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We don't need to sort the array! First we find the minimum by one pass. If 2*minimum is not less than the target, there is no such subset and the count is zero. Other wise, we do another pass and count all elements that minimum plus such element is less than the target, say we get N. Since any subset with the above property must be a subset of such elements, and vice versa, the answer is 2^N. So the solution is O(n)!
- Maryam March 14, 2017Note that there no repeated elements, otherwise we would need to sort.