What is Dynamic Programming? Smart Recursion!

Here we introduce the idea of "smart recursion", which is better known as "dynamic programming". We illustrate this with the calculation of the Fibonacci numbers, which give a horrendously slow algorithm if we don't keep previous calculations stored (i.e., we will repeat them). So we use "smart" recursion by saving calculations in a table, leading to a much faster algorithm.

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I am a professor of Computer Science, and am passionate about CS theory. I have taught many courses at several different universities, including several sections of undergraduate and graduate theory-level classes.