## Problem You have a container of width `W` and unlimited height. Blocks have varying widths `w_i` and heights `h_i`. Pack all blocks into the container in given order (left to right, then shelf by shelf). When a block does not fit on the current shelf, start a new shelf. A shelf's height equals the tallest block placed on it. Return the total container height used. ```python def container_height(blocks: list[tuple[int,int]], W: int) -> int: # blocks[i] = (width, height) ... ``` **Example:** ``` blocks = [(3,2),(4,5),(2,3),(5,1),(3,4)], W = 7 Shelf 1: (3,2),(4,5) -> width used=7, height=5 Shelf 2: (2,3),(5,1) -> width=7, height=3 Shelf 3: (3,4) -> width=3, height=4 Total height: 5+3+4 = 12 Output: 12 ``` ## Follow-ups - How would you minimize total height if you can reorder the blocks before packing? - What heuristic ordering (e.g., sort by height descending) tends to reduce wasted space? - Extend to a 2D bin-packing variant where the container has a fixed height as well -- how do you determine the minimum number of containers needed?

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Optimal Packing of Blocks in a Container - Coding Interview

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Problem You have a container of width W and unlimited height. Blocks have varying widths w_i and heights h_i. Pack all blocks into the container in given order (left to right, then shelf by shelf). When a block does not fit on the current shelf, start a new shelf. A shelf's height equals the tallest block placed on it. Return the total container height used. Example: Follow-ups How would you minimize total height if you can reorder the blocks before packing? What heuristic ordering (e.g., sort b…

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Optimal Packing of Blocks in a Container - Coding Interview

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