<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/description/

from typing import List

class Solution:
    def criticalConnections(self, n: int, connections: List[List[int]]) -> List[List[int]]:
        
        def dfs(node):
            nonlocal curr_time
            low_links[node] = curr_time
            times[node] = curr_time
            curr_time += 1

            for nei in adj_list[node]:
                if times[nei] == UNSET:
                    parents[nei] = node
                    dfs(nei)
                    if low_links[nei] > times[node]:
                        critical_edges.append([node, nei])
                if parents[node] != nei:
                    low_links[node] = min(low_links[nei], low_links[node])

        UNSET = -1
        low_links = [UNSET for _ in range(n)]
        times = [UNSET for _ in range(n)]
        parents = [None for _ in range(n)]
        critical_edges = []
        adj_list = [[] for _ in range(n)]
        curr_time = 0

        for _from, _to in connections:
            adj_list[_from].append(_to)
            adj_list[_to].append(_from)

        dfs(0)
        return critical_edges
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