How do you perform topological sort on a directed acyclic graph?
Reported in Palo Alto Networks USA engineering loops. Graph algorithm for task scheduling, build systems, and course prerequisites.
Interview scenario
Context for Palo Alto Networks candidates:
Detect cycle if present; otherwise return valid ordering of nodes.
Model answer
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Cover trade-offs, structure, and a concrete example before revealing the baseline response.
How to frame this at Palo Alto Networks: Connect your answer to measurable impact, clarity of thought, and trade-offs the team cares about. Below is a strong baseline response you can adapt with your own project examples.
Kahn's algorithm (BFS): compute in-degree for each node; enqueue nodes with in-degree 0; dequeue, append to order, decrement neighbors' in-degree; enqueue newly zero nodes. If order length < V, cycle exists.
DFS approach: post-order stack—after visiting all descendants, push node. Reverse stack for topological order. Track visiting/visited states for cycle detection (back edge).
Time O(V + E), space O(V). Applications: Maven/Gradle task order, course prerequisites, instruction scheduling in compilers.
Follow-up: longest path in DAG for critical path method; parallel topological levels for batch execution.
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