<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=1;
    vector<vector<int>>ans;

    void dfs(vector<vector<int>>&adj,vector<int>&vis,vector<int>&time,vector<int>&low,int node,int par) {
        vis[node]=1;
        time[node]=timer;
        low[node]=timer;
        timer++;
        for (auto ch:adj[node]) {
            if (ch==par) continue;
            if (vis[ch]) low[node]=min(low[node],low[ch]);
            else {
                dfs(adj,vis,time,low,ch,node);
                if (time[node]<low[ch]) ans.push_back({ch,node});
                low[node]=min(low[node],low[ch]);
            }
        }
    }

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