Recursive and iterative approaches to generate rotation Gray codes for stamp foldings and semi-meanders

TL;DR

This paper introduces the first known Gray codes for stamp foldings and semi-meanders, using recursive and iterative algorithms that generate these sequences efficiently and in constant amortized time.

Contribution

It presents the first known Gray codes for stamp foldings and semi-meanders, solving an open problem and providing efficient recursive and iterative algorithms.

Findings

Recursive algorithm generates cyclic rotation Gray codes.

Iterative algorithm produces the same Gray codes efficiently.

Both algorithms operate in constant or linear amortized time.

Abstract

We first present a simple recursive algorithm that generates cyclic rotation Gray codes for stamp foldings and semi-meanders, where consecutive strings differ by a stamp rotation. These are the first known Gray codes for stamp foldings and semi-meanders, and we thus solve an open problem posted by Sawada and Li in [Electron. J. Comb. 19(2), 2012]. We then introduce an iterative algorithm that generates the same rotation Gray codes for stamp foldings and semi-meanders. Both the recursive and iterative algorithms generate stamp foldings and semi-meanders in constant amortized time and $O(n)$-amortized time per string respectively, using a linear amount of memory.