<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:
    def criticalConnections(self, n: int, connections: List[List[int]]) -> List[List[int]]:
        graph = defaultdict(list)
        edges = set()
        for pair in  connections:
            u, v = pair[0], pair[1]
            graph[u].append(v)
            graph[v].append(u)
            edges.add((min(u, v), max(v, u)))
        rank = defaultdict(lambda: None)

        def dfs(node, discoverRank):
            if rank[node]:
                return rank[node]
            else:
                rank[node] = discoverRank
            
            minRank = discoverRank + 1
            for nei in graph[node]:
                if rank[nei] and rank[nei] == discoverRank - 1:
                    continue
                recursiveRank = dfs(nei, discoverRank + 1)
                if recursiveRank <= discoverRank:
                    edges.discard((min(node, nei), max(node, nei)))    
                minRank = min(minRank, recursiveRank)
            return minRank

        dfs(0, 0)
        return list(edges)        

        
80798