<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>

//9/11 class
//single forward looking dfs - tarjan's algorithm - to detect cycles 
//discovery
//lowest - earliest discovered node that i can reach from curr node is stored

//time: O(V+E)
//space: O(V+E)
class Solution {
    unordered_map<int, vector<int>> map;
    vector<int> discovery;
    vector<int> lowest;
    vector<vector<int>> result;
    int time;
public:
    vector<vector<int>> criticalConnections(int n, vector<vector<int>>& connections) {
        discovery.resize(n, -1);
        lowest.resize(n);
        time = 0;

        buildGraph(connections, n);
        dfs(0, -1);

        return result;
    }
private:
    void buildGraph(vector<vector<int>>& connections, int n) {
        for (int i = 0; i < n; i++) {
            map[i] = vector<int>();
        }

        for (const auto& edge : connections) {
            int first = edge[0];
            int second = edge[1];
            map[first].push_back(second);
            map[second].push_back(first);
        }
    }

    void dfs(int v, int u) {
        if (discovery[v] != -1) return;
        discovery[v] = lowest[v] = time++;

        for (int ne : map[v]) {
            if (ne == u) continue;
            if (discovery[ne] == -1) {
                dfs(ne, v);
                if (lowest[ne] > discovery[v]) {
                    result.push_back({ne, v});
                }
                lowest[v] = min(lowest[v], lowest[ne]);
            } else {
                lowest[v] = min(lowest[v], discovery[ne]);
            }
        }
    }
};
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