Introduction to Algorithms, Second Edition [Hardcover]

Thomas H. Cormen (Author), Charles E. Leiserson (Author), Ronald L. Rivest (Author), Clifford Stein (Author)

Book Description

Publication Date: September 1, 2001 | ISBN-10: 0262032937 | ISBN-13: 978-0262032933 | Edition: 2nd

The first edition won the award for Best 1990 Professional and Scholarly Book in Computer Science and Data Processing by the Association of American Publishers.

There are books on algorithms that are rigorous but incomplete and others that cover masses of material but lack rigor. Introduction to Algorithms combines rigor and comprehensiveness.

The book covers a broad range of algorithms in depth, yet makes their design and analysis accessible to all levels of readers. Each chapter is relatively self-contained and can be used as a unit of study. The algorithms are described in English and in a pseudocode designed to be readable by anyone who has done a little programming. The explanations have been kept elementary without sacrificing depth of coverage or mathematical rigor.

The first edition became the standard reference for professionals and a widely used text in universities worldwide. The second edition features new chapters on the role of algorithms, probabilistic analysis and randomized algorithms, and linear programming, as well as extensive revisions to virtually every section of the book. In a subtle but important change, loop invariants are introduced early and used throughout the text to prove algorithm correctness. Without changing the mathematical and analytic focus, the authors have moved much of the mathematical foundations material from Part I to an appendix and have included additional motivational material at the beginning.

Editorial Reviews

Amazon.com Review

Aimed at any serious programmer or computer science student, the new second edition of Introduction to Algorithms builds on the tradition of the original with a truly magisterial guide to the world of algorithms. Clearly presented, mathematically rigorous, and yet approachable even for the math-averse, this title sets a high standard for a textbook and reference to the best algorithms for solving a wide range of computing problems.

With sample problems and mathematical proofs demonstrating the correctness of each algorithm, this book is ideal as a textbook for classroom study, but its reach doesn't end there. The authors do a fine job of explaining each algorithm. (Reference sections on basic mathematical notation will help readers bridge the gap, but it will help to have some math background to appreciate the full achievement of this handsome hardcover volume.) Every algorithm is presented in pseudo-code, which can be implemented in any computer language, including C/C++ and Java. This ecumenical approach is one of the book's strengths. When it comes to sorting and common data structures, from basic linked lists to trees (including binary trees, red-black, and B-trees), this title really shines, with clear diagrams that show algorithms in operation. Even if you just glance over the mathematical notation here, you can definitely benefit from this text in other ways.

The book moves forward with more advanced algorithms that implement strategies for solving more complicated problems (including dynamic programming techniques, greedy algorithms, and amortized analysis). Algorithms for graphing problems (used in such real-world business problems as optimizing flight schedules or flow through pipelines) come next. In each case, the authors provide the best from current research in each topic, along with sample solutions.

This text closes with a grab bag of useful algorithms including matrix operations and linear programming, evaluating polynomials, and the well-known Fast Fourier Transformation (FFT) (useful in signal processing and engineering). Final sections on "NP-complete" problems, like the well-known traveling salesman problem, show off that while not all problems have a demonstrably final and best answer, algorithms that generate acceptable approximate solutions can still be used to generate useful, real-world answers.

Throughout this text, the authors anchor their discussion of algorithms with current examples drawn from molecular biology (like the Human Genome Project), business, and engineering. Each section ends with short discussions of related historical material, often discussing original research in each area of algorithms. On the whole, they argue successfully that algorithms are a "technology" just like hardware and software that can be used to write better software that does more, with better performance. Along with classic books on algorithms (like Donald Knuth's three-volume set, The Art of Computer Programming), this title sets a new standard for compiling the best research in algorithms. For any experienced developer, regardless of their chosen language, this text deserves a close look for extending the range and performance of real-world software. --Richard Dragan

