A greedy algorithm for making change is the cashier's algorithm, which all young wizards learn. Malfoy writes the following pseudocode on the whiteboard to illustrate it, where n is the amount of money to make change for and ? is a vector of the coin denominations: wizardChange(n, v): d[1 .. v. len()] =0//initial histogram of coin types in solution while n > 0 {k = r while (v[k] > n and k >= 0) {k--} if k==0 {return 'no solution'} else {d[k]++}} return d Hermione snorts and says Malfoy's code has bugs. Identify the bugs and explain why each would cause the algorithm to fail. (b) Sometimes the goblins at Gringotts Wizarding Bank run out of coins, and make change using whatever is left on hand. Identify a set of U. S. coin denominations for which the greedy algorithm does not yield an optimal solution. Justify your answer in terms of optimal substructure and the greedy-choice property. (The set should include a penny so that there is a solution for every value of n.)