<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 dfs(int node, int parent, vector<int> g[], vector<int> &discovered, vector<int> &low, unordered_map<int,bool> &visited, int &timer, vector<vector<int>> &ans){
        visited[node] = true;
        discovered[node] = low[node] = timer++;
        for(auto child: g[node]){
            if(child==parent){
                continue;
            }   
            else if(!visited[child]){
                dfs(child, node, g, discovered, low, visited, timer, ans);
                low[node] = min(low[child], low[node]);
                if(low[child]>discovered[node]){
                    vector<int> temp;
                    temp.push_back(child);
                    temp.push_back(node);
                    ans.push_back(temp);
                }
            } 
            else{ 
                low[node] = min(low[node], discovered[child]);
            }
        }
    }
    vector<vector<int>> criticalConnections(int n, vector<vector<int>>& connections) {
        int e = connections.size();
        vector<int> g[n];
        for(int i=0;i<e;i++){
            g[connections[i][0]].push_back(connections[i][1]);
            g[connections[i][1]].push_back(connections[i][0]);
        }
        vector<int> discovered(n), low(n);
        int parent = -1;
        unordered_map<int,bool> visited;
        for(int i=0;i<n;i++){
            discovered[i] = -1;
            low[i] = -1;
            visited[i] = false;
        }
        vector<vector<int>> ans;
        int timer = 0;
        for(int i=0;i<n;i++){
            if(!visited[i]){
                dfs(i,parent,g,discovered,low,visited,timer,ans);
            }
        }
        return ans;
    }
};
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