CPMagical CP Library

Problem solution · Python

Critical Connections in a Network

Critical Connections in a Network: a Python solution using depth-first search. Learn the idea, check the complexity, and read the full code, with credit to Kamyu LeetCode Solutions.

Technique
Depth-first search
Source
Kamyu LeetCode Solutions
Length
35 lines
Start with the idea.

Try the problem first. If you get stuck, read the approach below, then write your own solution. The full code is at the bottom.

Approach

Depth-first search

For Critical Connections in a Network, the implementation follows one branch at a time, making it suitable for components, trees, backtracking, or dependency exploration.

  1. Define the state carried into one recursive or stack frame.
  2. Mark or choose the current state before exploring children.
  3. Combine child results or undo the choice when the branch finishes.

Code notes

  • 35 lines of Python from the credited upstream file critical-connections-in-a-network.py.
  • The implementation visibly relies on sequence storage.
  • No explicit loop blocks detected, together with recursive traversal.

Complexity

Count unique states for graph traversal; for backtracking, count the branching factor and maximum depth.

Check the problem constraints before deciding whether this complexity will pass.

Source

Code and credit

This code comes from Kamyu LeetCode Solutions by kamyu104 and is used under the MIT licence.

Open problem ↗Original source ↗
Full codeCritical Connections in a Network · PythonPython
Use this to learn the idea, then write your own version.
# Time:  O(|V| + |E|)# Space: O(|V| + |E|) # variant of Tarjan's algorithm (https://www.geeksforgeeks.org/bridge-in-a-graph/)class Solution(object):    def criticalConnections(self, n, connections):        """        :type n: int        :type connections: List[List[int]]        :rtype: List[List[int]]        """        def dfs(edges, parent, u, idx, lowlinks, lookup, result):            if lookup[u]:                return              lookup[u] = True            curr_idx = lowlinks[u] = idx[0]            idx[0] += 1            for v in edges[u]:                if v == parent:                    continue                dfs(edges, u, v, idx, lowlinks, lookup, result)                lowlinks[u] = min(lowlinks[u], lowlinks[v])                if lowlinks[v] > curr_idx:                    # if any lowlink of neighbors is larger than curr_idx                    result.append([u, v])                edges = [[] for _ in xrange(n)]        idx, lowlinks, lookup = [0], [0]*n, [False]*n        result = []        for u, v in connections:            edges[u].append(v)            edges[v].append(u)        dfs(edges, -1, 0, idx, lowlinks, lookup, result)        return result

Keep practising

Did this explanation save you time? I'm a Grade 11 student building this free library to make difficult algorithms easier to understand.

Buy me a coffee ↗