<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:
    int timer = 0;
    void dfs(int node, int parent, vector<int> adj[], vector<int> &time, vector<int> &low, vector<int> &visited, vector<vector<int>> &bridges)
    {
        visited[node] = 1;
        time[node] = timer;
        low[node] = timer;
        timer++;
        for(auto x : adj[node])
        {
            if(x == parent)
                continue;
            if(visited[x] == 0){
                dfs(x, node, adj, time, low, visited, bridges);
                if(low[x] > time[node])
                    bridges.push_back({x, node});
            }
            else{
                    if(low[x] < low[node])
                        low[node] = low[x];
            }
            
        }

        for(auto x : adj[node])
        {
            if(x != parent && low[x] < low[node])
                low[node] = low[x];
        }

        



    }
    vector<vector<int>> criticalConnections(int n, vector<vector<int>>& edges) {
        vector<vector<int>> bridges;
        vector<int> adj[n];
        for(auto x : edges)
        {
            adj[x[0]].push_back(x[1]);
            adj[x[1]].push_back(x[0]);
        }
        vector<int> time(n);
        vector<int> low(n);
        vector<int> visited(n, 0);
        dfs(0, -1, adj, time, low, visited, bridges);
        return bridges;
    }
};
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