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The Art of Computer Programming

January 26, 2023

The Art of Computer Programming (TAOCP) is a comprehensive monograph written by the computer scientist Donald Knuth presenting programming algorithms and their analysis. Volumes 1–5 are intended to represent the central core of computer programming for sequential machines.

The Art of Computer Programming
The Art of Computer Programming, Volume 1: Fundamental Algorithms
AuthorDonald Knuth
CountryUnited States
LanguageEnglish
GenreNon-fiction
Monograph
PublisherAddison-Wesley
Publication date
1968– (the book is still incomplete)
Media typePrint (Hardcover)
ISBN0-201-03801-3
519
LC ClassQA76.75

When Knuth began the project in 1962, he originally conceived of it as a single book with twelve chapters. The first three volumes of what was then expected to be a seven-volume set were published in 1968, 1969, and 1973. Work began in earnest on Volume 4 in 1973, but was suspended in 1977 for work on typesetting prompted by the second edition of Volume 2. Writing of the final copy of Volume 4A began in longhand in 2001, and the first online pre-fascicle, 2A, appeared later in 2001.[1] The first published installment of Volume 4 appeared in paperback as Fascicle 2 in 2005. The hardback Volume 4A, combining Volume 4, Fascicles 0–4, was published in 2011. Volume 4, Fascicle 6 ("Satisfiability") was released in December 2015; Volume 4, Fascicle 5 ("Mathematical Preliminaries Redux; Backtracking; Dancing Links") was released in November 2019.

Volume 4B consists of material evolved from Fascicles 5 and 6. [2] The manuscript was sent to the publisher on August 1, 2022 and the volume was published in September 2022.[3] Fascicle 7, planned for Volume 4C, was the subject of Knuth's talk on August 3, 2022.[4]

History

 
Donald Knuth in 2005

After winning a Westinghouse Talent Search scholarship, Knuth enrolled at the Case Institute of Technology (now Case Western Reserve University), where his performance was so outstanding that the faculty voted to award him a master of science upon his completion of the bachelor degree. During his summer vacations, Knuth was hired by the Burroughs Corporation to write compilers, earning more in his summer months than full professors did for an entire year.[5] Such exploits made Knuth a topic of discussion among the mathematics department, which included Richard S. Varga.

In January 1962, when he was a graduate student in the mathematics department at Caltech, Knuth was approached by Addison-Wesley to write a book about compiler design, and he proposed a larger scope. He came up with a list of twelve chapter titles the same day. In the summer of 1962 he worked on a FORTRAN compiler for UNIVAC. During this time, he also came up with a mathematical analysis of linear probing, which convinced him to present the material with a quantitative approach. After receiving his Ph.D. in June 1963, he began working on his manuscript, of which he finished his first draft in June 1965, at 3000 hand-written pages.[6] He had assumed that about five hand-written pages would translate into one printed page, but his publisher said instead that about 1+1⁄2 hand-written pages translated to one printed page. This meant he had approximately 2000 printed pages of material, which closely matches the size of the first three published volumes. At this point, Knuth received support from Richard S. Varga, who was the scientific adviser to the publisher. Varga was visiting Olga Taussky-Todd and John Todd at Caltech. With Varga's enthusiastic endorsement, the publisher accepted Knuth's expanded plans. In its expanded version, the book would be published in seven volumes, each with just one or two chapters.[7] Due to the growth in Chapter 7, which was fewer than 100 pages of the 1965 manuscript, per Vol. 4A p. vi, the plan for Volume 4 has since expanded to include Volumes 4A, 4B, 4C, 4D, and possibly more.

In 1976, Knuth prepared a second edition of Volume 2, requiring it to be typeset again, but the style of type used in the first edition (called hot type) was no longer available. In 1977, he decided to spend some time creating something more suitable. Eight years later, he returned with TEX, which is currently used for all volumes.

The offer of a so-called Knuth reward check worth "one hexadecimal dollar" (100HEX base 16 cents, in decimal, is $2.56) for any errors found, and the correction of these errors in subsequent printings, has contributed to the highly polished and still-authoritative nature of the work, long after its first publication. Another characteristic of the volumes is the variation in the difficulty of the exercises. Knuth even has a numerical difficulty scale for rating those exercises, varying from 0 to 50, where 0 is trivial, and 50 is an open question in contemporary research.[8]

Knuth's dedication reads:

This series of books is affectionately dedicated
to the Type 650 computer once installed at
Case Institute of Technology,
with whom I have spent many pleasant evenings.[a]

Assembly language in the book

All examples in the books use a language called "MIX assembly language", which runs on the hypothetical MIX computer. Currently,[when?] the MIX computer is being replaced by the MMIX computer, which is a RISC version. Software such as GNU MDK[9] exists to provide emulation of the MIX architecture. Knuth considers the use of assembly language necessary for the speed and memory usage of algorithms to be judged.

