<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>

// https://leetcode.com/problems/critical-connections-in-a-network/

static const auto s_initialize = [] { std::ios::sync_with_stdio(false); std::cin.tie(nullptr); std::cout.tie(nullptr); return nullptr; }();

class Solution {
public:
    vector<vector<int>> criticalConnections(int n, vector<vector<int>>& connections) {
        return criticalConnections_v1(n, connections); // [325, 366] ms, 169.91 MB.
    }


private:
    // method 1. DFS, EntryTimeOfNode.
    //    https://cp-algorithms.com/graph/bridge-searching.html
    // O( V + E ); O( V ).
    //
    vector<vector<int>> criticalConnections_v1(const int n, const vector<vector<int>>& connections) {
        std::vector< std::vector<int> > vvEdge( n );
        for (const auto& conn: connections) {
            vvEdge[ conn[0] ].emplace_back( conn[1] );
            vvEdge[ conn[1] ].emplace_back( conn[0] );
        }
        std::vector< std::vector<int> > vvRes;
        std::vector<bool> vIsVisited(n);
        std::vector<int> vTin(n), vLow(n);
        int iTime = 0;
        std::function< void(const int, const int) > tDfs;
        tDfs = [=, &tDfs, &vvEdge, &vvRes, &vIsVisited, &vTin, &vLow, &iTime] (const int i, const int pa) -> void {
            vIsVisited[i] = true;
            vLow[i] = vTin[i] = (++iTime);
            for (const int ni: vvEdge[i]) {
                if (ni != pa) {
                    if (vIsVisited[ni]) {
                        vLow[i] = std::min(vLow[i], vTin[ni]);
                    } else {
                        tDfs(ni, i);
                        vLow[i] = std::min(vLow[i], vLow[ni]);
                        if (vLow[ni] > vTin[i]) {
                            vvRes.emplace_back( std::vector<int>{i, ni} );
                        }
                    }
                }
            }
        };
        tDfs(0, -1);
        return vvRes;
    }

};

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