BFS on graph
Last updated: February 13, 2026
Quick Overview
Implement the Breadth-First Search (BFS) algorithm to traverse a given undirected graph represented as an adjacency list. Your function should take the graph and a starting node as input, and return a list of nodes in the order they are visited. Ensure that your solution handles graphs with cycles and disconnected components appropriately.
Brex
February 13, 20262
12
3,291 solved
Implement the Breadth-First Search (BFS) algorithm to traverse a given undirected graph represented as an adjacency list. Your function should take the graph and a starting node as input, and return a list of nodes in the order they are visited. Ensure that your solution handles graphs with cycles and disconnected components appropriately.
This coding problem is frequently asked during Technical Screen at Brex. The interviewer is testing your ability to translate a problem into clean, working code while discussing time and space complexity. Brex expects candidates to write production-quality code, not just solve the puzzle.
What the Interviewer Expects
- Recognize the underlying problem pattern (sliding window, two pointers, BFS/DFS, etc.)
- Discuss multiple approaches and trade-offs before coding
- Implement an optimal solution with clean, production-quality code
- Handle all edge cases including boundary conditions and invalid input
- Optimize both time and space complexity with clear justification
- Test your solution systematically with well-chosen examples
Key Topics to Cover
How to Approach This
- Clarify input constraints and edge cases before writing code.
- Walk through your approach verbally and confirm with the interviewer before coding.
- Start with a brute force solution, then optimize. Mention time and space complexity.
- Test your solution with examples, including edge cases like empty input or duplicates.
- Consider common patterns: sliding window, two pointers, hash map, BFS/DFS, dynamic programming.
Possible Follow-up Questions
- How would you test this solution thoroughly?
- How would your solution change if the input was sorted?
- What is the worst-case input for your solution?
- How would you parallelize this solution?
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Problem Analysis
The problem requires implementing the Breadth-First Search (BFS) algorithm on an undirected graph represented as an adjacency list. BFS is suitable here because it explores all neighbors at the presen...
Approach
- Initialize Structures: Start by creating a queue to manage the nodes to visit and a set to track visited nodes.
- Enqueue Starting Node: Add the starting node to the queue and mark it as...
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