<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>> ans;
    vector<vector<int>> graph(n);

    for (const vector<int>& connection : connections) {
      const int u = connection[0];
      const int v = connection[1];
      graph[u].push_back(v);
      graph[v].push_back(u);
    }

    // rank[i] := the minimum node that node i can reach with forward edges
    // Initialize with NO_RANK = -2 to indicate not visited.
    getRank(graph, 0, 0, vector<int>(n, NO_RANK), ans);
    return ans;
  }

 private:
  static constexpr int NO_RANK = -2;

  // Gets the minimum rank that u can reach with forward edges.
  int getRank(const vector<vector<int>>& graph, int u, int currRank,
              vector<int>&& rank, vector<vector<int>>& ans) {
    if (rank[u] != NO_RANK)  // The rank is already determined.
      return rank[u];

    rank[u] = currRank;
    int minRank = currRank;

    for (const int v : graph[u]) {
      // visited || parent (that's why NO_RANK = -2 instead of -1)
      if (rank[u] == rank.size() || rank[v] == currRank - 1)
        continue;
      const int nextRank =
          getRank(graph, v, currRank + 1, std::move(rank), ans);
      // (u, v) is the only way for u go to v.
      if (nextRank == currRank + 1)
        ans.push_back({u, v});
      minRank = min(minRank, nextRank);
    }

    rank[u] = rank.size();  // Mark as visited.
    return minRank;
  }
};
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