<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);
        unordered_map<int, unordered_set<int>> uncriticals;
        vector<int> steps(n, -1);
        for (auto &c: connections) {
            graph[c[0]].push_back(c[1]);
            graph[c[1]].push_back(c[0]);
        }

        function<int(int, int, int)> dfs = [&](int begin, int prev, int step) {
            if (steps[begin] != -1) {
                return steps[begin];
            }
            steps[begin] = step;

            int minstep = step;
            for (auto neighbor: graph[begin]) {
                if (neighbor == prev) {
                    continue;
                }

                int tmp = dfs(neighbor, begin, step + 1);
                if (tmp <= step) {
                    uncriticals[begin].insert(neighbor);
                }
                minstep = min(minstep, tmp);
            }

            return minstep;
        };

        dfs(0, -1, 0);

        vector<vector<int>> ans;
        for (auto &c: connections) {
            if (uncriticals[c[0]].count(c[1]) || uncriticals[c[1]].count(c[0])) {
                continue;
            }
            ans.push_back(c);
        }

        return ans;
    }
};
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