An Introduction to Dynamic Programming

An Introduction to Dynamic Programming

An Introduction to Dynamic Programming: Although people make a big deal about how scary dynamic programming problems are, there’s really no need to be afraid of them.

Although people make a big deal about how scary dynamic programming problems are, there’s really no need to be afraid of them. In fact, once you get the hang of them, these can actually be very easy problems.

What is dynamic programming?

Dynamic programming is a technique to solve problems by breaking it down into a collection of sub-problems, solving each of those sub-problems just once and storing these solutions inside the cache memory in case the same problem occurs the next time. Dynamic Programming is mainly an optimization over plain [r_]( . Wherever we see a recursive solution that has repeated calls for same inputs, we can optimize it using Dynamic Programming. This simple optimization reduces the time complexities from exponential to polynomial.

Briefly speaking, dynamic programming is mostly just a matter of taking a recursive algorithm and finding the overlapping subproblems (that is, the repeated calls). You then cache those results for future recursive calls. Alternatively, you can study the pattern of the recursive calls and implement something iterative. You still “cache” previous work.

There are two different ways to store our values so that they can be reused. Let’s discuss both of them:

1. Tabulation or the Bottom Up approach.

2. Memoization or the Top Down Approach.

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Tabulation vs Memoization

A note on terminology: Some people call top-down dynamic programming “memoization” and only use “dynamic programming” to refer to bottom-up work.

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