<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 {
    void helper(int node, int parent, int &time, vector<vector<int>> &adj, vector<int> &visited, vector<int> &disc, vector<int> &low, vector<vector<int>> &res) {
        if(visited[node]) {
            return;
        }

        time++;

        visited[node] = 1;
        disc[node] = time;
        low[node] = time;
        int child = 0;

        for(auto neigh:adj[node]) {
            if(neigh == parent) {
                continue;
            }

            if(visited[neigh]) {
                low[node] = min(low[node], disc[neigh]);
            } else {
                helper(neigh, node, time, adj, visited, disc, low, res);
                low[node] = min(low[node], low[neigh]);
            
                if(parent != -1 && low[neigh] > disc[node]) {
                    res.push_back({node, neigh});
                }

                child++;
            }

            
        }
    }

public:
    vector<vector<int>> criticalConnections(int n, vector<vector<int>> connections) {
        connections.push_back({n, 0});
        n++;

        vector<vector<int>> adj(n);
        for(auto edge:connections) {
            int a = edge[0];
            int b = edge[1];


            adj[a].push_back(b);
            adj[b].push_back(a);
        }



        vector<int> visited(n, 0);
        vector<int> disc(n, 0);
        vector<int> low(n, 0);
        vector<vector<int>> res;

        int time = 0;
        helper(n-1, -1, time, adj, visited, disc, low, res);

        return res;
    }
};

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