The Art of Computer Programming, Volume 4, Fascicle 0 Introduction to Combinatorial Algorithms and Boolean Functions

by Knuth, Donald E.

• ISBN13: 9780321534965
• ISBN10: 0321534964
• Edition: 1st
• Format: Paperback
• Copyright: 2008-04-17
• Publisher: Addison-Wesley Professional
• More Book Details
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Summary

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 t regular intervals. Each fascicle will encompass a section or more of wholly new or evised 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. Volume 4, Fascicle 2This fascicle inaugurates the eagerly awaited publication of Knuth's The Art of Computer Programming, Volume 4: Combinatorial Algorithms. Part of what will be a long chapter on combinatorial searching, the fascicle begins his treatment of how to generate all possibilities. Specifically, it discusses the generation of all n-tuples, then extends those ideas to all permutations. Such algorithms provide a natural motivation by means of which many of the key ideas of combinatorial mathematics can be introduced and explored. In this and other fascicles of Volume 4, Knuth illuminates important theories by discussing related games and puzzles. Even serious programming can be fun.

Author Biography

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 his time to the completion of these fascicles and the seven volumes to which they belong.

Table of Contents

Combinatorial Searching	p. 1
Zeros and Ones	p. 47
Boolean Basics	p. 47
Boolean Evaluation	p. 96
Answers to Exercises	p. 134
Index and Glossary	p. 201
Table of Contents provided by Publisher. All Rights Reserved.

Excerpts

To put all the good stuff into one book is patently impossible, and attempting even to be reasonably comprehensive about certain aspects of the subject is likely to lead to runaway growth. GERALD B. FOLLAND "Editor's Corner" (2005) La derniere chose qu'on trouve en faisant un ouvrage est de savoir celle qu'il faut mettre la premiere. BLAISE PASCAL,Pensees740 (c. 1660) This booklet is Fascicle 0 ofThe Art of Computer Programming, Volume 4:Combinatorial Algorithms. As explained in the preface to Fascicle 1 of Volume 1, I'm circulating the material in this preliminary form because I know that the task of completing Volume 4 will take many years; I can't wait for people to begin reading what I've written so far and to provide valuable feedback. To put the material in context, this fascicle contains the opening sections intended to launch a long, long chapter on combinatorial algorithms. Chapter 7 is planned to be by far the longest single chapter ofThe Art of Computer Programming; it will eventually fill at least three volumes (namely Volumes 4A, 4B, and 4C), assuming that I'm able to remain healthy. Like the second-longest chapter (Chapter 5), it begins with pump-priming introductory material that comes before the main text, including dozens of exercises to get the ball rolling. A long voyage lies ahead, and some important provisions need to be brought on board before we embark. Furthermore I want to minimize the shock of transition between Chapter 6 and the new chapter, because Chapter 6 was originally written and published more than thirty years ago. Chapter 7 proper begins with Section 7.1: Zeros and Ones, which is another sort of introduction, at a different level. It dives into the all-important topics that surround the study of Boolean functions, which essentially underly everything that computers do. Subsection 7.1.1, "Boolean basics," attempts to erect a solid foundation of theoretical and practical ideas on which we shall build significant superstructures later; subsection 7.1.2, "Boolean evaluation," considers how to compute Boolean functions with maximum efficiency. The remaining parts of Section 7.1--namely 7.1.3, "Bitwise tricks and techniques," and 7.1.4, "Binary decision diagrams"--will be published soon as Volume 4, Fascicle 1. Then comes Section 7.2, Generating All Possibilities; the fascicles for Section 7.2.1, "Generating basic combinatorial patterns," have already appeared in print. Section 7.2.2 will deal with backtracking in general. And so it will go on, if all goes well; an outline of the entire Chapter 7 as currently envisaged appears on the taocp webpage that is cited on page ii. These introductory sections have turned out to have more than twice as many exercises as I had originally planned. In fact, the total number of exercises in this fascicle (366) is almost unbelievable. But many of them are quite simple, intended to reinforce the reader's understanding of basic definitions, or to acquaint readers with the joys ofThe Stanford GraphBase. Other exercises were simply irresistible, as they cried out to be included here--although, believe it or not, I did reject more potential leads than I actually followed up. I would like to express my indebtedness to the late Robert W Floyd, who made dozens of valuable suggestions when I asked him to look over the first draft of this material in 1977. Thanks also to Robin Wilson of the Open University for his careful reading and many detailed suggestions; and to hundreds of readers who provided fantastic feedback on early drafts that circulated on the Internet. I shall happily pay a finder's fee of $2.56 for each error in this fascicle when it is first reported to me, whether that error be typographical, technical, or historical. The same reward holds for items that I forgot to put in the index. And valuable suggestions for i