<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,vector<vector<int>>&adj,vector<bool>&visited,vector<int>&parent,vector<int>&low,vector<int>&disc,int timer,vector<vector<int>>&ans){
        low[node] = timer;
        disc[node] = timer;
        timer++;

        visited[node] = true;

        // nbrs
        for(int i=0;i<adj[node].size();i++){
            int nbr = adj[node][i];
            if(!visited[nbr]){
                parent[nbr] = node;
                dfs(nbr,adj,visited,parent,low,disc,timer,ans);
                low[node] = min(low[node] , low[nbr]);
                if(low[nbr]>disc[node]){
                    vector<int>bdg;
                    bdg.push_back(node);
                    bdg.push_back(nbr);
                    ans.push_back(bdg);
                }
            }
            else{
                if(parent[node] == nbr){
                    continue;
                }
                low[node] = min(low[node] , disc[nbr]);
            }
        }
    }
    vector<vector<int>> criticalConnections(int n, vector<vector<int>>& edges) {
        // make adj list
        vector<vector<int>>adj(n);
        for(int i=0;i<edges.size();i++){
            int u = edges[i][0];
            int v = edges[i][1];
            // undirected graph
            adj[u].push_back(v);
            adj[v].push_back(u);
            
        }

        vector<vector<int>>ans;

        vector<int>parent(n,-1);
        vector<bool>visited(n,false);
        vector<int>low(n,INT_MAX);
        vector<int>disc(n,INT_MAX);
        
        int timer = 0;

        for(int i=0;i<n;i++){
            if(!visited[i]){
                dfs(i,adj,visited,parent,low,disc,timer,ans);
            }
        }
        return ans;
    }
};
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