Critical response

Knuth was awarded the 1974 Turing Award "for his major contributions to the analysis of algorithms […], and in particular for his contributions to the 'art of computer programming' through his well-known books in a continuous series by this title."[10] American Scientist has included this work among "100 or so Books that shaped a Century of Science", referring to the twentieth century,[11]and within the computer science community it is regarded as the first and still the best comprehensive treatment of its subject.[failed verification] Covers of the third edition of Volume 1 quote Bill Gates as saying, "If you think you're a really good programmer… read (Knuth's) Art of Computer Programming… You should definitely send me a résumé if you can read the whole thing."[12] The New York Times referred to it as "the profession's defining treatise".[13]

Volumes

Completed

Planned

Chapter outlines

Completed

Volume 1 – Fundamental Algorithms

Volume 2 – Seminumerical Algorithms

  • Chapter 3 – Random Numbers
    • 3.1. Introduction
    • 3.2. Generating Uniform Random Numbers
      • 3.2.1. The Linear Congruential Method
        • 3.2.1.1. Choice of modulus
        • 3.2.1.2. Choice of multiplier
        • 3.2.1.3. Potency
      • 3.2.2. Other Methods
    • 3.3. Statistical Tests
      • 3.3.1. General Test Procedures for Studying Random Data
      • 3.3.2. Empirical Tests
      • 3.3.3. Theoretical Tests
      • 3.3.4. The Spectral Test
    • 3.4. Other Types of Random Quantities
      • 3.4.1. Numerical Distributions
      • 3.4.2. Random Sampling and Shuffling
    • 3.5. What Is a Random Sequence?
    • 3.6. Summary
  • Chapter 4 – Arithmetic

Volume 3 – Sorting and Searching

  • Chapter 5 – Sorting
    • 5.1. Combinatorial Properties of Permutations
      • 5.1.1. Inversions
      • 5.1.2. Permutations of a Multiset
      • 5.1.3. Runs
      • 5.1.4. Tableaux and Involutions
    • 5.2. Internal sorting
      • 5.2.1. Sorting by Insertion
      • 5.2.2. Sorting by Exchanging
      • 5.2.3. Sorting by Selection
      • 5.2.4. Sorting by Merging
      • 5.2.5. Sorting by Distribution
    • 5.3. Optimum Sorting
      • 5.3.1. Minimum-Comparison Sorting
      • 5.3.2. Minimum-Comparison Merging
      • 5.3.3. Minimum-Comparison Selection
      • 5.3.4. Networks for Sorting
    • 5.4. External Sorting
      • 5.4.1. Multiway Merging and Replacement Selection
      • 5.4.2. The Polyphase Merge
      • 5.4.3. The Cascade Merge
      • 5.4.4. Reading Tape Backwards
      • 5.4.5. The Oscillating Sort
      • 5.4.6. Practical Considerations for Tape Merging
      • 5.4.7. External Radix Sorting
      • 5.4.8. Two-Tape Sorting
      • 5.4.9. Disks and Drums
    • 5.5. Summary, History, and Bibliography
  • Chapter 6 – Searching
    • 6.1. Sequential Searching
    • 6.2. Searching by Comparison of Keys
      • 6.2.1. Searching an Ordered Table
      • 6.2.2. Binary Tree Searching
      • 6.2.3. Balanced Trees
      • 6.2.4. Multiway Trees
    • 6.3. Digital Searching
    • 6.4. Hashing
    • 6.5. Retrieval on Secondary Keys

Volume 4A – Combinatorial Algorithms, Part 1

Volume 4B – Combinatorial Algorithms, Part 2

Planned

Volume 4C, 4D – Combinatorial Algorithms

Volume 5 – Syntactic Algorithms

Volume 6 – The Theory of Context-free Languages[14]

Volume 7 – Compiler Techniques

English editions

Current editions

These are the current editions in order by volume number:

  • The Art of Computer Programming, Volumes 1-4B Boxed Set. (Reading, Massachusetts: Addison-Wesley, 2023), 3904pp. ISBN 978-0-13-793510-9, 0-13-793510-2
    • Volume 1: Fundamental Algorithms. Third Edition (Reading, Massachusetts: Addison-Wesley, 1997), xx+650pp. ISBN 978-0-201-89683-1, 0-201-89683-4. Errata: [1] (2011-01-08), [2] (2020-03-26, 27th printing). Addenda: [3] (2011).
    • Volume 2: Seminumerical Algorithms. Third Edition (Reading, Massachusetts: Addison-Wesley, 1997), xiv+762pp. ISBN 978-0-201-89684-8, 0-201-89684-2. Errata: [4] (2011-01-08), [5] (2020-03-26, 26th printing). Addenda: [6] (2011).
    • Volume 3: Sorting and Searching. Second Edition (Reading, Massachusetts: Addison-Wesley, 1998), xiv+780pp.+foldout. ISBN 978-0-201-89685-5, 0-201-89685-0. Errata: [7] (2011-01-08), [8] (2020-03-26, 27th printing). Addenda: [9] (2011).
    • Volume 4A: Combinatorial Algorithms, Part 1. First Edition (Upper Saddle River, New Jersey: Addison-Wesley, 2011), xv+883pp. ISBN 978-0-201-03804-0, 0-201-03804-8. Errata: [10] (2020-03-26?, 22nd printing).
    • Volume 4B: Combinatorial Algorithms, Part 2. First Edition (Upper Saddle River, New Jersey: Addison-Wesley, 2023), xviii+714pp. ISBN 978-0-201-03806-4, 0-201-03806-4(2022-11-??, 2nd printing).
  • Volume 1, Fascicle 1: MMIX – A RISC Computer for the New Millennium. (Addison-Wesley, 2005-02-14) ISBN 0-201-85392-2. Errata: [11] (2020-03-16) (will be in the fourth edition of volume 1)

