Result: Loopless Gray Code Enumeration and the Tower of Bucharest

Title:
Loopless Gray Code Enumeration and the Tower of Bucharest
Authors:
Herter, Felix, Rote, Günter
Source:
Theoretical Computer Science 748 (2018), 40-54
Publication Year:
2016
Collection:
Computer Science
Subject Terms:
Computer Science - Discrete Mathematics, Computer Science - Data Structures and Algorithms, 97R80, F.2.2
Document Type:
Report Working Paper
DOI:
10.1016/j.tcs.2017.11.017
Access URL:
http://arxiv.org/abs/1604.06707
Accession Number:
edsarx.1604.06707
Database:
arXiv

Further Information

We give new algorithms for generating all n-tuples over an alphabet of m letters, changing only one letter at a time (Gray codes). These algorithms are based on the connection with variations of the Towers of Hanoi game. Our algorithms are loopless, in the sense that the next change can be determined in a constant number of steps, and they can be implemented in hardware. We also give another family of loopless algorithms that is based on the idea of working ahead and saving the work in a buffer.
Comment: 16 pages plus 8 pages of appendix with Python programs, 6 figures. A Python script to extract the program code from the LaTeX file is attached to the sources