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The Art of Computer Programming, Volumes 1-4A Boxed Set 1st Edition
The bible of all fundamental algorithms and the work that taught many of today’s software developers most of what they know about computer programming.
—Byte, September 1995
Countless readers have spoken about the profound personal influence of Knuth’s work. Scientists have marveled at the beauty and elegance of his analysis, while ordinary programmers have successfully applied his “cookbook” solutions to their day-to-day problems. All have admired Knuth for the breadth, clarity, accuracy, and good humor found in his books.
I can’t begin to tell you how many pleasurable hours of study and recreation they have afforded me! I have pored over them in cars, restaurants, at work, at home… and even at a Little League game when my son wasn’t in the line-up.
—Charles Long
Primarily written as a reference, some people have nevertheless found it possible and interesting to read each volume from beginning to end. A programmer in China even compared the experience to reading a poem.
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.
—Bill Gates
Whatever your background, if you need to do any serious computer programming, you will find your own good reason to make each volume in this series a readily accessible part of your scholarly or professional library.
It’s always a pleasure when a problem is hard enough that you have to get the Knuths off the shelf. I find that merely opening one has a very useful terrorizing effect on computers.
—Jonathan Laventhol
In describing the new fourth volume, one reviewer listed the qualities that distinguish all of Knuth’s work.
[In sum:] detailed coverage of the basics, illustrated with well-chosen examples; occasional forays into more esoteric topics and problems at the frontiers of research; impeccable writing peppered with occasional bits of humor; extensive collections of exercises, all with solutions or helpful hints; a careful attention to history; implementations of many of the algorithms in his classic step-by-step form.
— Frank Ruskey
These four books comprise what easily could be the most important set of information on any serious programmer’s bookshelf.
- ISBN-100321751043
- ISBN-13978-0321751041
- Edition1st
- PublisherAddison-Wesley Professional
- Publication dateMarch 3, 2011
- LanguageEnglish
- Dimensions9 x 8.9 x 9 inches
- Print length3168 pages
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From the Publisher

Updated Box Set Now Available!
This new box set now includes Volume 4B - Combinatorial Algorithms, Part 2
"I've had loads of fun writing other parts of these volumes, but without doubt Section 7.2.2.1 [of Combinatorial Algorithms, Part 2] has been the funnest. And I know that my delight in good puzzles is shared by a significant number of leading computer scientists and mathematicians, who have told me that they chose their careers after having been inspired by such intellectual challenges."
— Donald Knuth
The Art of Computer Programming Volumes 1-4B
ISBN-10: 0137935102
Editorial Reviews
From the Back Cover
This boxed set consists of the following four volumes:
0201896834 / 9780201896831 Art of Computer Programming, Volume 1: Fundamental Algorithms
0201896842 / 9780201896848 Art of Computer Programming, Volume 2: Seminumerical Algorithms
0201896850 / 9780201896855 Art of Computer Programming, Volume 3: Sorting and Searching
0201038048 / 9780201038040 Art of Computer Programming, Volume 4A: Combinatorial Algorithms
About the Author
Donald E. Knuth is known throughout the world for his pioneering work on algorithms and programming techniques, for his invention of the TEX and METAFONT systems for computer typesetting, and for his prolific and influential writing. Professor Emeritus of The Art of Computer Programming at Stanford University, he currently devotes full time to the completion of these fascicles and the seven volumes to which they belong.
Product details
- Publisher : Addison-Wesley Professional; 1st edition (March 3, 2011)
- Language : English
- Hardcover : 3168 pages
- ISBN-10 : 0321751043
- ISBN-13 : 978-0321751041
- Item Weight : 12 pounds
- Dimensions : 9 x 8.9 x 9 inches
- Best Sellers Rank: #362,725 in Books (See Top 100 in Books)
- #23 in Computer Algorithms
- #94 in Programming Algorithms
- #236 in Computer Programming Languages
- Customer Reviews:
About the author

Donald E. Knuth was born on January 10, 1938 in Milwaukee, Wisconsin. He studied mathematics as an undergraduate at Case Institute of Technology, where he also wrote software at the Computing Center. The Case faculty took the unprecedented step of awarding him a Master's degree together with the B.S. he received in 1960. After graduate studies at California Institute of Technology, he received a Ph.D. in Mathematics in 1963 and then remained on the mathematics faculty. Throughout this period he continued to be involved with software development, serving as consultant to Burroughs Corporation from 1960-1968 and as editor of Programming Languages for ACM publications from 1964-1967.
