In this post, we return back to the combinatorial problem discussed in Introduction to Dynamic Programming and Memoization post. We will show that generating functions may work great not only for single variable case (see The Art of Generating Functions), but also could be very useful for hacking two-variable relations (and of course, in general for multivariate case too).
For making the post self-contained, we repeat the problem definition here.

In the post, we discuss the basics of Recursion, Dynamic Programming (DP), and Memoization. As an example, we take a combinatorial problem, which has very short and clear description. This allows us to focus on DP and memoization. Note that the topics are very popular in coding interviews. Hopefully, this article will help to somebody to prepare for such types of questions.
In the next posts, we consider more advanced topics, like The Art of Generating Functions and Cracking Multivariate Recursive Equations Using Generating Functions.

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