<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(map<int,vector<int>> &graph,vector<bool> &vis,int parent,int node,vector<vector<int>> &result,int timer,vector<pair<int,int>> &times){

        vis[node]=true;
        times[node].first=timer;
        times[node].second=timer;
        timer++;

        for(auto i:graph[node]){

            if(i == parent)     continue;
            if(!vis[i]){

                dfs(graph,vis,node,i,result,timer,times);
                times[node].second=min(times[node].second,times[i].second);
                if(times[i].second > times[node].first){
                    vector<int> store;
                    store.push_back(node);
                    store.push_back(i);
                    result.push_back(store);
                }

            }
            else{
                times[node].second=min(times[node].second,times[i].second);
            }
        }


    }

    vector<vector<int>> criticalConnections(int n, vector<vector<int>>& connections) {

        int edges=connections.size();
        vector<vector<int>> result;
        map<int,vector<int>> graph;
        vector<bool> vis(n,false);
        vector<pair<int,int>> times(n,{0,0});    //initial and lowest

        for(int i=0;i<edges;i++){

            int a=connections[i][0];
            int b=connections[i][1];

            graph[a].push_back(b);
            graph[b].push_back(a);
        }

        dfs(graph,vis,-1,0,result,1,times);

        return result;
    
    }
};
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