<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:

    map<int,vector<int>> adj;
    int visited[100001];
    int discoveryTime[100001];
    int lowestTime[100001];
    int idx=0;


    int dfs(int node,int parent)
    {
        visited[node] = 1;
        discoveryTime[node] = idx++;
        lowestTime[node] = discoveryTime[node];
        int temp = INT_MAX;
        for(auto it:adj[node])
        {
            if(!visited[it])
            {
                temp=min(temp,dfs(it,node));
                lowestTime[node] = min(lowestTime[node],temp);
            } 
            else if(it!=parent)
            {
                // backedge found
                lowestTime[node] = min(lowestTime[node],discoveryTime[it]);
            }
        }
        return lowestTime[node];
    }
    vector<vector<int>> criticalConnections(int n, vector<vector<int>>& v) {
        for(int i=0;i<n;i++) lowestTime[i] = INT_MAX;
        vector<vector<int>> ans;
        for(auto it:v)
        {
            adj[it[0]].push_back(it[1]);
            adj[it[1]].push_back(it[0]);
        }

        dfs(0,-1);
        // for(int i=0;i<n;i++)
        // {
        //     cout<<discoveryTime[i]<<' ';
        // }
        // cout<<endl;
        //  for(int i=0;i<n;i++)
        // {
        //     cout<<lowestTime[i]<<' ';
        // }
        for(auto it:v)
        {
            int x=it[0];
            int y=it[1];
            if(y<x) swap(x,y);
            if(lowestTime[y] > discoveryTime[x]) ans.push_back({x,y});
            
        }
        return ans;
    }
};
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