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

Donald Knuth



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Addison Wesley
22 November 2019
Algorithms & data structures; Client-Server networking
This multivolume work on the analysis of algorithms has long been recognised 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 marvelled 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 humour 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:

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.

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. Dancing Links: this section is related to 2 above. It develops an important data structure technique that is suitable for backtrack programming described above.
By:   Donald Knuth
Imprint:   Addison Wesley
Country of Publication:   United States
Dimensions:   Height: 230mm,  Width: 180mm,  Spine: 20mm
Weight:   739g
ISBN:   9780134671796
ISBN 10:   0134671791
Pages:   400
Publication Date:   22 November 2019
Audience:   Professional and scholarly ,  Undergraduate
Format:   Paperback
Publisher's Status:   Active
Preface iii Mathematical Preliminaries Redux 1 Chapter 7: Combinatorial Searching 7.2.2 Backtrack Programming 28 Dancing Links 63 Answers to Exercises 182 Appendix C: index to Algorithms and Theorems 357 Appendix E: Answers to Puzzles in the Answers 358 Index and Glossary 361

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.

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