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The Art of Computer Programming by Donald E. Knuth

by Donald E. Knuth.

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At the end of 1999, these books were named among the best twelve physical-science monographs of the century by American Scientist, along with: Dirac on quantum mechanics, Einstein on relativity, Mandelbrot on fractals, Pauling on the chemical bond, Russell and Whitehead on foundations of mathematics, von Neumann and Morgenstern on game theory, Wiener on cybernetics, Woodward and Hoffmann on orbital symmetry, Feynman on quantum electrodynamics, Smith on the search for structure, and Einstein's collected papers. Wow!

View “historic” publisher's brochure from the first edition of Volume 1 (1968)

A complimentary downloadable PDF containing the collected indexes is available from the publisher to registered owners of the five-volume boxed set. This PDF includes the complete indexes of Volumes 1, 2, 3, 4A, and 4B, as well as the index to Volume 1 Fascicle 1. Registered owners of the earlier four-volume boxed set are, similarly, entitled to download an earlier collection of indexes. This earlier collection includes Volumes 1, 2, 3, and 4A; Volume 1 Fascicle 1; and Volume 4 Fascicles 5 and 6.

eBook versions

These volumes are now available also in portable electronic form, using PDF format. Special care has been taken to make the search feature work well. Thousands of useful "clickable" cross-references are also provided — from exercises to their answers and back, from the index to the text, from the text to important tables and figures, etc.

Warning: Unfortunately, however, non-PDF versions have also appeared, against my recommendations, and those versions are frankly quite awful. A great deal of expertise and care is necessary to do the job right. If you have been misled into purchasing one of these inferior versions (for example, a Kindle edition), the publishers have told me that they will replace your copy with the PDF edition that I have personally approved. Do not purchase eTAOCP in Kindle format if you expect the mathematics to make sense. (The ePUB format may be just as bad; I really don't want to know, and I am really sorry that it was released.) Some non-PDF versions also masquerade as PDF.

The authorized PDF versions can be purchased at www.informit.com/taocp.

Please do not tell me about errors that you find in an eBook, whether it's PDF or not, unless the same errors are present in a printed copy; such mistakes should be reported directly to the publisher.

Volume 1

Fundamental Algorithms, Third Edition (Reading, Massachusetts: Addison-Wesley, 1997), xx+650pp. ISBN 0-201-89683-4

Translations of previous editions:

Chinese translation by Guan JiWen and Su Yunlin, Ji Suan Ji Cheng Xu She Ji Ji Qiao, 1. Juan: Ji Ben Suan Fa (Beijing: Defense Industry Publishing Co., 1980), 14+573pp.

Translations of the third edition:

Translations of fascicles:

Volume 2

Seminumerical Algorithms, Third Edition (Reading, Massachusetts: Addison-Wesley, 1997), xiv+762pp.

Translations of previous editions:

Romanian translation by Florian Petrescu, Ioan Georgescu, Rolanda Predescu, and Paul Zamfirescu, Tratat de programarea calculatoarelor, V. 2: Algoritmi seminumerici (Bucharest: Editura tehnica, 1983), 722pp.

Translations of the third edition:

Volume 3

Sorting and Searching, Second Edition (Reading, Massachusetts: Addison-Wesley, 1998), xiv+780pp.+foldout.

Translations of the first edition:

Translations of the second edition:

Volume 4A

Combinatorial Algorithms, Part 1 (Upper Saddle River, New Jersey: Addison-Wesley, 2011), xvi+883pp.

(Preliminary drafts were previously published as paperback fascicles; see below.)

Russian translation (Moscow: Dialektika, 2019), 955pp.

Volume 4B

Combinatorial Algorithms, Part 2 (Upper Saddle River, New Jersey: Addison-Wesley, 2023), xviii+714pp.

(Preliminary drafts were previously published as paperback fascicles; see below.)

Japanese translation by Hideya Iwasaki, Naoyuki Tamura, Minoru Terada, and Eiiti Wada, supervised by Eiiti Wada (Tokyo: ASCII DWANGO, 2023), xx+708pp.

Chinese translation by Xiongxin Yang, Guang Hu, Xihan Li, and Fei Liu (Beijing: Posts & Telecom Press, 2025), xviii+590pp.

The Remainder of Volume 4

Present plans are for Volumes 4A and 4B to be the first in a series of several subvolumes 4A, 4B, 4C, ... entitled Combinatorial Algorithms, Part 1, 2, 3, .... The remaining subvolumes, currently in preparation, will have the following general outline:

Paperback Fascicles

New material for Volume 4 will first appear in beta-test form as fascicles of approximately 128 pages each, issued approximately twice per year. These fascicles will represent my best attempt to write a comprehensive account; but computer science has grown to the point where I cannot hope to be an authority on all the material covered in these books. Therefore I'll need feedback from readers in order to prepare the official volumes later.

