Unformatted text preview: using the fewest coins possible has ༉ at most 2 dimes (2×10c), 1 nickel (1×5c), 4 pennies (4×1c), ༉ cannot have 2 dimes and a nickel (2×10c + 5c), and ༉ total amount of change in dimes, nickels, pennies must not exceed 24c. Proof: by contradiction ༉
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༉ If we had 3 dimes, we could replace them with a quarter and a nickel. If we had 2 nickels, we could replace them with 1 dime. If we had 5 pennies, we could replace them with a nickel (5c). ༉ If we had 2 dimes and 1 nickel, we could replace them with a quarter. ༉ The allowable combinations, have a maximum value of 24 cents. Otherwise, we could replace them with a quarter. Proving Op$mality for US Coins Theorem: the greedy change making algorithm for US coins produces change using the fewest coins possible. Proof: by contradiction. 1. A...
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 Spring '14
 M.Nojoumian
 Algorithms, Sort

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