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Dynamic Programming is a technique that you can use to construct your own algorithms to solve problems. The idea is to set up a recursive solution and then add memoization, which means storing each solution you’ve calculated along the way and reusing them any time the same recursive call arises. You might think “why does dynamic programming mean recursion with memory”? It’s a good question. It turns out the term was invented to sound cool so that the developer, Richard Bellman, could get more research funding, and doesn’t really mean anything! (Who wouldn’t want to fund dynamic programming? Sounds cool.) In any case, a dynamic programming algorithm needs to be set up this way:
The problem is broken down into a series of subproblems, which are often smaller versions of the main problem.
The subproblems are related recursively (that is, you determine a way to calculate each subproblem in terms of other smaller subproblems), with an ordering that will ultimately end up on a base case.
The solution to each subproblem is stored in a memo once it is calculated, usually a dictionary, so that if that subproblem is encountered again in a future recursive call, the solution can be recalled rather than recalculated.
When conceptualized this way, we can calculate the big-Oh of a dynamic programming algorithm by simply doing (number of subproblems) O(work per subproblem).
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