Mimi comments on The Best Textbooks on Every Subject - Less Wrong
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Well, let me do Jonathan's job for him on one of those.
Introduction to Algorithms by Cormen, Leiserson, Rivest, and (as of the second edition) Stein is a first-rate single-volume algorithms text, covering a good selection of topics and providing nice clean pseudocode for most of what they do. The explanations are clear and concise. (Readers whose tolerance for mathematics is low may want to look elsewhere, though.)
Two obvious comparisons: Knuth's TAOCP is wonderful but: very, very long; now rather outdated in the range of algorithms it covers; describes algorithms with wordy descriptions, flowcharts, and assembly language for a computer of Knuth's own invention. When you need Knuth, you really need Knuth, but mostly you don't. Sedgwick's Algorithms (warning: it's many years since I read this, and recent editions may be different) is shallower, less clearly written, and frankly never gave me the same the-author-is-really-smart feeling that CLRS does.
(If you're going to get two algorithms books rather than one, a good complement to CLRS might be Skiena's "The algorithm design manual", more comments on which you can find on my website.)
Manber's "Algorithms--a creative approach" is better than Cormen, which I agree is better than Knuth. It's also better than Aho's book on algorithms as well. It's better in that you can study it by yourself with more profit. On the other hand, Cormen's co-author has a series of video lectures at MIT's OCW site that you can follow along with.
What about Manber's book makes it more fruitful for self-study than CLRS? How does it compare with CLRS in other respects? (Coverage of algorithms and data structures; useful pseudocode; mathematical rigour; ...)