Topics covered: Overview of algorithms (including algorithms as a technology); designing and analyzing algorithms; asymptotic notation; recurrences and recursion; probabilistic analysis and randomized algorithms; heapsort algorithms; priority queues; quicksort algorithms; linear time sorting (including radix and bucket sort); medians and order statistics (including minimum and maximum); introduction to data structures (stacks, queues, linked lists, and rooted trees); hash tables (including hash functions); binary search trees; red-black trees; augmenting data structures for custom applications; dynamic programming explained (including assembly-line scheduling, matrix-chain multiplication, and optimal binary search trees); greedy algorithms (including Huffman codes and task-scheduling problems); amortized analysis (the accounting and potential methods); advanced data structures (including B-trees, binomial and Fibonacci heaps, representing disjoint sets in data structures); graph algorithms (representing graphs, minimum spanning trees, single-source shortest paths, all-pairs shortest paths, and maximum flow algorithms); sorting networks; matrix operations; linear programming (standard and slack forms); polynomials and the Fast Fourier Transformation (FFT); number theoretic algorithms (including greatest common divisor, modular arithmetic, the Chinese remainder theorem, RSA public-key encryption, primality testing, integer factorization); string matching; computational geometry (including finding the convex hull); NP-completeness (including sample real-world NP-complete problems and their insolvability); approximation algorithms for NP-complete problems (including the traveling salesman problem); reference sections for summations and other mathematical notation, sets, relations, functions, graphs and trees, as well as counting and probability backgrounder (plus geometric and binomial distributions).

From the Publisher

There are books on algorithms that are rigorous but incomplete and others that cover masses of material but lack rigor. Introduction to Algorithms combines rigor and comprehensiveness. The book covers a broad range of algorithms in depth, yet makes their design and analysis accessible to all levels of readers. Each chapter is relatively self-contained and can be used as a unit of study. The algorithms are described in English and in a pseudocode designed to be readable by anyone who has done a little programming. The explanations have been kept elementary without sacrificing depth of coverage or mathematical rigor.

The first edition became the standard reference for professionals and a widely used text in universities worldwide. The second edition features new chapters on the role of algorithms, probabilistic analysis and randomized algorithms, and linear programming, as well as extensive revisions to virtually every section of the book. In a subtle but important change, loop invariants are introduced early and used throughout the text to prove algorithm correctness. Without changing the mathematical and analytic focus, the authors have moved much of the mathematical foundations material from Part I to an appendix and have included additional motivational material at the beginning.

See all Editorial Reviews

Product Details

• Hardcover: 1184 pages
• Publisher: The MIT Press; 2nd edition (September 1, 2001)
• Language: English
• ISBN-10: 0262032937
• ISBN-13: 978-0262032933
• Product Dimensions: 9.1 x 8.1 x 2 inches
• Shipping Weight: 4.6 pounds
• Average Customer Review: 3.9 out of 5 stars  See all reviews (118 customer reviews)
• Amazon Best Sellers Rank: #350,655 in Books (See Top 100 in Books)

Most Helpful Customer Reviews

112 of 115 people found the following review helpful

4.0 out of 5 stars Great book with one major shortcoming February 11, 2007

By Ellis Whitehead

Format:Hardcover

What it is:
A very thick text book about a) the mathematics behind algorithms, and b) a treasure chest of random performance tips.

Who it's for:
This book is for those who want or need to gain a decent grasp of the math for analyzing algorithms, and already have a decent understanding of discrete mathematics and probability.

What's good about it:
I really like this book. It's very high quality, well written, concise, and clear, and it's sprinkled with clever little tips to improve the efficiency of common routines.

Tips:
You can watch video recordings of the MIT lectures based on the book. Check out "6.046J Introduction to Algorithms" by searching for "ocw 6.046J" in your favorite search engine. The mathematical prerequisite course is also available in text form on MIT's OpenCourseWare; it can be found by searching for "ocw 6.042J spring 2005".

Warnings:
* Don't bother with this book unless you have a high aptitude for math
* Don't bother with this book unless you're prepared to work at it
* It's not designed as a reference book; instead it's a study book.

Many reviewers have called this book a "reference", but I have to disagree. A good reference book makes information quickly accessible, but this book would require you to read way too much to be called a reference. A practical reference book for algorithms is "The Algorithm Design Manual" by Steven S. Skiena, assuming you don't require proofs.

The Major Shortcoming!
Given that the book's design is most appropriate for learning things you don't already know, it has one major shortcoming: there are no answers to any of the exercises or problems. That makes the book semi-useless for self-study as well as for instructors who believe in the pedagogic value of students being able to check their answers. The instructor's manual is only available to instructors on the condition that they don't make the answers available.

193 of 213 people found the following review helpful

3.0 out of 5 stars A definitive guide, but not perfect May 28, 2002

By Andrew McCaffrey VINE™ VOICE

Format:Hardcover

INTRODUCTION TO ALGORITHMS is pretty much the standard textbook in the field of algorithms. In its favor is the fact that it is quite comprehensive, covering a wide range of topics that the beginning student will need to know. On the other hand, it has a tendency towards the confusing and the obscure, with many of the example problems not making a lot of sense. If one decides to purchase this book (and the students will have no choice in this matter, being subject as they are to the whims of their professors), then I recommend that one immediately prints out the "bug correction" page available on the web, as there are several major howlers present in the book, and if one isn't careful then many hours will be lost while one checks and rechecks faulty pseudo-code. In one particularly confused portion of the book, the correction sheet completely replaces three entire pages of the text.

