In the Nikoli pencil-and-paper game Tatamibari, a puzzle consists of an $m \times n$ grid of cells, where each cell possibly contains a clue among +, -, |. The goal is to partition the grid into disjoint rectangles, where every rectangle contains exactly one clue, rectangles containing + are square, rectangles containing - are strictly longer horizontally than vertically, rectangles containing | are strictly longer vertically than horizontally, and no four rectangles share a corner. We prove this puzzle NP-complete, establishing a Nikoli gap of 16 years. Along the way, we introduce a gadget framework for proving hardness of similar puzzles involving area coverage, and show that it applies to an existing NP-hardness proof for Spiral Galaxies. We also present a mathematical puzzle font for Tatamibari.

中文翻译：

---

榻榻米是NP完全的

在 Nikoli 纸笔游戏 Tatamibari 中，拼图由 $m \times n$ 个单元格组成，其中每个单元格可能包含 +、-、| 之间的线索。目标是将网格划分为不相交的矩形，其中每个矩形只包含一个线索，包含 + 的矩形是正方形，包含 - 的矩形在水平方向上比垂直方向长，矩形包含 | 严格地垂直长于水平，并且没有四个矩形共享一个角。我们证明了这个谜题 NP-complete，建立了 16 年的 Nikoli 差距。在此过程中，我们引入了一个小工具框架，用于证明涉及区域覆盖的类似谜题的硬度，并表明它适用于螺旋星系的现有 NP 硬度证明。我们还为 Tatamibari 提供了一种数学拼图字体。