Openai·Software Engineer·Technical Phone Screen·Senior

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May 2026Remote

Summary

OpenAI software engineer interview with a meaty algorithmic simulation problem. The question had multiple layers and I definitely underestimated how far they wanted me to take it.

Questions Asked (2)

You're given two teams of monsters, each with HP and attack values. Simulate a turn-based battle where monsters exchange damage simultaneously each turn, a defeated monster is replaced by the next in line, and each side can revive one monster per battle at full HP. Start with the basic case: pick one monster from each side, simulate the duel, and return the survivor with remaining HP.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

The basic version felt like a warmup but I still spent too long on edge cases around simultaneous kills.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the basic duel mechanics: simultaneous damage each turn, HP reduction, and survivor determination. Then outline a simple simulation loop that continues until one monster's HP drops to zero or below, returning the other with remaining HP. Finally, briefly mention how this scales to the full problem with multiple monsters and revivals.

Pro tip: Demonstrate foresight by noting that simultaneous damage means both monsters can die in the same turn, requiring a tie-breaking rule (e.g., both defeated). This shows attention to edge cases and prepares for the extended scenario.

1. Clarify the rules

Confirm that damage is simultaneous, HP is reduced each turn, and a monster is defeated when HP <= 0. Ask about tie-breaking if both reach 0 in the same turn.

2. Define the simulation loop

While both monsters have HP > 0, subtract each monster's attack from the other's HP. This models simultaneous exchange.

3. Determine the survivor

After the loop, check which monster has HP > 0. If both have HP <= 0, apply the tie-breaking rule (e.g., both defeated). Return the survivor with remaining HP.

4. Extend to full problem

Briefly explain how to generalize: maintain queues of monsters, replace defeated ones with the next in line, and allow one revival per side at full HP when a monster is defeated.

Key Points to Mention

Simultaneous damage calculation: both monsters attack each turn regardless of order.
Termination condition: loop ends when at least one monster's HP <= 0.
Tie-breaking rule: if both monsters die in the same turn, define the outcome (e.g., both defeated).
Time complexity: O(ceil(min(HP1/atk2, HP2/atk1))) turns, which is efficient for the basic case.
Edge cases: initial HP <= 0, attack values of 0, or extremely high HP requiring optimization.
Scalability: how the basic duel logic fits into the larger simulation with multiple monsters and revivals.

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

Extend the simulation to find the optimal strategy for team A: search over all possible monster orderings and revival decisions to maximize the number of A's monsters that survive. Implement this using memoized DP with the state being the remaining monster sets for both sides, current active HP values, and whether each side has used their revival. Also discuss the state space size, how you'd key the memo table, and any pruning opportunities.

Algorithms & Data StructuresSystem DesignTechnical Trade-offs

Author's notes

This is where I started sweating.

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AI HintsAI Generated

Suggested Approach

Start by formalizing the problem as a two-player game with perfect information, then define the DP state to capture all relevant information: remaining monsters, active HP, and revival flags. Implement memoized recursion with minimax, optimizing state representation and pruning to handle the large state space. Finally, discuss complexity and trade-offs.

Pro tip: Emphasize that the state space is huge but many states are unreachable; use hashing and pruning to make it feasible. Also, mention that the optimal strategy can be extracted by storing the best move in each state.

1. Model the game

Define the rules: each turn, a side chooses an active monster (if none, they lose), attacks, and may revive a fainted monster if available. Clarify win conditions and how survival is counted.

2. Define DP state

State = (A_remaining, B_remaining, A_active_HP, B_active_HP, A_revival_used, B_revival_used). Use bitmasks for remaining sets and integers for HP and booleans for revival flags.

3. Design recursion and memoization

Use minimax: A maximizes surviving monsters, B minimizes. Recurse over all possible moves (switch, attack, revive). Memoize with a hash map keyed by a tuple or a compact encoding of the state.

4. Analyze state space and pruning

Estimate size: 2^N * 2^M * HP_A * HP_B * 4. Prune by ignoring dominated moves, using alpha-beta pruning, and noting that revival is only useful when a monster is fainted.

5. Discuss implementation and trade-offs

Choose between top-down memoization and bottom-up DP. Discuss memory vs time, and how to extract the optimal strategy by storing best moves.

Key Points to Mention

State representation using bitmasks for remaining monsters and integers for HP.
Minimax with memoization: A maximizes survival, B minimizes it.
Memo table key: tuple of (A_mask, B_mask, A_HP, B_HP, A_rev, B_rev) or a hash.
State space size: O(2^N * 2^M * HP_max^2 * 4) and pruning via alpha-beta or dominance.
Revival decision: only consider reviving when a monster is fainted and revival not used.
Extracting optimal strategy by storing best move in each state.

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