数独基于规则的逐步枚举算法设计  

Design of stepwise enumerative algorithm based on rule about Sudoku

作　　者：肖华勇[1] 田铮[1] 马雷[1] 

机构地区：[1]西北工业大学理学院数学系,陕西西安710072

出　　处：《计算机工程与设计》2010年第5期1035-1037,1113,共4页Computer Engineering and Design

基　　金：国家自然科学基金项目(60375003)

摘　　要：给出了数独(Sudoku)的6条性质,并在此基础上提出了6条推理规则,然后结合空格填写的一个一组,两个一组及更多个一组的枚举算法,在枚举中进行推理。使推理和枚举结合起来,对有唯一解的数独问题,其求解速度比回溯法快得多,同时也能完成许多数独软件无法进行推理计算的数独难题。用两个数独难题进行验证,表明该方法十分有效。Sudoku puzzle has become a very popular puzzle in the world. Firstly, six properties of Sudoku are given and six deductive rules are introduced. Then scanning on blank one bye, then two by two and so on, deduce the digit in the blank while stepwise enumeration. By deduction and enumeration, we solve the Sudoku faster than backtrack and finish many difficulty Sudoku puzzles that is not solved by deduction in many software about Sodnku. Two difficulty Sudoku puzzles are demonstated and solved easy with the mehod. That show the method is very effective.

关 键 词：数独 智力游戏 推理规则 逐步枚举 唯一解 

分 类 号：O157[理学—数学]