<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=1;
    void dfs(int node ,int parent ,vector<vector<int>> &adj,vector<int> &tin, vector<int> &lin, unordered_map<int,bool> &visited, vector<vector<int>> &bridge)
    {
        visited[node]=1;
        tin[node]=lin[node]=timer++;
        for(auto it:adj[node])
        {
            if(it==parent) continue;
            if(!visited[it])
            {
                dfs(it,node,adj,tin,lin,visited,bridge);
                lin[node]=min(lin[node],lin[it]);
                if(lin[it]>tin[node]) 
                {
                    bridge.push_back({it,node});
                }
            }
            else
            {
                lin[node]=min(lin[it],lin[node]);
            }
        }
    }
    vector<vector<int>> criticalConnections(int n, vector<vector<int>>& connections) {
       vector<vector<int>> adj(n);
       for(int i=0;i<connections.size();i++)
       {
          adj[connections[i][0]].push_back(connections[i][1]);
          adj[connections[i][1]].push_back(connections[i][0]);  
       }
       unordered_map<int,bool> visited;
       vector<int> tin(n);
       vector<int> lin(n);
       vector<vector<int>> bridge;
       dfs(0,-1,adj,tin,lin,visited,bridge);
       return bridge;
    }
};
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