Spent way too long on small helper functions early on and it cost me at the end.
Clarify the problem constraints and define the objective function precisely: minimize total capacity first, then minimize the number of properties. Then propose an algorithm that finds the optimal subset, such as dynamic programming or a greedy approach with sorting, and analyze its time and space complexity.
Pro tip: Discuss trade-offs between different algorithmic approaches (e.g., DP vs. greedy) and mention how you would handle large inputs or ties. Also, consider edge cases like no combination meeting the group size.
Ask clarifying questions to ensure you understand the problem: Are capacities integers? Can properties be used multiple times? What if no combination meets the group size? Confirm the tie-breaking rule.
Formalize the problem: Given a set of capacities, find a subset such that sum(capacities) >= groupSize, minimizing sum(capacities), and among those, minimizing the number of properties.
Propose an algorithm. For example, dynamic programming (knapsack-like) to find all achievable sums and track minimal count, or sort and use two-pointer/greedy if applicable. Explain why it works.
State the time and space complexity of your approach. For DP, it's O(n * groupSize) time and O(groupSize) space. Discuss if it's efficient for the expected input size.
Mention edge cases: no solution, exact match, large group size. Discuss possible optimizations or alternative approaches (e.g., branch and bound) if needed.
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