【发布时间】：2012-10-09 02:49:37
【问题描述】：
我正在为我的 Python 课程编写一个信用卡支付计算器。任务是为计算器编写一个定义，该计算器计算出在 x 个月内使您的余额为零所需的每月付款。
该定义采用 3 个参数：initialBalance、apr、months。
据我所知，作业的重点是让我们使用二分法来找到我们的答案，我还写了另外两个有助于作业的定义：
1) newBalance() - 确定付款后的新余额； 2) balances() - 在付款后返回余额列表；
鉴于此，balances()[-1] 返回最终余额，因此我的行动计划是评估列表中的最后一项等于 0（或至少在 0 的 0.005 范围内！），如果所以，退还让我到达那里的付款。
如果最终余额为负数（我付出了太多！）：payment = payment - (payment / 2); 如果余额为正（我还没有付足够的钱！）：付款=付款+（付款/2）；
尽我所能，我的算法最终应该得出结论，但它永远找不到足够接近的答案......
这是我的代码，（最后是教授的测试定义）：
def newBalance(prevBalance, apr, payment):
"""
- prevBalance: the balance on the credit card statement.
- apr: the annual percentage rate (15.9 here means 15.9%).
- payment: the amount paid this month to the credit card company.
- returns: the new balance that will be owed on the credit card
(assumes no purchases are made).
"""
interestCharge = float(((apr / 12.0) / 100) * prevBalance)
return float((interestCharge + prevBalance) - payment)
def balances(initialBalance, apr, payments):
"""
- initialBalance: the initial balance on the credit card.
- apr: the annual percentage rate (15.9 here means 15.9%).
- payments: a list of monthly payments made on the credit card.
- returns: a list giving the balance on the credit card each
month. The first number in the list is the initial
balance, the next number is the balance after the first
payment is made, and so on. Note that the length of the returned
list is len(payments) + 1.
"""
balancelist = []
balancelist.append(initialBalance)
for x in range(0, len(payments)):
balancelist.append(newBalance(balancelist[x], apr, payments[x]))
return balancelist
def findMonthlyPayment(initialBalance, apr, months):
"""
- initialBalance: the starting balance on the card.
- apr: the APR.
- months: the number of equal monthly payments you wish to
make in order to reduce the balance to zero.
- returns: the monthly payment amount needed to reduce the
balance to zero (well, "zero" to within $0.005, anyway)
in the given number of months.
"""
guess = float(initialBalance / months)
listo = months*[guess]
while True:
if abs(float(balances(initialBalance, apr, listo)[-1]) - initialBalance) < 0.006:
print "BINGO", guess ##for debugging
print balances(initialBalance, apr, listo)[-1]
return guess
else:
if float(balances(initialBalance, apr, listo)[-1]) < -0.005:
guess = guess - (guess / 2)
print "BOO", guess ##for debugging
print balances(initialBalance, apr, listo)[-1]
else:
guess = guess + (guess / 2)
print "NAY", guess ##for debugging
print balances(initialBalance, apr, listo)[-1]
listo = months*[guess]
def testFindMonthlyPayment():
answer = findMonthlyPayment(1000, 18.9, 60)
print
myString = "Monthly payment to pay off $%.2f in %d months at %.2f%% APR:"
print myString % (1000, 60, 18.9)
print "$%.2f" % answer
# Output should look approximately like this:
"""
iteration: 1 guess: 500.0 final bal: -46777.3384635
iteration: 2 guess: 250.0 final balance: -22111.7016729
iteration: 3 guess: 125.0 final balance: -9778.88327752
iteration: 4 guess: 62.5 final balance: -3612.47407985
iteration: 5 guess: 31.25 final balance: -529.269481021
iteration: 6 guess: 15.625 final balance: 1012.3328184
iteration: 7 guess: 23.4375 final balance: 241.531668687
iteration: 8 guess: 27.34375 final balance: -143.868906167
iteration: 9 guess: 25.390625 final balance: 48.83138126
iteration: 10 guess: 26.3671875 final balance: -47.5187624535
iteration: 11 guess: 25.87890625 final balance: 0.656309403241
iteration: 12 guess: 26.123046875 final balance: -23.4312265251
iteration: 13 guess: 26.0009765625 final balance: -11.387458561
iteration: 14 guess: 25.9399414062 final balance: -5.36557457885
iteration: 15 guess: 25.9094238281 final balance: -2.35463258781
iteration: 16 guess: 25.8941650391 final balance: -0.849161592282
iteration: 17 guess: 25.8865356445 final balance: -0.0964260945206
iteration: 18 guess: 25.8827209473 final balance: 0.27994165436
iteration: 19 guess: 25.8846282959 final balance: 0.0917577799204
iteration: 20 guess: 25.8855819702 final balance: -0.00233415730086
Monthly payment to pay off $1000.00 in 60 months at 18.90 APR:
$25.89
"""
感谢您的帮助。除非我用谷歌搜索的所有内容都在 stackoverflow 上，否则可能不会加入 compsci。
【问题讨论】：
-
它的实际作用是什么，你期望它做什么？
-
它在正确答案（25.89 美元）附近振荡，但从未得出该答案。我希望它会通过确定付款是否过高或过低来缩小结果范围（最终在我的 0.005 公差范围内并接受它）。