1. In this question we consider the change-making problem (as covered in recitation), of making change for n cents using the smallest number of coins. Suppose we have coins with denominations of v1 > U2 > ... > Ur for r coins types, where each coin's value vi is a positive integer. Your goal is to obtain a set of counts {d}}, one for each coin type, such that i-di = k and where k is minimized, and such that the sum of the values - div; = n. (a) A greedy algorithm for making change is the cashier's algorithm. Consider the following pseudocode-meant to implement the cashier's algorithm where n is the amount of money to make change for and v is a vector of the coin denominations: change(n,v,r): d[1 .. r] = 1 // initial histogram of coin types in solution while no{ k = r while (k> 0 and v[k] >n) { k++ } if k==0 { return 'no solution' } else { n = n - v[k] } return d This code has bugs. Identify the bugs and explain why each would cause the algorithm to fail