Openai·Software Engineer·Technical Phone Screen·Intermediate

IntermediatePrefer not to say

Jul 2026Remote

Summary

Got a general coding question for a SWE role at OpenAI that looked deceptively simple on the surface. The problem involved generating sequences with some prefix-balance constraints across three tags, and it took me longer than I'd like to admit to really internalize what the constraints were asking.

Questions Asked (1)

Given three tags (AI, Human, Task) and three allowed pairs (AI-Human, AI-Task, Human-Task), generate a sequence of N pairs such that for every prefix of the sequence, the absolute difference in occurrence counts between AI and Human is at most 1, and the absolute difference between AI and Task is also at most 1.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

I stared at this for a bit trying to figure out if there was a cycle pattern that just works.

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AI HintsAI Generated

Suggested Approach

Model the problem as a state machine where each state is the current count differences (AI-Human, AI-Task). Use a greedy algorithm that at each step picks an allowed pair that keeps both differences within [-1,1]. If greedy fails, backtrack or use BFS to find a valid sequence.

Pro tip: Mention that the constraints imply a periodic pattern (e.g., repeating AI-Human, AI-Task, Human-Task) and that you can precompute a valid sequence for any N by cycling through a small set of states. This shows you recognize the underlying structure and can optimize for large N.

1. Define state and constraints

Represent the state as (d1, d2) where d1 = count(AI) - count(Human) and d2 = count(AI) - count(Task). The constraints require |d1| <= 1 and |d2| <= 1 after each prefix.

2. Identify allowed transitions

For each allowed pair (AI-Human, AI-Task, Human-Task), determine how it updates (d1, d2). For example, AI-Human increments d1 by 1 and leaves d2 unchanged; AI-Task increments d2 by 1; Human-Task decrements d1 by 1 and increments d2 by 1.

3. Search for a valid sequence

Use BFS or DFS from the initial state (0,0) to find a path of length N that never leaves the valid states. Since the state space is small (9 states), this is efficient.

4. Handle edge cases and prove correctness

Check if N is feasible (e.g., N=1 works with AI-Human or AI-Task). Argue that if a solution exists, the search will find it, and if not, explain why (e.g., N=2 might be impossible? Actually test).

5. Optimize and generalize

If N is large, note that the sequence becomes periodic. Find a cycle in the state graph and repeat it to achieve any N beyond a small threshold.

Key Points to Mention

State representation using difference counts
Allowed transitions and their effects on differences
BFS/DFS for small state space
Periodicity and cycle detection for large N
Proof of correctness and feasibility conditions
Time and space complexity analysis

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