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

Art of Computer Programming, Volume 4, Fascicle 4,The: Generating All Trees--History of Combinatorial Generation
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Author(s): Donald E. Knuth
Publisher: Addison-Wesley Professional
Paperback: 128 pages
Language(s): English
ISBN: 0321335708
Published On: 2006-02-16
Studio: Addison-Wesley Professional
Product Description
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.
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Customer Reviews
"Computer Science Classic"
Written By: J. E. Sherman
Three classic volumes from Donald Knuth. I have the 3rd edition. Once your get pass understanding MIX ( MMIX, 4th edition), it is a great technical read. Bring so much to Computer Science. I used them in school. I use them today.
"Don't Program Without it!"
Written By: J. E. Sherman
Three classic volumes from Donald Knuth. I have the 3rd edition. Once your get pass understanding MIX ( MMIX, 4th edition), it is a great technical read. Bring so much to Computer Science. I used them in school. I use them today.
"Useful, but very brief"
Written By: wiredweird
First, the brevity. This book nominally contains 160 pages - take off a few for indicia and intro, and it's down to 150. Of those, page 87 and up are all "answers to exercises" - not really part of the exposition. Then, within those 86 pages, about 30 are exercises. Although helpful to the involved reader, they aren't direct exposition either.

The 50 or 60 pages left are good, though. They present the combinatorial content in deep detail, even if breadth sometimes seems to suffer. Proofs and analyses are thorough, but become lengthy and require fair bits of calculus. These discussions range across the width of contemporary math and the length of its last few generations of history.

That leaves the algorithms - a few good ones, but only a few. If you came to this as a cut-and-paster, you won't find much to take home. On the whole, it's a worthy addition to "The Art" and to the collection that makes up Volume 4. For many, however, it won't be the hardest-working reference on the shelf.

-- wiredweird
"Brief but worthwhile"
Written By: wiredweird
Combinatorial problems arise in a wide range of contexts. Among combinatorial problems, generation of all distinct sets of some size (tuples) or all rearrangements of the objects (permutations) occur commonly, often as the first step in a larger calculation. Knuth addresses some important classes of such problems in this book.

Even "all possible permutations" leaves a wide range of choices open. For example, should the list be in alphabetical order? Should it minimize the number of differences between consecutive elements? Many other constraints can be imposed as well, even esthetic ones! "Ringing the changes" on a carillon is one such combinatorial problem, with a long history and criteria for beauty all its own. However choices are made, the next step is to specify a way of creating the list. This can have constraints of its own. For example, it may be neccesary to create the next arrangement in the sequence knowing only the current element of the sequence. Knuth offers different algorithms for meeting different sets of constraints. If none of them match your needs, then the references will help you find something that does, or the discussion and exercises will help you develop one of your own.

Although useful, this book is very brief. 144 pages isn't a lot. Take away 45 pages just for solutions to exercises, then more for index and exercises, and the text is surprisingly brief. What's left carries its weight, though. It's a valuable addition to almost programmer's library.

-- wiredweird
" The Art of Computer Programming, Volume 4, Fascicle 4: Generating All Trees--History of Combinatorial Generation (Art of Compu"
Written By: P. Plunkett
The books are very detailed and take a lot of analysis... they are not written in a current Object Oriented Language... that was a disappointment but otherwise it is very good... just uses old "spaghetti code"
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