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You are given a database that describes N six-sided boxes, where one side of each box is open (no flaps). Each box has a unique integer ID and is defined by three dimensions: width, height, and length. Your task is to determine which boxes, if any, can fit inside other boxes, in order to consolidate space. A box A can fit inside box B if its base (length × width) can be completely placed within B’s base, in any rotational order. That means both dimensions of A’s base must be strictly smaller than the corresponding dimensions of B’s base, even after considering rotation (i.e., min(LA, WA) < min(LB, WB) and max(LA, WA) < max(LB, WB)). Additionally, box B’s height must be greater than or equal to box A’s height. You are expected to output valid box containment chains, where each box fits inside the next. An example of such an output chain might look like: A → C → Q → B or M → D → Z or R → O → E → Y, and so on. The idea is to show the maximum possible nesting or consolidation paths, based on the given dimension rules.
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Software Engineer New Grad

Interviewed at Bloomberg

4★
Apr 1, 2025

You are given a database that describes N six-sided boxes, where one side of each box is open (no flaps). Each box has a unique integer ID and is defined by three dimensions: width, height, and length. Your task is to determine which boxes, if any, can fit inside other boxes, in order to consolidate space. A box A can fit inside box B if its base (length × width) can be completely placed within B’s base, in any rotational order. That means both dimensions of A’s base must be strictly smaller than the corresponding dimensions of B’s base, even after considering rotation (i.e., min(LA, WA) < min(LB, WB) and max(LA, WA) < max(LB, WB)). Additionally, box B’s height must be greater than or equal to box A’s height. You are expected to output valid box containment chains, where each box fits inside the next. An example of such an output chain might look like: A → C → Q → B or M → D → Z or R → O → E → Y, and so on. The idea is to show the maximum possible nesting or consolidation paths, based on the given dimension rules.

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