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 Rust (1.15.1) (judge verdict: Accepted)

use std::io::*;
use std::str::FromStr;

pub fn read<T: FromStr>() -> T {
  let stdin = stdin();
  let stdin = stdin.lock();
  let token: String = stdin
    .bytes()
    .map(|c| c.expect("failed to read char") as char)
    .skip_while(|c| c.is_whitespace())
    .take_while(|c| !c.is_whitespace())
    .collect();
  token.parse().ok().expect("failed to parse token")
}

use std::collections::HashMap;

fn main() {
  let n = read::<usize>();
  let m = read::<usize>();
  // let mut graph: HashMap<i64, Vec<i64>> = HashMap::new();

  let mut map: Vec<Vec<usize>> = vec![vec![0; n]; n];
  let mut edges: Vec<Vec<usize>> = vec![];
  let mut cnt = 0;

  for _ in 0..m {
    let a = read::<usize>();
    let b = read::<usize>();
    map[a - 1][b - 1] = 1;
    map[b - 1][a - 1] = 1;
    edges.push(vec![a - 1, b - 1])
  }

  for i in edges {
    let a = i[0];
    let b = i[1];
    // 無効化
    map[a][b] = 0;
    map[b][a] = 0;

    // dfs
    let mut visited: Vec<usize> = vec![];
    let mut stack: Vec<usize> = vec![1];

    dfs(&mut visited, &mut stack, 0, &map);

    // println!("{:?}", visited);
    if visited.len() != n {
      cnt += 1;
    }

    // 戻す
    map[a][b] = 1;
    map[b][a] = 1;
  }

  println!("{:?}", cnt);
}

fn dfs(visited: &mut Vec<usize>, stack: &mut Vec<usize>, node: usize, map: &Vec<Vec<usize>>) {
  if visited.contains(&node) {
    return;
  }
  visited.push(node);
  for (i, v) in map[node].iter().enumerate() {
    if *v == 1 {
      dfs(visited, stack, i, map)
    }
  }
}