Python购房首付储蓄计算程序死循环问题求助

问题背景 #

我正在完成MIT购房首付储蓄计算练习题，需求如下：

• 梦想房屋总价为total_cost
• 首付比例portion_down_payment=0.25（25%）
• 当前储蓄current_savings初始为0美元
• 储蓄年回报率r=0.04，每月末收益为current_savings*r/12
• 年薪为annual_salary
• 每月储蓄工资比例portion_saved（小数形式，如10%为0.1）
• 每月末储蓄额增加投资收益+每月工资的对应比例（年薪/12）

程序需获取用户输入的annual_salary、portion_saved、total_cost，输出所需月数。测试用例：

1. 输入年薪120000、储蓄比例0.1、房价1000000，输出183个月
2. 输入年薪80000、储蓄比例0.15、房价500000，输出105个月

我的代码如下：

#variables and inputs:
current_savings=0
r=0.04
additional_current_savings=current_savings*r/12
annual_salary=float(input("Enter your annual salary: "))
portion_saved=float(input("Enter the percent of your salary to save, as a decimal: "))
total_cost=float(input("Enter the cost of your dream home: "))
portion_down_payment=0.25*total_cost
monthly_salary=annual_salary / 12
new_total_saving=0
number_of_months=0
total_saving=portion_saved+current_savings+additional_current_savings
#a program to calculate how many months it will take someone to save up enough money for a down payment:
while new_total_saving != portion_down_payment :
 new_total_saving += total_saving
 number_of_months += 1
print(f"Number of months: {number_of_months}")

运行时终端持续运行无输出，请求排查原因并解决。

问题排查与解决 #

核心问题分析 #

1. 死循环触发原因：
   • 循环条件使用new_total_saving != portion_down_payment，但浮点数运算存在精度误差，new_total_saving几乎不可能完全等于portion_down_payment，导致循环无限执行。
   • 每月储蓄额计算逻辑完全错误：total_saving=portion_saved+current_savings+additional_current_savings没有按照题目要求计算，正确逻辑应为当月工资储蓄部分 + 当前储蓄的月收益，且current_savings需要每月更新。
2. 逻辑错误细节：
   • additional_current_savings初始计算为0后就不再更新，忽略了每月储蓄增长后的收益变化。
   • total_saving直接把储蓄比例数值加进去，而非计算每月工资*储蓄比例。

修正后的代码 #

current_savings = 0.0
r = 0.04
annual_salary = float(input("Enter your annual salary: "))
portion_saved = float(input("Enter the percent of your salary to save, as a decimal: "))
total_cost = float(input("Enter the cost of your dream home: "))

portion_down_payment = 0.25 * total_cost
monthly_salary = annual_salary / 12
number_of_months = 0

# 循环条件改为储蓄额大于等于首付，避免浮点数精度问题
while current_savings < portion_down_payment:
    # 计算当月投资收益
    investment_income = current_savings * r / 12
    # 当月新增储蓄：工资储蓄部分 + 投资收益
    current_savings += portion_saved * monthly_salary + investment_income
    number_of_months += 1

print(f"Number of months: {number_of_months}")

修正说明 #

• 循环条件改为current_savings < portion_down_payment，只要储蓄额足够覆盖首付就停止循环，规避浮点数精确匹配的问题。
• 每月更新current_savings，包含当月工资储蓄和投资收益，严格符合题目中每月末更新储蓄的规则。
• 移除冗余变量，简化代码逻辑，提升可读性。

内容的提问来源于stack exchange，提问作者Oussama El Manar