I would strongly urge the OP to not use this book. I used it as my undergrad algorithms book and it is, quite frankly, far too obtuse and hard to understand. At first, I thought it was just me and that other people found the book readable. I eventually realized that the book itself is just bad for autodidacts.
Last month (about 5 years after I took the course), I went through to review some stuff that I'd looked at more recently. Specifically, I had worked out Dijkstra's algorithm on my own and finally understood how the heck it actually worked. I then opened CLRS to check their proof. What I saw blew my mind in terms of sheer obfuscation. Despite having a very clear understanding in my head of the core concept behind the algorithm, I read their proof and was just amazed at how little it actually explained about the simple idea that ties the whole thing together. That by itself isn't a huge deal, because some proofs are just hard to follow. What really upset me was that there was practically no surrounding discussion of the intuition behind the algorithm. Behind all the rigor of mathematics lies very simple and powerful ideas. This book did nothing to emphasize those simple ideas. It's a real travesty to be honest :(
If you're looking for something more accessible, I've heard that The Algorithm Design Manual[1] by Steve Skiena[2] is better. Whatever you choose, though, please stay away from CLRS.
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
As far as The Algorithm Design Manual and CLRS is concerned I would not say that they are comparable.
CLRS is about algorithm analysis and formally proving that they behave in certain ways - like proving that quicksort has a guaranteed worst case of O(n^2) and an average case of O(n log n). Being able to work with proofs such as those is fairly fundamental to being a Computer Scientist in the strict, academic, sense. That being said, it should not be used as book to teach data structures or algorithms without formal proofs having been taught first - without the maths background the book is going to be very hard going.
The Algorithm Design Manual on the other hand, is more like a literature review for a collection of algorithms/families of algorithms (75, claims the copy infront of me). For each of them it gives an overview of the class of problems you'd apply the algorithm to, a run through of the algorithm (some with pseudo code) and discussion about the algorithm and times when the author has used it, and then pointers to more in depth sources. CRLS and Knuth are cited considerably, which should give you an idea about the relative stature of the two books being compared here.
Ultimately, they're both good books but for different audiences. The Algorithm Design Manual is by far the easier read, not least of which because it's not trying to be an academic text and is replete with anecdotes from the author. It's an excellent overview of the techniques available to the practicing developer - the ones who work in fields where you might need to whip up a quick Bin Packing routine anyway. CLRS is a lot harder to get through, but it will teach you how to prove that your algorithms will do what they should.
When it comes down to it, I'd say that CLRS is for the Computer Scientist while TADM is for the practitioner and I'm glad I own both.
"Introduction to Algorithms" a.k.a. "CLRS" http://www.amazon.com/Introduction-Algorithms-Thomas-H-Corme...
I think this is all (and probably more than) you really "need" if you want to know CS for programming, and an enjoyable read too.