For example, the following fascicles appeared before the hardcover editions of Volumes 4A and 4B were complete.

Volume 4 Fascicle 0, Introduction to Combinatorial Algorithms and Boolean Functions (2008), xii+216pp. ISBN 0-321-53496-4

Translations of those fascicles:

The future Volume 4C is currently represented by

Volume 5

Syntactic Algorithms, in preparation.

Future plans

As I continue to write Volumes 4 and 5, I'll need to refer to topics that belong logically in Volumes 1--3 but weren't invented yet when I wrote those books. Instead of putting such material artificially into Volumes 4 or 5, I'll put it into fascicle form. The first such fascicle is in fact ready now (see above): It describes MMIX, a RISC machine that is used in Volume 4A; MMIX will also take the place of MIX in all subsequent editions of Volumes 1, 2, and 3.

Download the 16 Feb 2004 version of Volume 1 Fascicle 1 (583KB of compressed PostScript) (this old version is however no longer being maintained; see the errata below)

After Volume 5 has been completed, I will revise Volumes 1--3 again to bring them up to date. In particular, the new material for those volumes that has been issued in beta-test fascicles will be incorporated at that time.

Then I will publish a “reader's digest” edition of Volumes 1--5, condensing the most important material into a single book.

And after Volumes 1--5 are done, God willing, I plan to publish Volume 6 (the theory of context-free languages) and Volume 7 (Compiler techniques), but only if the things I want to say about those topics are still relevant and still haven't been said. Volumes 1--5 represent the central core of computer programming for sequential machines; the subjects of Volumes 6 and 7 are important but more specialized.

Volumes 1--4B are available from the publisher, Addison-Wesley Publishing Company.

MIXware

The MIX computer will soon be replaced by a RISC machine called MMIX. Meanwhile if you want to try out the existing programs for the original 60s-era machine, you might be able to find suitable software at the following sites:

(Please let me know of any other sites that I should add to this list.)

The MMIX Supplement

Martin Ruckert has written an excellent 200-page companion to Volumes 1, 2, and 3, intelligently translating all of the MIX programs into MMIX form. This booklet is jam-packed with instructive details and opportunities for self-instruction.

Errata et Addenda for Volume 1

The main changes between the second and third editions of Volume 1 are listed in the Errata for Volume 1 (2nd ed.) (335K bytes of compressed PostScript, 80pp)---an archival file that is not being kept up to date. But thousands of additional refinements appear in the 3rd edition; you really should ask someone to get it for you next Christmas.

The main changes to the third edition of Volume 1, made before the appearance of Volume 4A in 2011, are listed in the Earliest errata for Volume 1 (3rd ed.) (262K bytes of compressed PostScript, 50pp).

There's also another major list of changes, covering the period 2011--2021: Earlier changes for Volume 1 (3rd ed.) (143K bytes of compressed PostScript, 20pp).

There's also a (much shorter, last updated 31 May 2026) list of changes since the 49th printing was released in 2022, almost all of which have been made in more recent printings:

Note: You can't run that TeX file through TeX; it imports all kinds of other files that are private. But if you have no way to look at compressed PostScript files, you might try reading the TeX code as a last resort; at least you'll be able to figure out the page numbers on which corrections have been made.

And there's also a list of changes to Volume 1 Fascicle 1, last updated 08 January 2025:

Note: An unknown number of badly printed copies of Volume 1 Fascicle 1 were printed by mistake. Among other defects, the copyright page has incredibly poor resolution, and the MMIX summary chart has been omitted from the inside back cover. If you have purchased one of these monstrosities, the publishers assure me that they will replace your copy with a good one.

Errata et Addenda for Volume 2

The main changes between the second and third editions of Volume 2 are listed in the Errata for Volume 2 (2nd ed.) (555K bytes of compressed PostScript, 142pp)---an archival file that is not being kept up to date. But thousands of additional refinements appear in the 3rd edition; you really should ask someone to get it for you next Christmas.

The main changes to the third edition of Volume 2, made before the appearance of Volume 4A, are listed in the Earliest errata for Volume 2 (3rd ed.) (229K bytes of compressed PostScript, 50pp), dated 08 January 2011.

There's also another major list of changes, covering the period 2011--2021: Earlier changes for Volume 2 (3rd ed.) (133K bytes of compressed PostScript, 19pp).

There's also a (much shorter, last updated 09 June 2026) list of changes since the 45th printing was released in 2022, almost all of which have been made in more recent printings:

Note: You can't run that TeX file through TeX; it imports all kinds of other files that are private. But if you have no way to look at compressed PostScript files, you might try reading the TeX code as a last resort; at least you'll be able to figure out the page numbers on which corrections have been made.

