- Hardcover: 1184 pages
- Publisher: The MIT Press; 2nd edition (September 1, 2001)
- Language: English
- ISBN-10: 0262032937
- ISBN-13: 978-0262032933
- Product Dimensions: 8 x 2.2 x 9 inches
- Shipping Weight: 4.6 pounds (View shipping rates and policies)
- Average Customer Review: 584 customer reviews
- Amazon Best Sellers Rank: #610,539 in Books (See Top 100 in Books)
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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.
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Students will need a very strong mathematical background and a strong arm to even think about picking up this book because the it is heavy (both physically and metaphorically). Mastery of discrete math is a must, graph theory, programming, and, combinatorics will also help.
With that said, this book falls short in one MAJOR area, explanations. Too often explanations are left out and left as exercises and there are no solutions to the exercises! Or details are replaced by ambiguous statements such as of "cleary, this works", or "it is easy to see that this ...". I get the concept of learning by doing, really I do, but there should be some kind of solutions so the student can CHECK his/her understanding of the material and sometimes the exercises are not about advanced aspects of a concept, sometimes it is the core material. Even if the solution manual only contained a simple answer without the work. Not only would it help tremendously but the purpose of doing the exercises would be preserved; that is the student getting his/her "hands dirty" and working out a problem.
For the love everything good and pure in this universe, I really wish writers of mathematical books would stop using statements like "clearly this works" or "it is easy to see", "it is obvious" etc. While that may be true for you and your brilliant circle of colleagues, everything is not always clear and obvious to your readers. Save all of that ambiguity for your research paper.
A great book should deliver in two areas; it should challenge and it should inform. The challenge is there, no doubt. However in some ways it fails to inform the reader. The authors should really think about releasing a students solution manual to help students learn better. I take away two stars for the reasons stated about.
On the plus side, the text is, as my review title says, magisterial. It covers the field comprehensively and authoritatively. When one of the authors is the "R" in RSA, and others are well-known names, you can count on the text's expertise and accuracy. I've never found an error in this text.
BUT.... The pedagogy needs work. Explanations tend to jump too quickly to pure mathematical notation, and there are often insufficient concrete examples. The pseudocode has one-letter variable names that appear at times to be randomly generated :). At least the latest edition fixes what was a baffling indentation style. If you took a sample of 100 CS undergrads and asked them to learn algorithms principally from this text, I'd venture a guess that only the 10 brightest could do so. And even they'd be baffled at times.
I apologize for having to offer such an "emperor is naked" review to such a highly respected work, but it's time to consider more carefully pedagogical texts in the undergrad market.
For students of graph theory, you might find your knowledge solidly supplemented by the material in chapters 22 through 26 on graph algorithms. The last section of the book, "Selected Topics", goes over various specific algorithms from many fields using the knowledge of algorithm design and analysis you have learned up to this point in the book. Throughout, the text is very clear, and there are plenty of instructive diagrams and pseudocode.
One of the most interesting parts of the book is the chapter on NP-completeness. This is the study of problems for which no efficient algorithm has ever been found. These problems are interesting for two reasons. The first being that even though an efficient algorithm has never been found, there is no proof that one cannot exist. Second, if an efficient algorithm exists for one of them, then an efficient algorithm exists for all. Thus, if you are ever called upon to write an efficient algorithm for an NP-complete problem, you will be involved in a long fruitless search if you do not recognize the problem as NP-complete. If you can show the problem is NP-complete, you can go about producing an algorithm that gives a good solution, but not the best possible solution. This kind of knowledge is what separates a computer scientist from a mere programmer, and is one of many reasons to study this book's contents. I highly recommend this book to anyone who truly wants to be called a computer scientist.
To get the most from this book you should already be familiar with discrete mathematics and combinatorics, as this book makes heavy use of these subjects. Because this book contains no solutions to any of the exercises, might I suggest "Problems on Algorithms" by Ian Parberry as a companion to this book. It has a little bit of tutorial and a lot of exercises, many unsolved, but some with hints and others with solutions. Also, for more basic material, you might look at "Schaum's Outline of Discrete Mathematics". It's very inexpensive and can almost stand alone as a tutorial on the mathematics you need to know to succeed at understanding this book. The table of contents is not shown for this third edition of the book, so I supply that information next:
Table of Contents
1 The Role of Algorithms in Computing
2 Getting Started
3 Growth of Functions
5 Probabilistic Analysis and Randomized Algorithms
II Sorting and Order Statistics
8 Sorting in Linear Time
9 Medians and Order Statistics
III Data Structures
10 Elementary Data Structures
11 Hash Table
12 Binary Search Trees
13 Red-Black Trees
14 Augmenting Data Structures
IV Advanced Design and Analysis Techniques
15 Dynamic Programming
16 Greedy Algorithms
17 Amortized Analysis
V Advanced Data Structures
19 Binomial Heaps
20 Fibonacci Heaps
21 Data Structures for Disjoint Sets
VI Graph Algorithms
22 Elementary Graph Algorithms
23 Minimum Spanning Trees
24 Single-Source Shortest Paths
25 All-Pairs Shortest Paths
26 Maximum Flow
VII Selected Topics
27 Sorting Networks
28 Matrix Operations
29 Linear Programming
30 Polynomials and the FFT
31 Number-Theoretic Algorithms
32 String Matching
33 Computational Geometry
34 NP Completeness
35 Approximation Algorithms