This is bin packing and I knew that going in, which maybe made me overconfident.
Clarify the problem constraints (e.g., item sizes, batch capacity, whether items can be split) and then propose a greedy algorithm like First-Fit Decreasing (FFD) as a practical solution, while acknowledging the NP-hard nature of bin packing. Discuss the trade-offs between optimality and efficiency, and mention that for small inputs or when optimality is critical, exact methods like dynamic programming or branch-and-bound could be used.
Pro tip: Amazon values customer obsession and frugality, so emphasize how your algorithm minimizes the number of batches (reducing cost) while being efficient enough to scale; also mention that you would validate the solution with real-world constraints and consider edge cases like items larger than batch capacity.
Ask about the number of items, size distribution, batch capacity, whether items can be split, and if the goal is to minimize batches or maximize utilization. Confirm if an approximate solution is acceptable.
Recognize this as the bin packing problem, which is NP-hard. For practical purposes, propose a greedy heuristic like First-Fit Decreasing (FFD) or Best-Fit Decreasing (BFD) that sorts items descending and places each into the first batch that fits.
Explain the steps of FFD: sort items in descending order, then for each item, scan existing batches and place it in the first that has enough remaining capacity; if none, start a new batch. State time complexity O(n log n + n*m) where m is number of batches, and note that FFD guarantees at most 11/9 OPT + 6/9 batches.
Compare greedy heuristics with exact methods (e.g., dynamic programming, branch-and-bound) in terms of optimality, time, and implementation complexity. Mention that for large-scale systems, heuristics are preferred due to speed, but exact methods may be used for small inputs.
Propose optimizations like using a balanced binary search tree to find the best batch quickly, or pre-processing to remove items that exactly fill a batch. Address edge cases: items larger than capacity (impossible), empty list, and all items same size.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.