<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 parent ,vector<int>& visited ,vector<int>& low ,vector<int>& disc ,unordered_map<int,vector<int>>& adjL ,int i ,int time ,vector<vector<int>> &result){
        visited[i] = 1;
        disc[i] = low[i] = time++;
        for(auto neig : adjL[i]){
            if(neig == parent){
                continue;
            }
            if(visited[neig] == 0){
                dfs(i ,visited ,low ,disc ,adjL ,neig ,time ,result);
                low[i] = min(low[i],low[neig]);
                // check bridge
                if(disc[i] < low[neig]){
                    vector<int> ans;
                    ans.push_back(i);
                    ans.push_back(neig);
                    result.push_back(ans);
                }
            }
            else{
                low[i] = min(disc[neig] ,low[i]);
            }
        }
    }

    vector<vector<int>> criticalConnections(int n, vector<vector<int>>& connections) {
        vector<int> disc(n,-1);
        vector<int> low(n,-1);
        int parent = -1 ;
        vector<int> visited(n,0);
        unordered_map<int ,vector<int>> adjL; 
        for(int i = 0 ; i < connections.size() ;i++){
            adjL[connections[i][0]].push_back(connections[i][1]);
            adjL[connections[i][1]].push_back(connections[i][0]);
        }
        vector<vector<int>> result;
        int timer = 0;
        for(int i = 0 ;i < n ;i++ ){
            if(visited[i] != 1){
                dfs(parent, visited, low, disc, adjL, i, timer, result);
            }
        }
        return result;
    }
};

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