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.