# file: change.py
# author: Bob Muller
# 
# CS1101 Computer Science I
#
# Code implementing a greedy algorithm for making change. The
# algorithm returns the smallest list of coins adding up to a
# given amount. NB: this algorithm only works for certain sets
# of coins, including US coinage.

# getLargest : int list -> (int * int list)
#
# The call getLargest(coins) returns a pair (c, coins') where
# c is the largest coin in coins and coins' are the leftovers.
#
def getLargest(coins):
  big = max(coins)
  return (big, [ coin for coin in coins if coin <> big ])

# change : int * int list -> int list
#
# The call change(amount, coins) returns the fewest coins drawn
# from the list that add up to amount.
#
def change(amount, coins):
  if amount == 0:
    return []
  else:
    (largestCoin, otherCoins) = getLargest(coins)
    numLargest = amount / largestCoin
    residualAmount = amount % largestCoin
    return ([largestCoin] * numLargest) + change(residualAmount, otherCoins)