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The Art of Computer Programming, Vol. 1: Fundamental Algorithms, 3rd Edition 3rd Edition
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This magnificent tour de force presents a comprehensive overview of a wide variety of algorithms and the analysis of them. Now in its third edition, The Art of Computer Programming, Volume I: Fundamental Algorithms contains substantial revisions by the author and includes numerous new exercises.
Although this book was conceived several decades ago, it is still a timeless classic. One of the book's greatest strengths is the wonderful collection of problems that accompany each chapter. The author has chosen problems carefully and indexed them according to difficulty. Solving a substantial number of these problems will help you gain a solid understanding of the issues surrounding the given topic. Furthermore, the exercises feature a variety of classic problems.
Fundamental Algorithms begins with mathematical preliminaries. The first section offers a good grounding in a variety of useful mathematical tools: proof techniques, combinatorics, and elementary number theory. Knuth then details the MIX processor, a virtual machine architecture that serves as the programming target for subsequent discussions. This wonderful section comprehensively covers the principles of simple machine architecture, beginning with a register-level discussion of the instruction set. A later discussion of a simulator for this machine includes an excellent description of the principles underlying the implementation of subroutines and co-routines. Implementing such a simulator is an excellent introduction to computer design.
In the second section, Knuth covers data structures--stacks, queues, lists, arrays, and trees--and presents implementations (in MIX assembly) along with techniques for manipulating these structures. Knuth follows many of the algorithms with careful time and space analysis. In the section on tree structures, the discussion includes a series of interesting problems concerning the combinatorics of trees (counting distinct trees of a particular form, for example) and some particularly interesting applications. Also featured is a discussion of Huffmann encoding and, in the section on lists, an excellent introduction to garbage collection algorithms and the difficult challenges associated with such a task. The book closes with a discussion of dynamic allocation algorithms.
The clear writing in Fundamental Algorithms is enhanced by Knuth's dry humor and the historical discussions that accompany the technical matter. Overall, this text is one of the great classics of computer programming literature--it's not an easy book to grasp, but one that any true programmer will study with pleasure.
From the Back Cover
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.
—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.
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.
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.
This first volume in the series begins with basic programming concepts and techniques, then focuses more particularly on information structures—the representation of information inside a computer, the structural relationships between data elements and how to deal with them efficiently. Elementary applications are given to simulation, numerical methods, symbolic computing, software and system design. Dozens of simple and important algorithms and techniques have been added to those of the previous edition. The section on mathematical preliminaries has been extensively revised to match present trends in research.
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I think the most important is to study the Vol 1. It gives enough exposition to the Donald Knuth style and brilliant thinking. While the content is definitely important it is the level of thinking of the author that represents the main value of the book: you instantly understand the book was written by a great scientist and it does not matter much that now the contents of most chapters can be significantly improved using more modern sources. After all Vol 1 is more then a 30 years old book (it is older then Unix) and as such it should be outdated (we all believe in progress, don't we)... And it is not surprising that parts of Vol 1 on of TAOCP today look completely out of touch with reality especially MIX, the CPU instruction set that is used in all volumes.
Actually MIX instruction set (and thus assembler) was outdated even when the book was first published and more reflects unique Knuth's background with IBM 650. It was far from the state of hardware development even in late 60th when the first volume was published, the period when IBM/360 was the king of the hill.
Now IBM 650, a 1,966 lb machine that consumed almost 30 Kw of electricity looks more like a primitive calculator than a real computer: typical installation has the memory of just 10,000 decimal digits ( 1,000 words; 10 digit per word).
It's really sad that Knuth did not adopt System 360 architecture and PL/360 assembler (Wirth's structured assembler for S/360) for his books but we can do nothing about it. Still this is a book about timeless truths, not the book about the resent CS fashion like Java or you name it :-). It actually can serve as a perfect antidote against any current CS fashion.
And Knuth does provide pseudocode with his natural language algorithm description. And natural language pseudocode has an important advantage over 'structured pseudocode. The problem with a "structured pseudocode" is that the set of control structures is fixed and may not reflect the needs of a particular algorithms (branching out of loop is a common problem that is not addressed by structured programming well). Moreover it can cripple the algorithm by enforcing unnatural control structures, the structures that are absent in it but might be present in more modern languages. For example Perl has an interesting set of control structures that is superior to C. But even "Perl control structures set" can be improved further.
That's why assembler language is preferable: it never obscures "natural" control structures for each algorithms, structures that one day can be mapped into some new elegant language construct. Also as one review noted "sometimes high level languages with all their abstractions make things look more complex than they need be."
I would like to stress it again that each volume is very difficult to read; you really need to work on each chapter by reimplementing the examples that Knuth gives in your favorite language (assembler might help but is not essential).
Mathematical considerations as for average and worst running time of a particular algorithm can be largely ignored during the first couple of years of study of this book. Actually most mathematics in Vol. 1 can (and probably should) be initially completely ignored. See Softpanorama Classic Computer Books for more information.
On the negative side this is an overpriced book, if we are talking about students budget. To save money you can buy one of the first editions: there is not that much difference in content to justify the differences in price. The differences do not interfere with the study of the book. Knuth did an excellent work the first time he published each volume and for a significant improvement we probably need another century and another person.
My chief complaint of all of Knuth's "Art of" series is his incessant use of "MIX". MIX is Knuth's homebrew assembly language he uses to analyse the computer algorithms he describes. When Knuth first wrote the "Art of" series, assembly language was thankfully dying. 20 years later, no one but Knuth would even consider writing a book filled with such gibberish. There is no possible way at the end of the 1990s that this nonsense can be justified. Knuth has really missed the mark by insisting on having MIX in his books. What about C or C++, Pascal, BASIC, or even his own high-level psuedo-language? Here's the "God" of computer programming pushing this wretched gobbledygook on us. I can only attribute his horrid fascination with MIX to one of three things: Laziness (he doesn't want to rewrite his analysis - if this is true, then the new additions might need to be re-titled "The Art of Milking a Good Thing"), pride (he just can't give up his assembly language bastard-child he created), or ignorance. Either way, none of these are good justifications for why us plain mortals have to wade through this mine field of MIXed manure.
Get with it Don! Come down to our level, be a little bit humble and give us a decent high-level language analysis of your favorite algorithms.
MIX - R.I.P.