使用二分法计算购房最优储蓄率的Python代码为何出现无限循环？

• 初始年薪未重置：每次二分法测试新储蓄率时，annual_salary已经被上一次测试中的涨薪逻辑修改，不是用户输入的初始值，导致所有后续储蓄时长计算全部错误。
• 内层循环终止条件逻辑错误：原判断current_savings < portion_down_payment or current_savings-100< portion_down_payment等价于只要储蓄小于「首付+100」就会一直累加月数，无上限控制，极易陷入死循环。
• 二分终止条件过于严格：强制要求储蓄时长严格等于目标月数，实际场景中很可能不存在刚好卡着目标月数的储蓄率，会导致二分在两个相邻值之间反复横跳永远无法退出。
• 无边界校验逻辑：没有先判断100%储蓄率的情况下能不能在目标月数内凑够首付，如果连全额储蓄都达不到要求，二分永远找不到结果，直接死循环。

print('what is the cost of your dream home?')
total_cost = float(input())
print('what is your annual salary?')
annual_salary = float(input())
# 保存初始年薪副本，每次测试重置用
initial_annual_salary = annual_salary
portion_down_payment = 0.25 * total_cost
print('enter a semi-annual raise, as a decimal')
semi_annual_raise = float(input())
print('in how many months do you want to buy your house?')
target_months = int(input())

first = 0
last = 10000
steps_in_bisection = 0
# 先做边界校验：100%储蓄率能不能达到要求
test_saving = 0
test_months = 0
test_salary = initial_annual_salary
while test_saving < portion_down_payment and test_months <= target_months:
    test_saving += (1 * (test_salary/12)) + (test_saving * 0.04)/12
    test_months += 1
    if test_months %6 ==0:
        test_salary += semi_annual_raise * test_salary
if test_months > target_months:
    print("即便100%储蓄也无法在目标月数内凑够首付")
    exit()

# 二分搜索主逻辑
while last - first > 1:
    saving_rate = int((first + last)/2)
    current_savings = 0
    number_of_months = 0
    # 每次测试重置年薪为初始值
    current_annual = initial_annual_salary
    while current_savings < portion_down_payment:
        current_savings += ((saving_rate/10000) * (current_annual /12)) + (current_savings * 0.04)/12
        number_of_months += 1
        if number_of_months %6 ==0:
            current_annual += semi_annual_raise * current_annual
    # 调整二分边界
    if number_of_months > target_months:
        first = saving_rate
    else:
        last = saving_rate
    steps_in_bisection +=1

best_rate = last / 100
print(f"best savings rate: {best_rate}%")
print(f"number of bisection steps: {steps_in_bisection}")

内容的提问来源于stack exchange，提问作者abdelrahman moataz