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 Python (3.4.3) (judge verdict: Accepted)

from collections import deque

def check(st,en,ed):
    ed[st-1][en-1] -= 1
    ed[en-1][st-1] -= 1
    cnt = [0] * n
    q = deque()
    q.append(st)
    cnt[st-1] += 1
    while q:
        now = q.popleft()
        if ed[now-1][en-1] == 1:
            ed[st-1][en-1] += 1
            ed[en-1][st-1] += 1
            return False
        for r in range(n):
            if ed[now-1][r] == 1 and cnt[r] == 0:
                q.append(r+1)
                cnt[r] += 1
    ed[st-1][en-1] += 1
    ed[en-1][st-1] += 1
    return True

n, m = map(int, input().split())

edge = [[0] * n for _ in range(n)] 

nodes = []

for i in range(m):
    a, b = map(int, input().split())
    nodes.append((a,b))
    edge[a-1][b-1] += 1
    edge[b-1][a-1] += 1

ans = 0 
for node in nodes:
    a,b = node[0], node[1]
    if check(a,b,edge):
        ans += 1

print(ans)