Previous editions

Complete volumes

These volumes were superseded by newer editions and are in order by date.

Fascicles

Volume 4's fascicles 0–4 were revised and published as Volume 4A:

  • Volume 4, Fascicle 0: Introduction to Combinatorial Algorithms and Boolean Functions. (Addison-Wesley Professional, 2008-04-28) vi+240pp, ISBN 0-321-53496-4. Errata: [15] (2011-01-01).
  • Volume 4, Fascicle 1: Bitwise Tricks & Techniques; Binary Decision Diagrams. (Addison-Wesley Professional, 2009-03-27) viii+260pp, ISBN 0-321-58050-8. Errata: [16] (2011-01-01).
  • Volume 4, Fascicle 2: Generating All Tuples and Permutations. (Addison-Wesley, 2005-02-14) v+127pp, ISBN 0-201-85393-0. Errata: [17] (2011-01-01).
  • Volume 4, Fascicle 3: Generating All Combinations and Partitions. (Addison-Wesley, 2005-07-26) vi+150pp, ISBN 0-201-85394-9. Errata: [18] (2011-01-01).
  • Volume 4, Fascicle 4: Generating All Trees; History of Combinatorial Generation. (Addison-Wesley, 2006-02-06) vi+120pp, ISBN 0-321-33570-8. Errata: [19] (2011-01-01).

Volume 4's fascicles 5–6 were revised and published as Volume 4B:

  • Volume 4, Fascicle 5: Mathematical Preliminaries Redux; Backtracking; Dancing Links. (Addison-Wesley, 2019-11-22) xiii+382pp, ISBN 978-0-13-467179-6. Errata: [20] (2020-03-27)
  • Volume 4, Fascicle 6: Satisfiability. (Addison-Wesley, 2015-12-08) xiii+310pp, ISBN 978-0-13-439760-3. Errata: [21] (2020-03-26)

Pre-fascicles

Volume 4's pre-fascicles 5A, 5B, and 5C were revised and published as fascicle 5.

Volume 4's pre-fascicle 6A was revised and published as fascicle 6.

  • Volume 4, Pre-fascicle 7A: Constraint Satisfaction
  • Volume 4, Pre-fascicle 8A: Hamiltonian Paths and Cycles
  • Volume 4, Pre-fascicle 9B: A Potpourri of Puzzles
  • Volume 4, Pre-fascicle 12A: Components and Traversal (PDF Version)
  • Volume 4, Pre-fascicle 14A: Bipartite Matching

See also

References

Notes

  1. ^ The dedication was worded slightly differently in the first edition.

