**The time and space complexity in case of top-down DP with memoization should be O(Nx2^N)**

*This is because although the total sum is the upper boundary of all possible sum of subsets, the actual number of subsets that can be formed from a Set of N elements is 2^N.*

So instead of O(NxS) (where S is the total sum), it should be O(Nx2^N).

Consider this example to understand what I mean

Array = [100, 200, 300]

total sum = 600

total number of subsets possible = 2^3 = 8