Question: Given a set of non - negative integers S = { S 1 , S 2 , . . . , Sn } and a

Given a set of non-negative integers S ={S1, S2,..., Sn} and a value sum, the task is to check if there is a subset of the
given set S whose sum is equal to the given sum. For {3,34,4,12,5,2} and sum =9, there is a subset (4,5) with sum
9. For {3,34,4,12,5,2} and sum =30, there is no subset that adds up to 30.
a. Give an exhaustive and optimal algorithm to solve the problem. What is its time complexity?
b. Now, design a dynamic programming algorithm to solve the subset sum problem. What is its time
complexity?

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