Citations

  1. ^ "note for box 3, folder 1".
  2. ^ "Pearson InformIT webpage book Content tab".
  3. ^ "Pearson InformIT webpage".
  4. ^ "CP 2022 All Questions Answered, July 31–August 5, 2022, Haifa, Israel".
  5. ^ Frana, Philip L. (2001-11-08). "An Interview with Donald E. Knuth". hdl:11299/107413.
  6. ^ Knuth, Donald E. (1993-08-23). "This Week's Citation Classic" (PDF). Current Contents. p. 8.
  7. ^ Albers, Donald J. (2008). "Donald Knuth". In Albers, Donald J.; Alexanderson, Gerald L. (eds.). Mathematical People: Profiles and Interviews (2 ed.). A. K. Peters. ISBN 978-1-56881-340-0.
  8. ^ "Reflections on a year of reading Knuth". infinitepartitions.com. Retrieved 2020-07-25. I worked, or at least attempted to work, every single problem in the first volume. In some cases I settled for just understanding what the question was trying to ask for. In some cases I failed even to accomplish that (don't judge me until you try it yourself). Each problem is assigned a difficulty rating from 0-50 where 0 is trivial and 50 is "unsolved research problem" (in the first edition, Fermat's last theorem was listed as a 50, but since Andrew Wiles proved it, it's bumped down to a 45 in the current edition). I think I was able to solve most of the problems rated < 20 — it was hit and miss beyond that. Most of the problems fell into the 20-30 difficulty range, but Knuth's idea of "difficult" is subjective, and problems that he considers to be of average difficulty ended up stretching my comparatively tiny brain painfully. I've never climbed Mount Everest, but I imagine the whole ordeal feels similar: painful while you're going through it, but triumphant when you reach the pinnacle.
  9. ^ "GNU MDK - GNU Project - Free Software Foundation". www.gnu.org. Retrieved 2022-10-23.
  10. ^ "Donald E. Knuth – A. M. Turing Award Winner". AM Turing. Retrieved 2017-01-25.
  11. ^ Morrison, Philip; Morrison, Phylis (November–December 1999). . American Scientist. Sigma Xi, The Scientific Research Society. 87 (6). Archived from the original on 2008-08-20. Retrieved 2008-01-11.
  12. ^ Weinberger, Matt. "Bill Gates once said 'definitely send me a résumé' if you finish this fiendishly difficult book". Business Insider. Retrieved 2016-06-13.
  13. ^ Lohr, Steve (2001-12-17). "Frances E. Holberton, 84, Early Computer Programmer". The New York Times. Retrieved 2010-05-17.
  14. ^ "TAOCP – Future plans".
  15. ^ a b Wells, Mark B. (1973). "Review: The Art of Computer Programming, Volume 1. Fundamental Algorithms and Volume 2. Seminumerical Algorithms by Donald E. Knuth" (PDF). Bulletin of the American Mathematical Society. 79 (3): 501–509. doi:10.1090/s0002-9904-1973-13173-8.

Sources

External links

  • Overview of topics (Knuth's personal homepage)
  • Oral history interview with Donald E. Knuth at Charles Babbage Institute, University of Minnesota, Minneapolis. Knuth discusses software patenting, structured programming, collaboration and his development of TeX. The oral history discusses the writing of The Art of Computer Programming.
  • "Robert W Floyd, In Memoriam", by Donald E. Knuth - (on the influence of Bob Floyd)
  • TAoCP and its Influence of Computer Science (Softpanorama)

