<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;
    vector<int> low, vis;
    vector<vector<int>> ans;
    void dfs(int v, int p, vector<int> adj[])
    {
        vis[v] = low[v] = ++timer;
        for(auto &u: adj[v])
        {
            if(u==p) continue;
            if(vis[u]!=-1)
            {
                low[v] = min(vis[u], low[v]);
            }
            else
            {
                dfs(u, v, adj);
                if(vis[v]<low[u]) ans.push_back({v, u});
                low[v] = min(low[v], low[u]);
            }
        }
    }

    vector<vector<int>> criticalConnections(int n, vector<vector<int>>& connections) {
        low.assign(n, -1);
        vis.assign(n, -1);
        vector<int> adj[n];
        for(auto &e: connections)
        {
            adj[e[0]].push_back(e[1]);
            adj[e[1]].push_back(e[0]);
        }
        timer = 0;
        for(int i=0; i<n; i++)
        {
            if(vis[i]==-1)
            {
                dfs(i, -1, adj);
            }
        }
        return ans;
    }
};
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