Art of Computer Programming, The Combinatorial Algorithms, Volume 4A, Part 1

by Knuth, Donald E.

• ISBN13: 9780201038040
• ISBN10: 0201038048
• Edition: 1st
• Format: Hardcover
• Copyright: 2011-01-12
• Publisher: Addison-Wesley Professional

Summary

Knuthrs"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 Knuthrs"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 programmerrs"s library.

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 (26 books, 161 papers). Professor Emeritus of The Art of Computer Programming at Stanford University, he currently devotes full time to the completion of his seminal multivolume series on classical computer science, begun in 1962 when he was a graduate student at California Institute of Technology. Professor Knuth is the recipient of numerous awards and honors, including the ACM Turing Award, the Medal of Science presented by President Carter, the AMS Steele Prize for expository writing, and, in November, 1996, the prestigious Kyoto Prize for advanced technology. He lives on the Stanford campus with his wife, Jill.

Table of Contents

Preface

Notes on the Exercises

 

Chapter 7: Combinatorial Searching 1

7.1: Zeros and Ones 47

7.2: Generating All Possibilities 281

 

Answers to Exercises 514

 

Appendix A: Tables of Numerical Quantities 818

Appendix B: Index to Notations 822

Appendix C: Index to Algorithms and Theorems 828

Appendix D: Index to Combinatorial Problems 830

 

Index and Glossary 834