The Research of Efficient Algorithm to Generate Sudoku Puzzle

Abstract

AbstractMethod to solve a puzzle, evaluation of difficulty level, guaranteeing a single solution and time complexity are the main factors to generate Sudoku puzzles. This paper develops three kinds of Methods to generate a puzzle, namely Randomly Generating Method, Removal Generating Method and Construction Generating Method. Randomly Generating Method can generate simple puzzle with a high efficiency; Removal Generating Method is good at generating medium and difficult puzzles; Construction Generating Method has the latent capacity to generate those quite difficult puzzles. Then the complexity of algorithm is analyzed. Two techniques, Partly Greedy Strategy and Bit Wise Logical Operation, are used to reduce the complexity. Applying the two techniques generate a 9*9 Sudoku, the complexity is improved by 9^2 time theoretically. The algorithm can generate puzzles of high qualification with a high time efficiency, and the difficulty level of the puzzle must meet the requirement.KeywordsSudokuComplexityPartly greedyBit wise logical operation