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)

#[allow(unused_imports)]
use std::char::from_digit;
#[allow(unused_imports)]
use std::cmp::{max, min};
#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
#[allow(unused_imports)]
use std::fs::File;
#[allow(unused_imports)]
use std::io::prelude::*;
#[allow(unused_imports)]
use std::io::{stdin, stdout, BufReader, BufWriter, Stdin, Stdout, Write};
#[allow(unused_imports)]
use std::mem::swap;
#[allow(unused_imports)]
use std::str::FromStr;
 
type BoxResult<T> = Result<T, Box<std::error::Error>>;


fn main() {
    let mut scanner = Scanner::new(stdin());
    let line = scanner.read_vector::<usize>().unwrap();
    let (n, m) = (line[0], line[1]);
    let mut edges = vec![];
    for _ in 0..m {
        let line = scanner.read_vector::<usize>().unwrap();
        let (a, b) = (line[0] - 1, line[1] - 1);
        edges.push((a, b));
    }
    let mut ans = 0;
    for i in 0..m {
        if !is_connected(n, &edges, i) {
            ans += 1;
        }
    }
    println!("{}", ans);    
}

fn is_connected(n: usize, edges: &[(usize, usize)], skip_index: usize) -> bool {
    let mut uf = UnionFindTree::new(n);
    for i in 0..edges.len() {
        if i == skip_index {
            continue;
        }
        uf.unite(edges[i].0, edges[i].1);
    }
    return uf.group_num() == 1
}

struct UnionFindTree {
    parents: Vec<usize>,
    heights: Vec<usize>,
    sizes: Vec<usize>,
    group_num: usize,
}

impl UnionFindTree {
    fn new(size: usize) -> UnionFindTree {
        UnionFindTree {
            parents: (0..size).collect(),
            heights: vec![0; size],
            sizes: vec![1; size],
            group_num: size,
        }
    }

    fn climb_up(&mut self, node: usize) -> usize {
        let mut parents_to_root = vec![];
        let mut present = node;
        while self.parents[present] != present {
            parents_to_root.push(present);
            present = self.parents[present];
        }
        for &node in parents_to_root.iter() {
            self.parents[node] = present;
        }
        present
    }

    fn is_same_group(&mut self, x: usize, y: usize) -> bool {
        self.climb_up(x) == self.climb_up(y)
    }

    fn unite(&mut self, x: usize, y: usize) {
        let root_x = self.climb_up(x);
        let root_y = self.climb_up(y);
        if root_x == root_y {
            return;
        }
        if self.heights[root_x] > self.heights[root_y] {
            self.parents[root_y] = root_x;
            self.sizes[root_x] += self.sizes[root_y];
        } else if self.heights[root_x] < self.heights[root_y] {
            self.parents[root_x] = root_y;
            self.sizes[root_y] += self.sizes[root_x];
        } else {
            self.parents[root_y] = root_x;
            self.heights[root_x] += 1;
            self.sizes[root_x] += self.sizes[root_y];
        }
        self.group_num -= 1;
    }

    fn group_num(&self) -> usize {
        self.group_num
    }
}

#[allow(dead_code)]
struct Scanner<R> {
    reader: BufReader<R>,
    buffer: String,
}
impl<R> Scanner<R>
where
    R: Read,
{
    #[allow(dead_code)]
    fn new(inner: R) -> Scanner<R> {
        let reader = BufReader::new(inner);
        let buffer = String::new();
        Scanner {
            reader: reader,
            buffer: buffer,
        }
    }
    #[allow(dead_code)]
    fn with_capacity(capacity: usize, inner: R) -> Scanner<R> {
        let reader = BufReader::with_capacity(capacity, inner);
        let buffer = String::new();
        Scanner {
            reader: reader,
            buffer: buffer,
        }
    }
 
    #[allow(dead_code)]
    fn read_line(&mut self) -> BoxResult<String> {
        self.reader.read_line(&mut self.buffer)?;
        let cloned = self.buffer.trim().to_string();
        self.buffer.clear();
        Ok(cloned)
    }
 
    #[allow(dead_code)]
    fn read<T>(&mut self) -> BoxResult<T>
    where
        T: FromStr,
        T::Err: std::fmt::Debug,
        T::Err: std::error::Error,
        T::Err: 'static,
    {
        self.reader.read_line(&mut self.buffer)?;
        let parsed = self.buffer.trim().parse()?;
        self.buffer.clear();
        Ok(parsed)
    }
    #[allow(dead_code)]
    fn read_vector<T>(&mut self) -> BoxResult<Vec<T>>
    where
        T: FromStr,
        T::Err: std::fmt::Debug,
        T::Err: std::error::Error,
        T::Err: 'static,
    {
        self.reader.read_line(&mut self.buffer)?;
        let parsed_vec = self
            .buffer
            .trim()
            .split_whitespace()
            .map(|s| s.parse())
            .collect::<Result<Vec<_>, _>>()?;
        self.buffer.clear();
        Ok(parsed_vec)
    }
    #[allow(dead_code)]
    fn read_matrix<T>(&mut self, lines: usize) -> BoxResult<Vec<Vec<T>>>
    where
        T: FromStr,
        T::Err: std::fmt::Debug,
        T::Err: std::error::Error,
        T::Err: 'static,
    {
        let mut parsed_matrix = vec![];
        for _ in 0..lines {
            self.reader.read_line(&mut self.buffer)?;
            parsed_matrix.push(
                self.buffer
                    .trim()
                    .split_whitespace()
                    .map(|s| s.parse())
                    .collect::<Result<Vec<_>, _>>()?,
            );
            self.buffer.clear();
        }
        Ok(parsed_matrix)
    }
    #[allow(dead_code)]
    fn read_chars(&mut self) -> BoxResult<Vec<char>> {
        self.reader.read_line(&mut self.buffer)?;
        let chars = self.buffer.trim().chars().collect::<Vec<_>>();
        self.buffer.clear();
        Ok(chars)
    }
}