA++){//初期化
        can[loopA]=0;
    }
    can[0]=1;//絶対にありえる
    for(loopA=0;loopA<how_data;loopA++){
        for(loopB=how_can-1;loopB>=0;loopB--){
            if(can[loopB]==1 && loopB+data[loopA]<how_can){
                can[loopB+data[loopA]]=1;
            }
        }
    }
    for(loopA=0;loopA<how_can;loopA++){
        if(can[loopA]==1){
            ret++;
        }
    }
    return ret;
}
long array_max(long how_data,long *data){
    long loop;
    long ret=data[0];
    for(loop=0;loop<how_data;loop++){
        if(ret<data[loop])ret=data[loop];
    }
    return ret;
}
long array_min(long how_data,long *data){
    long loop;
    long ret=data[0];
    for(loop=0;loop<how_data;loop++){
        if(ret>data[loop])ret=data[loop];
    }
    return ret;
}
long array_sum(long how_data,long *data){
    long ret=0;
    long loop;
    for(loop=0;loop<how_data;loop++){
        ret+=data[loop];
    }
    return ret;
}
long Leven_dist(char *now , char *target){
    long loopA,loopB;
    //レーベンシュタイン距離を求める
    // 参考文献
    // http://nw.tsuda.ac.jp/class/algoB/c13.html  (アルゴリズム理解)
    // http://d.hatena.ne.jp/ohnishiakira/20090809/1249845529  (実装)
    long len_now=strlen(now)+1;
    long len_target=strlen(target)+1;
    long d[len_now][len_target]; //計算用
    for(loopA=0;loopA<len_now;loopA++) d[loopA][0]=loopA;
    for(loopA=0;loopA<len_target;loopA++) d[0][loopA]=loopA;
    for(loopA=1;loopA<len_now;loopA++){
        for(loopB=1;loopB<len_target;loopB++){
            long cost=(now[loopA-1]==target[loopB-1] ? 0:1);
            d[loopA][loopB]=sel_min(sel_min(d[loopA-1][loopB]+1,d[loopA][loopB-1]+1),d[loopA-1][loopB-1]+cost);
        }
    }
    return d[len_now-1][len_target-1];
}
void prime_fact(long target, long *data){
    long loopB=0;
    long loopA=2;
    long moto_target=target;
    while(target!=1){
        loopA-=1;
        while(1){
            loopA++;
            if(loopA>=sqrt(moto_target)+100){
                data[loopB]=target;
                target=1;
                break;
            }
            if(target%loopA==0){
                data[loopB]=loopA;
                target/=loopA;
                loopB++;
                break;
            }
        }
    }
    return ;
}
long get_digit(long target){
    return (long)(log10(target)+1);
}
long ncr(long n , long r){
    //パスカルの三角形
    long loopA,loopB;
    long pascal[100][102]={{0}};
    pascal[1][0]=1;
    pascal[1][1]=1;
    for(loopA=2;loopA<100;loopA++){
        pascal[loopA][0]=1;
        for(loopB=1;loopB<loopA;loopB++){
            pascal[loopA][loopB]=pascal[loopA-1][loopB-1]+pascal[loopA-1][loopB];
        }
        pascal[loopA][loopA]=1;
    }
    return pascal[n][r];
}
long npr(long n, long r){
    return ncr(n,r)*factorial(r);
}
long nhr(long n , long r){
    return ncr(n+r-1,r);
}


long BellmanFord(long how_tyouten,long how_hen,long start_ten,long goal_ten,wdg hen_data[]){
    long dist[100000];
    format_array(100000,dist,10000000000);
    dist[start_ten]=0;
    
    for(int loopA=0;loopA<how_tyouten;loopA++){
        for(int loopB=0;loopB<how_hen;loopB++){
            if(dist[hen_data[loopB].from]+hen_data[loopB].omomi<dist[hen_data[loopB].to]){
                dist[hen_data[loopB].to]=dist[hen_data[loopB].from]+hen_data[loopB].omomi;
            }
        }
    }
    
    return dist[goal_ten];
}

void dfs(long vertex,long habuku){
    //既に到達済み
    if(flag[vertex]){
        return; //再帰のアレをアレするためのアレ
    }
    
    //到達済みとして記憶
    flag[vertex]=1;
    
    //vertexと連結している頂点へ訪問、ただしhabukuをはぶく
    for(int i=0;i<how_hen;i++){
        if(i!=habuku){
            if(hen_data[i][0]==vertex){
                dfs(hen_data[i][1],habuku);
            }else if(hen_data[i][1]==vertex){
                dfs(hen_data[i][0],habuku);
            }
        }
    }
    return ;
}