章节目录
T A B L E O F C O N T E N T S Chapter One: Analysis of Algorithms 3 1.1 Why Analyze an Algorithm? 3 1.2 Theory of Algorithms 6 1.3 Analysis of Algorithms 13 1.4 Average-Case Analysis 16 1.5 Example: Analysis of Quicksort 18 1.6 Asymptotic Approximations 27 1.7 Distributions 30 1.8 Randomized Algorithms 33 Chapter Two: Recurrence Relations 41 2.1 Basic Properties 43 2.2 First-Order Recurrences 48 2.3 Nonlinear First-Order Recurrences 52 2.4 Higher-Order Recurrences 55 2.5 Methods for Solving Recurrences 61 2.6 Binary Divide-and-Conquer Recurrences and Binary Numbers 70 2.7 General Divide-and-Conquer Recurrences 80 Chapter Three: Generating Functions 91 3.1 Ordinary Generating Functions 92 3.2 Exponential Generating Functions 97 3.3 Generating Function Solution of Recurrences 101 3.4 Expanding Generating Functions 111 3.5 Transformations with Generating Functions 114 3.6 Functional Equations on Generating Functions 117 3.7 Solving the Quicksort Median-of-Three Recurrence with OGFs 120 3.8 Counting with Generating Functions 123 3.9 Probability Generating Functions 129 3.10 Bivariate Generating Functions 132 3.11 Special Functions 140 Chapter Four: Asymptotic Approximations 151 4.1 Notation for Asymptotic Approximations 153 4.2 Asymptotic Expansions 160 4.3 Manipulating Asymptotic Expansions 169 4.4 Asymptotic Approximations of Finite Sums 176 4.5 Euler-Maclaurin Summation 179 4.6 Bivariate Asymptotics 187 4.7 Laplace Method 203 4.8 “Normal” Examples from the Analysis of Algorithms 207 4.9 “Poisson” Examples from the Analysis of Algorithms 211 Chapter Five: Analytic Combinatorics 219 5.1 Formal Basis 220 5.2 Symbolic Method for Unlabelled Classes 221 5.3 Symbolic Method for Labelled Classes 229 5.4 Symbolic Method for Parameters 241 5.5 Generating Function Coefficient Asymptotics 247 Chapter Six: Trees 257 6.1 Binary Trees 258 6.2 Forests and Trees 261 6.3 Combinatorial Equivalences to Trees and Binary Trees 264 6.4 Properties of Trees 272 6.5 Examples of Tree Algorithms 277 6.6 Binary Search Trees 281 6.7 Average Path Length in Catalan Trees 287 6.8 Path Length in Binary Search Trees 293 6.9 Additive Parameters of Random Trees 297 6.10 Height 302 6.11 Summary of Average-Case Results on Properties of Trees 310 6.12 Lagrange Inversion 312 6.13 Rooted Unordered Trees 315 6.14 Labelled Trees 327 6.15 Other Types of Trees 331 Chapter Seven: Permutations 345 7.1 Basic Properties of Permutations 347 7.2 Algorithms on Permutations 355 7.3 Representations of Permutations 358 7.4 Enumeration Problems 366 7.5 Analyzing Properties of Permutations with CGFs 372 7.6 Inversions and Insertion Sorts 384 7.7 Left-to-Right Minima and Selection Sort 393 7.8 Cycles and In Situ Permutation 401 7.9 Extremal Parameters 406 Chapter Eight: Strings and Tries 415 8.1 String Searching 416 8.2 Combinatorial Properties of Bitstrings 420 8.3 Regular Expressions 432 8.4 Finite-State Automata and the Knuth-Morris-Pratt Algorithm 437 8.5 Context-Free Grammars 441 8.6 Tries 448 8.7 Trie Algorithms 453 8.8 Combinatorial Properties of Tries 459 8.9 Larger Alphabets 465 Chapter Nine: Words and Mappings 473 9.1 Hashing with Separate Chaining 474 9.2 The Balls-and-Urns Model and Properties of Words 476 9.3 Birthday Paradox and Coupon Collector Problem 485 9.4 Occupancy Restrictions and Extremal Parameters 495 9.5 Occupancy Distributions 501 9.6 Open Addressing Hashing 509 9.7 Mappings 519 9.8 Integer Factorization and Mappings 532 List of Theorems 543 List of Tables 545 List of Figures 547 Index 551
内容简介
《算法分析导论（第2版）（英文版）》全面介绍了算法的数学分析中所涉及的主要技术。涵盖的内容来自经典的数学课题（包括离散数学、初等实分析、组合数学），以及经典的计算机科学课题（包括算法和数据结构）。《算法分析导论（第2版）（英文版）》的重点是“平均情况”或“概率性”分析，书中也论述了“最差情况”或“复杂性”分析所需的基本数学工具。 《算法分析导论（第2版）（英文版）》第 1 版为行业内的经典著作，本版不仅对书中图片和代码进行了更新，还补充了新章节。全书共 9 章，第 1 章是导论 ；第 2~5 章介绍数学方法 ；第 6~9 章介绍组合结构及其在算法分析中的应用。除每章包含的大量习题以及参考文献外，《算法分析导论（第2版）（英文版）》特设配套免费学习网站，为读者提供了很多关于算法分析的补充材料，包括课件和相关网站的链接，帮助读者提高学习兴趣，完成更深入的学习。 《算法分析导论（第2版）（英文版）》适合作为高等院校数学、计算机科学以及相关专业的本科生和研究生的教材，也可供相关技术人员和爱好者学习参考。
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