The Art of Computer Programming.VoLume 3,Sorting and Searching
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ISBN：9787302058168
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简介
为反映计算机领域的最新发展，Knuth二十多年来第一次将三卷书全部做了修订。他的修订主要集中在自上一版以来得到众人认可的新知识，已经解决的问题，以及有所变化的问题。为保持本书的权威性，在必要的地方对计算机领域先驱工作的历史信息做了更新；为维护作者苦心孤诣追求至善至美的盛誉，新版本对读者发现的少量技术性错误做了更正；为增加本书的挑战性，作者还添加了数百道习题。本套书由3卷组成。 第1卷 基本算法 -------------- 第1卷首先介绍编程的基本概念和技术，然后详细讲解信息结构方面的内容，包括信息在计算机内部的表示方法、数据元素之间的结构关系，以及有效的信息处理方法。此外，书中还描述了编程在模拟、数值方法、符号计算、软件与系统设计等方面的初级应用。新版本增加了数十项简单但重要的算法和技术，并根据当前研究发展趋势在数学预备知识方面做了大量修改。 第2卷 半数值算法 ---------------- 第2卷对半数值算法领域做了全面介绍，分“随机数”和“算术”两章。本卷总结了主要算法范例及这些算法的基本理论，广泛剖析了计算机程序设计与数值分析间的相互联系。第3版中最引人注目的是，Knuth对随机数生成器进行了重新处理，对形式幂级数计算作了深入讨论。 第3卷 排序和查找 ---------------- 这是对第3卷的头一次修订，不仅是对经典计算机排序和查找技术的最全面介绍，而且还对第1卷中的数据结构处理技术作了进一步的扩充，通盘考虑了将大小型数据库和内外存储器。它遴选了一些经过反复检验的计算机方法，并对其效率做了定量分析。第3卷的突出特点是对“最优排序”一节作了修订，对排列论原理与通用散列法作了全新讨论。 本套书适用于所有需要深入学习编程的计算机人员，也可以作为计算机专业的教材。
目录
height=1 width='100%'> Chapter 1 Basic Concepts
1.1. Algorithms
1.2. Mathematical Preliminaries
1.2.1. Mathematical Induction
1.2.2. Numbers, Powers, and Logarithms
1.2.3. Sums and Products
1.2.4. Integer Functions and Elementary Number Theory
1.2.5. Permutations and Factorials
1.2.6. Binomial Coefficients
1.2.7. Harmonic Numbers
1.2.8. Fibonacci Numbers
1.2.9. Generating Functions
1.2.10. Analysis of an Algorithm
*1.2.11. Asymptotic Representations
*1.2.11.1. The O-notation
*1.2.11.2. Euler's summation formula
*1.2.11.3. Some asymptotic calculations
1.3. MIX 124
1.3.1. Description of MIX
1.3.2. The MIX Assembly Language
1.3.3. Applications to Permutations
1.4. Some Fundamental Programming Techniques
1.4.1. Subroutines
1.4.2. Goroutines
1.4.3. Interpretive Routines
1.4.3.1. A MIX simulator
*1.4.3.2. Trace routines
1.4.4. Input and Output
1.4.5. History and Bibliography
Chapter 2 Information Structures
2.1. Introduction
2.2. Linear Lists
2.2.1. Stacks, Queues, and Deques
2.2.2. Sequential Allocation
2.2.3. Linked Allocation
2.2.4. Circular Lists
2.2.5. Doubly Linked Lists
2 2.6. Arrays and Orthogonal Lists
2.3. Trees
2.3.1. Traversing Binary Trees
2.3.2. Binary Tree Representation of Trees
2.3.3. Other Representations of Trees
2.3.4. Basic Mathematical Properties of Trees
2.3.4.1. Free trees
2.3.4.2. Oriented trees
*2.3.4.3. The 'infinity lemma'
*2.3.4.4. Enumeration of trees
2.3.4.5. Path length
*2.3.4.6. History and bibliography
2.3.5. Lists and Garbage Collection
2.4. Multilinked Structures
2.5. Dynamic Storage Allocation
History and Bibliography
Answers to Exercises
Appendix A Tables of Numerical Quantities
1. Fundamental Constants (decimal)
2. Fundamental Constants (octal)
3. Harmonic Numbers, Bernoulli Numbers, Fibonacci Numbers
Appendix B Index to Notations
Index and Glossary
Excerpt
Chapter 3 Random Numbers.
