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::prelude::*;

fn input<T>() -> T
where
    T: std::str::FromStr,
{
    let stdin = std::io::stdin();
    let token: String = stdin
        .lock()
        .bytes()
        .map(|c| c.unwrap() as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().unwrap()
}

fn main() {
    let n: usize = input();
    let m: usize = input();
    let ab: Vec<Vec<i64>> = (0..m)
        .map(|_| {
            let a = input();
            let b = input();
            vec![a, b]
        })
        .collect();

    let mut ans = 0;
    for i in 0..m {
        let mut uf = UnionFind::new(n);
        for j in 0..m {
            if i == j {
                continue;
            }

            uf.connect(ab[j][0] - 1, ab[j][1] - 1);
        }
        if uf.size(0) < n {
            ans += 1;
        }
    }

    println!("{}", ans);
}

struct UnionFind {
    parent: Vec<i64>,
}

impl UnionFind {
    fn new(n: usize) -> UnionFind {
        UnionFind {
            parent: vec![-1; n],
        }
    }

    fn root(&mut self, i: i64) -> i64 {
        if self.parent[i as usize] < 0 {
            i
        } else {
            let p = self.parent[i as usize];
            self.parent[i as usize] = self.root(p);
            self.parent[i as usize]
        }
    }

    fn connect(&mut self, i: i64, j: i64) {
        let i = self.root(i);
        let j = self.root(j);
        if i == j {
            return;
        }

        if i < j {
            self.parent[i as usize] += self.parent[j as usize];
            self.parent[j as usize] = i;
        } else {
            self.parent[j as usize] += self.parent[i as usize];
            self.parent[i as usize] = j;
        }
    }

    fn size(&mut self, i: i64) -> usize {
        let ri = self.root(i);
        (-self.parent[ri as usize]) as usize
    }
}