A number as it's prime number parts

Question

I have to print the number of ways you can represent a given number as it\'s prime number parts.

Let me clarify: Let\'s say I have been given this number 7. Now, fir

Answer 1

Dynamic programming is your friend here.

Consider the number 27.

If 7 has 5 results, and 20 has 732 results, then you know that 27 has at least (732 * 5) results. You can use a two variable system (1 + 26, 2 + 25 ... etc) using the precomputed values for those as you go. You don't have to recompute 25 or 26 because you already did them.