Search Monster Battle Strategies
Company: OpenAI
Role: Machine Learning Engineer
Category: Coding & Algorithms
Difficulty: hard
Interview Round: Onsite
Quick Answer: This question evaluates algorithmic problem-solving around deterministic simulation and state-space exploration, focusing on handling transient state (health and single-use revives), turn-based interactions, and optimal sequencing of choices; it tests Coding & Algorithms skills including state representation, search strategies, memoization, and complexity reasoning. It is commonly asked to gauge a candidate's ability to reason about reachable states and optimal strategies in adversarial systems, and sits at the intersection of conceptual understanding (state-space and game-theoretic reasoning) and practical implementation (efficient simulation and caching).
Part 1: Duel Between Two Monsters
Constraints
- 1 <= hp, attack <= 10^18
- 0 <= revive_hp <= 10^18
- Each monster may revive at most once
Examples
Input: ((10, 4, 0), (9, 3, 0))
Expected Output: 'A'
Explanation: A needs 3 hits to defeat B, while B needs 4 hits to defeat A.
Input: ((7, 3, 5), (10, 4, 0))
Expected Output: 'A'
Explanation: Both sides need 4 attacks to finish the other permanently, so A wins because it attacks first.
Input: ((1, 100, 0), (1, 1, 1))
Expected Output: 'B'
Explanation: A kills B's first life instantly, but B revives immediately and still attacks back that round, defeating A.
Input: ((5, 5, 5), (5, 5, 5))
Expected Output: 'A'
Explanation: Each monster effectively has two one-hit lives, so the first attacker wins.
Hints
- First compute how many successful attacks A needs to permanently remove B, including B's revive life if it has one.
- If A needs k attacks to finish B, then B gets to attack back after only the first k - 1 of those attacks.
Part 2: Fixed-Order Team Battle
Constraints
- 0 <= len(team_a), len(team_b) <= 2 * 10^5
- 1 <= hp, attack <= 10^18 for every monster
- 0 <= revive_hp <= 10^18 for every monster
- Both teams must be simulated in order; do not reorder monsters
Examples
Input: ([(10, 4, 0)], [(9, 3, 0)])
Expected Output: 'A'
Explanation: This is the same as a single duel, and Team A wins.
Input: ([(5, 5, 0), (10, 3, 0)], [(6, 2, 0), (8, 4, 0)])
Expected Output: 'A'
Explanation: A1 beats B1, loses to B2 after weakening it, and A2 finishes B2.
Input: ([(10, 3, 0), (10, 3, 0)], [(15, 5, 0)])
Expected Output: 'B'
Explanation: The single Team B monster defeats both Team A monsters in sequence.
Input: ([(4, 3, 5)], [(6, 4, 2)])
Expected Output: 'A'
Explanation: Revives matter on both sides; Team A still wins because of the first-attack advantage.
Input: ([], [(1, 1, 0)])
Expected Output: 'B'
Explanation: Edge case: Team A starts with no monsters.
Hints
- For a duel between the current two monsters, you can compute the winner from the number of hits needed instead of simulating round by round.
- When one monster survives a duel, update its remaining health after exactly the number of counterattacks it actually suffered.
Part 3: Winning Strategy with Dynamic Choices
Constraints
- 0 <= len(team_a), len(team_b) <= 6
- 1 <= hp, attack <= 20 for every monster
- 0 <= revive_hp <= 20 for every monster
- An exact state-search solution with memoization is expected
Examples
Input: ([(10, 4, 0)], [(9, 3, 0)])
Expected Output: True
Explanation: With only one choice, Team A simply wins the duel.
Input: ([(6, 5, 0), (10, 2, 0)], [(7, 1, 0), (12, 5, 0)])
Expected Output: True
Explanation: Choosing the second Team A monster first is winning; after it softens the second enemy, the first monster can finish the battle.
Input: ([(5, 2, 0), (5, 2, 0)], [(8, 3, 0), (8, 3, 0)])
Expected Output: False
Explanation: No matter which monster Team A sends first, Team B eventually survives with enough health to win.
Input: ([(4, 3, 5), (8, 2, 0)], [(6, 4, 2), (7, 3, 0)])
Expected Output: True
Explanation: Revives create more possible states, but Team A can still force a win.
Input: ([], [(1, 1, 0)])
Expected Output: False
Explanation: Edge case: Team A has no monster to send.
Hints
- A full state must capture every monster's current health and whether its revive is still unused.
- From a decision state, picking one Team A monster leads to a deterministic sequence of fights until that chosen monster dies or Team B is gone.