<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]]:
        cMap = {i: [] for i in range(n)}
        for i, j in connections:
            cMap[i].append(j)
            cMap[j].append(i)
        
        lows = [n] * n
        res = []
        
        def dfs(node, dt, parent):
            if lows[node] == n:
                lows[node] = dt
                for neighbor in cMap[node]:
                    if neighbor != parent:
                        expected_dt = dt+1
                        actual_dt = dfs(neighbor, expected_dt, node)
                        #print(node, dt, expected_dt, actual_dt)
                        if actual_dt >= expected_dt:
                            res.append((node, neighbor))
                        lows[node] = min(lows[node], actual_dt)
            return lows[node]
        
        dfs(n-1, 0, -1)
        
        #for i in cMap.keys():
        #    if len(cMap[i]) == 1:
        #        for j in connections:
        #            if i in j and j not in res:
        #                res.append(j)
        return res
71805