<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:

    int timer = 0;
    vector<int> tin, low;
    vector<vector<int>> bridges;
    vector<bool> visited;

    void dfs(int node, int parent, vector<int>* adj) {
        // cout << node << " => ";
        visited[node] = true;
        tin[node] = low[node] = ++timer;
        // cout << tin[node] << endl;
        for(int child: adj[node]) {
            // cout << child << endl;
            if(child == parent) continue;
            if(visited[child]) {
                low[node] = min(low[node], tin[child]);
                continue;
            }   
            dfs(child, node, adj);
            // cout << node << " " << child << " " << low[child] << " " << tin[node] << endl;
            if(low[child] > tin[node]) {
                bridges.push_back({node, child});
            }
            low[node] = min(low[node], low[child]);
        }
    }

    vector<vector<int>> criticalConnections(int n, vector<vector<int>>& connections) {
        tin = low = vector<int> (n, -1);
        visited = vector<bool> (n, false);
        vector<int> adj[n];
        for(auto connection: connections) {
            int u = connection[0], v = connection[1];
            adj[u].push_back(v);
            adj[v].push_back(u);
        }
        for(int i = 0; i < n; ++i) {
            if(!visited[i]) {
                dfs(i, -1, adj);
            }
        }
        return bridges;
    }
};
192478