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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Scanner;

public class Main {
    int n, m;
    boolean[][] es;
    int[] as, bs;
    public static void main(String[] args) {
        Main m = new Main();
        m.read();
        m.solve();
    }

    private void read() {
        Scanner sc = new Scanner(System.in);
        n = sc.nextInt();
        m = sc.nextInt();
        es = new boolean[n][n];
        as = new int[m];
        bs = new int[m];
        for (int i = 0; i < m; i++) {
            int a = sc.nextInt() - 1;
            int b = sc.nextInt() - 1;
            es[a][b] = es[b][a] = true;
            as[i] = a;
            bs[i] = b;
        }
    }

    private void solve() {
        int ans = 0;
        for (int i = 0; i < m; i++) {
            int a = as[i];
            int b = bs[i];
            es[a][b] = es[b][a] = false;
            if (!check())
                ans++;
            es[a][b] = es[b][a] = true;
        }
        System.out.println(ans);
    }

    private boolean check() {
        boolean[] fs = new boolean[n];
        dfs(0, 0, fs);
        boolean ret = true;
        for (boolean b: fs)
            ret &= b;
        return ret;
    }

    private void dfs(int node, int depth, boolean[] used) {
        if (used[node])
            return;
        used[node] = true;
        for (int i = 0; i < n; i++) {
            if (es[node][i] && !used[i])
                dfs(i, depth+1, used);
        }
    }

}