Table of contents

• Problem
• Computational complexity
• Solution

# Problem

http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_3_B

# Computational complexity

$O(V+E)$

# Solution

// C++ 14
#include <iostream>
#include <string>
#include <vector>
#include <list>
#include <algorithm>
#include <queue>
#include <stack>
#include <set>
#include <map>
#include <unordered_map>
#include <math.h>

#define ll long long
#define Int int
#define loop(x, start, end) for(Int x = start; x < end; x++)
#define loopdown(x, start, end) for(int x = start; x > end; x--)
#define rep(n) for(int x = 0; x < n; x++)
#define span(a,x,y) a.begin()+x,a.begin()+y
#define span_all(a) a.begin(),a.end()
#define len(x) (x.size())
#define last(x) (*(x.end()-1))

using namespace std;

#define MAX_V 10000

vector<Int> graph[MAX_V];
bool used_v[MAX_V],used_e[MAX_V][MAX_V];
Int ord[MAX_V],lowlink[MAX_V];
Int k=0;
vector<pair<Int, Int> > bridges;

bool compare (pair<Int, Int> a, pair<Int, Int> b) {
  if (a.first != b.first)  return a.first < b.first;
  if (a.second != b.second) return a.second < b.second;
  return false;
}

void dfs(Int v, Int parent) {
  used_v[v] = true;
  ord[v]=lowlink[v]=k++;
  
  for (Int u: graph[v]) {
    if(!used_v[u]) {
      used_e[v][u] = true;
      dfs(u, v);
      lowlink[v] = min(lowlink[v], lowlink[u]);
      if (ord[v] < lowlink[u]) {
        if (v < u) bridges.push_back(make_pair(v, u));
        else bridges.push_back(make_pair(u, v));
      }
    }
    else if(!used_e[u][v]) {
      lowlink[v] = min(lowlink[v], ord[u]);
    }
  }
}

Int main(void) {
  Int n, e, u, v;
  cin >> n >> e;
  loop(i,0,e) {
    cin >> u >> v;
    graph[u].push_back(v);
    graph[v].push_back(u);
  }
  dfs(0, -1);
  sort(bridges.begin(), bridges.end(), compare);
  for (auto b: bridges) cout << b.first << ' ' << b.second << endl;
}