<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 solve(int src, int parent, unordered_map<int, list<int>>& adj, int& timer, vector<vector<int>>& ans, vector<int>& tin, vector<int>& low, vector<bool>& vis) {
    vis[src] = true;
    tin[src] = low[src] = timer++;
    
    // Traverse the neighbors
    for (auto nbr : adj[src]) {
        if (nbr == parent) {
            // Ignore the edge to the parent node
            continue;
        }
        if (!vis[nbr]) {
            // Recursive call for the neighbor
            solve(nbr, src, adj, timer, ans, tin, low, vis);
            
            // Update the low time of the current node
            low[src] = min(low[src], low[nbr]);
            
            // Check if the current edge is a bridge
            if (low[nbr] > tin[src]) {
                ans.push_back({src, nbr});
            }
        } else {
            // Update the low time if the neighbor is already visited
            low[src] = min(low[src], tin[nbr]);
        }
    }
}

vector<vector<int>> criticalConnections(int n, vector<vector<int>>& connections) {
    unordered_map<int, list<int>> adj;
    for (auto vec : connections) {
        int u = vec[0];
        int v = vec[1];
        adj[u].push_back(v);
        adj[v].push_back(u);
    }
    
    // Main logic
    int timer = 0;
    vector<vector<int>> ans;
    vector<int> tin(n, -1);
    vector<int> low(n, -1);
    vector<bool> vis(n, false);
    
    // Assume that node 0 is part of the graph and connected
    solve(0, -1, adj, timer, ans, tin, low, vis);
    
    return ans;
}
};
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