The Art of Computer Programming Volume 3: Sorting and Searching

The bible of all fundamental algorithms and the work that taught many of today's software developers most of what they know about computer programming. #x2014;Byte, September 1995 I can't begin to tell you how many pleasurable hours of study and recreation they have afforded me! I have pored over them in cars, restaurants, at work, at home... and even at a Little League game when my son wasn't in the line-up. #x2014;Charles Long If you think you're a really good programmer... read [Knuth's] Art of Computer Programming... You should definitely send me a resume if you can read the whole thing. #x2014;Bill Gates It's always a pleasure when a problem is hard enough that you have to get the Knuths off the shelf. I find that merely opening one has a very useful terrorizing effect on computers. #x2014;Jonathan Laventhol The first revision of this third volume is the most comprehensive survey of classical computer techniques for sorting and searching. It extends the treatment of data structures in Volume 1 to consider both large and small databases and internal and external memories. The book contains a selection of carefully checked computer methods, with a quantitative analysis of their efficiency. Outstanding features of the second edition include a revised section on optimum sorting and new discussions of the theory of permutations and of universal hashing.

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.

Cookery is become an art, a noble science; cooks are gentlemen. TITUS LIVIUS,Ab Urbe ConditaXXXIX.vi (Robert Burton,Anatomy of Melancholy1.2.2.2) This book forms a natural sequel to the material on information structures in Chapter 2 of Volume 1, because it adds the concept of linearly ordered data to the other basic structural ideas. The title "Sorting and Searching" may sound as if this book is only for those systems programmers who are concerned with the preparation of general-purpose sorting routines or applications to information retrieval. But in fact the area of sorting and searching provides an ideal framework for discussing a wide variety of important general issues: How are good algorithms discovered? How can given algorithms and programs be improved? How can the efficiency of algorithms be analyzed mathematically? How can a person choose rationally between different algorithms for the same task? In what senses can algorithms be proved ''best possible''? How does the theory of computing interact with practical considerations? How can external memories like tapes, drums, or disks be used efficiently with large databases? Indeed, I believe that virtually every important aspect of programming arises somewhere in the context of sorting or searching! This volume comprises Chapters 5 and 6 of the complete series. Chapter 5 is concerned with sorting into order; this is a large subject that has been divided chiefly into two parts, internal sorting and external sorting. There also are supplementary sections, which develop auxiliary theories about permutations (Section 5.1) and about optimum techniques for sorting (Section 5.3). Chapter 6 deals with the problem of searching for specified items in tables or files; this is subdivided into methods that search sequentially, or by comparison of keys, or by digital properties, or by hashing, and then the more difficult problem of secondary key retrieval is considered. There searching related to sorting is a surprising amount of interplay between both chapters, with strong analogies tying the topics together. Two important varieties of information structures are also discussed, in addition to those considered in Chapter 2, namely priority queues (Section 5.2.3) and linear lists represented as balanced trees (Section 6.2.3). Like Volumes 1 and 2, this book includes a lot of material that does not appear in other publications. Many people have kindly written to me about their ideas, or spoken to me about them, and I hope that I have not distorted the material too badly when I have presented it in my own words. I have not had time to search the patent literature systematically; indeed, I decry the current tendency to seek patents on algorithms (see Section 5.4.5). If somebody sends me a copy of a relevant patent not presently cited in this book, I will dutifully refer to it in future editions. However, I want to encourage people to continue the centuries-old mathematical tradition of putting newly discovered algorithms into the public domain. There are better ways to earn a living than to prevent other people from making use of one's contributions to computer science. Before I retired from teaching, I used this book as a text for a student's second course in data structures, at the junior-to-graduate level, omitting most of the mathematical material. I also used the mathematical portions of this book as the basis for graduate-level courses in the analysis of algorithms, emphasizing especially Sections 5.1, 5.2.2, 6.3, and 6.4. A graduate-level course on concrete computational complexity could also be based on Sections 5.3, and 5.4.4, together with Sections 4.3.3, 4.6.3, and 4.6.4 of Volume 2. For the most part this book is self-contained, except for occasional discussions relating to the MIX computer explained in Volume 1. Appendix B MIX computer contains a summary