I have been given N coins and given there denominations, and a number K. I want to calculate all the subsets of N that can make the sum of K. I know the solution using Bit masking technique but, since it takes the exponential time it will not be good for N>=20 so is there any other faster way to nail this problem.
hey What do you mean by subsets if duplicate denomination are allowed then maybe this recurrence can help you
Rec(Pos, Sum) ---: Rec(Pos + 1, Sum)
+
Rec(Pos + 1, Sum - Array[Pos]) IF Sum >= Array[Pos]
Call this function Rec(0, K) and Array contain denominations now you have to do 2 work
(i) Define Base Condition
(ii) Memorize it 
If still didn’t get you can ask