On the complexity of the game of set
msra(2003)
摘要
Set R © is a card game played with a deck in which each card has four properties. Each property takes on one of three values. Players compete to quickly find sets of three cards such that for each property, the cards have all the same or all different values. We show that a natural generalization of the game, where the number of properties and values vary, is NPcomplete. We also study the case where the number of values is fixed at 3, as in the classic game, and the number of properties p varies. In a restricted model involving checking pairs of cards, we give an exactly (not just asymptotically) optimum Θ(n2p)-time algorithm.
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