我正在尝试使用以下方法计算每月支付的最低金额以支付贷款：
balance = 999999
annualInterestRate = .18
monthlyInterestRate = annualInterestRate/12
balanceCOPY = balance
#Bisection search parameters
lo = balance/12
hi = (balance*(1+monthlyInterestRate**12))/12
epsilon = .01
guess = (lo + hi)/2
while True:
for month in range(1,13):
balance = balance - guess
balance = balance + (monthlyInterestRate*balance)
if balance > 0 and balance > epsilon:
lo = guess
balance = balanceCOPY
elif balance < 0 and balance < -epsilon:
hi = guess
balance = balanceCOPY
else:
print('Lowest payment: ',str(round(guess,2)))
break
guess = (lo + hi)/2
但是，我似乎陷入某种无限循环，我的guess变量没有被更新。如何突破无限循环并更新guess变量？
问题出在我的数学上。我打算说
hi = (balance*(1+monthlyInterestRate)**12)/12
感谢所有人的帮助！
答案 0 :(得分：6)
首先，如果您正在进行MITx练习并完成之前的测试（只是在猜测中增加10），那么您只需要迈出一小步。只需要对条件进行一些调整并检查年度结果。
关于二分法搜索我会尝试澄清这个概念。你总会有两个肢体，最小值和最大值。而且总是会在四肢中间开始猜测。
在第一次猜测之后，您需要根据年度结果调整四肢。如果在一年之后支付最低限度的饮料，女孩，程序书籍和其他你没有支付总余额的东西，你肯定需要增加最低限度。否则，例如，如果您在第10个月支付总余额，那么明年你需要多喝酒并结识新女孩！开玩笑......你需要减少最低限度。这是在完成一年的硬支付后您需要进行的检查
在练习中，我们有：
第一个猜测是（最小+最大）/ 2我称之为guessMinimum：
guessMinimum = (minimum + maximum)/2
所以你将开始使用第一个猜测（guessMinimum）。一年后，你会检查剩余的。 如果遗骸是负数，则表示您已经支付了太多。你需要减少每月付款。另外，如果一个月后剩余是积极的（例如，超过你的精确度（例如0.10））你需要减少每月付款，好吗？！
试图设计思路......
+------------------------------------------------+
| /\ /\ /\ |
| \/------------------\/-------------------\/ |
|MINIMUM guess MAXIMUM|
| Minimum |
+------------------------------------------------+
如果一年后，“保持”是负面的（例如）。意味着'guessMinimum'非常多！你需要......不是你，程序!!程序需要调整它，降低最小值......
+---------------------------------------------------+
| Got negative 'remain' |
| ++ |
| /\ || /\ /\ |
| \/-------------||---\/-------------------\/ |
| MINIMUM || guess MAXIMUM |
| ++ Minimum-, |
| ', |
| `. |
| `., |
| ', |
| ', |
| `. |
| ` |
| /\ /\ /\ |
| \/------------------\/-------------------\/ |
| MINIMUM guess MAXIMUM |
+---------------------------------------------------+
对不起伙计们。我试图插入图像，但作为新成员。我不能。需要至少10个声望....帮助我!!!!使用角色的工作太多!!!!
并且CODE需要做这项艰苦的工作来调整最小值，直到“保持”是可接受的（在你的精度，epsilon，或任何字母或变量之内或者......好吧。）
在理解了概念和图纸之后..让我们检查一下代码。
balance = 999999;
annualInterestRate = 0.18
monthlyInterestRate = annualInterestRate / 12
minimum = balance / 12
maximum = (balance * (1 + monthlyInterestRate)**12) / 12.0
guessMinimum = (minimum + maximum)/2
remain = balance #if you payed nothin, the remain is the balance!!!!
precision = 0.10 #you choose....
while (remain >= precision):
guessMinimum = (minimum + maximum)/2
for i in range (1,13):
newBalance = remain - guessMinimum
monthInterest = annualInterestRate/12*newBalance
remain = newBalance+monthInterest
# after one month, the CODE need to check about the remain
if (remain < 0): #paying too much.... need to decrease the value
maximum = guessMinimum #remember my beautiful draw above!!
remain = balance # reset the remain to start again!!
elif (remain > precision): #paying less .... need to increase the value
minimum = guessMinimum
remain = balance # reset the remain to start again!!