January 26, 2023
computer, programming, taocp, comprehensive, monograph, written, computer, scientist, donald, knuth, presenting, programming, algorithms, their, analysis, volumes, intended, represent, central, core, computer, programming, sequential, machines, volume, fundame. The Art of Computer Programming TAOCP is a comprehensive monograph written by the computer scientist Donald Knuth presenting programming algorithms and their analysis Volumes 1 5 are intended to represent the central core of computer programming for sequential machines The Art of Computer ProgrammingThe Art of Computer Programming Volume 1 Fundamental AlgorithmsAuthorDonald KnuthCountryUnited StatesLanguageEnglishGenreNon fiction MonographPublisherAddison WesleyPublication date1968 the book is still incomplete Media typePrint Hardcover ISBN0 201 03801 3Dewey Decimal519LC ClassQA76 75When Knuth began the project in 1962 he originally conceived of it as a single book with twelve chapters The first three volumes of what was then expected to be a seven volume set were published in 1968 1969 and 1973 Work began in earnest on Volume 4 in 1973 but was suspended in 1977 for work on typesetting prompted by the second edition of Volume 2 Writing of the final copy of Volume 4A began in longhand in 2001 and the first online pre fascicle 2A appeared later in 2001 1 The first published installment of Volume 4 appeared in paperback as Fascicle 2 in 2005 The hardback Volume 4A combining Volume 4 Fascicles 0 4 was published in 2011 Volume 4 Fascicle 6 Satisfiability was released in December 2015 Volume 4 Fascicle 5 Mathematical Preliminaries Redux Backtracking Dancing Links was released in November 2019 Volume 4B consists of material evolved from Fascicles 5 and 6 2 The manuscript was sent to the publisher on August 1 2022 and the volume was published in September 2022 3 Fascicle 7 planned for Volume 4C was the subject of Knuth s talk on August 3 2022 4 Contents 1 History 2 Assembly language in the book 3 Critical response 4 Volumes 4 1 Completed 4 2 Planned 5 Chapter outlines 5 1 Completed 5 1 1 Volume 1 Fundamental Algorithms 5 1 2 Volume 2 Seminumerical Algorithms 5 1 3 Volume 3 Sorting and Searching 5 1 4 Volume 4A Combinatorial Algorithms Part 1 5 1 5 Volume 4B Combinatorial Algorithms Part 2 5 2 Planned 5 2 1 Volume 4C 4D Combinatorial Algorithms 5 2 2 Volume 5 Syntactic Algorithms 5 2 3 Volume 6 The Theory of Context free Languages 14 5 2 4 Volume 7 Compiler Techniques 6 English editions 6 1 Current editions 6 2 Previous editions 6 2 1 Complete volumes 6 2 2 Fascicles 6 2 3 Pre fascicles 7 See also 8 References 9 External linksHistory Edit Donald Knuth in 2005 After winning a Westinghouse Talent Search scholarship Knuth enrolled at the Case Institute of Technology now Case Western Reserve University where his performance was so outstanding that the faculty voted to award him a master of science upon his completion of the bachelor degree During his summer vacations Knuth was hired by the Burroughs Corporation to write compilers earning more in his summer months than full professors did for an entire year 5 Such exploits made Knuth a topic of discussion among the mathematics department which included Richard S Varga In January 1962 when he was a graduate student in the mathematics department at Caltech Knuth was approached by Addison Wesley to write a book about compiler design and he proposed a larger scope He came up with a list of twelve chapter titles the same day In the summer of 1962 he worked on a FORTRAN compiler for UNIVAC During this time he also came up with a mathematical analysis of linear probing which convinced him to present the material with a quantitative approach After receiving his Ph D in June 1963 he began working on his manuscript of which he finished his first draft in June 1965 at 3000 hand written pages 6 He had assumed that about five hand written pages would translate into one printed page but his publisher said instead that about 1 1 2 hand written pages translated to one printed page This meant he had approximately 2000 printed pages of material which closely matches the size of the first three published volumes At this point Knuth received support from Richard S Varga who was the scientific adviser to the publisher Varga was visiting Olga Taussky Todd and John Todd at Caltech With Varga s enthusiastic endorsement the publisher accepted Knuth s expanded plans In its expanded version the book would be published in seven volumes each with just one or two chapters 7 Due to the growth in Chapter 7 which was fewer than 100 pages of the 1965 manuscript per Vol 4A p vi the plan for Volume 4 has since expanded to include Volumes 4A 4B 4C 4D and possibly more In 1976 Knuth prepared a second edition of Volume 2 requiring it to be typeset again but the style of type used in the first edition called hot type was no longer available In 1977 he decided to spend some time creating something more suitable Eight years later he returned with TEX which is currently used for all volumes The offer of a so called Knuth reward check worth one hexadecimal dollar 100HEX base 16 cents in decimal is 2 56 for any errors found and the correction of these errors in subsequent printings has contributed