Introduction.
Generating Uniform Random Numbers.
The Linear Congruential Method.
Other Methods.
Statistical Tests.
General Test Procedures for Studying Random Data.
Empirical Tests.
Theoretical Tests.
The Spectral Test.
Other Types of Random Quantities.
Numerical Distributions.
Random Sampling and Shuffling.
What Is a Random Sequence?
Summary.
Chapter 4 Arithmetic.
Positional Number Systems.
Floating Point Arithmetic.
Single-Precision Calculations.
Accuracy of Floating Point Arithmetic.
Double-Precision Calculations.
Distribution of Floating Point Numbers.
Multiple Precision Arithmetic.
The Classical Algorithms.
Modular Arithmetic.
How Fast Can We Multiply?.
Radix Conversion.
Rational Arithmetic.
Fractions.
The Greatest Common Divisor.
Analysis of Euclid's Algorithm.
Factoring into Primes.
Polynomial Arithmetic.
Division of Polynomials.
Factorization of Polynomials.
Evaluation of Powers.
Evaluation of Polynomials.
Manipulation of Power Series.
Answers to Exercises.
Appendix A: Tables of Numerical Quantities.
Fundamental Constants (decimal).
Fundamental Constants (octal).
Harmonic Numbers, Bernoulli Numbers, Fibonacci Numbers.
Appendix B: Index to Notations.
Index and Glossary.
Chapter 5 Sorting.
Combinatorial Properties of Permutations.
Inversions.
Permutations of a Multiset.
Runs.
Tableaux and Involutions.
Internal sorting.
Sorting by Insertion.
Sorting by Exchanging.
Sorting by Selection.
Sorting by Merging.
Sorting by Distribution.
Optimum Sorting.
Minimum-Comparison Sorting.
Minimum-Comparison Merging.
Minimum-Comparison Selection.
Networks for Sorting.
External Sorting.
Multiway Merging and Replacement Selection.
The Polyphase Merge.
The Cascade Merge.
Reading Tape Backwards.
The Oscillating Sort.
Practical Considerations for Tape Merging.
External Radix Sorting.
Two-Tape Sorting.
Disks and Drums.
Summary, History, and Bibliography.
Chapter 6 Searching.
Sequential Searching.
Searching by Comparison of Keys.
Searching an Ordered Table.
Binary Tree Searching.
Balanced Trees.
Multiway Trees.
Digital Searching.
Hashing.
Retrieval on Secondary Keys.
Answers to Exercises.
Appendix A: Tables of Numerical Quantities.
Fundamental Constants (decimal).
Fundamental Constants (octal).
Harmonic Numbers, Bernoulli Numbers, Fibonacci Numbers.
Appendix B:Index to Notations.
Index and Glossary.
