Explain your reasoning and show calculations$/$steps$,$ please. This task is known as the coin change problem.

Given the currency denominations for Norwegian krone coins $C=\{1,5,10,20\},$ we devise a greedy

algorithm to give change while using the fewest number of coins possible.

When returning an amount $V,$ we will give a coin of the largest value possible that does not take

us over the amount we have left to pay, and repeat so until we reach $V.$

a$)$ Is this algorithm optimal?

b$)$ Suppose we introduce a $7$ kroner coin. Is the algorithm still optimal?