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.
The Art of Computer Programming, Volumes 1-4A Boxed Set, 3/e
Please visit the companion site at http://www-cs-faculty.stanford.edu/~knuth/.
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
Download the Preface for this book.
Please also visit the companion site at for additional updates http://www-cs-faculty.stanford.edu/~knuth/.
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