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 Ruby (2.3.3) (judge verdict: Accepted)

class UnionFind
  def initialize(n)
    @root = Array.new(n)
    @rank = Array.new(n)
    @size = Array.new(n)
    (0...n).each do |i|
      @root[i] = i
      @rank[i] = 0
      @size[i] = 1
    end
  end

  def find(x)
    if @root[x] == x
      x
    else
      @root[x] = find(@root[x])
    end
  end

  def unite(x, y)
    x_root = find(x)
    y_root = find(y)
    return if x_root == y_root

    if @rank[x_root] < @rank[y_root]
      @root[x_root] = y_root
      @size[y_root] += @size[x_root]
    else
      @root[y_root] = x_root
      @size[x_root] += @size[y_root]
      if @rank[x_root] == @rank[y_root]
        @rank[x_root] += 1
      end
    end
    nil
  end

  def size(x)
    x_root = find(x)
    @size[x_root]
  end

  def same?(x, y)
    find(x) == find(y)
  end
end

N, M = gets.split.map(&:to_i)
ab_list = M.times.map { gets.split.map(&:to_i) }
ans = 0
(0...(ab_list.size)).each do |i|
  a, b = ab_list[i]
  uf = UnionFind.new(N)
  (0...(ab_list.size)).each do |j|
    next if j == i
    _a, _b = ab_list[j]
    uf.unite(_a - 1, _b - 1)
  end
  ans += 1 unless uf.same?(a - 1, b - 1)
end
puts ans