I'm trying to stack $n$ rectangles with size $a \times b$ to minimize the distance from the origin to the furthest point ($L$).
I attach a couple of images to clarify.
Thanks for you help!
Jorge
2026-03-26 02:44:41.1774493081
Smallest packaging of rectangles
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A greedy algorithm will work.
It suffices to show that if we have two boxes stack on top of each other, the higher one will have a greater L. Hence we just maintain a priority queue of all the possible locations to put a box, then choose the one with the smallest L, place it and insert the new possible locations into the priority queue.