Mathematical Theory in Sudoku Puzzle
首发时间:2009-03-12
Abstract:Solving a Sudoku is an NP problem. How to solve a Sudoku puzzle effectively is already a complex problem. To generate a validated Sudoku puzzle of desirable difficulty level is more complex. In this paper, an effective generating algorithm and a simple but efficient difficulty level are proposed. Firstly some common Logical Techniques and Brute Force Search Technique are introduced to solve a Sudoku puzzle. After that, demonstrate an generic generating algorithm, which uses a difficulty level based Analytic Hierarchy Process (AHP). This difficulty level is very reasonable by considering various factors. Some intelligent techniques and sub-processes are used to guarantee this generating algorithm efficient and correct. And the method to generate symmetrical Sudoku Puzzles is put forward just follow it. At last , some useful conclusion is obtained.
keywords: Sudoku Puzzle Logical Technique Brute Force Search Technique Metric of Difficulty Level Generating Algorithm
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数独游戏中的数学理论
摘要:求解数独游戏是有名的NP问题.怎样高效的解决它本身是比较复杂的.因此,产生一个任意难度的数独题目就更加困难.本文给出了一种简单而且能够高效产生不同难度数独题目的算法. 首先,提出了一些常用的逻辑方法和遍历方法来求解数独问题.然后,利用层次分析法定义的难度,提出了一个产生一般数独问题的算法.所定义的难度也是有道理的,因为它考虑了许多因素.为保证生成算法高效准确,一些灵活的技术和方法也运用其中.紧接着,一种产生对称数独游戏的方法也被提出. 最后,进行了一些有用的讨论.
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