1192. Critical Connections in a Network

Hard

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There are n servers numbered from 0 to n - 1 connected by undirected server-to-server connections forming a network where connections[i] = [ai, bi] represents a connection between servers ai and bi. Any server can reach other servers directly or indirectly through the network.

A critical connection is a connection that, if removed, will make some servers unable to reach some other server.

Return all critical connections in the network in any order.

Example 1:

Input: n = 4, connections = [[0,1],[1,2],[2,0],[1,3]]
Output: [[1,3]]
Explanation: [[3,1]] is also accepted.

Example 2:

Input: n = 2, connections = [[0,1]]
Output: [[0,1]]

Constraints:

• 2 <= n <= 105

• n - 1 <= connections.length <= 105

• 0 <= ai, bi <= n - 1

• ai != bi

• There are no repeated connections.

class Solution:
    def criticalConnections(self, n: int, connections: List[List[int]]) -> List[List[int]]:
        self.visited = set()
        self.low = {}
        self.d = defaultdict(list)
        self.result = []
        for source, destination in connections:
            self.d[source].append(destination)
            self.d[destination].append(source)
        self.dfs(0,-1,0)
        return self.result
    
    def dfs(self, node, parent, rank):
        self.low[node] = rank
        self.visited.add(node)
        for adj in self.d[node]:
            if adj == parent:
                continue
            if adj not in self.visited:
                self.dfs(adj, node, rank+1)
            self.low[node] = min(self.low[node], self.low[adj])
            if rank < self.low[adj]:
                self.result.append([node, adj])