Art of Computer Programming, Volume 4, Fascicle 4,The: Generating All Trees--History of Combinatorial Generation

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 4

This latest fascicle covers the generation of all trees, a basic topic that has surprisingly rich ties to the first three volumes of The Art of Computer Programming. In thoroughly discussing this well-known subject, while providing 124 new exercises, Knuth continues to build a firm foundation for programming. To that same end, this fascicle also covers the history of combinatorial generation. Spanning many centuries, across many parts of the world, Knuth tells a fascinating story of interest and relevance to every artful programmer, much of it never before told. The story even includes a touch of suspense: two problems that no one has yet been able to solve.

Table of Contents

Chapter 7 Combinatorial Searching 1

7.2. Generating All Possibilities 1

7.2.1. Generating Basic Combinatorial Patterns 1

7.2.1.1. Generating all n-tuples 1

7.2.1.2. Generating all permutations 1

7.2.1.3 Generating all combinations 1

7.2.1.4 Generating all partitions 1

7.2.1.5 Generating all set partitions 2

7.2.1.6 Generating all trees 2

7.2.1.7 History and further references 48

Answers to Exercises 76

Index and Glossary 112