An efficient algorithm for generating symmetric ice piles

Abstract

Abstract. We define the Symmetric Ice Pile Model SIPM k (n), a generalization of the Ice Pile Model IPM k (n), and we show an efficient algorithm for generating the symmetric ice piles with n grains. More precisely, we show how to exploit an existing algorithm for generating IPM k (n) in order to generate SIPM k (n) in amortized time O(1) and in space O( √ kn).

On the Generation of 2-Polyominoes

“…The algorithm is based on an idea that was already used for other exhaustive generation algorithms (for instance, [12,11,13]) and it is inspired by discrete . .…”