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 (1.42.0) (judge verdict: Accepted)

use proconio::{input, marker::Usize1};

pub struct UnionFind {
    dim: usize,
    par: Vec<usize>,
}

impl UnionFind {
    pub fn new(d: usize) -> UnionFind {
        let mut list = vec![0; d];
        for i in 0..d {
            list[i] = i;
        }
        UnionFind { dim: d, par: list }
    }

    pub fn dim(self) -> usize {
        self.dim
    }

    pub fn union(&mut self, x: usize, y: usize) {
        let x_root = self.find(x);
        let y_root = self.find(y);
        if x_root > y_root {
            self.union(y, x);
        } else if x_root < y_root {
            self.par[y_root] = x_root;
        }
    }

    pub fn find(&mut self, x: usize) -> usize {
        if self.par[x] == x {
            return x;
        }
        self.par[x] = self.find(self.par[x]);
        self.par[x]
    }

    pub fn same(&mut self, x: usize, y: usize) -> bool {
        return self.find(x) == self.find(y);
    }
}

pub struct AdjList {
    dim: usize,
    list: Vec<Vec<usize>>,
}

impl AdjList {
    pub fn new(d: usize) -> AdjList {
        AdjList {
            dim: d,
            list: vec![vec![]],
        }
    }

    pub fn dim(&self) -> usize {
        self.dim
    }

    pub fn add_edge(&mut self, from: usize, to: usize) {
        self.list.get_mut(from).unwrap().push(to);
    }

    pub fn add_undirected_edge(&mut self, from: usize, to: usize) {
        self.list.get_mut(from).unwrap().push(to);
        self.list.get_mut(to).unwrap().push(from);
    }

    pub fn out_edges(&mut self, vertex: usize) -> Vec<usize> {
        self.list.get_mut(vertex).unwrap().to_vec()
    }

    pub fn in_edges(&mut self, v: usize) -> Vec<usize> {
        let mut res = vec![];
        for l in 0..self.dim() {
            if let Some(list) = self.list.get(l) {
                if list.contains(&v) {
                    res.push(l);
                }
            }
        }

        res
    }
}

fn main() {
    input! {
        n: usize,
        m: usize,
        edges: [(Usize1, Usize1); m]
    }

    let mut res = 0;
    for i in 0..m {
        // iは使わないもの
        let mut uf = UnionFind::new(n);
        for j in 0..m {
            if j != i {
                uf.union(edges[j].0, edges[j].1);
            }
        }

        // つなげたので連結性判定
        let mut f = true;
        for j in 0..n {
            f &= uf.find(j) == 0;
        }
        if !f {
            res += 1;
        }
    }
    println!("{}", res);
}