He joined Stanford University as Professor of Computer Science in 1968, and was appointed to Stanford's first endowed chair in computer science nine years later. As a university professor he introduced a variety of new courses into the curriculum, notably Data Structures and Concrete Mathematics. In 1993 he became Professor Emeritus of The Art of Computer Programming. He has supervised the dissertations of 28 students.
Knuth began in 1962 to prepare textbooks about programming techniques, and this work evolved into a projected seven-volume series entitled The Art of Computer Programming. Volumes 1-3 first appeared in 1968, 1969, and 1973. Having revised these three in 1997, he is now working full time on the remaining volumes. Volume 4A appeared at the beginning of 2011. More than one million copies have already been printed, including translations into ten languages.
He took ten years off from that project to work on digital typography, developing the TeX system for document preparation and the METAFONT system for alphabet design. Noteworthy by-products of those activities were the WEB and CWEB languages for structured documentation, and the accompanying methodology of Literate Programming. TeX is now used to produce most of the world's scientific literature in physics and mathematics.
His research papers have been instrumental in establishing several subareas of computer science and software engineering: LR(k) parsing; attribute grammars; the Knuth-Bendix algorithm for axiomatic reasoning; empirical studies of user programs and profiles; analysis of algorithms. In general, his works have been directed towards the search for a proper balance between theory and practice.
Professor Knuth received the ACM Turing Award in 1974 and became a Fellow of the British Computer Society in 1980, an Honorary Member of the IEEE in 1982. He is a member of the American Academy of Arts and Sciences, the National Academy of Sciences, and the National Academy of Engineering; he is also a foreign associate of l'Academie des Sciences (Paris), Det Norske Videnskaps-Akademi (Oslo), Bayerische Akademie der Wissenschaften (Munich), the Royal Society (London), and Rossiiskaya Akademia Nauk (Moscow). He holds five patents and has published approximately 160 papers in addition to his 28 books. He received the Medal of Science from President Carter in 1979, the American Mathematical Society's Steele Prize for expository writing in 1986, the New York Academy of Sciences Award in 1987, the J.D. Warnier Prize for software methodology in 1989, the Adelskøld Medal from the Swedish Academy of Sciences in 1994, the Harvey Prize from the Technion in 1995, and the Kyoto Prize for advanced technology in 1996. He was a charter recipient of the IEEE Computer Pioneer Award in 1982, after having received the IEEE Computer Society's W. Wallace McDowell Award in 1980; he received the IEEE's John von Neumann Medal in 1995. He holds honorary doctorates from Oxford University, the University of Paris, St. Petersburg University, and more than a dozen colleges and universities in America.
Professor Knuth lives on the Stanford campus with his wife, Jill. They have two children, John and Jennifer. Music is his main avocation.
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Customers find this programming book set fundamental for computer scientists and excellent for advanced programmers. The writing is well-explained, with one customer specifically praising Knuth's clear explanation of searching and sorting. Customers consider the set worth the money and appreciate its beautiful presentation, with one noting its good glossy cover.
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Customers praise these programming books as fundamental reads for computer scientists and advanced programmers, describing them as an excellent collection of classic computer science material.
"...What an excellent authoritive masterful survey - up to 2011 - of combinatorial exhaustive search techniques ......" Read more
"...There is a lot of history which Knuth makes interesting by stating which algorithms were remarkable discoveries and which were logical extensions of..." Read more
"...This is a book to learn and appreciate and not to copy code from. Anyways, does it matter if he wrote in c++,c,python or assembly?..." Read more
"...the world is deep and complicated." I think that they are great for reference...." Read more
Customers praise the writing quality of the book, finding it well-explained and superbly written, with one customer noting how it blends programming with higher-level mathematics.
"...Excellent and comprehensive chapter on bitwise tips and techniques, and all sorts of other obscure techniques such as resolution and radix sorting..." Read more
"...Knuth's writing is excellent. Each sentence is clear and communicates in a way that makes computer history interesting...." Read more
"...I also recommend to get facsimile 0 (MMIX) The math is so clear and well explained. The fact that he uses MIX (and MMIX) it is fine...." Read more
"...The contents are simply fabulous, and the print quality and the paper inside are great." Read more
Customers find the book set worth the money, with one mentioning it's a perfect collection to invest in.
