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 Scala (2.11.7) (judge verdict: Accepted)

import java.io.{BufferedReader, InputStreamReader}

object Main extends App {

  val in = new BufferedReader(new InputStreamReader(System.in))
  val Array(n, m) = in.readLine.split(" ").map(_.toInt)
  val edges = Iterator.continually(in.readLine)
    .take(m)
    .map(_.split(" ").map(_.toInt))
    .toArray

  val graph = {
    val arr = Array.ofDim[Boolean](n+1,n+1)
    for(edge <- edges) {
      arr(edge(0))(edge(1)) = true
      arr(edge(1))(edge(0)) = true
    }
    arr
  }
  var visit = Array.ofDim[Boolean](n+1)

  def dfs(v:Int):Unit = {
    if(visit(v)) return
    visit(v) = true
    for(i <- 1 to n) {
      if(graph(v)(i)) dfs(i)
    }
  }

  val ans = {
    for(edge <- edges) yield {
      visit = Array.fill(n+1)(false)
      graph(edge(0))(edge(1)) = false
      graph(edge(1))(edge(0)) = false
      dfs(edge(0))
      // println(visit.mkString(" "))
      graph(edge(0))(edge(1)) = true
      graph(edge(1))(edge(0)) = true
      visit.tail.forall(_ == true)
    }
  }

  println(ans.count(_ == false))
}