What technique do I use for when I want to check all possible combinations of a set?

Question

I\'m working through an interview question that goes like:

Given an array of integers and sum, check whether any combination adds up to the sum.

Answer 1

I see two options:

1. Compute the Power Set of the input array and check the sum of each element in the power set (see http://en.wikipedia.org/wiki/Power_set). This is probably O(2^N) and not good for large N
2. Try something with the 0-1 Knapsack problem (see http://en.wikipedia.org/wiki/Knapsack_problem). This should either find the greatest sum less than your desired value, a sum that is your desired value, or not find anything. Based on the output, you can answer your original question. 0-1 Knapsack is nice because it runs in polynomial time O(N^c) where c is constant. I don't remember if it works for negative numbers though.