The behaviour of a bad Tetris player suggests a class of polyominoes that we call prefix-closed. Such a class contains all polyominoes P such that for any integer i > 0 the first i columns of P form a polyomino. We provide a simple discrete dynamical system that allows us to define an algorithm for generating all prefix- closed polyominoes of size n in constant amortized time using O(n) space.
From Tetris to polyominoes generation
MASSAZZA, PAOLO;
2017-01-01
Abstract
The behaviour of a bad Tetris player suggests a class of polyominoes that we call prefix-closed. Such a class contains all polyominoes P such that for any integer i > 0 the first i columns of P form a polyomino. We provide a simple discrete dynamical system that allows us to define an algorithm for generating all prefix- closed polyominoes of size n in constant amortized time using O(n) space.
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