 The Art of Computer Programming, Volume 1: Fundamental Algorithms | |
| Author | Donald Knuth |
|---|---|
| Language | English |
| Genre | Non-fiction Monograph |
| Publisher | Addison-Wesley |
Publication date | 1968– (the book is still incomplete) |
| Publication place | United States |
| Media type | Print (Hardcover) |
| ISBN | 0-201-03801-3 |
| 519 | |
| LC Class | QA76.75 |
The Art of Computer Programming (TAOCP) is a comprehensive multi-volumemonograph written by the computer scientistDonald Knuth presentingprogrammingalgorithms andtheir analysis. As of 2025[update] it consists of published volumes 1, 2, 3, 4A, and 4B, with more expected to be released in the future. The Volumes 1–5 are intended to represent the central core of computer programming for sequential machines; the subjects of Volumes 6 and 7 are important but more specialized.[1]
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 ontypesetting 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.[2] The first published installment of Volume 4 appeared in paperback asFascicle 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.[3] The manuscript was sent to the publisher on August 1, 2022, and the volume was published in September 2022.[4] Fascicle 7 ("Constraint Satisfaction"), planned for Volume 4C, was the subject of Knuth's talk on August 3, 2022[5] and was published on February 5, 2025.[6]
After winning aWestinghouse Talent Search scholarship, Knuth enrolled at the Case Institute of Technology (nowCase Western Reserve University), where his performance was so outstanding that the faculty voted to award him amaster of science upon his completion of thebachelor's degree. During his summer vacations, Knuth was hired by theBurroughs Corporation to writecompilers, earning more in his summer months than full professors did for an entire year.[7] Such exploits made Knuth a topic of discussion among the mathematics department, which includedRichard S. Varga.
In January 1962, when he was a graduate student in the mathematics department at Caltech, Knuth was approached byAddison-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 aFORTRAN compiler forUNIVAC, considering that he had "sold my soul to the devil" to develop a FORTRAN compiler[8]: 15 afterALGOL developments with Burroughs. He remained as a consultant to Burroughs over the period 1960 to 1968 while writing Volume 1 "Fundamental Algorithms".
During this time, he also developed a mathematical analysis oflinear 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, at3000 hand-written pages.[9] He had assumed that about five hand-written pages would translate into one printed page, but his publisher said instead that about1+1⁄2 hand-written pages translated to one printed page. This meant he had approximately2000 printed pages of material, which closely matches the size of the first three published volumes.
The first volume of "The Art of Computer Programming", "Fundamental Algorithms", took five years to complete between 1963 and 1968 while working at both Caltech and Burroughs.
Knuth's dedication in Volume 1 reads:
This series of books is affectionately dedicated
to theType 650 computer once installed at
Case Institute of Technology,
in remembrance of many pleasant evenings.[a]
In the preface, he thanks first his wife Jill, then Burroughs for the use of B220 and B5500 computers in testing most of the programs, and Caltech, the National Science Foundation, and the Office of Naval Research.[10]: xii
Section 2.5 of "Fundamental Algorithms" is onDynamic Storage Allocation. Parts of this are used in the Burroughs approach to memory management. Knuth claims credit for: “the “boundary-tag” method, introduced in Section 2.5, was designed by the author in 1962 for use in a control program for the B5000 computer.”[10]: 460
Knuth received support from Richard S. Varga, who was the scientific adviser to the publisher. Varga was visitingOlga Taussky-Todd andJohn Todd atCaltech. 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.[11] 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 betypeset again, but the style of type used in the first edition (calledhot type) was no longer available. In 1977, he decided to spend some time creating something more suitable. Eight years later, he returned withTEX, which is currently used for all volumes.
Another characteristic of the volumes is the variation in the difficulty of the exercises including a numerical rating varying from 0 to 50, where 0 is trivial, and 50 is an open question in contemporary research.
The offer of a so-calledKnuth reward check worth "one hexadecimal dollar" (100HEXbase 16 cents, indecimal, 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.
All examples in the books use a hypothetical language called "MIX assembly language" (MIXAL), which runs on "a mythical computer called MIX". Currently,[when?] the MIX computer is being replaced by theMMIX computer, which is aRISC version. The conversion from MIX to MMIX was a large ongoing project for which Knuth solicited volunteers for help. Software such asGNU MDK[12] exists to provideemulation of the MIX architecture. Knuth considers the use ofassembly language necessary for the speed and memory usage of algorithms to be judged.
According to Knuth, MIX was much like any computer then in existence, but nicer.[13] The name 'MIX' is 1009 in Roman numerals and this is given by a formula involving series numbers of several computers of the time: (360 + 650 + 709 + U3 + SS80 + 1107 + 1604 + G2- + B220 + S2000 + 920 + 601 + H800 + PDP-4 + 11)/16 = 1009 or MIX.[how?] The name MMIX is 2009 in Roman numerals and Knuth claims MMIX is even nicer than MIX.
Knuth was awarded the 1974Turing Award "for his major contributions to theanalysis 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."[14]American Scientist has included this work among "100 or so Books that shaped a Century of Science", referring to the twentieth century.[15] Covers of the third edition of Volume 1 quoteBill 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."[16]The New York Times referred to it as "the profession's defining treatise".[17]
These are the current editions in order by volume number:
These volumes were superseded by newer editions and are in order by date.
Volume 4,Fascicles 0–4 were revised and published as Volume 4A.
Volume 4, Fascicles 5–6 were revised and published as Volume 4B.
Volume 1
Volume 4
The remaining pre-fascicles contain draft material that is set to appear in future fascicles and volumes.
Notes
Citations
Now 82, he's hard at work on part B of volume 4, and he anticipates that the book will have at least parts A through F.
Sources
