The naive approach is obvious, loop over every order for every set and do a linear scan for the right container.
First, clarify the problem constraints and edge cases (e.g., order volumes, container capacities, exact match, invalid sets). Then, outline a brute-force solution that iterates through each container set, checks validity, and computes total waste using binary search for efficiency. Finally, discuss potential optimizations and trade-offs, such as sorting capacities and early termination.
Pro tip: Demonstrate awareness of real-world constraints: in pharma, waste minimization is critical due to cost and regulatory factors, so emphasize exact matches and efficient search. Also, mention that ties are resolved by index, so iterate in order and update only when strictly better.
Ask about input sizes, whether container capacities are sorted, if multiple containers can be used per order (no, exactly one), and what constitutes waste (unused capacity). Confirm that invalid sets are those where no container fits an order.
For each container set, iterate through orders. For each order, find the smallest container that fits (using binary search if capacities are sorted). If none fits, mark set invalid. Otherwise, accumulate waste (container capacity - order volume).
Sort each container set's capacities once. For each order, binary search takes O(log m) where m is number of containers. Total per set: O(n log m). Overall: O(k * n log m) where k is number of sets. Discuss if pre-sorting all sets is beneficial.
Track the minimum total waste and the corresponding set index. Since ties go to lower index, only update when waste is strictly less than current minimum. Return -1 if no valid set.
Walk through a simple example, test exact matches, invalid sets, multiple sets with same waste, and large inputs to ensure efficiency. Mention potential pitfalls like integer overflow in waste sum.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.