Comment by btilly

There is only one efficient solution that can be described as bottom up, and that one is in fact dynamic programming.

A top-down solution in this case is in fact strictly worse. Why? Because while both take similar numbers of operations, in the bottom up solution you can throw away a row once you've processed the one above it. But in a top-down solution, you never know when you might call a particular recursive call again.

This is very common. In a bottom up approach, we often know when we're done with data and can throw it away. This memory savings is the reason why people try to learn a bottom up approach. But it does come with the price of trying to figure out various kinds of "tricks". (That in complicated cases, may not be findable.)