<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 curr,int parent,int timer,vector<int> &discovery,vector<int> &lowest,unordered_map<int,vector<int>> &adj,
    unordered_map<int,bool> &visited,
    vector<vector<int>> &result){
        visited[curr]=true;
        lowest[curr]=discovery[curr]=timer++;
        for(auto ele:adj[curr]){
            if(ele==parent){
                continue;
            }
            if(visited[ele]==false){
                dfs(ele,curr,timer,discovery,lowest,adj,visited,result);
                lowest[curr]=min(lowest[ele],lowest[curr]);
                //for bridge
                if(lowest[ele]>discovery[curr]){
                    vector<int> out={curr,ele};
                    result.push_back(out);
                }

            }
            else{
                lowest[curr]=min(lowest[curr],discovery[ele]);

            }
        }
        return;
    }
    vector<vector<int>> criticalConnections(int n, vector<vector<int>>& connections) {
        unordered_map<int,vector<int>> adj;
        for(int i=0;i<connections.size();i++){
            int u=connections[i][0];
            int v=connections[i][1];
            adj[u].push_back(v);
            adj[v].push_back(u);
        }
        vector<vector<int>> result;
        vector<int> discovery(n,-1);
        vector<int> lowest(n,-1);
        unordered_map<int,bool> visited;
        int parent=-1;
        int timer=0;
        for(int i=0;i<n;i++){
            if(visited[i]==false){
                dfs(i,parent,timer,discovery,lowest,adj,visited,result);
            }
        }
        return result;
    }
};
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