print "Lowest Payment: %.2f" %(guessMinimum)
就是这样。
答案 1 :(得分：5)
我认为这个解决方案应该有效，
balance = 999999
annualInterestRate = 0.18
monthlyInterestRate = annualInterestRate / 12
lowerBound = balance / 12
upperBound = (balance * (1 + annualInterestRate / 12) ** 12) / 12
originalBalance = balance
lowestBalance = 0.01 # Error margin e.g. $0.01
# Keep testing new payment values until the balance is +/- lowestBalance
while abs(balance) > lowestBalance:
# Reset the value of balance to its original value
balance = originalBalance
# Calculate a new monthly payment value from the bounds
payment = (upperBound - lowerBound) / 2 + lowerBound
# Test if this payment value is sufficient to pay off the entire balance in 12 months
for month in range(12):
balance -= payment
balance *= 1 + monthlyInterestRate
# Reset bounds based on the final value of balance
if balance > 0:
# If the balance is too big, need higher payment so we increase the lower bound
lowerBound = payment
else:
# If the balance is too small, we need a lower payment, so we decrease the upper bound
upperBound = payment
# When the while loop terminates, we know we have our answer!
print "Lowest Payment:", round(payment, 2)
答案 2 :(得分：3)
要弄清楚这样的错误，一个好方法就是添加一些打印，例如，我在代码中添加了以下内容：
print(balance, lo, hi, guess)
然后看看会发生什么，你可以弄清楚发生了什么。事实证明：
hi = (balance*(1+monthlyInterestRate**12))/12
计算上限太低。也许你的意思是：
hi = (balance*(1+monthlyInterestRate*12))/12
答案 3 :(得分：3)
我将您的代码更改为：
balance = 999999
annualInterestRate = .18
monthlyInterestRate = annualInterestRate / 12
balanceCOPY = balance
#Bisection search parameters
low = balance / 12
high = (balance * (1 + monthlyInterestRate ** 12)) / 12
epsilon = .01
print "starting high and low guesses"
print "high: %s" % high
print "Low: %s" % low
print "\n"
guess = (low + high) / 2
for i in range(5):
print "Type of balance: %s" % type(balance)
print "Balance is: %s" % balance
print "Low: %s" % low
print "High: %s" % high
print "Guess: %s" % guess
print "monthly interest %s" % (monthlyInterestRate * balance)
for month in range(1, 13):
balance -= guess
balance += monthlyInterestRate * balance
print "balance after %s" % balance
if balance > 0 and balance > epsilon:
print "Change low"
low = guess
balance = balanceCOPY
elif balance < 0 and balance > -epsilon:
high = guess
balance = balanceCOPY
else:
print('Lowest payment: ', str(round(guess, 2)))
break
guess = (low + high) / 2
print "\n"
几点说明： 我将“hi”和“lo”改为“high”和“low”。最好不截断变量名，因为截断的变量名不太可读。
我添加了显示各种变量值的调试语句。
以下是运行上述内容的结果：
starting high and low guesses
high: 83333.25
Low: 83333
Type of balance: <type 'int'>
Balance is: 999999
Low: 83333
High: 83333.25
Guess: 83333.125
monthly interest 14999.985
balance after 92550.599997
Change low
Type of balance: <type 'int'>
Balance is: 999999
Low: 83333.125
High: 83333.25
Guess: 83333.1875
monthly interest 14999.985
balance after 92549.7726951
Change low
Type of balance: <type 'int'>
Balance is: 999999
Low: 83333.1875
High: 83333.25
Guess: 83333.21875
monthly interest 14999.985
balance after 92549.3590442
Change low
Type of balance: <type 'int'>
Balance is: 999999
Low: 83333.21875
High: 83333.25
Guess: 83333.234375
monthly interest 14999.985
balance after 92549.1522187
Change low
Type of balance: <type 'int'>
Balance is: 999999
Low: 83333.234375
High: 83333.25
Guess: 83333.2421875
monthly interest 14999.985
balance after 92549.048806
Change low
通过此，您可以看到您的低值正在收敛到您的高价值。换句话说，您的初始高值不够高。一旦它们具有相同的价值，循环将永远不会改变任何东西，并将永远持续下去。
我认为这一行：
elif balance < 0 and balance < -epsilon:
应为：
elif balance < 0 and balance > -epsilon:
因为我认为您需要在0和-epsilon之间取得平衡而不是-epsilon
另外，正如@WinstonEwert所说：
hi = (balance*(1+monthlyInterestRate**12))/12
应该是
hi = (balance*(1+monthlyInterestRate)**12)/12
答案 4 :(得分：1)
以下是我提出的有效方法。我通常会为这些类型的东西编写函数，以便它可以重复使用，即使我没有这样做，因为它让我习惯了这样做，并给了我一些额外的练习。
balance = 320000
annualInterestRate=0.2
monthlyIntRate= annualInterestRate/12.0
getpayment=True
ranonce=False
MoMin = balance/12
MoMax = (balance*(1+monthlyIntRate)**12)/12.0
MoPayment = (MoMin+MoMax)/2
NewBal=0
#Create a function to run 12 months of payments, and then create a loop to re-run the function if the Ending Balance is not close enough to 0.
