对分搜索实现错误以计算理想的储蓄率

问题描述

我一直在尝试在MIT OCW 6.0001（Python的CS简介）PSET 1 C部分中实现对分搜索算法，但是它不起作用。目标是根据用户的输入工资（在我的代码中均定义了固定变量）找到理想的储蓄率，以支付新房的首付。我是二等分搜索的新手，并且在尝试实现此代码方面确实很挣扎。

semi_annual_raise = 0.07
r = 0.04
total_cost = 1000000
down_payment = 0.25 * total_cost
annual_salary = int(input("Enter your annual salary: "))
current_savings = 0
epsilon = 100
low = 0
high = 10000
savings_rate = ((high + low)/2)
num_guesses = 0

#to find: best rate of savings to achieve the money

month = 0

while current_savings <= down_payment - epsilon and month < 37:
    if (month != 0 and month % 6 == 0):
        annual_salary += annual_salary*semi_annual_raise
    current_savings += ((annual_salary/12 *savings_rate/(10**4)) + current_savings*r/12)
    if current_savings < down_payment - epsilon:
        low = savings_rate
    else:
        high = savings_rate
    savings_rate = (high + low)/2
    num_guesses+=1
    month += 1
        
if (month > 36 or current_savings < down_payment - epsilon):
    print("Sorry,can't afford that")
else:
    print("Best savings rate: ",savings_rate/10**4)
    print("Steps in bisection search: ",num_guesses)

理想的输出：

Enter your annual salary: 150000
Best Savings rate: 0.4411
Steps in bisection search: 12

我的代码的输出：

Enter your annual salary: 150000
Best savings rate:  0.9999971389770508
Steps in bisection search:  19

该问题表明，根据我实现对分搜索的方式，我的值可能与理想的输出语句略有不同。但是我很难为正确理解这意味着什么。

解决方法

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