to the highly polished and still authoritative nature of the work long after its first publication Another characteristic of the volumes is the variation in the difficulty of the exercises Knuth even has a numerical difficulty scale for rating those exercises varying from 0 to 50 where 0 is trivial and 50 is an open question in contemporary research 8 Knuth s dedication reads This series of books is affectionately dedicatedto the Type 650 computer once installed atCase Institute of Technology with whom I have spent many pleasant evenings a Assembly language in the book EditAll examples in the books use a language called MIX assembly language which runs on the hypothetical MIX computer Currently when the MIX computer is being replaced by the MMIX computer which is a RISC version Software such as GNU MDK 9 exists to provide emulation of the MIX architecture Knuth considers the use of assembly language necessary for the speed and memory usage of algorithms to be judged Critical response EditKnuth was awarded the 1974 Turing Award for his major contributions to the analysis of algorithms and in particular for his contributions to the art of computer programming through his well known books in a continuous series by this title 10 American Scientist has included this work among 100 or so Books that shaped a Century of Science referring to the twentieth century 11 and within the computer science community it is regarded as the first and still the best comprehensive treatment of its subject failed verification Covers of the third edition of Volume 1 quote Bill Gates as saying If you think you re a really good programmer read Knuth s Art of Computer Programming You should definitely send me a resume if you can read the whole thing 12 The New York Times referred to it as the profession s defining treatise 13 Volumes EditCompleted Edit Volume 1 Fundamental Algorithms Chapter 1 Basic concepts Chapter 2 Information structures Volume 2 Seminumerical Algorithms Chapter 3 Random numbers Chapter 4 Arithmetic Volume 3 Sorting and Searching Chapter 5 Sorting Chapter 6 Searching Volume 4A Combinatorial Algorithms Chapter 7 Combinatorial searching part 1 Volume 4B Combinatorial Algorithms Chapter 7 Combinatorial searching part 2 Planned Edit Volume 4C Combinatorial Algorithms chapters 7 amp 8 released in several subvolumes Chapter 7 Combinatorial searching continued Chapter 8 Recursion Volume 5 Syntactic Algorithms Chapter 9 Lexical scanning also includes string search and data compression Chapter 10 Parsing techniques Volume 6 The Theory of Context Free Languages Volume 7 Compiler TechniquesChapter outlines EditCompleted Edit Volume 1 Fundamental Algorithms Edit 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 MMIX MIX in the hardback copy but updated by fascicle 1 1 3 1 Description of MMIX 1 3 2 The MMIX Assembly Language 1 3 3 Applications to Permutations 1 4 Some Fundamental Programming Techniques 1 4 1 Subroutines 1 4 2 Coroutines 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 topological sorting 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 2 6 History and BibliographyVolume 2 Seminumerical Algorithms Edit Chapter 3 Random Numbers 3 1 Introduction 3 2 Generating Uniform Random Numbers 3 2 1 The Linear Congruential Method 3 2 1 1 Choice of modulus 3 2 1 2 Choice of multiplier 3 2 1 3 Potency 3 2 2 Other Methods 3 3 Statistical Tests 3 3 1 General Test Procedures for Studying Random Data 3 3 2 Empirical Tests 3 3 3 Theoretical Tests 3 3 4 The Spectral Test 3 4 Other Types of Random Quantities 3 4 1 Numerical Distributions 3 4 2 Random Sampling and Shuffling 3 5 What Is a Random Sequence 3 6 Summary Chapter 4 Arithmetic 4 1 Positional Number Systems 4 2 Floating Point Arithmetic 4 2 1 Single Precision Calculations 4 2 2 Accuracy of Floating Point Arithmetic 4 2 3 Double Precision Calculations 4 2 4 Distribution of Floating Point Numbers 4 3 Multiple Precision Arithmetic 4 3 1 The Classical Algorithms 4 3 2 Modular Arithmetic 4 3 3 How Fast Can We Multiply 4 4 Radix Conversion 4 5 Rational Arithmetic 4 5 1 Fractions 4 5 2 The Greatest Common Divisor 4 5 3 Analysis of Euclid s Algorithm 4 5 4 Factoring into Primes 4 6 Polynomial Arithmetic 4 6 1 Division of Polynomials 4 6 2 Factorization of Polynomials 4 6 3 Evaluation of Powers addition chain exponentiation 4 6 4 Evaluation of Polynomials 4 7 Manipulation of Power SeriesVolume 3 Sorting and Searching Edit Chapter 5 Sorting 5 1 Combinatorial Properties of Permutations 5 1 1 Inversions 5 1 2 Permutations of a Multiset 5 1 3 Runs 5 1 4 Tableaux and Involutions 5 2 Internal sorting 5 2 1 Sorting by Insertion 5 2 2 Sorting by Exchanging 5 2 3 Sorting by Selection 5 2 4 Sorting by Merging 5 2 5 Sorting by Distribution 5 3 Optimum Sorting 5 3 1 Minimum Comparison Sorting 5 3 2 Minimum Comparison Merging 5 3 3 Minimum Comparison Selection 5 3 4 Networks for Sorting 5 4 External Sorting 5 4 1 Multiway Merging and Replacement Selection 5 4 2 The Polyphase Merge 5 4 3 The Cascade Merge 5 4 4 Reading Tape Backwards 5 4 5 The Oscillating Sort 5 4 6 Practical Considerations for Tape Merging 5 4 7 External Radix Sorting 5 4 8 Two Tape Sorting 5 4 9 Disks and Drums 5 5 Summary History and Bibliography Chapter 6 Searching 6 1 