Op's saying (I think) that the difference between brute force recursion and DP ( top down ) is memoization, and that the language / library construct lru_cache will perform that memoization for you.

Its not a fascinating insight. If you can express a problem as a recursive brute force solution and there's a least a little recalculation involved, you're one step from DP. The lru_cache just does that step.

Just google lru_cache

edit: "op"

it is a particular part of the Python 3 standard library. it is one extra line of code to automatically memoize a recursive function.

you just do:

    from functools import lru_cache
    
    @lru_cache(maxsize=None)
    def brute_recursive_func(x):
        ...

And you're good to go.

Very nice! I often forget this handy thing during interviews. Good thing to impress your interviewer with :)

One thing of note: The arguments to the method you are memoizing need to be hashable. For example, if you want to memoize a method call whose parameters include a list, you will get an error!