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 is a slight modification of the change making problem. You should be able to find plenty of papers on this problem, and a dynamic programming solution would take no more than 20 lines of code.

http://en.wikipedia.org/wiki/Change-making_problem