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The Art of Computer Programming, Volume 4, Fascicle 2 - Generating All Tuples and Permutations
 
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The Art of Computer Programming, Volume 4, Fascicle 2 - Generating All Tuples and Permutations [Paperback]

Donald E. Knuth

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The Art of Computer Programming, Volume 4, Fascicle 2 - Generating All Tuples and Permutations + The Art of Computer Programming, Volume 4, Fascicle 3 - Generating All Combinations and Partitions + The Art of Computer Programming: Bitwise Tricks and Techniques; Binary Decision Diagrams v. 4, Fascicle 1
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Donald E. Knuth
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Product Description

Product Description

Finally, after a wait of more than thirty-five years, the first part of Volume 4 is at last ready for publication. Check out the boxed set that brings together Volumes 1 - 4A in one elegant case, and offers the purchaser a $50 discount off the price of buying the four volumes individually.

 

The Art of Computer Programming, Volumes 1-4A Boxed Set, 3/e

ISBN: 0321751043 

 

 

 

Art of Computer Programming, Volume 4, Fascicle 2, The: Generating All Tuples and Permutations: Generating All Tuples and Permutations

 

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 t regular intervals. Each fascicle will encompass a section or more of wholly new or evised 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 2

This fascicle inaugurates the eagerly awaited publication of Knuth's The Art of Computer Programming, Volume 4: Combinatorial Algorithms. Part of what will be a long chapter on combinatorial searching, the fascicle begins his treatment of how to generate all possibilities. Specifically, it discusses the generation of all n-tuples, then extends those ideas to all permutations. Such algorithms provide a natural motivation by means of which many of the key ideas of combinatorial mathematics can be introduced and explored. In this and other fascicles of Volume 4, Knuth illuminates important theories by discussing related games and puzzles. Even serious programming can be fun.



 

 

From the Back Cover

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 t regular intervals. Each fascicle will encompass a section or more of wholly new or evised 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 2

This fascicle inaugurates the eagerly awaited publication of Knuth's The Art of Computer Programming, Volume 4: Combinatorial Algorithms. Part of what will be a long chapter on combinatorial searching, the fascicle begins his treatment of how to generate all possibilities. Specifically, it discusses the generation of all n-tuples, then extends those ideas to all permutations. Such algorithms provide a natural motivation by means of which many of the key ideas of combinatorial mathematics can be introduced and explored. In this and other fascicles of Volume 4, Knuth illuminates important theories by discussing related games and puzzles. Even serious programming can be fun.




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Amazon.com:  6 reviews
10 of 10 people found the following review helpful
Combinatorial Programming Simplified! 11 Oct 2006
By John G. Gephart - Published on Amazon.com
Format:Paperback
First, I would like to say this is the first Donald Knuth book I have read, only because every programmer respects TAOCP so much that they say it is too hard for the hobby programmer. I have a small background in Computer Science, and some mid-level Math; yet Knuth walks you through some of the most exciting Computer Science problems you could ever dream of with ease! I came to find this book perfect, mostly because my favorite Programming problem is the Traveling Salesman, this book as well as fasicles 3 and 4, are the perfect reference to find great ways to venture into the unsolved TSP Algorithm, and the feared Hamilitonian Cycle.

Reading about gray generation I immediatly found so much more value to this book than I ever expected. As well, the book then jumps into ways to use loopless generation( which blew my mind! ). Then the best part comes in the second half of the book, "Generating All Permutations" First it starts with a brute force method for achieving all permutations, then Algorithm L to G(my favorite algorithm in the book...) is the largest hurtle in the book; I actually bought the whole TAoCP volumes so I could get through this part because it goes over permutation pre-multiplication ( Knuth has a better way of defining this ), although the idea is simple, an effective way to implement and explore pre-multiplication I found to be extremely important and should not be over looked. Then after that the diffictulty goes to equal as the first half.

In summary this book is deffinitly worth the wait, and it helps a person, no matter how experienced, to explore new ways to venture out of the straight and narrow, and into an arena of problems that few dare to venture.
25 of 32 people found the following review helpful
a solid compendium of challenging problems 25 April 2005
By W Boudville - Published on Amazon.com
Format:Paperback
This preliminary excerpt from Knuth's Volume 4 will please all the fans of his seminal first three volumes. The didactic style is the same. So too is the very distinctive Tex typeface. (You know that he invented Tex, don't you?)

Of course, there are the problem sets. This little book has two sections. In each are 112 problems. Strewth! Knuth thoughtfully gives an estimate next to each of how long it will take you to solve it. Those estimates probably refer to someone of his calibre. I've attempted most of the problems in his earlier volumes and could typically only get within a factor of two of the time estimate. And this was only when I could actually solve a problem.

The book addresses a gap in the literature of computer science. Research papers in journals or books of conference proceedings do not usually present you with problems. While introductory texts do, but those are simple. Very difficult to find a solid compendium of challenging problems.

Such is the attraction of this book to me and perhaps to you. The potential readership is exclusive and self selecting. The only drawback is the wait for the rest of Volume 4.
3 of 4 people found the following review helpful
Brief but worthwhile 12 Aug 2007
By wiredweird - Published on Amazon.com
Format:Paperback
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

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