| 关于Hex博弈最优获胜策略的一种新方法* |
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| 引用本文： | 彭元,许晓东,罗海鹏,崔岫峰.关于Hex博弈最优获胜策略的一种新方法*[J].计算机应用研究,2010,27(2):498-499. |
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| 作者姓名： | 彭元 许晓东 罗海鹏 崔岫峰 |
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| 作者单位： | 1. 广西科学院,南宁,530007
2. 齐齐哈尔大学,网络信息中心,黑龙江,齐齐哈尔,161006 |
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| 基金项目： | 广西自然科学基金资助项目（0991074）；广西科学院基本科研业务费资助项目(09YJ17XX01) |
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| 摘 要： | Hex博奕Hex(n)是一种在六边形拼接的n×n棋盘上进行的二人博奕，博奕中二人轮流下红色和蓝色棋子，先构造出一条从一边连到对边的单色路者为胜者。Hex博奕中先手有必胜策略。设δ(n)为Hex(n)中先手能保证获胜所需的最少步数，Garikai Campbell通过研究其他对象间接地证明了δ(n)>n对任意n≥4成立。利用新的方法来分析对称性,给出了δ(n)>n一个直接而简单的证明，并在此基础上利用计算证明了δ(5)=7。
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| 关 键 词： | Hex博弈 步数 最优策略 |
New approach on optimal play in Hex game |
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| PENG Yuan,XU Xiao-dong,LUO Hai-peng,CUI Xiu-feng.New approach on optimal play in Hex game[J].Application Research of Computers,2010,27(2):498-499. |
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| Authors: | PENG Yuan XU Xiao-dong LUO Hai-peng CUI Xiu-feng |
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| Affiliation: | (1.Guangxi Academy of Sciences, Nanning 530007, China; 2. Network Information Center, Qiqihar University, Qiqihar Heilongjiang 161006, China) |
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| Abstract: | Hex game Hex(n) is a two person game played on an n×n board of hexagonal tiles,in which the players take turns trying to construct paths from one side of the board to the other.There exists a winning strategy for the first player.Let δ(n) be the minimum number of moves that player one must make to guarantee a win in Hex(n),Garikai Campbell proved δ(n)>n for any n≥4 by studying another question.In this note,gave a directed and much simpler proof based on a new approach,based on what proved δ(5)=7 by computing. |
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| Keywords: | Hex game moves optimal play |
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