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 C++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
using Graph= vector<vector<int>>;

void DFS(const Graph gph, int from, int to, unordered_map<int, int> *pre, unordered_map<int, int> *low, set<pair<int, int>> *bridges){
  int pre_to= pre->size();
  pre->operator[](to)= pre_to;
  low->operator[](to)= pre_to;

  for(auto ngh:gph.at(to)){
    if(ngh != from){
      if(!pre->count(ngh)){
        DFS(gph, to, ngh, pre, low, bridges);
      }
      low->at(to)= min(low->at(to), low->at(ngh));
    }
  }
  if(from != -1 && pre->at(to)==low->at(to)){
    bridges->insert(make_pair(from, to));
  }
}

int main(){
  int N,M;
  cin >> N >> M;

  Graph gph= vector<vector<int>>(N);
  int v1,v2;
  for(int j=0; j<M; j++){
    cin >> v1 >> v2;
    v1--; v2--; // 1-indexed -> 0-indexed
    gph.at(v1).emplace_back(v2);
    gph.at(v2).emplace_back(v1);
  }

  unordered_map<int, int> pre;
  unordered_map<int, int> low;
  set<pair<int, int>> bridges;
  DFS(gph, -1, 0, &pre, &low, &bridges);

  int ans= bridges.size();
  cout << ans << endl;
}