I just finished a fantastic book called “Algorithms”, by Sanjoy Dasgupta, Christos Papadimitriou and Umesh Vazirani. Even better: this book is free and can be downloaded in PDF form.
At 300+ pages, it’s not lightweight either, but the authors have done a fantastic job at explaining the main foundations of essential algorithms in simple terms that even developer who don’t have a CS degree will find easy to read and to absorb. You will see a few mathematics formulas and proofs here and there, but you can safely skip them if you are not comfortable with them and just take away the very natural and friendly wordings that the authors never omit to make when they are trying to get you to understand the overall idea behind an algorithm.
The book is very extensive and covers the most important algorithms you will ever come across in your life as a developer, starting with the introduction of the “big O” notation, and then progressively moving to more complex topics such as graphs, dynamic programming (nothing to do with dynamic languages), linear programming and culminating this area with the Simplex algorithm (I loved this section).
I would consider the chapters that follow as a “second part” of the book (even though it’s not structured as such) since they cover more advanced (and sometimes, still not completely understood yet) problems such as NP completeness and quantum programming.
A must-read for any developer who never got a chance to understand how all these algorithms work or who simply want to get a refresher…
And hats off to Sanjoy, Christos and Umesh for making such a great contribution to the computing world!