This book covers a huge amount of material, and many of the topics are described quite adequately. Although readers may already be familiar with the numerous data structures that are discussed, the book doesn't assume prior knowledge and goes into quite a lot of detail concerning them. These sections, in particular, are illustrated clearly and offer great reference material that every programmer should have access to. This portion on data structures is one area where the book's conciseness is an advantage. It's simple enough for the beginner to learn from, but it contains more than enough information for the advanced user in need of mental refreshing.

The opening sections that discuss the rudiments of algorithm analysis are also covered competently. The easier subjects don't suffer from the book's shortcomings, as these ideas aren't quite as difficult to understand. For a simple introduction to the easier-to-grasp concepts in Algorithms, these sections simply can't be bettered. It's not until later chapters that some of the material appears incomprehensible.

Other parts of the book are very confusing to the beginning students who, presumably, make up the bulk of the target audience. If this text is used as an accompaniment to a class (as it usually is), then you'll probably do all right. One really needs to have some other source of information, because this book tends to get quite confusing. The problem sets included are frequently obscure, and don't always relate to the material in that chapter. The fact that many of the problems have no given solution (even if one attempts to contact the authors!) is quite telling. The style of the book is extremely dry and occasionally impenetrable, even when compared to other computer science textbooks.

If you're looking at this page, then no doubt you're looking mainly for pricing information, since this book is the definitive standard on the subject. Keep in mind that "definitive" doesn't necessarily mean perfect, and, alas, this book is far from perfection. But if you have an alternative method of learning the material, then this is an excellent book to have as accompaniment. And once you've learned the material, you'll find this to be a great resource.

142 of 160 people found the following review helpful

3.0 out of 5 stars Academic Masterpiece, Practical White Elephant September 5, 2005

By David A. Lessnau

Format:Hardcover|Amazon Verified Purchase

First, the good part: this book is an intellectual and academic masterpiece. It would be great for people doing algorithm or other Computer Science research. It's an amazing synthesis of much of the core of a Computer Science degree with Discrete Math and Probability. Oddly, it's more like a math book than a CS book.

Now, the not so good part: for implementers (i.e., programmers), this book is not all that useful. The biggest technical negative is that, for the most part, the authors ignore memory hierarchies and treat everything as if it were running on a computer with infinite cache memory and having everything already loaded there. Granted, the authors spend a huge chunk of time teaching the readers how to do (and prove) cost (or efficiency) analysis on algorithms. So, readers should be able to figure out actual, real-world efficiencies on their own (although there's nothing in this book to illustrate how to modify the analysis to do that). But, since memory hierarchies drastically change the relative efficiencies of algorithms, they should be considered in the original algorithmic analysis and ranking.

From a methodology point of view, another problem is that the authors assume the readers have full knowledge of the algorithms covered in the book. In general, they don't even try to teach the actual algorithms, how they came about, the reasoning behind them, or any method of thought for coming up with other, similar, algorithms. Instead, the authors merely focus on proving the correctness and cost of the pre-existing algorithms. It's like the authors present a beautiful, theoretical, shiny structure sparkling and spinning in the ether. They then explain what parts make up this structure, how they're put together, and how long it takes to use such a structure. But, what would be far more useful is if the authors started from the more common position where someone has a problem and a big pile of parts. They need to know how to determine the best thing to make from all those parts to fix the problem, and how to put it together in the most efficient way. Essentially, it's the difference between a reference book and a teaching book.

On the level of irritations, the authors leave a LOT of core stuff as exercises for the student. This is bad enough on its own (and is one of my pet peeves in the math world). However, making this even worse is the fact that NONE of the exercises are answered. So, firstly, that makes these exercises useless to self-studyers (i.e., me). And, secondly, that makes the "proof is left as an exercise to the student" core parts of the book entirely inaccesible to self-studyers.

I can't emphasize enough that academically and intellectually, the scope and depth of this book is amazing. If I were someone doing pure research in computer science algorithms, I'd rate it at 5 stars out of 5. But, as a lowly nouveaux-programmer trying to improve my mind, the best I can give it is an OK 3 stars out of 5.