<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:
    vector<int> discovery_time;
    vector<int> lowest_time;
    vector<bool> visited;
    vector<vector<int>> ans;
    
    vector<vector<int>> criticalConnections(int n, vector<vector<int>>& connections) 
    {
        vector<vector<int>> graph (n);
        discovery_time.resize(n, 0);
        lowest_time.resize(n, 0);
        visited.resize(n, false);
        
        for (auto conn : connections) {
            auto u = conn[0];
            auto v = conn [1];
            graph[u].push_back(v);
            graph[v].push_back(u);
        }
        
        for (int i = 0; i < n; i++) {
            if (visited[i] == false) {
                int timestamp = 0;
                int parent = -1;
                dfs(graph, i, timestamp, parent);
            }
        }
        return ans;
    }
    
    void dfs(const vector<vector<int>>& graph, int node, int timestamp, int parent)
    {
        visited[node] = true;
        ++timestamp;
        discovery_time[node] = lowest_time[node] = timestamp;
        
        for (auto neigh : graph[node]) {
            if (!visited[neigh]) {
                dfs(graph, neigh, timestamp, node);
                lowest_time[node] = min(lowest_time[node], lowest_time[neigh]);
                
                if (lowest_time[neigh] > discovery_time[node]) {
                    ans.push_back({node, neigh});
                }
                
            } else if (neigh != parent) {
                lowest_time[node] = min(lowest_time[node], discovery_time[neigh]);
            }
        }
    }
};
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