Equal sum subsets hybrid

Question

The problem is the following:

You are given a set of positive integers { a1 , a2 , a3 , ... , an } in which there are no same numbers ( a1 exists only once ,a2 exist

Answer 1

This problem seems to be at least as hard as SUBSET-SUM. If we can find two subsets of A: B = {b1,...,bp} and C = {c1,...,cq} such that b1+...+bp = -c1-...-cq, or if we determine that none exist, then we have solved SUBSET-SUM(A) (ignoring the trivial case where 0 ∈ A).

I'm not sure what you mean by it is not obligatory for B and C to cover A, so the problem isn't automatically reduced to the subset sum problem. Please check the definition of SUBSET-SUM.