The complexity of Solitaire
Mathematical Foundations of Computer Science(2009)
摘要
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 AC0 and in NL respectively. When a single suit is allowed, the problem drops in complexity down to AC0[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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关键词
computational complexity,arbitrary number,problem drop,n-card klondike initial configuration,solitaire,single suit,opposite color,52-card solitaire game,completeness,games,constant-depth unbounded-fan-in
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