<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:
//tarjan algo -->Finding bridges
int timer=1;
 vector<vector<int>>ans;

void dfs(int node,int parent,vector<int>&vis,vector<int> adj[],vector<int>&tin,vector<int>&low)
{
  vis[node]=1;
  tin[node]=timer;
  low[node]=timer;
  timer++;

  for(auto it:adj[node])
  {
    if(!vis[it])
    {
      dfs(it,node,vis,adj,tin,low);

      low[node]=min(low[node],low[it]);

      if(tin[node]<low[it])
      {
        //it is a bridge
        ans.push_back({node,it});

      }


    }
    else {
        if(it==parent)
        {
            continue;
        }
        low[node]=min(low[node],low[it]);
    }
  }
}
 

    vector<vector<int>> criticalConnections(int n, vector<vector<int>>& connections) {
        vector<int> adj[n];
        for(auto it:connections)
        {
            int a=it[0];
            int b=it[1];
            adj[a].push_back(b);
            adj[b].push_back(a);

        }

        vector<int>tin(n);
        vector<int>low(n); //minimum time of insertion of all adjacent nodes apart from the parent
        vector<int>vis(n,0);
        dfs(0,-1,vis,adj,tin,low);
        return ans;


    }
};
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