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 <stdlib.h>
#include <string.h>

int isconnected(int *a, int *b, int N, int M, int without){

	int isvisited[N];
	memset(isvisited, 0, sizeof(int) * N);

	isvisited[0] = 1;

	for(int i = 0; i < M; i++){
		for(int j = 0; j < M; j++){
			if(j == without) continue;
			if(isvisited[a[j]]) isvisited[b[j]] = 1;
			if(isvisited[b[j]]) isvisited[a[j]] = 1;
		}
	}

	for(int i = 0; i < N; i++){
		if(!isvisited[i]){
			return 0;
		}
	}
	return 1;

}

int main(int argc, char** argv){

	int N, M;
	int *a, *b;

	scanf("%d %d", &N, &M);

	a = malloc(sizeof(int) * M);
	b = malloc(sizeof(int) * M);

	for (int i = 0; i < M; i++){
		scanf("%d %d", a + i, b + i);
		a[i]--; b[i]--;
	}

	int ret = 0;
	for (int i = 0; i < M; i++){
		if(!isconnected(a, b, N, M, i)) ret++;
	}

	printf("%d\n", ret);
	
	free(a);
	free(b);
	return 0;
}