Question 1) (20 points) Suppose that we are given an array A of n non-negative integers A[1], A[2], ..., A[n]. We would like to decide if there exists subset of the elements of the array A such that the sum of the elements in this subset is exactly S. We would like to construct a dynamic programming algorithm to solve this problem. As it is typical for dynamic programming algorithms, we introduce a function to characterize the solution. Let us assume that we introduce the function D[i,j] with the following meaning: D[i, j] will be set to TRUE if and only if there exists a subset of the elements A[i], A[i+1], A[i+2),..., A[n] such that the sum of this subset is exactly Here we have, 1