Lookup table and dynamic programming

Question

In old games era, we are used to have a look-up table of pre-computed values of sin and cos,..etc, due to the slowness of computing those values in that old CPUs.

Is that considered a dynamic programming technique ? or dynamic programming must solve a recursive function that is always computed or sort of ?

Update: In dynamic programming the key is to have a memoization table, which is the solution for the sin,cos look up table, so what is really the difference in the technique ?

Answer 1

I'd say for what I see in your question no it's not dynamic programming. Dynamic programming is more about solving problems by solving smaller subproblem and create way to get solution of problem from smaller subproblem.

Your situation looks more like memoization.

For me it could be considered DP if your problem was to compute cos N and you have formula to calculate cos i from array of cos 0, cos 1, ..., cos i - 1, so you calculate cos 1, sin 1 and run you calculation for i from 0 to N.

May be somebody will correct me :)

There's also interesting quote about how dynamic programming differ from divide-and-conquer paradigm:

There are two key attributes that a problem must have in order for dynamic programming to be applicable: optimal substructure and overlapping subproblems. If a problem can be solved by combining optimal solutions to non-overlapping subproblems, the strategy is called "divide and conquer" instead. This is why mergesort and quicksort are not classified as dynamic programming problems.