Openai·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Jun 2026

Summary

Interviewed at OpenAI for what seemed like a software engineering role. The technical portion zeroed in on complexity analysis for a simulation problem, which sounds routine until you're actually in the hot seat trying to justify every nested loop.

Questions Asked (1)

Walk through the time and space complexity of your simulation implementation, accounting for the number of steps, the data structure sizes, and any nested operations.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

I had the code in front of me and still fumbled a bit.

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AI HintsAI Generated

Suggested Approach

Start by defining the simulation's parameters (e.g., number of steps N, number of entities M) and the core data structures used. Then, systematically analyze the time complexity by breaking down each operation within a single step, including any nested loops or data structure operations. Finally, aggregate these costs over all steps and analyze the space complexity by summing the sizes of all data structures and any auxiliary space.

Pro tip: Always discuss both average and worst-case complexities, and mention any optimizations or trade-offs you made (e.g., using a hash map for O(1) lookups at the cost of extra space). This shows you think beyond just the code and consider practical performance implications.

1. Define Parameters and Data Structures

Clearly state the variables that affect complexity, such as number of simulation steps (N), number of entities (M), and the data structures used (e.g., arrays, hash maps, queues).

2. Analyze Per-Step Time Complexity

Break down the operations performed in a single simulation step. Identify loops, nested loops, and operations on data structures, and determine their individual time complexities.

3. Aggregate Time Complexity Over All Steps

Multiply or sum the per-step complexities across all N steps to get the total time complexity. Consider if the per-step cost changes over time (e.g., due to growing data structures).

4. Analyze Space Complexity

Calculate the total memory used by all data structures, including any auxiliary space for temporary variables or recursion. Express it in terms of N and M.

5. Discuss Trade-offs and Optimizations

Mention any trade-offs made between time and space, and potential optimizations (e.g., using a more efficient data structure) that could improve complexity.

Key Points to Mention

Big-O notation for time and space complexity, with clear definitions of variables (e.g., N = steps, M = entities).
Identification of nested operations and their impact on complexity (e.g., O(N*M) vs O(N+M)).
Data structure choices and their operation complexities (e.g., array access O(1), hash map lookup O(1) average, tree operations O(log M)).
Amortized analysis if applicable (e.g., dynamic array resizing).
Space-time trade-offs (e.g., caching results to reduce time at the cost of memory).
Worst-case vs average-case scenarios and how they affect the simulation's performance.

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