Sequential Searching 6 2 Searching by Comparison of Keys 6 2 1 Searching an Ordered Table 6 2 2 Binary Tree Searching 6 2 3 Balanced Trees 6 2 4 Multiway Trees 6 3 Digital Searching 6 4 Hashing 6 5 Retrieval on Secondary KeysVolume 4A Combinatorial Algorithms Part 1 Edit Chapter 7 Combinatorial Searching 7 1 Zeros and Ones 7 1 1 Boolean Basics 7 1 2 Boolean Evaluation 7 1 3 Bitwise Tricks and Techniques 7 1 4 Binary Decision Diagrams 7 2 Generating All Possibilities 7 2 1 Generating Basic Combinatorial Patterns 7 2 1 1 Generating all n tuples 7 2 1 2 Generating all permutations 7 2 1 3 Generating all combinations 7 2 1 4 Generating all partitions 7 2 1 5 Generating all set partitions 7 2 1 6 Generating all trees 7 2 1 7 History and further referencesVolume 4B Combinatorial Algorithms Part 2 Edit Chapter 7 Combinatorial Searching continued 7 2 Generating all possibilities continued 7 2 2 Backtrack programming published in Fascicle 5 7 2 2 1 Dancing links includes discussion of Exact cover published in Fascicle 5 7 2 2 2 Satisfiability published in Fascicle 6 Planned Edit Volume 4C 4D Combinatorial Algorithms Edit Chapter 7 Combinatorial Searching continued 7 2 Generating all possibilities continued 7 2 2 Backtrack programming continued 7 2 2 3 Constraint satisfaction online draft in pre fascicle 7A 7 2 2 4 Hamiltonian paths and cycles online draft in pre fascicle 8A 7 2 2 5 Cliques 7 2 2 6 Covers Vertex cover Set cover problem Exact cover Clique cover 7 2 2 7 Squares 7 2 2 8 A potpourri of puzzles online draft in pre fascicle 9B includes Perfect digital invariant 7 2 2 9 Estimating backtrack costs chapter 6 of Selected Papers on Analysis of Algorithms and Fascicle 5 pp 44 47 under the heading Running time estimates 7 2 3 Generating inequivalent patterns includes discussion of Polya enumeration theorem see Techniques for Isomorph Rejection chapter 4 of Classification Algorithms for Codes and Designs by Kaski and Ostergard 7 3 Shortest paths 7 4 Graph algorithms online draft in pre fascicle 12A 7 4 1 Components and traversal online draft in pre fascicle 12A 7 4 1 1 Union find algorithms online draft in pre fascicle 12A 7 4 1 2 Depth first search online draft in pre fascicle 12A 7 4 1 3 Vertex and edge connectivity 7 4 2 Special classes of graphs 7 4 3 Expander graphs 7 4 4 Random graphs 7 5 Graphs and optimization online draft in pre fascicle 14A 7 5 1 Bipartite matching including maximum cardinality matching Stable marriage problem Mariages Stables online draft in pre fascicle 14A 7 5 2 The assignment problem 7 5 3 Network flows 7 5 4 Optimum subtrees 7 5 5 Optimum matching 7 5 6 Optimum orderings 7 6 Independence theory 7 6 1 Independence structures 7 6 2 Efficient matroid algorithms 7 7 Discrete dynamic programming see also Transfer matrix method 7 8 Branch and bound techniques 7 9 Herculean tasks aka NP hard problems 7 10 Near optimization Chapter 8 Recursion chapter 22 of Selected Papers on Analysis of Algorithms Volume 5 Syntactic Algorithms Edit Chapter 9 Lexical scanning includes also string search and data compression Chapter 10 Parsing techniquesVolume 6 The Theory of Context free Languages 14 Edit Volume 7 Compiler Techniques EditEnglish editions EditCurrent editions Edit These are the current editions in order by volume number The Art of Computer Programming Volumes 1 4B Boxed Set Reading Massachusetts Addison Wesley 2023 3904pp ISBN 978 0 13 793510 9 0 13 793510 2 Volume 1 Fundamental Algorithms Third Edition Reading Massachusetts Addison Wesley 1997 xx 650pp ISBN 978 0 201 89683 1 0 201 89683 4 Errata 1 2011 01 08 2 2020 03 26 27th printing Addenda 3 2011 Volume 2 Seminumerical Algorithms Third Edition Reading Massachusetts Addison Wesley 1997 xiv 762pp ISBN 978 0 201 89684 8 0 201 89684 2 Errata 4 2011 01 08 5 2020 03 26 26th printing Addenda 6 2011 Volume 3 Sorting and Searching Second Edition Reading Massachusetts Addison Wesley 1998 xiv 780pp foldout ISBN 978 0 201 89685 5 0 201 89685 0 Errata 7 2011 01 08 8 2020 03 26 27th printing Addenda 9 2011 Volume 4A Combinatorial Algorithms Part 1 First Edition Upper Saddle River New Jersey Addison Wesley 2011 xv 883pp ISBN 978 0 201 03804 0 0 201 03804 8 Errata 10 2020 03 26 22nd printing Volume 4B Combinatorial Algorithms Part 2 First Edition Upper Saddle River New Jersey Addison Wesley 2023 xviii 714pp ISBN 978 0 201 03806 4 0 201 03806 4 2022 11 2nd printing Volume 1 Fascicle 1 MMIX A RISC Computer for the New Millennium Addison Wesley 2005 02 14 ISBN 0 201 85392 2 Errata 11 2020 03 16 will be in the fourth edition of volume 1 Previous editions Edit Complete volumes Edit These volumes were superseded by newer editions and are in order by date Volume 1 Fundamental Algorithms First edition 1968 xxi 634pp ISBN 0 201 03801 3 15 Volume 2 Seminumerical Algorithms First edition 1969 xi 624pp ISBN 0 201 03802 1 15 Volume 3 Sorting and Searching First edition 1973 xi 723pp foldout ISBN 0 201 03803 X Errata 12 Volume 1 Fundamental Algorithms Second edition 1973 xxi 634pp ISBN 0 201 03809 9 Errata 13 Volume 2 Seminumerical Algorithms Second edition 1981 xiii 688pp ISBN 0 201 03822 6 Errata 14 The Art of Computer Programming Volumes 1 3 Boxed Set Second Edition Reading Massachusetts Addison Wesley 1998 pp ISBN 978 