Suppose that the coins of the fictional country of Combinatoria come in the denominations, d₁, d₂,...,d_k, where d₁ = 1 and the other d_i values form a set of distinct integers greater than 1. Given an integer, n > 0, the problem of making change is to find the fewest number of Combinatorian coins whose values sum to n. 

(a) Give an instance of the making-change problem for which it is suboptimal to use the standard greedy algorithm, which repeatedly chooses a highest-valued coin whose value is at most n until the sum of chosen coins equals n. 

(b) Describe an efficient algorithm for solving the problem of making change. What is the running time of your algorithm?