Clarify the problem constraints and assumptions, then derive a mathematical formula for rounds and remaining HP per wave. Validate with a simple example and discuss edge cases and trade-offs.
Pro tip: Mention that the number of rounds is ceil(heroHP / monsterDamage) and remaining HP is heroHP - (rounds-1)*monsterDamage, but also consider if the hero attacks first or the monster attacks first, as this affects the outcome.
Ask about attack order, damage calculation, and whether HP can go negative. Confirm if waves are independent or if hero HP carries over.
For a single wave, compute rounds = ceil(heroHP / monsterDamage) if hero attacks first, or ceil((heroHP + monsterDamage - 1) / monsterDamage) if monster attacks first. Remaining HP = heroHP - (rounds-1)*monsterDamage (if hero attacks first) or heroHP - rounds*monsterDamage (if monster attacks first).
Walk through a concrete example (e.g., hero HP=10, monster damage=3) to verify the formula and ensure the hero survives if remaining HP > 0.
Discuss cases where hero HP <= 0 initially, monster damage = 0, or hero HP exactly divisible by monster damage. Also consider if hero damage affects rounds (if monster has HP).
Talk about time complexity for multiple waves, potential for simulation vs. formula, and how to handle large numbers or multiple monsters.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
First, clarify the problem constraints and define the objective precisely (maximize waves survived or minimize rounds). Then, model it as an optimization problem over permutations, likely reducible to a scheduling problem, and propose an algorithm (e.g., greedy with exchange argument or DP) with complexity analysis.
Pro tip: Discuss the trade-off between optimality and efficiency: for large N, a greedy heuristic may be necessary, but prove its optimality under certain conditions or provide approximation guarantees.
Ask about wave properties (e.g., fixed order within a wave, hero's state changes), objective (max waves vs min rounds), and input size. This ensures you solve the right problem.
Define variables, state transitions, and objective function. Recognize it as a permutation optimization, possibly equivalent to scheduling with precedence or resource constraints.
Look for properties like monotonicity, exchange arguments, or optimal substructure. For example, if waves have independent effects, a greedy sort by some key might work.
Describe a concrete algorithm (e.g., DP over subsets, greedy with proof, or heuristic) and analyze time/space complexity. Discuss optimality or approximation ratio.
Compare exact vs heuristic approaches, scalability, and potential ML integration (e.g., learning a policy). Mention edge cases and testing strategy.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Honestly the most fun part of the problem.
Start by outlining a modular architecture that separates core simulation logic from ability effects, then discuss how to model abilities as composable actions with targeting constraints. For optimal targeting, frame it as a decision problem under uncertainty, comparing search-based methods (e.g., minimax, MCTS) with learned policies (e.g., reinforcement learning) and explaining trade-offs.
Pro tip: Emphasize that optimal targeting often depends on the objective (e.g., maximize damage vs. minimize risk) and that a hybrid approach—using search for short horizons and learned value functions for long-term planning—can balance optimality and scalability.
Specify how each ability modifies state: healing restores HP, shields absorb damage, AoE affects multiple targets within a radius. Represent abilities as data-driven actions with parameters (cost, range, cooldown).
Use an entity-component-system (ECS) or similar pattern to decouple abilities from entities. Implement an effect system that applies changes to game state, allowing new abilities to be added without modifying core logic.
Formulate targeting as maximizing a utility function (e.g., expected damage, survival probability) over possible targets. Consider constraints like range, line-of-sight, and resource costs.
For small state spaces, use exhaustive search or minimax; for large, use Monte Carlo Tree Search (MCTS) or reinforcement learning. Discuss how to handle partial observability and stochastic outcomes.
Define metrics (e.g., win rate, average reward) and test against baselines. Use simulation to generate data for training ML models, and consider online learning to adapt to opponent behavior.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Binary search on HP and ATK separately, running the simulation as the check function.
Clarify the problem as a dynamic programming or binary search optimization: for a given HP and attack, simulate the game to check if all waves can be cleared without dying. Then binary search on HP and attack to find the minimum pair that works, or use DP to compute the Pareto frontier of feasible (HP, attack) pairs.
Pro tip: Discuss the trade-off between HP and attack: increasing attack reduces the number of enemy turns, which indirectly reduces required HP. This interdependence means you can't optimize them independently; you need to search over both dimensions or use a multi-objective optimization approach.
Ask about game mechanics: turn order, damage calculation, wave composition, and whether HP/attack can be upgraded between waves. Confirm that 'without dying' means HP > 0 at all times.
Given fixed HP and attack, simulate the game wave by wave, ensuring the hero survives each wave. This check runs in O(total enemies) time.
If the search space is small, brute-force all pairs. Otherwise, use binary search on one stat while computing the minimum required other stat via simulation, or use dynamic programming to find the Pareto-optimal frontier.
Compare approaches: binary search with simulation (O(N log M) where N is enemies, M is stat range) vs. DP (O(N * HP * ATK) if discretized). Discuss memory vs. time trade-offs.
Test with minimal stats, single enemy, multiple waves, and scenarios where attack is very high or very low. Ensure the solution handles ties and returns the minimum pair correctly.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.