Leetcode #1192: Critical Connections in a Network
In this guide, we solve Leetcode #1192 Critical Connections in a Network in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
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.
Quick Facts
- Difficulty: Hard
- Premium: No
- Tags: Depth-First Search, Graph, Biconnected Component
Intuition
The data forms a graph, so we should explore nodes and edges systematically.
A traversal ensures we visit each node once while maintaining the needed state.
Approach
Build an adjacency list and traverse with BFS or DFS.
Aggregate results as you visit nodes.
Steps:
- Build the graph.
- Traverse with BFS/DFS.
- Accumulate the required output.
Example
Input: n = 4, connections = [[0,1],[1,2],[2,0],[1,3]]
Output: [[1,3]]
Explanation: [[3,1]] is also accepted.
Python Solution
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
Complexity
The time complexity is O(V+E). The space complexity is O(V).
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.