How do I generate integer partitions?

Question

I have a list of numbers like 1,2,3 and I want to find all the combination patterns that sum up to a particular number like 5. For example:

Sum=5
Numbers:1,2         


        

Answer 1

This problem is known as a "doubly restricted integer partition." If the numbers "allowed" to sum to 5 were from a set V, then it is known as "multiply restricted integer partition." There is a paper by Riha and James: "Algorithm 29: Efficient algorithms for doubly and multiply restricted partitions" Computing Vol 16, No 1-2, pp 163-168 (1976). You should read that paper and implement their algorithm. Understanding how to do it will allow you to implement optimizations unique to your specific problem.