Customer Reviews

Introduction to Algorithms: A Creative Approach

5 star:		(3)
4 star:		(5)
3 star:		(2)
2 star:		(1)
1 star:		(1)

 

 

This book is much more than a catalog of algorithms (e.g., CLR): its purpose is to train your intuition to recognize mathematical structure in abstract problems. What does it matter if you know Dijkstra's algorithm? It's much more valuable to have good intuitions and a inductive reasoning tool chest with which to smash apart all of the variations of the shortest path problem (for example.)

The reviewers who wrote that the book "assumes you are a math wiz" and that it provides "little or no guidance for solving an arbitrary problem of the same type" didn't get it. This book is trying very hard to make you into a wiz by forcing you to really interact with mathematics, rather than working through a set of nearly identical problems (--what passes for "education" in North America.)

I was just going to leave my review at that, but since the reviews that people find "helpful" are so way off base, I think I should throw in a relevant story.

When my friend was in grade 11, he showed up to the Canadian Computing Competition finals, placing 14th. The guy who won told him, "if you want to win, read this book." Two years later, he won the CCC against 2000 other students. This book is the best introduction you can give a budding mathematician.

Sure, you can cough up what you've memorized from CLR during your university algorithms course. But, do you want to learn to invent algorithms yourself?

Math is not something handed down generations in big, dry textbooks. Like all knowledge, math is organically discovered Truth, and you have learn to discover it for yourself.

I like this book a lot. I think it's a good reference and introductory text, maybe as a supplement. It's much easier to read than Cormen's, but not half as deep.

Pros:
- Easy to read. You can understand an algorithm much faster if you go to this book first.
- Good examples and pictures.
- Explain the ideas that lead to efficient algorithmic designs.

Cons:
- Doesn't go into enough details about the proofs of correctness and complexity.
- The approach is different than most books and may take some time to get used to.

I really like this book as a supplement to the algorithm bible (Introduction to Algorithms, Thomas Cormen et al). This book is tiny and portable yet every major algorithm is covered. Basics, like mathematical induction are reviewed and illustrated with relevant examples.

One of the ways that Udi Manber packs so much information into such a small package is by keeping verbosity to a minimum. In his proofs, only the most complicated steps are justified or explained. As a result the reader may find herself spending time justifying steps in the proofs that are unrelated to the problem at hand. I did not mind doing this; others may. Regardless, the persistent reader will find that within the pages of this book lies all of the information required to understand all of the algorithms covered (and of course, it never hurts to keep a notebook, pencil and several erasers handy).

I would not recommend this book as a reference; rather, it provides a refreshingly new perspective on algorithms that may seem old and dusty. I've spent more time and energy per page on this book than any other CS book I've had but the ROI has been well worth the effort.

I wonder why this book is not as popular as it should be. Although the CLR is the mandatory book of most introduction to algorithm classes, it does not say much of how they came up with those algorithms which is the role of this book. The unique interesting thing is it uses induction to explain how each algorithm was developed, however I guess it's not the primary objective of the author. He wanted readers to read the description of the problems that those algorithms try to solve, and learn to apply induction to solve them on their own. If you like solving puzzle, you will love it.

A good introduction to the study of algorithms with its terse description and selective content, especially for a one-semester course. However, I highly recommend some additional reference material to supplement and provide more indepth coverage to topics highlighted in this book. My personal favorite supplementary reference is Cormen, Leiserson, and Rivest's excellent Introduction to Algorithms (ISBN 0-262-03141-8 MIT Press)

Most books I have read on the subject seem to be simply a collection of algorithmic tricks and techniques. There's no single universal idea, except for this book by Udi Manber. The cover picture says it all. In my opinion, the most fundamental and universal concept in algorithmic design is the idea of induction, recursion, and building bigger desired solutions from smaller already-constructed ones. The experts establish this as their intuition and perhaps take it for granted. But as a beginning algorist, when you have to ask yourself how do I solve/optimize/approximate this problem, I think you'll find this idea so important. This book attempts to make this concept your algorithmic intuition, and that's I think is a good thing.

That said, it should be read along with other books in algorithms design and analysis.

Although this book covers a large area its coverage is somewhat incomplete. The first thing you notice is the bad formatting of this book making the examples and explanations hard to follow. Mathematical proofs and algorithms are placed, bit by bit, into a paragraph of text i.e.

"...When we substitute -x for x in (9.8), we get P(-x)=Pe(x^2)+(-x)Po(x^2). To evaluate (9.7), we need to compute P(x-i) and P(-xi), for 0<i<n/2. To do that..." --Udi Manber, Intro to Algorithms

This combined with the assumption that the reader already understands the subject and the maths behind it makes it an unsuitable introductory text. Its only redeeming feature is its wide range of topics, if this is the only Algorithmics book you are likely to by at this time look elsewhere, if you need a second or third book to clarify some points this may just be the one you are after.

The book is complete and correct, no argument there. However, I had a lot of trouble learning from it. I had to re-read the same paragraph a number of times in order to derive comprehensive meaning from the author's scant explanations. The author usually walks through a sample problem, but then provides little or no guidance for solving an arbitrary problem of the same type. Likewise, although the book centers on induction, it was extremely difficult to follow with no prior induction education.

The author often presents the answer to some given problem with words like "obviously" or "clearly" without making things at all clear or obvious to the student. I kept wishing that the author wouldn't be so tight-lipped and would spend some extra time clarifying the issues at hand.

This book is for people who already understand the subject and need a condensed reference to refer to. This book does not explain problems or have meaningful examples to follow. Cormen et al's book is worlds better for someone just learning the subject.

...I changed my mind after trying to use this book alone to implement FFT. Its description is quite clear and simple, much simpler than the Rivest et al book or wikipedia. Unfortunately, though clear, it is not complete and it is not possible to actually implement FFT using this book alone. I ended up having to use the Rivest et al book (which I had on CD via DDJ) along with this book to implement it. (Wikipedia was truly hopeless for trying to understand the FFT algorithm.) I was able to implement FFT in a single page of Python code because of Manber's description.

For giving very simple explanations of a number of algorithms, this book is fantastic. Just don't rely on it for the technical details.