<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:

    void dfs(int node,vector<int> &disc, vector<int>&low, vector<bool> &visited, int parent, int timer,unordered_map<int, vector<int>> &adjL , vector<vector<int>>&result  )
    {
        visited[node]= true ;
        disc[node] = low[node]= timer++;

        for(auto nbr : adjL[node])
        {
            if(nbr == parent)
            {
                continue;
            }

            if(!visited[nbr])
            {
                dfs(nbr, disc, low, visited, node, timer, adjL, result);
                low[node] = min(low[node], low[nbr]);
                //check if the edge is a bridge or not ?

                if(low[nbr] > disc[node])
                {
                    vector<int>temp ;
                    temp.push_back(node);
                    temp.push_back(nbr);

                    result.push_back(temp);
                }
            }
            else
            {
                low[node] = min(low[node], disc[nbr]);
            }
        }
    }
    vector<vector<int>> criticalConnections(int n, vector<vector<int>>& connections) {

        // making of adjacency list 
        unordered_map<int, vector<int>>adjL ;

        for(int i = 0 ;i<connections.size();i++)
        {
            int a = connections[i][0];
            int b = connections[i][1];

            adjL[a].push_back(b);
            adjL[b].push_back(a);
       
        }

        int timer = 0 ;
        int parent = -1 ;
        vector<int>disc(n, -1);
        vector<int>low(n, -1);

        vector<bool>visited(n, false);

        vector<vector<int>>result;

        for(int i = 0 ;i<n;i++)
        {
            if(!visited[i])
            {
                dfs(i, disc, low, visited, parent,timer, adjL, result);
            }
        }

        return result ;
        
    }
};
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