1.1. Algorithms
1.2. Mathematical Preliminaries
1.2.1. Mathematical Induction
1.2.2. Numbers, Powers, and Logarithms
1.2.3. Sums and Products
1.2.4. Integer Functions and Elementary Number Theory
1.2.5. Permutations and Factorials
1.2.6. Binomial Coefficients
1.2.7. Harmonic Numbers
1.2.8. Fibonacci Numbers
1.2.9. Generating Functions
1.2.10. Analysis of an Algorithm
*1.2.11. Asymptotic Representations
*1.2.11.1. The O-notation
*1.2.11.2. Euler's summation formula
*1.2.11.3. Some asymptotic calculations
1.3. MIX 124
1.3.1. Description of MIX
1.3.2. The MIX Assembly Language
1.3.3. Applications to Permutations
1.4. Some Fundamental Programming Techniques
1.4.1. Subroutines
1.4.2. Goroutines
1.4.3. Interpretive Routines
1.4.3.1. A MIX simulator
*1.4.3.2. Trace routines
1.4.4. Input and Output
1.4.5. History and Bibliography
Chapter 2 Information Structures
2.1. Introduction
2.2. Linear Lists
2.2.1. Stacks, Queues, and Deques
2.2.2. Sequential Allocation
2.2.3. Linked Allocation
2.2.4. Circular Lists
2.2.5. Doubly Linked Lists
2 2.6. Arrays and Orthogonal Lists
2.3. Trees
2.3.1. Traversing Binary Trees
2.3.2. Binary Tree Representation of Trees
2.3.3. Other Representations of Trees
2.3.4. Basic Mathematical Properties of Trees
2.3.4.1. Free trees
2.3.4.2. Oriented trees
*2.3.4.3. The 'infinity lemma'
*2.3.4.4. Enumeration of trees
2.3.4.5. Path length
*2.3.4.6. History and bibliography
2.3.5. Lists and Garbage Collection
2.4. Multilinked Structures
2.5. Dynamic Storage Allocation
History and Bibliography
Answers to Exercises
Appendix A Tables of Numerical Quantities
1. Fundamental Constants (decimal)
2. Fundamental Constants (octal)
3. Harmonic Numbers, Bernoulli Numbers, Fibonacci Numbers
Appendix B Index to Notations
Index and Glossary
Excerpt
Chapter 3 Random Numbers.
Introduction.
Generating Uniform Random Numbers.
The Linear Congruential Method.
Other Methods.
Statistical Tests.
General Test Procedures for Studying Random Data.
Empirical Tests.
Theoretical Tests.
The Spectral Test.
Other Types of Random Quantities.
Numerical Distributions.
Random Sampling and Shuffling.
What Is a Random Sequence?
Summary.
Chapter 4 Arithmetic.
Positional Number Systems.
Floating Point Arithmetic.
Single-Precision Calculations.
Accuracy of Floating Point Arithmetic.
Double-Precision Calculations.
Distribution of Floating Point Numbers.
Multiple Precision Arithmetic.
The Classical Algorithms.
Modular Arithmetic.
How Fast Can We Multiply?.
Radix Conversion.
Rational Arithmetic.
Fractions.
The Greatest Common Divisor.
Analysis of Euclid's Algorithm.
Factoring into Primes.
Polynomial Arithmetic.
Division of Polynomials.
Factorization of Polynomials.
Evaluation of Powers.
Evaluation of Polynomials.
Manipulation of Power Series.
Answers to Exercises.
Appendix A: Tables of Numerical Quantities.
Fundamental Constants (decimal).
Fundamental Constants (octal).
Harmonic Numbers, Bernoulli Numbers, Fibonacci Numbers.
Appendix B: Index to Notations.
Index and Glossary.
Chapter 5 Sorting.
Combinatorial Properties of Permutations.
Inversions.
Permutations of a Multiset.
Runs.
Tableaux and Involutions.
Internal sorting.
Sorting by Insertion.
Sorting by Exchanging.
Sorting by Selection.
Sorting by Merging.
Sorting by Distribution.
Optimum Sorting.
Minimum-Comparison Sorting.
Minimum-Comparison Merging.
Minimum-Comparison Selection.
Networks for Sorting.
External Sorting.
Multiway Merging and Replacement Selection.
The Polyphase Merge.
The Cascade Merge.
Reading Tape Backwards.
The Oscillating Sort.
Practical Considerations for Tape Merging.
External Radix Sorting.
Two-Tape Sorting.
Disks and Drums.
Summary, History, and Bibliography.
Chapter 6 Searching.
Sequential Searching.
Searching by Comparison of Keys.
Searching an Ordered Table.
Binary Tree Searching.
Balanced Trees.
Multiway Trees.
Digital Searching.
Hashing.
Retrieval on Secondary Keys.
Answers to Exercises.
Appendix A: Tables of Numerical Quantities.
Fundamental Constants (decimal).
Fundamental Constants (octal).
Harmonic Numbers, Bernoulli Numbers, Fibonacci Numbers.
Appendix B:Index to Notations.
Index and Glossary.
The Art of Computer Programming.VoLume 3,Sorting and Searching
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