Errata et Addenda for Volume 3

The main changes between the first and second editions of Volume 3 are listed in the Errata for Volume 3 (1st ed.) (430K bytes of compressed PostScript, 109pp)---an archival file that is not being kept up to date. But thousands of additional refinements appear in the 2nd edition; you really should ask someone to get it for you next Christmas.

The main changes to the second edition of Volume 3, made before the appearance of Volume 4A in 2011, are listed in the Earliest errata for Volume 3 (2nd ed.) (226K bytes of compressed PostScript, 43pp).

There's also another major list of changes, covering the period 2011--2021: Earlier changes for Volume 3 (2nd ed.) (117K bytes of compressed PostScript, 15pp).

There's also a (much shorter, last updated 09 June 2026) list of changes since the 45th printing was released in 2022, almost all of which have been made in more recent printings:

Note: You can't run that TeX file through TeX; it imports all kinds of other files that are private. But if you have no way to look at compressed PostScript files, you might try reading the TeX code as a last resort; at least you'll be able to figure out the page numbers on which corrections have been made.

Errata et Addenda for Volume 4A

The following corrections to the paperback fascicles that preceded Volume 4A will make them essentially consistent with the first hardcover printing of that volume. (These errata files reached their final form on 01 January 2011, and they won't be updated again; see below for additional amendments and corrections to the hardcover printing.)

The main changes to the first edition of Volume 4A, made before the appearance of Volume 4B in 2022, are listed in the Earliest errata for Volume 4A (225K bytes of compressed PostScript, 44pp).

There's also a (much shorter, last updated 09 September 2025) list of changes since the 20th printing was released in 2022, almost all of which have been made in more recent printings:

Note: You can't run that TeX file through TeX; it imports all kinds of other files that are private. But if you have no way to look at compressed PostScript files, you might try reading the TeX code as a last resort; at least you'll be able to figure out the page numbers on which corrections have been made.

Errata et Addenda for Volume 4B

The following corrections to the paperback fascicles that preceded Volume 4B will make them essentially consistent with the first hardcover printing of that volume. (These errata files reached their final form on 26 July 2022, and they won't be updated again; see below for additional amendments and corrections to the hardcover printing.)

And there's also a list of changes to Volume 4 Fascicle 6:

Here's the current list of changes to the hardcover edition of Volume 4B, last updated 16 April 2026:

Note: You can't run that TeX file through TeX; it imports all kinds of other files that are private. But if you have no way to look at compressed PostScript files, you might try reading the TeX code as a last resort; at least you'll be able to figure out the page numbers on which corrections have been made.

Errata et Addenda for Volume 4C

Volume 4C is just getting started, as stated above. So far at least its first couple hundred pages are available as Volume 4 Fascicle 7. Here are the corrections that I've made so far to my master copy of that fascicle (last updated 01 July 2026):

Note: You can't run that TeX file through TeX; it imports all kinds of other files that are private. But if you have no way to look at compressed PostScript files, you might try reading the TeX code as a last resort; at least you'll be able to figure out the page numbers on which corrections have been made.

Rewards

The first finder of any error in my books receives 0x$1.00 ($2.56), deposited to their account at the Bank of San Serriffe; significant suggestions are also worth 0x$0.20 ($0.32) each. If you are a really careful reader, you may be able to recoup more than the cost of the books this way, and you'll be helping future readers too.

However, people who have read the book Eats, Shoots & Leaves should not expect a reward for criticizing the ways in which I use commas. Punctuation is extremely important to me, but I insist on doing it my own way.

Similarly, you can save yourself valuable time by not trying to get me to change ‘awhile’ to ‘a while’.

As mentioned above, I take no responsibility for errors in the eBook editions that do not use PDF format. I would soon go broke if I had to pay for all of them! Such errors should be reported directly to the publisher, not to me, and you should request a replacement copy.

Please send your comments either by email to taocp@cs.stanford.edu or by old-fashioned mail to

Donald E. Knuth

In either case please include your postal address, so that I can mail an official certificate of deposit as a token of thanks for any improvements to which you have contributed.

SPECIAL NOTE TO THE SPEAKERS OF FRENCH AND OTHER EXOTIC LANGUAGES: Numerous quotations and bibliographic citations found in these books have been copied verbatim from the original sources. If you believe you have found a typographic error, you must prove it by showing that the original was incorrectly transcribed; believe it or not, your language has changed over the years, just as English has.

Although I'm working full time on Volume 4C these days, I will try to reply to all such messages within nine months of receipt.

BUT PLEASE DO NOT SEND EMAIL TO TAOCP EXCEPT TO REPORT ERRORS IN THE ART OF COMPUTER PROGRAMMING. And if you do report an error via email, please do not include attachments of any kind; your message should be readable on brand-X operating systems for all values of X. (Encrypted messages that I get from "gmail.com" are also gibberish and unreadable without great pain.) Send PLAIN ASCII TEXT ONLY.

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