贪心算法无法正常运行

Question

这个代码应该给我最少数量的硬币（硬币、硬币、镍和便士），加起来就是所欠的金额。 当我输入 0.25 的倍数的值时，它可以无缝工作。但是当我在终端中输入其他值时，它只是插入一个新行而不做任何事情。我怎么搞砸了？

owed = float(input("how much change is owed?"))
coins = 0

if owed % 0.25 == 0:
    coins = owed / 0.25
    print(int(coins))
    exit()
elif owed % 0.25 != 0:
    while owed > 0:
        if (owed - 0.25) >= 0:
            coins += 1
            owed -= 0.25
        elif (owed - 0.10) >= 0:
            coins += 1
            owed -= 0.10
        elif (owed - 0.05) >= 0:
            coins += 1
            owed -= 0.05
        elif (owed - 0.01) >= 0:
            coins += 1
            owed -= 0.01
    print(int(coins))
    exit()

Answer 1

由于浮点数的内部表示引起的与浮点值相关的一些舍入错误，您的程序正在运行无限 while 循环。因此，为了修复这些错误，我们可以使用round() 函数在每个while 循环迭代结束时将owed 的值四舍五入：

elif owed % 0.25 != 0:
    while owed > 0:
        if (owed - 0.25) >= 0:
            coins += 1
            owed -= 0.25
        elif (owed - 0.10) >= 0:
            coins += 1
            owed -= 0.10
        elif (owed - 0.05) >= 0:
            coins += 1
            owed -= 0.05
        elif (owed - 0.01) >= 0:
            coins += 1
            owed -= 0.01
        owed = round(owed, 3) # In this line, we roundoff the value of owed
    print(int(coins))
    exit()

这很好用。

希望这会有所帮助:)

Answer 2

由于浮点错误，您的程序卡在while 循环中。尝试在while 循环中添加以下代码，您会看到虽然owed 确实变得无限小，但它永远不会变为零：

...
while owed > 0:
    print(owed)
    ...

输出：

...
8.326672684688674e-17
8.326672684688674e-17
8.326672684688674e-17
8.326672684688674e-17
...

考虑将输入乘以100，然后将其作为整数处理：

owed = int(float(input("How much change is owed? $")) * 100)

quarters = int(owed / 25)
dimes = int((owed - quarters * 25) / 10)
nickels = int((owed - quarters * 25 - dimes * 10) / 5)
cents = int((owed - quarters * 25 - dimes * 10 - nickels * 5))

coins = (quarters + dimes + nickels + cents)

print('Quarters (${}): {}'.format(quarters*0.25, quarters))
print('Dimes (${}): {}'.format(dimes*0.1, dimes))
print('Nickels (${}): {}'.format(nickels*0.05, nickels))
print('Cents (${}): {}'.format(cents, cents))
print('Coins:', coins)

或者如果你想坚持使用贪心算法：

owed = int(float(input("How much change is owed? $")) * 100)

while owed > 0:
    if (owed - 25) >= 0:
        coins += 1
        owed -= 25
    elif (owed - 10) >= 0:
        coins += 1
        owed -= 10
    elif (owed - 5) >= 0:
        coins += 1
        owed -= 5
    elif (owed - 1) >= 0:
        coins += 1
        owed -= 1

coins = (quarters + dimes + nickels + cents)

print('Quarters (${}): {}'.format(quarters*0.25, quarters))
print('Dimes (${}): {}'.format(dimes*0.1, dimes))
print('Nickels (${}): {}'.format(nickels*0.05, nickels))
print('Cents (${}): {}'.format(cents, cents))
print('Coins:', coins)

输出

>>> How much change is owed? $1.42
Quarters ($1.25): 5
Dimes ($0.1): 1
Nickels ($0.05): 1
Cents ($2): 2
Coins: 9

有关浮点限制的更多信息，请查看以下内容：https://docs.python.org/3.8/tutorial/floatingpoint.html