Is Critical Connections in a Network easy or hard?

The problem is rated Hard on LeetCode because it requires understanding Tarjan's algorithm and low-link values. While the DFS traversal itself is straightforward, correctly maintaining discovery times and detecting bridges requires solid graph theory knowledge.

Critical Connections in a Network Python/Java solution

Most implementations use Tarjan's DFS algorithm with adjacency lists. The same logic works across Python, Java, C++, and JavaScript: track discovery time, maintain low values, and record edges where low[v] > disc[u]. This produces all bridges in O(V + E) time.

How to solve Critical Connections in a Network in O(n)?

Solve it with Tarjan's bridge-finding algorithm. Run a DFS while storing discovery times and low-link values for every node. When exploring an edge (u, v), if low[v] becomes greater than disc[u], that edge is a bridge. This processes all vertices and edges once, giving O(V + E) complexity.

What is the best approach for Critical Connections in a Network?

The best approach uses Tarjan's Algorithm with a Depth-First Search. It tracks discovery time and low-link values for each node to identify bridge edges. If low[v] > disc[u], the edge (u, v) is a critical connection. This algorithm runs in O(V + E) time and processes each node and edge once.

Is Critical Connections in a Network asked at Google/Amazon/Meta?

Critical bridge detection problems frequently appear in interviews at companies like Amazon, Google, and Meta because they test deep graph knowledge. Variations often require detecting bridges, articulation points, or biconnected components using DFS-based algorithms.

What data structure is used in Critical Connections in a Network?

The core data structure is an adjacency list representing the graph. The algorithm also uses arrays or lists to store discovery times, low-link values, and visited states during DFS. Some alternative implementations experiment with Union-Find structures for connectivity checks.

What is the time complexity of Critical Connections in a Network?

The optimal Tarjan DFS solution runs in O(V + E) time with O(V) space. Each node is visited once and each edge is examined during the DFS traversal. Brute force approaches that remove edges and recheck connectivity can take O(E * (V + E)) time.

Description Hints 1 Solution Video 29:14

1192. Critical Connections in a Network

Hard60.6% acceptance8 companies

There are n servers numbered from 0 to n - 1 connected by undirected server-to-server connections forming a network where connections[i] = [a_i, b_i] represents a connection between servers a_i and b_i. 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 <= a_i, b_i <= n - 1
a_i != b_i
There are no repeated connections.

Asked at 8 companies

Kla Tencor Akuna Capital Flipkart ServiceNow Amazon

Google Microsoft Bloomberg

Topics

Hints open one at a time

Hint 1

Use Tarjan's algorithm.

29:14

Still stuck?Read 3 approaches, or watch a walkthrough.

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1class Solution:
2    def criticalConnections(self, n: int, connections: List[List[int]]) -> List[List[int]]:
3        

Starter codePython 3Spaces: 4

Examples

Case 1Case 2

Input

4
[[0,1],[1,2],[2,0],[1,3]]

Input

2
[[0,1]]

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