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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Published in | Theoretical computer science Vol. 410; no. 50; pp. 5252 - 5260 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Elsevier B.V
17.11.2009
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Subjects | |
Online Access | Get full text |
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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. |
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Bibliography: | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
ISSN: | 0304-3975 1879-2294 |
DOI: | 10.1016/j.tcs.2009.08.027 |