Art of Computer Programming, Volume 4, Fascicle 3, The: Generating All Combinations and Partitions, 1st edition

  • Donald E. Knuth

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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

ISBN: 0321751043 



Art of Computer Programming, Volume 4, Fascicle 3, The: Generating All Combinations and Partitions: Generating All Combinations and Partitions


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 3

This fascicle continues Knuth's authoritative chapter on combinatorial algorithms, ultimately to be included in Volume 4 of The Art of Computer Programming. The previous fascicle from Volume 4, which covered the generation of all tuples and permutations, is now complemented by techniques for generating all combinations and partitions. In Knuth's thorough discussion of these two topics, readers will find much that is new, as well as surprisingly rich ties to material in Volumes 1 through 3 and to other aspects of computer science and mathematics. As usual, this fascicle includes a bounty of creative exercises, as well as intriguing challenges posed by yet-unsolved questions.



Table of contents

Chapter 7 Combinatorial Searching

7.2. Generating All Possibilities 0

7.2.1. Generating Basic Combinatorial Patterns 0 Generating all n-tuples 0 Generating all permutations 0 Generating all combinations 1 Generating all partitions 36 Generating all set partitions 61

Answers to Exercises 87

Index and Glossary 144

Published by Addison-Wesley Professional (July 26th 2005) - Copyright © 2006