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.*;

class UnionFind {
    int[] roots;
	
	public UnionFind(int N) {
		this.roots = new int[N];
		for(int i = 0; i < N; ++i) this.roots[i] = i;
	}
	
	int getRoot(int x) {
		if(this.roots[x] == x) return x;
		else return this.roots[x] = getRoot(this.roots[x]);
	}
	
	boolean isSameSet(int x, int y) {
		return getRoot(x) == getRoot(y);
	}
	
	void unite(int x, int y) {
	    int rx = getRoot(Math.max(x, y));
	    int ry = getRoot(Math.min(x, y));
	    if(rx == ry) return;
	    roots[rx] = ry;
	}
}

public class Main {
    static Scanner sc = new Scanner(System.in);
    static final int SIZE = 55;
    static int N = 0;
    static int M = 0;
    static int[] a = new int[SIZE];
    static int[] b = new int[SIZE];
    
    public static void main (String[] args) {
        N = sc.nextInt();
        M = sc.nextInt();
        for(int i = 0; i < M; ++i) {
            a[i] = sc.nextInt() - 1;
            b[i] = sc.nextInt() - 1;
        }
        
        int ans = 0;
        for(int i = 0; i < M; ++i) {
            if(isBridge(i)) ++ans;
        }
        System.out.println(ans);
    }
    
    static boolean isBridge(int num) {
        UnionFind uf = new UnionFind(N);
        for(int i = 0; i < M; ++i) {
            if(i != num) uf.unite(a[i], b[i]);
        }
        return isNotConnected(uf);
    }
    
    static boolean isNotConnected(UnionFind uf) {
        for(int i = 0; i < N - 1; ++i) {
            for(int j = i + 1; j < N; ++j) {
                if(!uf.isSameSet(i, j)) return true;
            }
        }
        return false;
    }
}