don’t you understand this explanation?
We already know that the 2 subsets we are looking for have the same sum which is equal to the sum of all the elements in the set / 2, so we only need to find the elements of 1 of the 2 subsets. A neat solution would be splitting the set into 2 random disjoint subsets of size N / 2, namely A and B. Then we insert each sum of every combination of elements from A into a hash table. We then check the sums of every combination of elements from B i. e. for a sum K, if S / 2 - K is in the hash, then we have a solution. Final complexity: O(2 ^ (N / 2 + 1)). An alternative to this solution would be a well implemented algorithm which randomly moves elements from one subset to the other. This outperforms the 2 ^ (N / 2) algorithm on memory and may even have better results on time.