I stared at this for a bit before realizing the two constraints interact in a non-obvious way.
Clarify the problem constraints and edge cases first, then model it as a bin packing problem with per-item type constraints. Discuss greedy heuristics and potential exact algorithms, analyzing trade-offs in time complexity and optimality.
Pro tip: Mention that while the problem is NP-hard, in practice Amazon uses efficient heuristics with guarantees, and always validate with test cases including edge cases like zero counts or capacity smaller than a single item.
Ask about input size, whether items of the same category can be split across trucks, and if there are any other constraints like truck capacity being uniform.
Define it as a bin packing variant where each bin has a capacity and a per-category limit; identify it as NP-hard and discuss implications.
Outline a greedy algorithm (e.g., first-fit decreasing) and an exact approach (e.g., integer programming or branch-and-bound) with complexity analysis.
Compare time vs. optimality, discuss when greedy suffices, and mention handling of edge cases like zero counts or infeasible limits.
Walk through a small example to verify the algorithm and discuss how to test with random and adversarial inputs.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.