Building Boxes: coding question

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Place n unit cubes into stacks on an n×n floor with the rule that a cube can be stacked only if the supporting cube's four lateral faces are each adjacent to a wall or another cube—this enforces that column heights form a 2D nonincreasing (Young diagram) layout. Compute the minimum number of floor cells (columns) that must be occupied by choosing column heights that sum to n under that monotonicity constraint.

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Leetcode 1739. Building Boxes
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Building Boxes
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Building Boxes
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Building Boxes

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Building Boxes

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