<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:
    // rank based dfs
    int dfs(int n, vector<vector<int>>& graph, std::vector<int>& rank, int node, int curRank, std::set<std::pair<int, int>>& conn_dict) {
        if (rank[node] != -2) {
            return rank[node];
        }
        rank[node] = curRank;
        int minRank = curRank;
        for (int neigh: graph[node]) {
            if (rank[neigh] != curRank - 1) {
                int ret = dfs(n, graph, rank, neigh, curRank + 1, conn_dict);
                if (ret <= curRank) {
                    rank[node] = curRank;
                    int u = min(node, neigh);
                    int v = max(node, neigh);
                    conn_dict.erase({u, v});
                }
                minRank = min(minRank, ret);
            }
        }
        return minRank;
    }

    vector<vector<int>> criticalConnections(int n, vector<vector<int>>& connections) {
        // adjacency list
        std::set<std::pair<int, int>> conn_dict = {};
        std::vector<std::vector<int>> graph(n);
        for (std::vector<int>& connection : connections) {
            graph[connection[0]].push_back(connection[1]);
            graph[connection[1]].push_back(connection[0]);
            int u = min(connection[0], connection[1]);
            int v = max(connection[0], connection[1]);
            conn_dict.insert({u, v});
        }

        std::vector<int> rank(n, -2);
        dfs(n, graph, rank, 0, 0, conn_dict);
        vector<vector<int>> res = {};
        for (auto [u,v] :  conn_dict) {
            res.push_back({u, v});
        }
        return res;
    }
};
190843