二分搜索导致无限循环答案

【问题标题】：bisection search causes infinite loop二分搜索导致无限循环
【发布时间】：2017-06-17 21:57:55
【问题描述】：

我想使用二等分搜索来找出每月需要支付多少才能在 12 个月内支付用户输入的全部余额。然而，我写的这段代码进入了无限循环，显示“低、高、月支付无限次”。我不知道哪个代码会导致这个问题，因为条件语句对我来说似乎是正确的。

initialBalance = float(raw_input('Enter the outstanding balance on your           credit card'))
annualInterestrate = float(raw_input('Enter the annual credit card  interest rate as a decimal'))
monthlyInterestrate = round(annualInterestrate, 2)

balance = initialBalance
while balance > 0:
    numMonth = 0
    balance = initialBalance
    low = balance/12.0
    high = (balance*(1+(annualInterestrate/12.0))**12.0)/12.0
    epsilon = 0.01
    monthlyPayment = round((high + low)/2.0, 2)
    while abs(monthlyPayment*12.0 - initialBalance) >= epsilon:
        print 'low =', low, 'high =', high, 'monthlyPayment =', round(monthlyPayment,2)
        if monthlyPayment*12.0 < balance:
            low = monthlyPayment
        else:
            high = monthlyPayment
        monthlyPayment = round((high + low)/2.0, 2)
        while balance > 0 and numMonth < 12:
            numMonth += 1
            interest = monthlyInterestrate * balance
            balance -= monthlyPayment
            balance += interest
balance = round(balance, 2)

print 'RESULT'
print 'monthly payment to pay off debt in 1 year:', monthlyPayment
print 'Number of months needed:', numMonth
print 'Balance:',balance

【问题讨论】：

循环中的第二行：balance = initialBalance。是故意的，还是偶然的？
我想知道通过反复试验找出近似结果的意义何在，而您可以颠倒公式并立即获得确切结果？
balance = initialBalance 是多余的，但我认为这不是导致此问题的原因。这是我正在研究 MIT Open 课件的问题集，它指定使用 bisect search 。
你能添加导致无限循环的输入吗？
这些是输入：Enter the outstanding balance on your credit card: 320000Enter the annual credit card interest rate as a decimal: .2

标签： python

【解决方案1】：

我已将上述问题重新编码为

balance = 120000
annualInterestRate = 0.1
rate=annualInterestRate/12.0
high=(balance * (1 + rate)**12) / 12.0
low=balance/12.0
payment=0
bal_ref=balance
unpaid=balance
N=0
while (abs(unpaid) > .01):
    month=0
    pay=(high+low)/2
    balance=bal_ref
    while(month < 12):
        unpaid=balance-pay
        balance=unpaid + (unpaid * rate)
        month +=1
    if (abs(unpaid) < .01):
        payment=pay
        break
    elif (unpaid > .01):
        low=pay
    elif (unpaid < -.01):
        high=pay
    N+=1
print("Payment:",round(pay,2))

【讨论】：

请解释一下，你改变了什么。