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Another excellent algorithms book that never seems to get any attention is Udi Manber's "Introduction to Algorithms: A Creative Approach". Unlike the standard "algorithm catalog" books, where the standard algorithms are merely presented, it really gives you an idea of how one could come up with them in the first place, focusing on arguments by mathematical induction which then naturally translate into recursion/iteration. It's really invaluable for being able to come up with your own algorithms, when a non-standard problem hits you.

The slight downside is that sometimes the given algorithms are not quite as worked out in detail as in some other textbooks. Yet it's probably the algorithms book that has taught me the most.

I came here to make exactly the same recommendation about Udi Manber's book.

When designing an algorithm, you ought to make sure that it actually works. At some point, then, you're going to have to prove it. Which for most people is hard, in part because most algorithms books present the proofs as a fait accompli. They just show up, fully formed.

But Manber argues, and demonstrates convincingly in his book, that the design and the proof both become easier if you do them together. The design guides the proof, the proof the design.

He's right. Since reading the book, I don't do it any other way.

The book, tragically, costs about $110. But if you care about this stuff, it's worth it.

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