The complexity of Solitaire

Klondike is the well-known 52-card Solitaire game available on almost every computer. The problem of determining whether an n -card Klondike initial configuration can lead to a win is shown NP -complete. The problem remains NP -complete when only three suits are allowed instead of the usual four. Wh...

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Bibliographic Details
Published inTheoretical computer science Vol. 410; no. 50; pp. 5252 - 5260
Main Authors Longpré, Luc, McKenzie, Pierre
Format Journal Article
LanguageEnglish
Published Elsevier B.V 17.11.2009
Subjects
Completeness
Computational complexity
Games
Solitaire
Computational complexity
Completeness
Solitaire
Games
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Summary:Klondike is the well-known 52-card Solitaire game available on almost every computer. The problem of determining whether an n -card Klondike initial configuration can lead to a win is shown NP -complete. The problem remains NP -complete when only three suits are allowed instead of the usual four. When only two suits of opposite color are available, the problem is shown NL -hard. When the only two suits have the same color, two restrictions are shown in AC 0 and in NL respectively. When a single suit is allowed, the problem drops in complexity down to AC 0 [3], that is, the problem is solvable by a family of constant-depth unbounded-fan-in { and, or, mod 3 }-circuits. Other cases are studied: for example, “no King” variant with an arbitrary number of suits of the same color and with an empty “pile” is NL -complete.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2009.08.027