Consider the following problem, which we will call the card sum problem. Suppose that we
are given a set of cards H, each of which has a positive integer value, and a positive integer
target C. Our goal is to find a subset of cards so that the sum of their values is as close as
possible to C without exceeding C.
(a) [1 mark] What is a feasible solution to the card sum problem?
(b) [1 mark] What is an optimal solution to the card sum problem?
(c) [2 marks] State the optimal substructure property for the card sum problem.
You
may not use the words āgreedy choiceā, āitemā, āsolutionā, āfeasibleā, or āoptimalā
(āmaximalā or āminimalā are fine).