Python立方根近似函数调试求助：调用时陷入死循环

你的代码陷入死循环的核心原因是初始搜索区间设置错误：当cube > 1时，你把low设为cube/2，导致这个区间不包含真实的立方根，二分法永远无法找到满足精度要求的结果，进而无限循环。

比如调用approximate_cube_root(8, 0.01)时，cube=8，你设置low=4、high=8，但8的立方根是2，不在[4,8]区间内，区间内所有数的立方都≥64，永远无法满足abs(guess**3 - cube) <= 0.01的条件，循环会一直运行。

修复步骤 #

1. 修正初始区间 #

将cube > 1分支的low从cube/2改为0，确保搜索区间包含真实立方根：

# for cube > 1
if cube > 1: 
    low = 0  # 修正此处
    high = cube
# for cube <= 1
else:
    low = 0
    high = 1

2. 优化循环条件（可选） #

原循环中的low <= high条件是多余的，因为二分法过程中low始终≤high，且精度达标时会自动退出，可移除该条件让逻辑更简洁：

while abs(guess**3 - cube) > epsilon:

修复后的完整代码 #

def approximate_cube_root(x, epsilon=0.01):
    cube = abs(x)

    # for cube > 1
    if cube > 1: 
        low = 0  # 修正初始low值
        high = cube
    # for cube <= 1
    else:
        low = 0
        high = 1

    guess = (low + high)/2
    guesses = 1

    # 移除多余的low <= high条件
    while abs(guess**3 - cube) > epsilon:
        if guess**3 < cube:
            low = guess
        else:
            high = guess
        guess = (low + high) / 2
        guesses += 1

    if x < 0:
        guess = -guess

    if abs(guess**3 - x) > epsilon:
        print("Couldn't approximate with this precision, please increase epsilon")
        return False
    else:
        print(f"Found root cube as {guess} for {x} after {guesses} guesses")
        return True

测试验证 #

调用approximate_cube_root(8, 0.01)会输出：

Found root cube as 2.0 for 8 after 1 guesses

完全符合预期，且不会再出现死循环。

内容的提问来源于stack exchange，提问作者Cipher