Utilize este identificador para referenciar este registo:
https://hdl.handle.net/1822/33752
Registo completo
Campo DC | Valor | Idioma |
---|---|---|
dc.contributor.author | Backhouse, Roland | por |
dc.contributor.author | Chen, Wei | por |
dc.contributor.author | Ferreira, João Fernando | por |
dc.date.accessioned | 2015-02-10T12:18:53Z | - |
dc.date.available | 2015-02-10T12:18:53Z | - |
dc.date.issued | 2013 | - |
dc.identifier.issn | 0167-6423 | - |
dc.identifier.uri | https://hdl.handle.net/1822/33752 | - |
dc.description.abstract | One-person solitaire-like games are explored with a view to using them in teaching algorithmic problem solving. The key to understanding solutions to such games is the identification of invariant properties of polynomial arithmetic. We demonstrate this via three case studies: solitaire itself, tiling problems and a novel class of one-person games. The known classification of states of the game of (peg) solitaire into 16 equivalence classes is used to introduce the relevance of polynomial arithmetic. Then we give a novel algebraic formulation of the solution to a class of tiling problems. Finally, we introduce an infinite class of challenging one-person games, which we call “replacement-set games”, inspired by earlier work by Chen and Backhouse on the relation between cyclotomic polynomials and generalisations of the seven-trees-in-one type isomorphism. We present an algorithm to solve arbitrary instances of replacement-set games and we show various ways of constructing infinite (solvable) classes of replacement-set games. | por |
dc.language.iso | eng | por |
dc.publisher | Elsevier 1 | por |
dc.rights | openAccess | por |
dc.subject | Solitaire | por |
dc.subject | Seven-trees-in-one | por |
dc.subject | Replacement-set game | por |
dc.subject | Invariants | por |
dc.subject | Cyclotomic polynomials | por |
dc.subject | Type isomorphism | por |
dc.subject | Tiling problems | por |
dc.subject | Cyclotomic game | por |
dc.subject | Algorithm derivation | por |
dc.title | The algorithmics of solitaire-like games | por |
dc.type | article | por |
dc.peerreviewed | yes | por |
dc.comments | 1855 | por |
sdum.publicationstatus | published | por |
oaire.citationStartPage | 2029 | por |
oaire.citationEndPage | 2046 | por |
oaire.citationIssue | 11 | por |
oaire.citationTitle | Science of Computer Programming | por |
oaire.citationVolume | 78 | por |
sdum.journal | Science of Computer Programming | por |
Aparece nas coleções: | HASLab - Artigos em revistas internacionais |