<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:
    vector<vector<int>> criticalConnections(int n, vector<vector<int>>& connections) {
        vector<vector<int>> graph(n);

        for (auto& conn: connections) {
            graph[conn[0]].push_back(conn[1]);
            graph[conn[1]].push_back(conn[0]);
        }

        vector<char> visited(n);
        vector<int> lowest(n);
        vector<int> nums(n);
        int num = 0;

        vector<vector<int>> result;
        findCycle(graph, -1, 0, num, visited, nums, lowest, result);

        return result;
    }
private:
    int findCycle(vector<vector<int>>& graph, int prevNode, int node, int& num, vector<char>& visited, vector<int>& nums, vector<int>& lowest, vector<vector<int>>& result) {
        visited[node] = 1;
        ++num;
        nums[node] = num;
        lowest[node] = num;
        int& low = lowest[node];

        for (int near: graph[node]) {
            if (near == prevNode) { continue; }
            
            if (visited[near]) {
                low = min(low, nums[near]);
            } else {
                low = min(low, findCycle(graph, node, near, num, visited, nums, lowest, result));
            }

            if (nums[node] < lowest[near]) {
                result.push_back({node, near});
            }
        }

        return low;
    }
};
167953