The Art of Computer Programming, Volume 1: Fundamental Algorithms

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 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 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. -Bill Gates 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 This first volume in the series begins with basic programming concepts and techniques, then focuses more particularly on information structures-the representation of information inside a computer, the structural relationships between data elements and how to deal with them efficiently. Elementary applications are given to simulation, numerical methods, symbolic computing, software and system design. Dozens of simple and important algorithms and techniques have been added to those of the previous edition. The section on mathematical preliminaries has been extensively revised to match present trends in research. Ebook (PDF version) produced by Mathematical Sciences Publishers (MSP), http: //msp.org The Art of Computer Programming, Volume 4A: Combinatorial Algorithms, Part 1 Knuth's multivolume analysis of algorithms is widely recognized as the definitive description of classical computer science. The first three volumes of this work have long comprised a unique and invaluable resource in programming theory and practice. Scientists have marveled at the beauty and elegance of Knuth's analysis, while practicing programmers have successfully applied his “cookbook” solutions to their day-to-day problems. The level of these first three volumes has remained so high, and they have displayed so wide and deep a familiarity with the art of computer programming, that a sufficient “review” of future volumes could almost be: “Knuth, Volume n has been published.” —Data Processing Digest Knuth, Volume n has been published, where n = 4A. In this long-awaited new volume, the old master turns his attention to some of his favorite topics in broadword computation and combinatorial generation (exhaustively listing fundamental combinatorial objects, such as permutations, partitions, and trees), as well as his more recent interests, such as binary decision diagrams. The hallmark qualities that distinguish his previous volumes are manifest here anew: 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. There is an amazing amount of information on each page. Knuth has obviously thought long and hard about which topics and results are most central and important, and then, what are the most intuitive and succinct ways of presenting that material. Since the areas that he covers in this volume have exploded since he first envisioned writing about them, it is wonderful how he has managed to provide such thorough treatment in so few pages. —Frank Ruskey, Department of Computer Science, University of Victoria The book is Volume 4A, because Volume 4 has itself become a multivolume undertaking. Combinatorial searching is a rich and important topic, and Knuth has too much to say about it that is new, interesting, and useful to fit into a single volume, or two, or maybe even three. This book alone includes approximately 1500 exercises, with answers for self-study, plus hundreds of useful facts that cannot be found in any other publication. Volume 4A surely belongs beside the first three volumes of this classic work in every serious programmer's library. Finally, after a wait of more than thirty-five years, the first part of Volume 4 is at last ready for publication. Check out the boxed set that brings together Volumes 1 - 4A in one elegant case, and offers the purchaser a $50 discount off the price of buying the four volumes individually. Ebook (PDF version) produced by Mathematical Sciences Publishers (MSP), http://msp.org The Art of Computer Programming, Volumes 1-4A Boxed Set, 3/e The Art of Computer Programming, Volume 4 Combinatorial Algorithms, Part 1 Knuths multivolume analysis of algorithms is widely recognized as the definitive description of classical computer science. The first three volumes of this work have long comprised a unique and invaluable resource in programming theory and practice. Scientists have marveled at the beauty and elegance of Knuths analysis, while practicing programmers have successfully applied his cookbook solutions to their day-to-day problems. The level of these first three volumes has remained so high, and they have displayed so wide and deep a familiarity with the art of computer programming, that a sufficient review of future volumes could almost Knuth, Volume n has been published. Data Processing Digest Knuth, Volume n has been published, where n = 4A. In this long-awaited new volume, the old master turns his attention to some of his favorite topics in broadword computation and combinatorial generation (exhaustively listing fundamental combinatorial objects, such as permutations, partitions, and trees), as well as his more recent interests, such as binary decision diagrams. The hallmark qualities that distinguish his previous volumes are manifest here 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. There is an amazing amount of information on each page. Knuth has obviously thought long and hard about which topics and results are most central and important, and then, what are the most intuitive and succinct ways of presenting that material. Since the areas that he covers in this volume have exploded since he first envisioned writing about them, it is wonderful how he has managed to provide such thorough treatment in so few pages . Frank Ruskey, Department of Computer Science, University of Victoria The book is Volume 4A, because Volume 4 has itself become a multivolume undertaking. Combinatorial searching is a rich and important topic, and Knuth has too much to say about it that is new, interesting, and useful to fit into a single volume, or two, or maybe even three. This book alone includes approximately 1500 exercises, with answers for self-study, plus hundreds of useful facts that cannot be found in any other publication. Volume 4A surely belongs beside the first three volumes of this classic work in every serious programmers library. Finally, after a wait of more than thirty-five years, the first part of Volume 4 is at last ready for publication. Check out the boxed set that brings together Volumes 1 - 4A in one elegant case, and offers the purchaser a $50 discount off the price of buying the four volumes individually. Ebook (PDF version) produced by Mathematical Sciences Publishers (MSP), The Art of Computer Programming, Volumes 1-4A Boxed Set, 3/e 0321751043 Cover......Page 1 Title Page......Page 5 Preface......Page 7 Preface to the Third Edition......Page 13 Procedure for Reading......Page 15 Notes on the Exercises......Page 17 Contents......Page 20 Algorithms......Page 23 Mathematical Preliminaries......Page 32 Mathematical Induction......Page 33 Numbers, Powers, and Logarithms......Page 43 Sums and Products......Page 49 Integer Functions and Elementary Number Theory......Page 61 Permutations and Factorials......Page 67 Binomial Coefficients......Page 74 Harmonic Numbers......Page 97 Fibonacci Numbers......Page 101 Generating Functions......Page 109 Analysis of an Algorithm......Page 118 * The O-notation......Page 129 * Euler's summation formula......Page 133 * Some asymptotic calculations......Page 138 Description of MIX......Page 146 The MIX Assembly Language......Page 166 Applications to Permutations......Page 186 Subroutines......Page 208 Coroutines......Page 215 Interpretive Routines......Page 222 A MIX simulator......Page 224 * Trace routines......Page 234 Input and Output......Page 237 History and Bibliography......Page 251 Introduction......Page 254 Stacks, Queues, and Deques......Page 260 Sequential Allocation......Page 266 Linked Allocation......Page 276 Circular Lists......Page 295 Doubly Linked Lists......Page 302 Arrays and Orthogonal Lists......Page 320 Trees......Page 330 Traversing Binary Trees......Page 340 Binary Tree Representation of Trees......Page 356 Other Representations of Trees......Page 370 Basic Mathematical Properties of Trees......Page 384 Free trees......Page 385 Oriented trees......Page 394 * The ``infinity lemma''......Page 404 * Enumeration of trees......Page 408 Path length......Page 421 * History and bibliography......Page 428 Lists and Garbage Collection......Page 430 Multilinked Structures......Page 446 Dynamic Storage Allocation......Page 457 History and Bibliography......Page 479 Answers to Exercises......Page 488 1. Fundamental Constants (decimal)......Page 641 2. Fundamental Constants (octal)......Page 642 3. Harmonic Numbers, Bernoulli Numbers, Fibonacci Numbers......Page 643 Appendix B: Index to Notations......Page 645 Appendix C: Index to Algorithms and Theorems......Page 650 Index and Glossary......Page 652

