Introduction to Algorithms [Paperback]

I haven't seen a better textbook ! Here are some reasons:

1. The discrete mathematics foundations are present in the first few chapters of this book and so, you can quickly brush up on any discrete math background that you may require while using this book.

2. The style of writing is very light and at the same time, rigorous - almost as if you are in the middle of a lecture while reading the book.

3. The material is comprehensive and serves as an excellent reference for other courses and in your future career.

4. The exercises and problems provide a very good learning experience.

5. It's a good-looking book !

This covers a lot of topics, and covers them in some level of mathematical rigor. For example, all assertions about algorithm efficiency are backed up with *proofs*, and key concepts like asymptotics, and big-O notation are covered. To those who think proofs are not essential -- as a mathematician, I'd counter that proofs are absolutely necessary, because you don't know something until you've proven it -- it's easy to make wrong "guesses", or even wrong hand-waving arguments. The examples are all in pseudo-code. Personally, I liked this as it makes implementing the data structures an interesting exercise that forces the reader to think.

The subject matter covered is quite broad, see below. There are some interesting topics that don't get covered (eg AVL trees), but this book does a good job at laying down the foundation.

Some might be intimidated by the theoretical approach, but I for one like it. It's written for computer scientists (or "software engineers"), not get-rich-quick wannabees. This book will force you to think, and if you don't like that, well you can (and should) buy "learn algorithms in 21 seconds" from SAMS or something.

You'll need some background to digest this material. Someone with a year of programming and some discreet math should be ready for it. Note that you won't learn any programming *language* from this book (unless you count pseudo-coed), so you'd better know some before starting !

Summary: PartI: Intro, Growth of functions,Summations, Recurrences, Sets, Counting and Probability

Part II: Heapsort,Quicksort, Sorting in linear time, Medians/order statistics

Part III: Stacks/Queues/Linked lists, Hash tables, Binary search trees, Red-Black trees, Augmented data structures

Part IV: Dynamic programming,Greedy algorithms, Amortized analysis

Part V: B-trees, Binomial heaps, fibonacci heaps, data structures for disjoint sets

Part VI: Elementary graph algorithms, Minimal spanning trees, single-source shortes paths, all pairs shortest paths, maximum flow

Part VII: sorting networks, arithmatic circuits, algorithms for parallel computers, matrix operations, polynomials and fft, number theoretic algorithms, string matching, computational geometry, NP-completeness, Approximation algorithms.

This is the definitive reference for algorithms with a firm theoretical and mathematical foundation. Algorithms are treated with a thorough theoretical introduction often with a complete mathematical walkthrough, a clearly thought out solution, a discussion of its pros and cons, lots of clear and consisive diagrams, a pseudocode implementation, and a good deal of serious optimisation discussion. It's written in an accessible manner, starting with the elementary issues, progressing to the advanced and complex thinking needed to conquer them, so you'll find you have to give it your full concentration.

This book will not disappoint. Its explanations are rigorous and its coverage spans all the general purpose algorithms with little focus on their applications but rather on the algorithms themselves. The book covers such major areas as sorting, data structures, advanced design and analysis techniques, graphs, each about a hundred pages on average, and a selection of specialised algorithms such as parallel programming, string matching and computational geometry. Because these algorithms are used everywhere, from games, graphics and simulations to electrical engineering it will have a broad audience and will find a home almost anywhere there is serious programming involved. Each chapter is a unit in itself which means you don't need to read it cover to cover, since they all start off smoothly and handhold you through. Clearly written by professionals, this is the book I know contains the information that I can't find elsewhere.