def CCPayment(balance, monthlyIntRate, MoPay):
global NewBal
Month = 1 #Month begins at 1
while Month <= 12:
balance = (balance - MoPay)
balance = balance + (monthlyIntRate * balance)
NewBal=balance #sets the var NewBal to be used globally
Month += 1
if (balance < .02) and (balance > -0.02) : #cannot evaluate to '0' as you are evaluating a float and it will 'inf loop'. Must evaluate it to a number 'close enough'
return MoPayment
else:
return False
while getpayment==True:
if CCPayment(balance, monthlyIntRate, MoPayment):
getpayment=False
print "Lowest Payment: ", round(CCPayment(balance, monthlyIntRate, MoPayment),2)
else:
if NewBal < 0.01: #paid too much! Lower the max payment and rerun function
if ranonce == True: #Bool check to avoid resetting the Min/Max values before running it once
MoMax=MoPayment #sets the Max payment to the current monthly payment
MoPayment=(MoMin+MoMax)/2 #sets the Monthly payment to average the Min/Max payments
ranonce = True
CCPayment(balance, monthlyIntRate, MoPayment)
elif NewBal > 0.01: #didn't pay enough! Raise min payment and rerun function
if ranonce == True: #Bool check to avoid resetting the Min/Max values before running it once
MoMin=MoPayment #sets the Min payment to the current monthly payment
MoPayment=(MoMin+MoMax)/2 #sets the Monthly payment to average the Min/Max payments
ranonce = True
CCPayment(balance, monthlyIntRate, MoPayment)
答案 5 :(得分：0)
monthlyInterestRate = annualInterestRate / 12
monthlyPaymentLowerBound = balance / 12
monthlyPaymentUpperBound = (balance * (1 + monthlyInterestRate)**12) / 12
epsilon = 0.01
while True:
unpaidBalance = balance
minimumFixedMonthlyPayment = (monthlyPaymentLowerBound + monthlyPaymentUpperBound) / 2
for i in range(12):
if i == 0:
unpaidBalance = balance - minimumFixedMonthlyPayment
else:
updatedBalance = unpaidBalance + (monthlyInterestRate * unpaidBalance)
unpaidBalance = updatedBalance - minimumFixedMonthlyPayment
if unpaidBalance > 0 and abs(unpaidBalance) > epsilon:
monthlyPaymentLowerBound = minimumFixedMonthlyPayment
minimumFixedMonthlyPayment = (minimumFixedMonthlyPayment + monthlyPaymentUpperBound) / 2
continue
elif unpaidBalance < 0 and abs(unpaidBalance) > epsilon:
monthlyPaymentUpperBound = minimumFixedMonthlyPayment
minimumFixedMonthlyPayment = (monthlyPaymentLowerBound + minimumFixedMonthlyPayment) / 2
else:
break
print(round(minimumFixedMonthlyPayment, 2))
答案 6 :(得分：0)
Python 3回答：
balance = 999999
annualInterestRate = .18
monthlyInterestRate = annualInterestRate / 12.0
lowBound = balance / 12
hiBound = (balance*(1+monthlyInterestRate)**12)/12.0
epsilon = 0.01
newBalance = balance
while abs(newBalance) > epsilon:
minPay = (lowBound + hiBound) / 2
newBalance = balance
for month in range(12):
monthlyUnpaid = newBalance - minPay
newBalance = monthlyUnpaid + (monthlyInterestRate * monthlyUnpaid)
if newBalance > epsilon:
lowBound = minPay
elif newBalance < epsilon:
hiBound = minPay
print ("Lowest Payment: ", round(minPay, 2))
答案 7 :(得分：0)
balance = balance
annualInterestRate = annualInterestRate
monthlyInterestRate = annualInterestRate/12
balanceCOPY = balance
#Bisection search parameters
lo = balance/12
hi = (balance*(1+monthlyInterestRate)**12)/12
epsilon = .01
guess = (lo + hi)/2
while True:
for month in range(1,13):
balance = balance - guess
balance = balance + (monthlyInterestRate*balance)
if balance > 0 and balance > epsilon:
lo = guess
balance = balanceCOPY
elif balance < 0 and balance < -epsilon:
hi = guess
balance = balanceCOPY
else:
print('Lowest payment: ',str(round(guess,2)))
break
guess = (lo + hi)/2