1192. Critical Connections in a Network

Author: Partho Biswas

leetcode.com/python/1192_Critical_Connections_in_a_Network.py

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+# Source: https://tinyurl.com/yc2tzb4k
+import collections
+
+
+class Solution(object):
+    def criticalConnections(self, n, connections):
+        """
+        :type n: int
+        :type connections: List[List[int]]
+        :rtype: List[List[int]]
+        """
+        graph = defaultdict(list)
+        for connection in connections:
+            x, y = connection
+            graph[x].append(y)
+            graph[y].append(x)
+
+        criticalConnections = set(map(tuple, map(sorted, connections)))
+        serverRank = [-2] * n
+        self.dfsServerSearch(0, 0, graph, serverRank, criticalConnections,
+                             n)  # since this is a connected graph, we don't have to loop over all nodes.
+        return list(criticalConnections)
+
+    def dfsServerSearch(self, serverNode, depth, graph, serverRank, criticalConnections, n):
+        if serverRank[serverNode] >= 0:
+            return serverRank[serverNode]  # # visiting (0<=serverRank<n), or visited (serverRank=n)
+        serverRank[serverNode] = depth
+        minBackDepth = n
+        for neighbour in graph[serverNode]:
+            if serverRank[neighbour] == depth - 1:
+                continue  # don't immmediately go back to parent. that's why i didn't choose -1 as the special value, in case depth==0.
+            backDepth = self.dfsServerSearch(neighbour, depth + 1, graph, serverRank, criticalConnections, n)
+            if backDepth <= depth:
+                criticalConnections.discard(tuple(sorted((serverNode, neighbour))))
+            minBackDepth = min(minBackDepth, backDepth)
+        return minBackDepth