2022年美国数学建模单词 .pdf

1 马氏链2 遗传算法,represent 代表 present 展现demonstrate表明 handle 处理 For each case对于每一种情况 resistance阻力 therefore因此a safety margin安全裕 cost-effective成本效益好的column：纵列inherently 天性的 be content to 满足于 algorithm 运算法则 contradict 反驳streamline;使合理化，使成流线型metrics;度量 terminology 术语capital，uppercase大写字母upper-left 左上角that is significant but not too large，不是很大的量。involves many complex interactions 包括许多复杂的内部作用。As a convention, 按照惯例we aim to create an algorithm with the following properties:我们可以得出具备以下特性的一种算法。These indices are related by the following functions: 这些量之间有下面一些关系式！决定：determine，decide，design 进一步：Furthermore in addition 另外取决于： depend on 从那时以来since then 估计 estimate derive from 来源于使之服从于subject to 说明explain Criteria 标准Similarly 同样的Initial modelling 最初模型rough 粗糙的thus 这样adjustment factor调整因素remove 去除eliminate calibrate 调整Recommendation 推荐信problematic 有问题的dynamic ratio 动态参数flow rates 流动比例a fixed constant 固定的常数flowchart 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 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 Statement 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 . . . . . . . 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 . . . . . . . . . . . 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 Basis 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 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 Uniqueness 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 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 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 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 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 various 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 - - - - - - - - -