0 201 48541 7 0 201 48541 9 The Art of Computer Programming Volumes 1 4A Boxed Set Third Edition Reading Massachusetts Addison Wesley 2011 3168pp ISBN 978 0 321 75104 1 0 321 75104 3Fascicles Edit Volume 4 s fascicles 0 4 were revised and published as Volume 4A Volume 4 Fascicle 0 Introduction to Combinatorial Algorithms and Boolean Functions Addison Wesley Professional 2008 04 28 vi 240pp ISBN 0 321 53496 4 Errata 15 2011 01 01 Volume 4 Fascicle 1 Bitwise Tricks amp Techniques Binary Decision Diagrams Addison Wesley Professional 2009 03 27 viii 260pp ISBN 0 321 58050 8 Errata 16 2011 01 01 Volume 4 Fascicle 2 Generating All Tuples and Permutations Addison Wesley 2005 02 14 v 127pp ISBN 0 201 85393 0 Errata 17 2011 01 01 Volume 4 Fascicle 3 Generating All Combinations and Partitions Addison Wesley 2005 07 26 vi 150pp ISBN 0 201 85394 9 Errata 18 2011 01 01 Volume 4 Fascicle 4 Generating All Trees History of Combinatorial Generation Addison Wesley 2006 02 06 vi 120pp ISBN 0 321 33570 8 Errata 19 2011 01 01 Volume 4 s fascicles 5 6 were revised and published as Volume 4B Volume 4 Fascicle 5 Mathematical Preliminaries Redux Backtracking Dancing Links Addison Wesley 2019 11 22 xiii 382pp ISBN 978 0 13 467179 6 Errata 20 2020 03 27 Volume 4 Fascicle 6 Satisfiability Addison Wesley 2015 12 08 xiii 310pp ISBN 978 0 13 439760 3 Errata 21 2020 03 26 Pre fascicles Edit Volume 4 s pre fascicles 5A 5B and 5C were revised and published as fascicle 5 Volume 4 s pre fascicle 6A was revised and published as fascicle 6 Volume 4 Pre fascicle 7A Constraint Satisfaction Volume 4 Pre fascicle 8A Hamiltonian Paths and Cycles Volume 4 Pre fascicle 9B A Potpourri of Puzzles Volume 4 Pre fascicle 12A Components and Traversal PDF Version Volume 4 Pre fascicle 14A Bipartite MatchingSee also EditIntroduction to AlgorithmsReferences EditNotes The dedication was worded slightly differently in the first edition Citations note for box 3 folder 1 Pearson InformIT webpage book Content tab Pearson InformIT webpage CP 2022 All Questions Answered July 31 August 5 2022 Haifa Israel Frana Philip L 2001 11 08 An Interview with Donald E Knuth hdl 11299 107413 Knuth Donald E 1993 08 23 This Week s Citation Classic PDF Current Contents p 8 Albers Donald J 2008 Donald Knuth In Albers Donald J Alexanderson Gerald L eds Mathematical People Profiles and Interviews 2 ed A K Peters ISBN 978 1 56881 340 0 Reflections on a year of reading Knuth infinitepartitions com Retrieved 2020 07 25 I worked or at least attempted to work every single problem in the first volume In some cases I settled for just understanding what the question was trying to ask for In some cases I failed even to accomplish that don t judge me until you try it yourself Each problem is assigned a difficulty rating from 0 50 where 0 is trivial and 50 is unsolved research problem in the first edition Fermat s last theorem was listed as a 50 but since Andrew Wiles proved it it s bumped down to a 45 in the current edition I think I was able to solve most of the problems rated lt 20 it was hit and miss beyond that Most of the problems fell into the 20 30 difficulty range but Knuth s idea of difficult is subjective and problems that he considers to be of average difficulty ended up stretching my comparatively tiny brain painfully I ve never climbed Mount Everest but I imagine the whole ordeal feels similar painful while you re going through it but triumphant when you reach the pinnacle GNU MDK GNU Project Free Software Foundation www gnu org Retrieved 2022 10 23 Donald E Knuth A M Turing Award Winner AM Turing Retrieved 2017 01 25 Morrison Philip Morrison Phylis November December 1999 100 or so Books that shaped a Century of Science American Scientist Sigma Xi The Scientific Research Society 87 6 Archived from the original on 2008 08 20 Retrieved 2008 01 11 Weinberger Matt Bill Gates once said definitely send me a resume if you finish this fiendishly difficult book Business Insider Retrieved 2016 06 13 Lohr Steve 2001 12 17 Frances E Holberton 84 Early Computer Programmer The New York Times Retrieved 2010 05 17 TAOCP Future plans a b Wells Mark B 1973 Review The Art of Computer Programming Volume 1 Fundamental Algorithms and Volume 2 Seminumerical Algorithms by Donald E Knuth PDF Bulletin of the American Mathematical Society 79 3 501 509 doi 10 1090 s0002 9904 1973 13173 8 Sources Slater Robert 1987 Portraits in Silicon MIT Press ISBN 0 262 19262 4 Shasha Dennis Lazere Cathy 1995 Out of Their Minds The Lives and Discoveries of 15 Great Computer Scientists Copernicus ISBN 0 387 97992 1 External links EditOverview of topics Knuth s personal homepage Oral history interview with Donald E Knuth at Charles Babbage Institute University of Minnesota Minneapolis Knuth discusses software patenting structured programming collaboration and his development of TeX The oral history discusses the writing of The Art of Computer Programming Robert W Floyd In Memoriam by Donald E Knuth on the influence of Bob Floyd TAoCP and its Influence of Computer Science Softpanorama Retrieved from https en wikipedia org w index php title The Art of Computer Programming amp oldid 1135703885, wikipedia, wiki, book, books, library,

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