2022年美国数学建模单词 .pdf

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4、wchart 流程图depends only on 仅仅取决于weighting 加权real root 实根that is 即apart from 除了（相当于besides ）名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 1 页，共 5 页 - - - - - - - - - empirical 凭经验的refine 改进Prior to the start of， ， ，在开始之前，beforecoherently 连贯性transition 过渡转变extrapolated

5、 推测informed decision 明智的决定out of 由于，用材料rigid body 刚体运动intuitively 凭直觉的respectively 相应的flaw 瑕疵postulate 假设impending 即将发生的recede 后退assist in 帮助note that 既然基本框架名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 2 页，共 5 页 - - - - - - - - - summary 1 1 Introduction 3 1.1 Stat

6、ement of Problem . . . . . . . . . 3 1.2 Relevance of Sudoku . . . . . . . . . 3 1.3 Goals . . . . . . . . . . . . . . . . . . 3 1.4 Rules of Sudoku . . . . . . . . . . . . 3 1.5 Terminology and Notation . . . . . . 3 1.6 Indexing . . . . . . . . . . . . . . . . 4 1.7 Formal Rules of Sudoku . . . .

7、. . . 5 1.8 Example Puzzles . . . . . . . . . . . 5 2 Background 5 2.1 Common Solving Techniques . . . . 5 2.1.1 Naked Pair . . . . . . . . . . 5 2.1.2 Naked Triplet . . . . . . . . . 5 2.1.3 Hidden Pair . . . . . . . . . . 6 2.1.4 Hidden Triplet . . . . . . . . . 6 2.1.5 Multi-Line . . . . . . . .

8、. . . 6 2.2 Previous Works . . . . . . . . . . . . 7 2.2.1 SudokuExplainer . . . . . . . 7 2.2.2 QQWing . . . . . . . . . . . . 7 2.2.3 GNOME Sudoku . . . . . . . 7 3 Metric Design 10 3.1 Overview . . . . . . . . . . . . . . . . 10 3.2 Assumptions . . . . . . . . . . . . . . 10 3.3 Mathematical Basi

9、s for WNEF . . . 10 3.3.1 Complexity . . . . . . . . . . . 10 4 Metric Calibration and Testing 11 4.1 Control Puzzle Sources . . . . . . . . 11 4.2 Testing Method . . . . . . . . . . . . 12 4.2.1 Defining Difficulty Ranges . . 12 4.2.2 Information Collection . . . . 12 4.2.3 Statistical Analysis of

10、Control Puzzles . . . . . . . . . . . 12 4.3 Choice of Weight Function. . . . . . . 12 5 Generator Algorithm 12 5.1 Overview . . . . . . . . . . . . . . . . 12 5.2 Detailed Description . . . . . . . . . 14 5.2.1 Completed Puzzle Generation 14 5.2.2 Cell Removal . . . . . . . . . . 14 5.2.3 Uniquenes

11、s Testing . . . . . . 15 5.3 Pseudocode . . . . . . . . . . . . . . . 15 5.3.1 Completed Board Generation 15 5.3.2 Random Masking . . . . . . . 16 5.3.3 Tuned Masking . . . . . . . . 17 名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 3 页，共 5 页 - - - - - - - - - 5.3.4

12、Uniqueness Testing . . . . . . 17 5.4 Complexity Analysis . . . . . . . . . 18 5.4.1 Parameterization . . . . . . . 18 5.4.2 Complexity of Completed Puzzle Generation . . . . . . . 18 5.4.3 Complexity of Uniqueness Testing and Random Filling . 18 5.4.4 Profiling Method . . . . . . . 18 5.4.5 WNEF vs

13、 Running Time . . . 19 5.5 Testing . . . . . . . . . . . . . . . . . 19 5.5.1 WNEF as a Function of Design Choices . . . . . . . . . . 19 5.5.2 Hypothesis Testing . . . . . . 19 6 Strengths and Weaknesses 19 7 Conclusions 21 References 21 1 Source Code 23 2 Screenshots of Puzzle Generator 62 List of

14、 Figures 1 Demonstration of indexing schemes. 6 2 Puzzle generated by WebSudoku (ranked as “ Easy” ). . . . . . . . . . . 63 Top 1465 Number 77. . . . . . . . . . 7 4 An example of a hand-made Nikoli puzzle. . . . . . . . . . . . . . . . . . 7 5 Example of the Naked Pair rule. . . 8 6 Example of the

15、 Naked Triplet rule. . 8 7 Example of the Hidden Pair rule. . . 8 8 Example of the Hidden Triplet rule. 9 9 Example of the Multi-Line rule. . . . 9 10 Examples of choice histograms. . . . 11 11 WNEF for control puzzles by difficulty. . . . . . . . . . . . . . . . . . . 13 12 WNEF correlations for va

16、rious weighting functions. . . . . . . . . . . 13 13 Running time as a function of the obtained WNEF. . . . . . . . . . . . . 20 14 WNEF as a function of allowed failures. . . . . . . . . . . . . . . . . . . . 20 15 Screenshots of puzzle generator. . . . 62 名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 4 页，共 5 页 - - - - - - - - - 名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 5 页，共 5 页 - - - - - - - - -