"...First of all, if you divide the price of the bundle /4 is a great deal. I also recommend to get facsimile 0 (MMIX)..." Read more
"...looking to enhance their knowledge base, this is the perfect book set to invest in." Read more
"...Definitely worth the money, and good luck getting through it." Read more
"...While it is not a cheap purchase, it is well worth it for the material presented inside...." Read more
Customers find the book beautiful, with one mentioning its good glossy cover.
"...The box set itself is beautiful and the paper is high quality. I wish I could give more than 5 stars for the review." Read more
"...They are beautiful, the off-white coloured dust jackets make a pleasing change to the other pure white books that I have on my desk, and the box..." Read more
"...They look beautiful in the boxed set with high quality covers as well as pages...." Read more
"...I was expecting a book with a good glossy cover (talk about judging a book by its cover!)...." Read more
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Top reviews from the United States
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- Reviewed in the United States on April 4, 2013Since receipt of volume 4A two days ago, I have been dipping into this and that topic via the indexes ...
What an excellent authoritive masterful survey - up to 2011 - of combinatorial exhaustive search techniques ...
And, some focus on application to business usable sorting and searching techniques ...
Excellent and comprehensive chapter on bitwise tips and techniques, and all sorts of other obscure techniques such as resolution and radix sorting that may not be obvious to information systems graduates who don't have to study algorithms in depth.
(Must confess I've seen earlier editions of volumes 1 to 3 before!)
Donald Knuth is not averse to explaining some things in terms of history or heuristic ... the only heuristic explanation I'm familiar with he doesn't raise are the ones based on the laws of thermodynamics. There is this argument that to understand sorting algorithms one must consider the entrophy gains and losses as the system becomes more ordered and the consequent radiated heat somewhere else in the universe. The related argument from nuclear cell division DNA replication - in science fiction called sometimes the life force - is that when one duplicates information there is a consequent 'life force' heat side effect from the physical law of the conservation of information in quantum mechanics equations. The heuristic explanation then is that if we can minimise the heat from the sorting, we'll have found the best sorting algorithm. Now quicksort wastes more fractions of distinguishment than multi-pass-N-way merge sorting in theory ... so there is more tiny fractions of wasted bits caused by the comparisions. If the exchanges are free and there is unlimited memory then less wasted bit fractions of distinguishment would mean less heat therefore quicksort should on average be slower ... but practical tests proves quicksort faster!
That's the problem with heuristics!
However, reading through some fo Knuth's essays on exhaustive searching may suggest a solution ... that if we have 64K 32 bit integers, to minimise comparisions we precompute all partitions of the 64K into several thousand sequences of varying length less than length 17, use table driven state machines to optimally sort these sequences in place, and check each resultant multi-pass-N-way merge sort for total wasted bits of distinguishment to find the best breakdown to compare quicksort with. This impossible to conduct experiment would then show the validity or invalidity of applying thermodynamics to the problem ...
Unfortunately for me I bought this volume hoping to get a survey of the latest news on the P-NP completeness problem. I will have to await volume 4B for that!
- Reviewed in the United States on February 9, 2016I read this book cover to cover which took me over 3 months, and I was extremely impressed with this collection. Knuth turns computer programming into an art form as the title suggests.
There is a lot of history which Knuth makes interesting by stating which algorithms were remarkable discoveries and which were logical extensions of other algorithms. The analysis is much more in depth than other authors especially with regards to run time performance.
At the end of each section there are tons of problems to solve, and full answers are in the back. I especially liked how each problem has a rating on its difficulty. For example, a problem with a rating 10 is easy, rating 25 might take an hour... up to rating 50 which is an unsolved problem in computer science.
Volume one starts with the first 150 pages being math related to computer science. Then the assembly language is introduced which many of the algorithms are written in. The choice for assembly was made so as to not commit to one specific language's paradigm.
Volume two gets into the heart of the algorithms. A lot of interesting things about floating point calculations, and prime number discovery. My overall understanding of computer science improved a ton here.
Volume three was my personal favorite. Knuth explains searching and sorting very well. The evolution of the "trie" data structure was impressive. At first he shows a way to make a trie in a way I had never seen before. Then he showed another way, and finally he got to the modern way I had seen. With this knowledge, I understood how the trie was discovered, how it was improved, and then improved again. Every other algorithm book just shows the modern trie without explaining how they got there.
