Topological Sort on grid
Last updated: December 5, 2025
Quick Overview
Given a 2D grid consisting of cells that can either be empty or contain a directed edge to another cell, implement a function to perform a topological sort on the grid. The function should return a list of cells in a valid topological order, or indicate if a cycle exists in the directed graph represented by the grid. The input will be a 2D array, and the output should be a list of coordinates representing the sorted order or an indication of a cycle.
Palo Alto Networks
December 5, 2025120
12
2,898 solved
Given a 2D grid consisting of cells that can either be empty or contain a directed edge to another cell, implement a function to perform a topological sort on the grid. The function should return a list of cells in a valid topological order, or indicate if a cycle exists in the directed graph represented by the grid. The input will be a 2D array, and the output should be a list of coordinates representing the sorted order or an indication of a cycle.
Palo Alto Networks uses this problem in the Onsite to evaluate your algorithmic thinking. They expect you to discuss multiple approaches, analyze trade-offs between them, and implement the optimal solution with clean, readable code.
What the Interviewer Expects
- Quickly identify the optimal approach and its theoretical basis
- Handle complex algorithm design with multiple interacting components
- Write concise, elegant code under time pressure
- Prove correctness of your approach and discuss alternative solutions
- Optimize beyond the obvious: discuss constant factor improvements
- Address follow-up variations and explain how the solution generalizes
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?
- Can you solve this iteratively instead of recursively (or vice versa)?
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Practice DSA ProblemsSample Answer
Problem Analysis
This problem can be approached as a graph problem where each cell in the grid represents a node, and the directed edges represent dependencies (i.e., which cell must be processed before another). A to...
Approach
- Graph Representation: Convert the 2D grid into a graph representation using an adjacency list. Each cell will point to its directed neighbors based on the directed edges defined in the grid. 2....
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