Critical Connections in a Network
<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://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/1100-1199/1192.Critical%20Connections%20in%20a%20Network/images/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>
Depth-First Search; Graph; Biconnected Component
class Solution:
    def criticalConnections(
        self, n: int, connections: List[List[int]]
    ) -> List[List[int]]:
        def tarjan(a: int, fa: int):
            nonlocal now
            now += 1
            dfn[a] = low[a] = now
            for b in g[a]:
                if b == fa:
                    continue
                if not dfn[b]:
                    tarjan(b, a)
                    low[a] = min(low[a], low[b])
                    if low[b] > dfn[a]:
                        ans.append([a, b])
                else:
                    low[a] = min(low[a], dfn[b])

        g = [[] for _ in range(n)]
        for a, b in connections:
            g[a].append(b)
            g[b].append(a)

        dfn = [0] * n
        low = [0] * n
        now = 0
        ans = []
        tarjan(0, -1)
        return ans
