<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<int> graph[n];
        for (auto& conn : connections) {
            graph[conn[0]].push_back(conn[1]);
            graph[conn[1]].push_back(conn[0]);
        }
        
        int ranks[n];
        fill_n(ranks, n, NO_RANK);
        vector<vector<int>> result;
        // Because whole graph is connected, there is no need to loop through every node.
        criticalConnections(graph, n, 0, 0, ranks, result);        
        
        return result;
    }
private:
    int NO_RANK=-2;

    int criticalConnections(vector<int> graph[], int n, int node, int myRank, int ranks[], vector<vector<int>>& result) {
        if (ranks[node] != NO_RANK) {
            return ranks[node];
        }

        int lowestRank = myRank;
        ranks[node] = myRank;
        for (auto neighbor : graph[node]) {
            if (ranks[neighbor] == myRank - 1 || ranks[neighbor] == n) {
                continue;
            }
            
            int neighborRank = criticalConnections(graph, n, neighbor, myRank + 1, ranks, result);
            lowestRank = min(lowestRank, neighborRank);
            if (neighborRank > myRank) {
                result.push_back({min(node, neighbor), max(node, neighbor)});
            }
            
        }
        
        ranks[node] = n;
        return lowestRank;
    }
};
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