Describe an efficient greedy algorithm for making changes for a specified value using a minimum number of coins, assuming there are four denominations of coins (called quarters, dimes, nickels, and pennies) with values D_1 = 25, D_2 = 10, D_3 = 5, D_4 = 1, respectively. Argue why your algorithm is correct. If a new 20-cent coin (D_5 = 20) is created for the coin set, we can no longer use the greedy strategy to return change with the fewest number of coins. Devise a dynamic programming formulation that determines the fewest number of coins to return as change for coin denominations