<p>There are <code>n</code> servers numbered from <code>0</code> to <code>n - 1</code> connected by undirected server-to-server <code>connections</code> forming a network where <code>connections[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> represents a connection between servers <code>a<sub>i</sub></code> and <code>b<sub>i</sub></code>. Any server can reach other servers directly or indirectly through the network.</p>

<p>A <em>critical connection</em> is a connection that, if removed, will make some servers unable to reach some other server.</p>

<p>Return all critical connections in the network in any order.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2019/09/03/1537_ex1_2.png" style="width: 198px; height: 248px;" />
<pre>
<strong>Input:</strong> n = 4, connections = [[0,1],[1,2],[2,0],[1,3]]
<strong>Output:</strong> [[1,3]]
<strong>Explanation:</strong> [[3,1]] is also accepted.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 2, connections = [[0,1]]
<strong>Output:</strong> [[0,1]]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>2 &lt;= n &lt;= 10<sup>5</sup></code></li>
	<li><code>n - 1 &lt;= connections.length &lt;= 10<sup>5</sup></code></li>
	<li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt;= n - 1</code></li>
	<li><code>a<sub>i</sub> != b<sub>i</sub></code></li>
	<li>There are no repeated connections.</li>
</ul>

class Solution {
public:
    int timer=0;
    vector<int>insert_time;
    vector<int>low_time;
    vector<vector<int>>store;
    void dfs(int index,int parent,vector<int>adj[],vector<bool>&visited){
        insert_time[index]=timer;
        low_time[index]=timer;
        visited[index]=true;
        timer++;
        for(auto child:adj[index]){
            if(child!=parent){
                if(visited[child]==false)
                {
                    dfs(child,index,adj,visited);
                    if(low_time[child]>insert_time[index])
                    {
                        store.push_back({index,child});
                        
                    }
                    low_time[index]=min(low_time[index],low_time[child]);
                   
                }
                else{
                   low_time[index]=min(low_time[index],low_time[child]);   
                }
                
            }
        }
    }
    


    
    vector<vector<int>> criticalConnections(int n, vector<vector<int>>& e) {
       vector<int>adj[n] ;
       insert_time.resize(n);
       low_time.resize(n);
      for(auto it:e)
      {
         adj[it[0]].push_back(it[1]);
         adj[it[1]].push_back(it[0]);
      }
      vector<bool>visited(n+1,false);
      dfs(0,-1,adj,visited);
      return store;
    

        
    }
};
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