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

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

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.

—Bill Gates

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

The first revision of this third volume is the most comprehensive survey of classical computer techniques for sorting and searching. It extends the treatment of data structures in Volume 1 to consider both large and small databases and internal and external memories. The book contains a selection of carefully checked computer methods, with a quantitative analysis of their efficiency. Outstanding features of the second edition include a revised section on optimum sorting and new discussions of the theory of permutations and of universal hashing.

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 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 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. –Bill Gates 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 The first revision of this third volume is the most comprehensive survey of classical computer techniques for sorting and searching. It extends the treatment of data structures in Volume 1 to consider both large and small databases and internal and external memories. The book contains a selection of carefully checked computer methods, with a quantitative analysis of their efficiency. Outstanding features of the second edition include a revised section on optimum sorting and new discussions of the theory of permutations and of universal hashing. Ebook (PDF version) produced by Mathematical Sciences Publishers (MSP),http://msp.org 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 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 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. –Bill Gates 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 The second volume offers a complete introduction to the field of seminumerical algorithms, with separate chapters on random numbers and arithmetic. The book summarizes the major paradigms and basic theory of such algorithms, thereby providing a comprehensive interface between computer programming and numerical analysis. Particularly noteworthy in this third edition is Knuth's new treatment of random number generators, and his discussion of calculations with formal power series. Ebook (PDF version) produced by Mathematical Sciences Publishers (MSP),http://msp.org This multivolume work on the analysis of algorithms has long been recognized as the definitive description of classical computer science. The three complete volumes published to date already comprise a unique and invaluable resource in programming theory and practice. Countless readers have spoken about the profound personal influence of Knuth's writings. Scientists have marveled at the beauty and elegance of his analysis, while practicing 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.To begin the fourth and later volumes of the set, and to update parts of the existing three, Knuth has created a series of small books called fascicles, which will be published at regular intervals. Each facicle will encompass a section or more of wholly new or revised material. Ultimately, the content of these fascicles will be rolled up into the comprehensive, final versions of each volume, and the enormous undertaking that began in 1962 will be complete. __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____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.____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.____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.__Ebook (PDF version) produced by Mathematical Sciences Publishers (MSP), http: //msp.org The first revision of this third volume is the most comprehensive survey of computer techniques for sorting and searching. It extends the treatment of data structures in Volume 1 to consider both large and small databases and internal and external memories. The book contains a selection of carefully checked computer methods, with a quantitative analysis of their efficiency. Outstanding features of the second edition include a revised section on optimum sorting and a new discussion of the theory of permutations and of universal hashing. The bible of programming theory and practice is being updated for the first time in more than 20 years. The book is concerned with information structures--the representation of information within a computer, the structural interrelations between data elements and how to work with them efficiently, and applications to simulation, numerical methods and software design Donald Knuth is Professor Emeritus of the Art of Computer Programming at Stanford University, and is well-known worldwide as the creator of the Tex typesetting language. Here he presents the second volume of his guide to computer programming Donald Knuth is Professor Emeritus of the Art of Computer Programming at Stanford University, and is well-known worldwide as the creator of the Tex typesetting language. Here he presents the third volume of his guide to computer programming V. 1. Fundamental Algorithms -- V. 2. Seminumerical Algorithms -- V. 3. Sorting And Searching. Donald E. Knuth. Vol. 3 Published As 2nd Ed. Includes Indexes. v. 1. Fundamental algorithms v. 2. Seminumerical algorithms v. 3. Sorting and searching v. 4, fascicule 3. Generating all combinations and partitions.