Chapter 1 Basic Concepts 1
1.1. Algorithms 1
1.2. Mathematical Preliminaries 10
1.2.1. Mathematical Induction 11
1.2.2. Numbers, Powers, and Logarithms 21
1.2.3. Sums and Products 27
1.2.4. Integer Functions and Elementary Number Theory 39
1.2.5. Permutations and Factorials 45
1.2.6. Binomial Coefficients 52
1.2.7. Harmonic Numbers 75
1.2.8. Fibonacci Numbers 79
1.2.9. Generating Functions 87
1.2.10. Analysis of an Algorithm 96
*1.2.11. Asymptotic Representations 107
*1.2.11.1. The O-notation . 107
* 1.2.11.2. Euler's summation formula 111
* 1.2.11.3. Some asymptotic calculations 116
1.3. MIX 124
1.3.1. Description of MIX 124
1.3.2. The NIX Assembly Language 144
1.3.3. Applications to Permutations 164
1.4. Some Fundamental Programming Techniques 180
1.4.1. Subroutines 180
1.4.2. Coroutines 193
1.4.3. Interpretive Routines 200
1.4.3.1. A NIX simulator 202
"1.4.3.2. Trace routines 212
1.4.4. Input and Output 215
1.4.5. History and Bibliography 229
Chapter 2 Information Structures 232
2.1. Introduction 232
2.2. Linear Lists 238
2.2.1. Stacks, Queues, and Deques 238
2.2.2. Sequential Allocation 244
2.2.3. Linked Allocation 254
2.2.4. Circular Lists 273
2.2.5. Doubly Linked Lists 280
2.2.6. Arrays and Orthogonal Lists 298
2.3. Trees 308
2.3.1. Traversing Binary Trees 318
2.3.2. Binary Tree Representation of Trees 334
2.3.3. Other Representations of Trees 348
2.3.4. Basic Mathematical Properties of Trees 362
2.3.4.1. Free trees 363
2.3.4.2. Oriented trees 372
*2.3.4.3. The "infinity lemma" 382
*2.3.4.4. Enumeration of trees 386
2.3.4.5. Path length 399
*2.3.4.6. History and bibliography 406
2.3.5. Lists and Garbage Collection 408
2.4. Multilinked Structures 424
2.5. Dynamic Storage Allocation 435
2.6. History and Bibliography 457
Answers to Exercises 466
Appendix A Tables of Numerical Quantities 619
1. Fundamental Constants (decimal) 619
2. Fundamental Constants (octal) 620
3. Harmonic Numbers, Bernoulli Numbers, Fibonacci Numbers 621
Appendix B Index to Notations 623
Index and Glossary 628
· · · · · · (收起)
1.1. Algorithms 1
1.2. Mathematical Preliminaries 10
1.2.1. Mathematical Induction 11
1.2.2. Numbers, Powers, and Logarithms 21
1.2.3. Sums and Products 27
1.2.4. Integer Functions and Elementary Number Theory 39
1.2.5. Permutations and Factorials 45
1.2.6. Binomial Coefficients 52
1.2.7. Harmonic Numbers 75
1.2.8. Fibonacci Numbers 79
1.2.9. Generating Functions 87
1.2.10. Analysis of an Algorithm 96
*1.2.11. Asymptotic Representations 107
*1.2.11.1. The O-notation . 107
* 1.2.11.2. Euler's summation formula 111
* 1.2.11.3. Some asymptotic calculations 116
1.3. MIX 124
1.3.1. Description of MIX 124
1.3.2. The NIX Assembly Language 144
1.3.3. Applications to Permutations 164
1.4. Some Fundamental Programming Techniques 180
1.4.1. Subroutines 180
1.4.2. Coroutines 193
1.4.3. Interpretive Routines 200
1.4.3.1. A NIX simulator 202
"1.4.3.2. Trace routines 212
1.4.4. Input and Output 215
1.4.5. History and Bibliography 229
Chapter 2 Information Structures 232
2.1. Introduction 232
2.2. Linear Lists 238
2.2.1. Stacks, Queues, and Deques 238
2.2.2. Sequential Allocation 244
2.2.3. Linked Allocation 254
2.2.4. Circular Lists 273
2.2.5. Doubly Linked Lists 280
2.2.6. Arrays and Orthogonal Lists 298
2.3. Trees 308
2.3.1. Traversing Binary Trees 318
2.3.2. Binary Tree Representation of Trees 334
2.3.3. Other Representations of Trees 348
2.3.4. Basic Mathematical Properties of Trees 362
2.3.4.1. Free trees 363
2.3.4.2. Oriented trees 372
*2.3.4.3. The "infinity lemma" 382
*2.3.4.4. Enumeration of trees 386
2.3.4.5. Path length 399
*2.3.4.6. History and bibliography 406
2.3.5. Lists and Garbage Collection 408
2.4. Multilinked Structures 424
2.5. Dynamic Storage Allocation 435
2.6. History and Bibliography 457
Answers to Exercises 466
Appendix A Tables of Numerical Quantities 619
1. Fundamental Constants (decimal) 619
2. Fundamental Constants (octal) 620
3. Harmonic Numbers, Bernoulli Numbers, Fibonacci Numbers 621
Appendix B Index to Notations 623
Index and Glossary 628
· · · · · · (收起)
具體描述
《計算機程序設計藝術》係列著作對計算機領域産生瞭深遠的影響。這一係列堪稱一項浩大的工程，自1962年開始編寫，計劃齣版7捲，目前已經齣版瞭4捲。《美國科學傢》雜誌曾將這套書與愛因斯坦的《相對論》等書並列稱為20世紀最重要的12本物理學著作。目前Knuth正將畢生精力投入到這部史詩性著作的撰寫中。想瞭解本書最新信息，請訪http://www-cs-faculty.stanford.edu/~knuth/taocp.html。
用戶評價
評分
##人和計算機的算法的區彆P139，算法和程序的關係，重要的組閤學公式，簡單的計算機模型。
評分##人和計算機的算法的區彆P139，算法和程序的關係，重要的組閤學公式，簡單的計算機模型。
評分##1.3之後就看不下去瞭。數學書也能引經據典寫齣錢鍾書散文的感覺
評分##編程的兩極，數學和物理。看來數學路綫比較適閤我。
評分##人和計算機的算法的區彆P139，算法和程序的關係，重要的組閤學公式，簡單的計算機模型。
評分厚顔無恥地標記一下，雖然隻讀瞭字麵而已。我猜測，缺乏底層知識和數學技巧是第一道坎，估計還是需要有匯編底子，過一遍《具體數學》。
評分##1.3之後就看不下去瞭。數學書也能引經據典寫齣錢鍾書散文的感覺
評分##終於讀完瞭第一捲。。。傳奇的作者不朽的傑作啊。。。
評分##閱讀思考的過程是甘苦交加的，算是正式開瞭3、4、5、6的頭吧。
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