115 lines
3.4 KiB
Python
Executable File
115 lines
3.4 KiB
Python
Executable File
# A set of functions to deal with bags of money.
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#
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# JMR 2017
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# Face values of coins (in cents):
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COINS = [200, 100, 50, 20, 10, 5, 2, 1]
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def value(bag):
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"""Return total amount in a bag."""
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totalValue = 0
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for coin in bag:
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totalValue += bag[coin] * coin
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return totalValue
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def transfer1coin(bag1, c, bag2):
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"""Try to transfer one coin of value c from bag1 to bag2.
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If possible, transfer coin and return True, otherwise return False."""
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if bag1[c] == 0:
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return False
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bag1[c] -= 1
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bag2[c] = 1 if c not in bag2 else bag2[c] + 1
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return True
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def transfer(bag1, amount, bag2):
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"""Try to transfer an amount from bag1 to bag2.
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If possible, transfer coins and return True,
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otherwise, return False and leave bags with same values."""
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# Uses a support method not to reuse the coins if they will make the process not possible
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return transferProcess(bag1, amount, bag2, COINS)
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def transferProcess(bag1, amount, bag2, coins):
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bagBackup = (bag1.copy(), bag2.copy())
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amountBackup = amount
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firstUsedCoin = None
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for coin in coins:
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while amount >= coin and transfer1coin(bag1, coin, bag2) and amount > 0:
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amount -= coin
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if firstUsedCoin is None:
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firstUsedCoin = coin
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if amount == 0:
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return True
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for coin in COINS:
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bag1[coin] = bagBackup[0][coin] if coin in bagBackup[0] else 0
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bag2[coin] = bagBackup[1][coin] if coin in bagBackup[1] else 0
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if len(coins) == 1:
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return False
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return transferProcess(bag1, amountBackup, bag2, COINS[COINS.index(firstUsedCoin) + 1:])
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def strbag(bag):
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"""Return a string representing the contents of a bag."""
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# You may want to change this to produce a more user-friendly
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# representation such as "4x200+3x50+1x5+3x1=958".
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string = ""
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for coin in bag:
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if bag[coin] != 0:
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string = f"+{bag[coin]}x{coin}{string}"
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string = f"{string[1:]}={value(bag)}"
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return string
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def main():
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# A bag of coins is represented by a dict of {coin: number} items
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bag1 = {1: 4, 2: 0, 5: 1, 10: 0, 20: 5, 50: 4, 100: 2, 200: 1}
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bag2 = {}
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# Test the value function.
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assert value({}) == 0
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assert value({1: 7, 5: 2, 20: 4, 100: 1}) == 197
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# Test the strbag function.
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print(strbag({1: 7, 5: 2, 20: 4, 100: 1})) # 1x100+4x20+2x5+7x1=197
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print(strbag({1: 7, 5: 2, 10: 0, 20: 4, 100: 1})) # 1x100+4x20+2x5+7x1=197
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print("bag1:", strbag(bag1)) # bag1: 1x200+2x100+4x50+5x20+1x5+4x1=709
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print("bag2:", strbag(bag2)) # bag2: =0
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print(transfer1coin(bag1, 10, bag2)) # False!
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print("bag1:", strbag(bag1)) # bag1: 1x200+2x100+4x50+5x20+1x5+4x1=709
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print("bag2:", strbag(bag2)) # bag2: =0
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print(transfer1coin(bag1, 20, bag2)) # True
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print("bag1:", strbag(bag1)) # bag1: 1x200+2x100+4x50+4x20+1x5+4x1=689
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print("bag2:", strbag(bag2)) # bag2: 1x20=20
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print(transfer1coin(bag1, 20, bag2)) # True
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print("bag1:", strbag(bag1)) # bag1: 1x200+2x100+4x50+3x20+1x5+4x1=669
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print("bag2:", strbag(bag2)) # bag2: 2x20=40
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print(transfer(bag1, 157, bag2)) # True (should be easy)
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print("bag1:", strbag(bag1)) # bag1: 1x200+1x100+3x50+3x20+2x1=512
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print("bag2:", strbag(bag2)) # bag2: 1x100+1x50+2x20+1x5+2x1=197
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print(transfer(bag1, 60, bag2)) # not easy, but possible...
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print("bag1:", strbag(bag1))
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print("bag2:", strbag(bag2))
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return
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if __name__ == "__main__":
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main()
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