On the exhaustive generation of k-convex polyominoes
نویسندگان
چکیده
منابع مشابه
On the exhaustive generation of k-convex polyominoes
We present an algorithm to compute the degree of convexity of a convex polyomino P , defined as the smallest integer k such that any two cells of P can be joined by a path in P with at most k changes of direction. The algorithm is used to generate in amortized time O(1) all k-convex polyominoes of size n.
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We present a simple but efficient method for generating the set LPol(n) of L-convex polyominoes of size n. We show a bijection between LPol(n) and a suitable set of pairs of integer sequences. This lets us design a CAT (Constant Amortized Time) algorithm for generating LPol(n) using O( √ n) space.
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We compute an asymptotic estimate of a lower bound of the number of k-convex polyominoes of semiperimeter p. This approximation can be written as μ(k)p4p where μ(k) is a rational fraction of k which up to μ(k) is the asymptotics of convex polyominoes. A polyomino is a connected set of unit square cells drawn in the plane Z × Z [7]. The size of a polyomino is the number of its cells. A central p...
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A permutomino of size n is a polyomino determined by a pair (π1, π2) of permutations of size n + 1, such that π1(i) 6= π2(i), for 1 ≤ i ≤ n+ 1. In this paper, after recalling some enumerative results about permutominoes, we give a first algorithm for the exhaustive generation of a particular class of permutominoes, the convex permutominoes, proving that its cost is proportional to the number of...
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In the plane Z× Z a cell is a unit square and a polyomino is a finite connected union of cells. Polyominoes are defined up to translations. Since they have been introduced by Golomb [20], polyominoes have become quite popular combinatorial objects and have shown relations with many mathematical problems, such as tilings [6], or games [19] among many others. Two of the most relevant combinatoria...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2017
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2016.02.006