Fast solution to Subset sum

Question

Consider this way of solving the Subset sum problem:

def subset_summing_to_zero (activities):
  subsets = {0: []}
  for (activity, cost) in activities.iterit         


        

Answer 1

I don't know much python, but there is an approach called meet in the middle. Pseudocode:

Divide activities into two subarrays, A1 and A2
for both A1 and A2, calculate subsets hashes, H1 and H2, the way You do it in Your question.
for each (cost, a1) in H1
     if(H2.contains(-cost))
         return a1 + H2[-cost];

This will allow You to double the number of elements of activities You can handle in reasonable time.