algorithm - Python二分搜索逻辑错误-返回不准确的结果

Question

我正在尝试解决这个 MIT OCW assignment 上的第三个问题.它要求您使用二等分搜索方法计算一年内清算给定债务所需的每月付款。我得到了预期的输出类型，但结果非常不准确。有人可以指出我哪里出错了吗？谢谢

# Problem Set 1("C")
# Time Spent: xx hours

def payInOne_BisectionSearch (balance,annualRate):
    #initialize variables
    initialBalance = balance
    monthlyRate = float(annualRate/12.0)
    minMonthly = float(balance/12.0)
    maxMonthly = float((balance * (1 + monthlyRate ** 12.0 ))/12.0)
    monthlyPayment = float((minMonthly + maxMonthly)/2)
    numMonths = 1
    #define function to check balance after 12 months       
    def balanceAfterYear (balance, monthlyRate, monthlyPayment):
        for numMonths in range (1,13):
            interest = balance * monthlyRate
            balance += interest - monthlyPayment
            if balance <= 0:
                  break
        return [balance, numMonths]

    while maxMonthly - minMonthly >= .005:
        balance = initialBalance
        monthlyPayment = float((minMonthly + maxMonthly)/2)
        if balanceAfterYear(balance,monthlyRate,monthlyPayment)[0] < 0:#paying too much
            maxMonthly = monthlyPayment
        elif balanceAfterYear(balance,monthlyRate,monthlyPayment)[0] > 0:#paying too little
            minMonthly = monthlyPayment
        else:
            break
    print "Monthly payment to pay off debt in 1 year:", round(monthlyPayment,2)
    print "Number of months needed:", round(balanceAfterYear(balance,monthlyRate,monthlyPayment)[1], 2) 
    print "Balance:", round(balanceAfterYear(balance,monthlyRate,monthlyPayment)[0], 2) 

payInOne_BisectionSearch (float(raw_input("Enter the outstanding balance")),float(raw_input("Enter annual rate as a decimal")))


    '''Test Case Expected:
       Enter the outstanding balance on your credit card: 320000
       Enter the annual credit card interest rate as a decimal: .2
       RESULT
       Monthly payment to pay off debt in 1 year: 29643.05
       Number of months needed: 12
       Balance: -0.1

       Test Case Actual Output:
       Enter the outstanding balance320000
       Enter annual rate as a decimal.2
       Monthly payment to pay off debt in 1 year: 26666.67
       Number of months needed: 12.0
       Balance: 39179.43'''

Answer 1

您的问题在于您的初始 maxMonthly 值。我想你真正想要的是将它定义为

maxMonthly = float((balance * ((1 + monthlyRate) ** 12.0 ))/12.0)

否则 monthlyRate**12 的计算结果将接近于零(对于介于 0 和 1 之间的 monthlyRate)，这将使 maxMonthly 的计算结果为 balance/12.0 与您的 minMonthly 相同，这将使最后的 while 循环永远不会开始。