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Try to put at least one box in the house pushing it from either side.
Once you put one box to the house, you can solve the problem with the same logic used to solve version I. You have a warehouse open from the left only and a warehouse open from the right only.
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Sorting ensures that smaller boxes are used to fill the most restrictive warehouse slots. This prevents large boxes from occupying spaces that could later block smaller ones, which helps maximize the number of boxes placed.
Yes, variations of warehouse packing and greedy placement problems appear in interviews at major tech companies. They test understanding of greedy strategies, sorting, and reasoning about constraints across arrays.
The optimal approach uses a greedy strategy combined with sorting. Boxes are sorted so smaller boxes fill tighter positions first, while prefix and suffix minimum heights help determine the effective capacity from each side. A two-pointer traversal of the warehouse places boxes where they best fit.
Arrays are sufficient for this problem, along with auxiliary arrays to track prefix and suffix minimum heights. Two pointers are then used to evaluate placements from the left and right ends efficiently.