The Art of Computer Programming, Volume 4, Fascicle 1: Bitwise Tricks and Techniques

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 fascicle 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.

Volume 4, Fascicle 1

This fascicle, enlivened by a wealth of Knuth’s typically enjoyable examples, describes basic “broadword” operations and an important class of data structures that can make computer programs run dozens–even thousands–of times faster. The author brings together and explains a substantial amount of previously scattered but eminently practical information known only to a few specialists. The book also includes nearly five-hundred exercises for self-study, with detailed answers given in nearly every case; dozens of these exercises present original material that has never before been published. Simply put, this fascicle is a must-have for anybody who is faced with tough problems of a combinatorial flavor. It demonstrates how ordinary programmers can make use of powerful techniques that heretofore seemed to be available only to people who used specialized languages and software. It shows how ideas once thought to be “far out” are now ready to become a part of the programming mainstream.

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.

The Art of Computer Programming, Volumes 1-4A Boxed Set, 3/e

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.

Chapter 7: Combinatorial Searching    1

7.1 Zeroes and Ones    1

    7.1.1 Boolean Basics    1

    7.1.2 Boolean Evaluation    1

    7.1.3 Bitwise Tricks and Techniques    1

    7.1.4 Binary Decision Diagrams    70

Answers to Exercises    149

Index and Glossary    244