Both top down and bottom up approaches can be used with dynamic programming. DP is about how you approach solving a problem by breaking it into subproblems (see

Both top down and bottom up approaches can be used with dynamic programming. DP is about how you approach solving a problem by breaking it into subproblems (see the term used, "optimal substructure"). Whether you use that information for a top-down (often memoized) solution or a bottom-up solution is a choice for the implementor (and which depends on how you're using your solver and solutions). If you need to solve one problem, bottom-up is often most efficient. But if you need to solve many related problems (say trialing many different initial conditions) then you may want the memoized solution.