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"