<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(vector<vector<int>> &ans,vector<int> adj[],int i,int parent,vector<int> &tin,vector<int> &low,vector<int> &vis,int val)
    {
        vis[i]=1;
        tin[i]=val;
        low[i]=val;
        for(auto it:adj[i])
        {
            if(vis[it]==1)
            {
                if(it!=parent&&low[it]<low[i])
                low[i]=low[it];
            }
            else
            {
                dfs(ans,adj,it,i,tin,low,vis,val+1);
                //can bridge
                if(tin[i]<low[it])
                {
                    vector<int> v(2,0);
                    v[0]=i;
                    v[1]=it;
                    ans.push_back(v);
                }
                low[i]=min(low[i],low[it]);
                
            }

        }
    }
    vector<vector<int>> criticalConnections(int n, vector<vector<int>>& connections) {
        vector<int>adj[n];
        for(int i=0; i<connections.size(); i++){
            adj[connections[i][0]].push_back(connections[i][1]);
            adj[connections[i][1]].push_back(connections[i][0]);
        }
        vector<vector<int>> ans;
        vector<int> tin(n,0);
        vector<int> low(n,0);
        vector<int> vis(n,0);
        dfs(ans,adj,0,-1,tin,low,vis,0);
        return ans;

    }
};
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