<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 i,int parent,int currStep,vector<bool> &visited,vector<int> &step,vector<int> &minStep,vector<int> adj[],vector<vector<int>> &ans){
        visited[i] = true;
        step[i] = currStep;
        minStep[i] = currStep;
        currStep++;
        for(int it : adj[i]){
            if(it == parent) continue;
            if(visited[it]){
                minStep[i] = min(minStep[i],minStep[it]);
            }else{
                dfs(it,i,currStep,visited,step,minStep,adj,ans);
                minStep[i] = min(minStep[i],minStep[it]);
                if(minStep[it] > step[i]){
                    ans.push_back({i,it});
                }
            }
        }
    }
    vector<vector<int>> criticalConnections(int n, vector<vector<int>>& connections) {
        vector<int> adj[n];
        for(auto conn : connections){
            adj[conn[0]].push_back(conn[1]);
            adj[conn[1]].push_back(conn[0]);
        }
        vector<bool> visited(n);
        vector<int> step(n),minStep(n);
        vector<vector<int>> ans;
        dfs(0,-1,1,visited,step,minStep,adj,ans);
        return ans;
    }
};
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