<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 {
    int t = 0;
private:
    void dfs(int node, int parent, vector<int>& vis, vector<vector<int>>& graph, vector<int>& in,
    vector<int>& low, vector<vector<int>>& ans){
        vis[node] = 1;
        in[node] = t;
        low[node] = t;
        t = t + 1;

        for(int k : graph[node]){
            if(k == parent) continue;
            if(!vis[k]){
                dfs(k, node, vis, graph, in, low, ans);
                low[node] = min(low[node], low[k]);
                if(in[node] < low[k]){
                    ans.push_back({node, k});
                }
            }
            else{
                low[node] = min(low[node], low[k]);
            }
        }
       
    }

public:
    vector<vector<int>> criticalConnections(int n, vector<vector<int>>& connections) {
        vector<vector<int>> graph(n);

        for(auto vec : connections){
            int u = vec[0];
            int v = vec[1];

            graph[u].push_back(v);
            graph[v].push_back(u);
        }

        vector<int> vis(n, 0);

        vector<int> in(n);
        vector<int> low(n);

        vector<vector<int>> ans;

        for(int i = 0; i < n; i++){
            if(!vis[i]){
                dfs(i, -1, vis, graph, in, low, ans);
            }
        }

        return ans;
    }
};
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