"Given a list A = [a1, a2,. .., an] of positive integers, and a positive integer k," "give a dynamic programming algorithm that determines if there exists a subset S of indices {1, 2,. .., n} such that"

"You can use each element of A at most once. All elements of A are distinct (i.e., no repeats). You dont need to output the subset." "Example: a1 = 5, a2 = 10, a3 = 2. For k = 12 there is a solution (using a2" "and a3). For k = 14 there is no solution." "(Faster (and correct) algorithm in O() notation is worth more credit.)"

"(a) Define the entries of your table in words. E.g., T (i) is ..., or T (i, j) is ...." "(b) State the recurrence for the entries of your table in terms of smaller subproblems." "(c) Write pseudocode for your algorithm to solve this problem." "(d) Analyze the running time of your algorithm."

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