<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 {
private:
    void checkCriticalConnection(int i, int timer, int parent,
                                 vector<int>& lowTime, vector<int>& tin,
                                 vector<bool>& visited,
                                 vector<vector<int>>& ans,
                                 vector<vector<int>>& adj) 
    {
        lowTime[i] = tin[i] = timer++;
        visited[i] = true;

        for (auto& it : adj[i]) 
        {
            if (it == parent)
                continue;

            if (!visited[it]) 
            {
                checkCriticalConnection(it, timer, i, lowTime, tin, visited, ans, adj);
                lowTime[i] = min(lowTime[i], lowTime[it]);

                if (lowTime[it] > tin[i])
                    ans.push_back({i, it});
            } 
            else
                lowTime[i] = min(lowTime[i], lowTime[it]);
        }
    }

public:
    vector<vector<int>> criticalConnections(int n,
                                            vector<vector<int>>& connections) 
    {
        vector<int> tin(n), lowTime(n);
        vector<bool> visited(n), marked(n);
        vector<vector<int>> adj(n);
        vector<vector<int>> ans;

        for (auto& it : connections) 
        {
            adj[it[0]].push_back(it[1]);
            adj[it[1]].push_back(it[0]);
        }

        for (int i = 0; i < n; i++) 
        {
            if (!visited[i])
                checkCriticalConnection(i, 0, -1, lowTime, tin, visited, ans,
                                        adj);
        }

        return ans;
    }
};
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