Volume four is heavy on math again with a lot about permutations and combinatorics. This was the most difficult of the books I felt but also rewarding.
Knuth's writing is excellent. Each sentence is clear and communicates in a way that makes computer history interesting.
The box set itself is beautiful and the paper is high quality. I wish I could give more than 5 stars for the review.
- Reviewed in the United States on October 17, 2011Hi,
AMAZING . The book is extremely fun !
I purchased the book and have begun reading it. I love it. I'm going slow, to better enjoy it! First of all, if you divide the price of the bundle /4 is a great deal. I also recommend to get facsimile 0 (MMIX)
The math is so clear and well explained.
The fact that he uses MIX (and MMIX) it is fine. I don't see what is the big deal that some people make about this. If you want something in a specific language, there is plenty of books out there...
This is a book to learn and appreciate and not to copy code from. Anyways, does it matter if he wrote in c++,c,python or assembly? who cares, it is all the same... if you are reading this book and you are not able to read the mix code, then don't bother.
I sow some reviews in the previous bundle that were surprising. Someone claimed that people buy this book to look smarter? Well, I have them in my house, so I guess when I look at them, should I think that I'm smarter ?
Also this reviewer claimed that Knuth paid his student to give better review... does he know since what year he stop being an active professor?
Anyways, just to rant about that reviewer.
- Reviewed in the United States on March 11, 2024The work of a lifetime of a real genius, a work still in progress. A must have reference for anyone who involves in serious computer programming. This edition comes in a nice boxed set that just calls for volume 4B as a proper companion.
Top reviews from other countries
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THReviewed in Germany on June 6, 2020
5.0 out of 5 stars Nicht nur inhaltlich höchste Qualität
Über den Inhalt dieses Jahrhundertwerks wurde schon reichlich geschrieben, dem lässt sich nicht mehr viel hinzufügen. Ich beschränke mich daher auf den Hinweis, dass in Volume 1 bis 3 noch MIX verwendet wird und in Volume 4A bereits MMIX. Als Ergänzung bietet sich daher Volume 1 Fascicle 1 (9780201853926) vom selben Autor an, in dem die neue Beispielarchitektur erklärt wird. Optional kann mit dem Buch The MMIX Supplement (9780133992311) von Martin Ruckert, das alle Programme der Volume 1 bis 3 für MMIX enthält, die Zeit überbrückt werden, bis Knuth diese für MMIX überarbeitet. Wollen wir hoffen, dass ihm noch ausreichend Lebenszeit und Gesundheit verbleiben.
Nun ist Knuth aber nicht nur ein begnadeter Mathematiker und Informatiker, sondern auch Spezialist für Buchsatz, speziell im mathematisch-technischen Bereich. Man könnte sogar so weit gehen zu sagen, er wäre ein Connoisseur für Bücher, speziell Lehrbücher. Siehe dazu die empfehlenswerte zweiteilige Interviewserie Oral History des Computer History Museums in Mountain View, Kalifornien mit ihm aus dem Jahr 2007.
Aus diesem Grund möchte ich noch zur Qualität der Bücher abseits des Inhaltes etwas sagen, nicht zuletzt weil es kürzlich eine englischsprachige Rezension hierzu gab die von einer schlechten Papierqualität sprach. Ich kann diese aktuelle vierbändige Ausgabe mit dem 10. Druck der vorherigen, dreibändigen Ausgabe vergleichen.
Die Druck- und Papierqualität ist herausragend. Im Vergleich zur dreibändigen Ausgabe wirkt das Papier etwas glatter und insbesondere erscheint mir der Kontrast des Druckes jetzt höher zu sein, was mir sehr entgegen kommt. An der Papierqualität im Sinne von Gewicht pro Fläche, hat sich nichts geändert, für Volume 1 war der ermittelte Gewichtsunterschied der zwei Drucke mit nur 4 Gramm vernachlässigbar.
Leider finde ich keine Angabe, welches Papier genau verwendet wurde. In Concrete Mathematics (Graham, Knuth, Patashnik, 9780201558029), das übrigens auch eine sehr sinnvolle Ergänzung darstellt und auf das im Kapitel 1.2 regelmäßig Bezug genommen wird, befindet sich diese unterhalb der Tabellenübersicht, am Ende des Indexes. Es handelt sich um ein für die Langzeitarchivierung geeignetes Papier, das mehrere hundert Jahre haltbar ist. Es erscheint daher logisch, dass bei Knuths Hauptwerk sicher kein schlechteres Papier verwendet wurde. Das Papier der vierbändigen Ausgabe ist ein Anderes, stärker und dadurch etwas weniger durchscheinend als Concrete Mathematics.
