The Art of Computer Programming

The Art of Computer Programming

The Art of Computer Programming, Volume 1: Fundamental Algorithms
Author Donald Knuth
Country United States
Language English
Genre Non-fiction
Publisher Addison-Wesley
Publication date
1968– (the book is still incomplete)
Media type Print (Hardcover)
ISBN 0-201-03801-3

The Art of Computer Programming (sometimes known by its initials TAOCP) is a comprehensive monograph written by Donald Knuth that covers many kinds of programming algorithms and their analysis.

Knuth began the project, originally conceived as a single book with twelve chapters, in 1962. The first three volumes of what was then expected to be a seven-volume set were published in 1968, 1969, and 1973. The first installment of Volume 4 (a paperback fascicle) was published in 2005. The hardback Volume 4A, combining Volume 4, Fascicles 0–4, was published in 2011. Additional fascicle installments are planned for release approximately biannually; Volume 4, Fascicle 6 ("Satisfiability") was released in December 2015.


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 baccalaureate degree. During his summer vacations, Knuth was hired by Burroughs to write compilers, earning more in his summer months than full professors did for an entire year.[1] Such exploits made Knuth a topic of discussion among the mathematics department, which included Richard S. Varga.

Knuth started to write a book about compiler design in 1962, and soon realized that the scope of the book needed to be much larger. In June 1965, Knuth finished the first draft of what was originally planned to be a single volume of twelve chapters. His hand-written first-draft manuscript (completed in 1966) was 3,000 pages long: he had assumed that about five hand-written pages would translate into one printed page, but his publisher said instead that about 1½ hand-written pages translated to one printed page. This meant the book would be approximately 2,000 pages in length. The publisher was nervous about accepting such a project from a graduate student. At this point, Knuth received support from Richard S. Varga, who was the scientific advisor 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.[2] Due to the growth in the material, 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. The level of difficulty ranges from "warm-up" exercises to unsolved research problems. 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.[lower-alpha 1]

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, the MIX computer is being replaced by the MMIX computer, which is a RISC version. Software such as GNU MDK 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

American Scientist has included this work among "100 or so Books that shaped a Century of Science", referring to the twentieth century,[3] and within the computer science community it is regarded as the first and still the best comprehensive treatment of its subject. 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."[4] The New York Times referred to it as “the profession's defining treatise”.[5]


  • Chapter 1 – Basic concepts
  • Chapter 2 – Information structures
  • Chapter 7 – Combinatorial searching
  • Chapter 8 Recursion

Chapter outline of published volumes

Outline of unpublished sections

English editions

Current editions

These are the current editions in order by volume number:

Previous editions

Complete volumes

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


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

Volume 2, Seminumerical Algorithms and Volume 4A Combinatorial Algorithms appear in the film Pixels.

See also



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


  2. Donald J. Albers (2008). "Donald Knuth". In Donald J. Albers, Gerald L. Alexanderson. Mathematical People: Profiles and Interviews (2 ed.). A K Peters. ISBN 1-56881-340-6
  3. 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). Retrieved 2008-01-11.
  4. Matt Weinberger. "Bill Gates once said 'definitely send me a résumé' if you finish this fiendishly difficult book". Retrieved 13 June 2016.
  5. Lohr, Steve (2001-12-17). "Frances E. Holberton, 84, Early Computer Programmer". The New York Times. Retrieved 2010-05-17.
  6. TAOCP Future plans
  7. 1 2 Wells, Mark B. (1973). "Review: The Art of Computer Programming, Volume 1. Fundamental Algorithms and Volume 2. Seminumerical Algorithms by Donald E. Knuth" (PDF). Bull. Amer. Math. Soc. 79 (3): 501–509. doi:10.1090/s0002-9904-1973-13173-8.


  • Slater, Robert (1987). Portraits in Silicon. MIT Press. ISBN 0-262-19262-4. 
  • Shasha, Dennis; Cathy Lazere (1995). Out of Their Minds: The Lives and Discoveries of 15 Great Computer Scientists. Copernicus. ISBN 0-387-97992-1. 
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