The Art of Computer Programming, Volume 4, Fascicle 5: Mathematical Preliminaries Redux; Introduction to Backtracking; Dancing Links

About

Features

• The Art of Computer Programming is the most influential work ever written on the subject
• Knuth is the foremost authority in the world on computer algorithms and programming

Description

This multivolume work on the analysis of algorithms has long been recognized as the definitive description of classical computer science. The four 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 continue the fourth and later volumes of the set, and to update parts of the existing volumes, Knuth has created a series of small books called fascicles, which are published at regular intervals. Each fascicle encompasses 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.

This fascicle covers three separate topics:

1. Mathematical Preliminaries.  Knuth writes that this portion of fascicle 5 "extends the ‘Mathematical Preliminaries’ of Section 1.2 in Volume 1 to things that I didn't know about in the 1960s. Most of this new material deals with probabilities and expectations of random events; there's also an introduction to the theory of martingales."
2. Backtracking: this section is the counterpart to section 7.2.1 which covered the generation of basic combinatorial patterns.  This section covers non-basic patterns, ones where the developer needs to make tentative choices and then may need to backtrack when those choices need revision.
3. Dancing Links: this section is related to 2 above.  It develops an important data structure technique that is suitable for backtrack programming described above.

Sample Content

Table of Contents

Preface iii

Mathematical Preliminaries Redux 1

Chapter 7: Combinatorial Searching7.2.2 Backtrack Programming 28
7.2.2.1 Dancing Links 63
Answers to Exercises 182Appendix C: index to Algorithms and Theorems 357Appendix E: Answers to Puzzles in the Answers 358

Index and Glossary 361

Updates

Updates & Corrections

A note on the PDF edition of Volume 4, Fascicle 5
The authorized PDF version of Volume 4, Fascicle 5 was not created by Mathematical Sciences Publishers (MSP). The typeface of this PDF is lighter than those produced by MSP, and it includes all the correct links, renders code correctly, and has been approved by Donald Knuth.

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