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    <p>I think the best way to learn algorithms are through the various competition sites. </p> <ul> <li><a href="http://ace.delos.com/usacogate" rel="noreferrer">USACO</a> - my personal favorite, as it gives a clear path through the material</li> <li><a href="http://www.topcoder.com/" rel="noreferrer">TopCoder</a> - already mentioned</li> <li><a href="http://www.spoj.pl/" rel="noreferrer">Sphere Online Judge</a> - great if you want to work in another language other than C/C++/Java</li> </ul> <p>As far as books, the best single intro I've seen for the non-math specialist is <a href="http://www.brpreiss.com/books/opus4/" rel="noreferrer">Data Structures and Algorithms</a>. It takes you through an algorithm line by line and shows you how it decomposes mathematically, something CLRS's otherwise excellent analysis section is a little less clear on. </p> <p>Skiena's <a href="http://rads.stackoverflow.com/amzn/click/1848000693" rel="noreferrer">Algorithm Design Manual</a> is also excellent, as is his <a href="http://rads.stackoverflow.com/amzn/click/0387001638" rel="noreferrer">Programming Challenges</a>, which is essentially a tutorial through the Valladolid Online Judge. </p> <p>Honestly, though, I think the single most helpful thing a beginner can do is to implement the various algorithms -- merge sort, say, followed by Quicksort -- and time them against variously sized inputs. Create a spreadsheet with a graph that shows their growth over time. Very few non-specialists will have the patience or the know-how to set up a recurrence relation and solve their way through it. But you must understand the effect of, say O n^2 growth over time, and there's no better way to learn this than to watch your own program blow through its memory stack. :)</p> <p>I say this as a non-CS, non-math programmer who has spent a good couple of months wrapping my mind around algorithmic analysis. </p>
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    1. COthere is not competition in here, only colleague
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    2. CO@none - I call them "competition sites" because they're set up specifically to allow people to train for the various algorithmic competitions. They are excellent learning tools.
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