Die Qualität dieser Bücher stimmt also in jeglicher Hinsicht. Man sieht aber leicht, dass The Art of Computer Programming nach wie vor ein unvollendetes Werk ist, eine Baustelle gar, wie der Autor selber unumwunden zugibt. Ob also genau jetzt der richtige Zeitpunkt ist, diese vierbändige Ausgabe zu kaufen, muss jeder mit sich selber ausmachen. Für mich den Ausschlag gegeben hat der aktuell günstige Preis, die Tatsache dass mir Volume 4A fehlte und dass im Vergleich zu meinem 10. Druck eine Vielzahl an Fehlerbereinigungen eingeflossen sind und die verbleidende Errata wesentlich kürzer ist. Die etwas bessere Lesbarkeit durch den höheren Kontrast war ein willkommener Bonus.
Als letzten Hinweis möchte ich noch unterbringen, dass es die Bücher zwischenzeitlich auch in einer offiziellen PDF-Version zu kaufen gibt.
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WelingtonReviewed in Brazil on December 21, 2016
5.0 out of 5 stars Primoroso
Das primeiras impressões que tive deste texto, são bem interessantes. Meu professor da faculdade, de Estrutura de Dados (professor Antônio Carlos de Oliveira Leigo) sempre sugeriu o material do senhor Knuth para ser estudado e degustado com "farinha" (ou seja, tem de ser literatura básica para quem quer ser um profissional sério na área de desenvolvimento de software). Hoje, pegando esta publicação e folheando o material e, depois de 19 anos no mercado de TI, realmente tenho que cravar: me professor tinha razão. Então, adquiri o livro; aqui a 1 ano e meio, após de estudos pesados por sobre ele, darei minhas impressões, mas, de início, vale sua aquisição, pois vale cada real gasto para tornar-se um profissional minimamente aceitável no mercado.
Abraço!Algoritmos. Teoria e Prática
WelingtonPrimoroso
Reviewed in Brazil on December 21, 2016
Abraço!Algoritmos. Teoria e Prática
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GooseReviewed in Spain on March 2, 2017
5.0 out of 5 stars Una edición cuidada para bibliografía de referencia
La presentación de los libros me ha gustado. El estuche no ajusta en exceso por lo que no castigas los libros al sacarlos y meterlos en él. Las sobrecubiertas son espartanas (la lectura es más cómoda quitándola). Las tapas tienen un estilo clásico que me resulta bastante agradable. La calidad de las páginas se percibe como muy buena (en cuanto a tacto y color, al menos).
El contenido está hecho todo en Latex (obvio teniendo en cuenta que el mismo autor del libro es a quien se le debe la existencia de Latex), lo que, desde mi punto de vista, facilita la lectura.
Por lo demás, el texto es muy asequible para un persona con conocimientos medios de inglés (el lenguaje utilizado es claro, el vocabulario bastante asequible), y a pesar de su estilo académico, se hace ameno.
- SonChakrReviewed in India on March 31, 2018
5.0 out of 5 stars Most comprehensive and definitive guide on Algorithms ever!
I read specific chapters from the book back during my college days, not as part of curriculum but out of my own interest.
There isn't much to say here, except that the book is the largest collection and the most well organized one too, on algorithms and mathematical methods for programming that you will ever find. Knuth formalized the study of algorithms when he first wrote the series of books back in the 60s.
I love especially the concept of a hypothetical machine that he invents to demonstrate algorithmic complexities, independent of the choice of high level programming language, which sometimes masks the underlying time (and space) requirements to execute programs. It helped me grasp how algorithmic complexity measurements are an independent phenomenon.
- Jirvin LohReviewed in Canada on October 16, 2014
5.0 out of 5 stars Inspiring!
First of all, I am not a programmer, but by far a hobbyist or enthusiast – if really want to link up to Windows programming. Reading all these definitely going to be a taxing and yet fascinating tasks – even without any of the academic pressure. I've certainly got no intend to send a copy of my résumé to Mr. Bill. I am glad to have a set of this.