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> They're not just functionally equivalent. They are the same thing. There are two things you need for a dynamic programming solution At a high level they are

> They're not just functionally equivalent. They are the same thing. There are two things you need for a dynamic programming solution At a high level they are the same, but it makes sense to distinguish between the techniques based on whether you need random access to the already-computed data. For example, if you are computing the nth fibonacci number f(n), a DP solution needs only the state f(n-1) and f(n), but a typical memoized solution keeps around all the state f(1) through f(n-1). For tougher problems, you can't always convert between them trivially while keeping performance the same.

thaumasiotes 4y ago
> if you are computing the nth fibonacci number f(n), a DP solution needs only the state f(n-1) and f(n), but a typical memoized solution keeps around all the state f(1) through f(n-1) That's all true, but is it comparing like with like? The "generic DP" solution to the problem is to allocate an array of n elements and fill it in from f(1) to f(n). That's the same amount of storage the "typical" memoized solution uses; cutting it down to an array of 2 elements plus an (implicit) offset between the part of the array that's in use and the full array seems to be an optimization on top of the DP solution. You could apply the same optimization to a memoized form of the solution. I certainly agree that you most likely wouldn't do that, but you could. What do we learn by comparing a tightly optimized DP solution against a "typical" memoized solution? Why do we give the DP solution credit for not using what it "doesn't need" while penalizing the memoized solution for what the programmer probably added unnecessarily?