Recursive and iterative approaches to generate rotation Gray codes for stamp foldings and semi-meanders
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913574375391232 |
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| author | Liu, Bowie Wong, Dennis Lam, Chan-Tong Im, Marcus |
| author_facet | Liu, Bowie Wong, Dennis Lam, Chan-Tong Im, Marcus |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_05458 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Recursive and iterative approaches to generate rotation Gray codes for stamp foldings and semi-meanders Liu, Bowie Wong, Dennis Lam, Chan-Tong Im, Marcus Data Structures and Algorithms 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. |
| title | Recursive and iterative approaches to generate rotation Gray codes for stamp foldings and semi-meanders |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2411.05458 |