Roblox·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Jun 2026

Summary

Roblox technical phone screen for a software engineer role, basically one meaty graph problem that spiraled into a full complexity analysis discussion. Felt pretty solid on the core algorithm but the tie-breaking extension and the DFS contrast tripped me up a bit.

Questions Asked (1)

Given a DAG of N tasks with directed prerequisite edges, return a valid execution order. When multiple tasks are ready to run at the same time, break ties using a provided ordering criterion (like ascending task ID, descending priority, or a custom comparator). Also detect and report cycles if no valid order exists.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

I jumped straight to Kahn's algorithm which was the right call, but I fumbled the tie-breaking part for a bit.

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AI HintsAI Generated

Suggested Approach

Use Kahn's algorithm (BFS-based topological sort) with a priority queue to break ties according to the given ordering criterion. Track in-degrees, enqueue all initially ready tasks, and repeatedly extract the highest-priority task, decrementing in-degrees of its dependents. If the output order doesn't include all tasks, report a cycle.

Pro tip: Mention that Kahn's algorithm naturally detects cycles: if the final order has fewer than N tasks, a cycle exists. Also, discuss how the choice of data structure (e.g., binary heap vs. bucket queue) affects time complexity, especially if the ordering criterion is dynamic or custom.

1. Clarify requirements and assumptions

Confirm the ordering criterion (e.g., ascending ID, descending priority) and whether the graph is guaranteed to be a DAG. Ask about input size and performance expectations.

2. Choose the algorithm

Select Kahn's algorithm for its simplicity and natural cycle detection. Explain that DFS-based topological sort is an alternative but requires separate cycle detection.

3. Design the data structures

Use an adjacency list for the graph, an array for in-degrees, and a priority queue (or custom heap) to efficiently retrieve the next ready task according to the tie-breaking rule.

4. Walk through the algorithm

Initialize in-degrees, enqueue all tasks with in-degree 0, then repeatedly extract the highest-priority task, append to order, and decrement in-degrees of its neighbors, enqueueing those that become 0.

5. Handle cycles and edge cases

After processing, if the order length is less than N, a cycle exists; report it (optionally identify the cycle). Discuss edge cases like empty graph, single node, or multiple components.

Key Points to Mention

Kahn's algorithm vs. DFS-based topological sort: trade-offs in cycle detection and implementation complexity.
Priority queue implementation: binary heap vs. bucket queue for O((N+E) log N) vs. O(N+E) when priorities are small integers.
Cycle detection: how to report the cycle (e.g., by tracking remaining nodes or using DFS to find a back edge).
Time and space complexity: O(N+E) for basic Kahn's, O((N+E) log N) with a binary heap, and O(N+E) with bucket queue if priorities are bounded.
Handling custom comparators: ensuring the priority queue supports arbitrary ordering (e.g., using a comparator function).
Real-world considerations: parallel execution, dynamic task addition, or distributed scheduling (if relevant to Roblox's scale).

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.