<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>

from collections import defaultdict

class Crit:
    def __init__(self, connections):
        self._critical = {(min(a,b), max(a,b)): True for a,b in connections}

    def set_noncritical(self, a, b):
        #print(a,b)
        self._critical[(min(a,b), max(a,b))] = False

    def get_critical(self):
        return [edge for edge, val in self._critical.items() if val is True]

class Solution:
    def criticalConnections(self, n: int, connections: List[List[int]]) -> List[List[int]]:
        DEBUG = False
        def dprint(*args):
            if DEBUG: print(*args)
        nbd = defaultdict(list)
        for a, b in connections:
            nbd[a].append(b)
            nbd[b].append(a)
        rank = {i: None for i in range(n)}
        critical = Crit(connections)
        def dfs(a, r=0):
            """a,b are nbd, but we can't follow a->b link"""
            dprint("call", a, r, rank)
            if rank[a] is not None:
                dprint("return", a)
                return rank[a]
            else:
                rank[a] = r
                min_r = r + 1
                for x in nbd[a]:
                    if rank[x] == r-1: # parent
                        dprint("skip par", x)
                        continue
                    r_x = dfs(x, r+1)
                    dprint("xx", a, x, r_x, r)
                    if r_x <= r:
                        critical.set_noncritical(a, x)
                    min_r = min(min_r, r_x)
                return min_r

        dfs(0)  # don't need other starting points, by assumption this will reach the whole network
        return critical.get_critical()
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