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python - 循环函数的输出不正确（For 和 While）

问题描述

对于我的课堂作业，我正在编写代码，该代码使用循环利用 Heron 的方法来查找平方根的估计值，同时还显示迭代和相对变化。

我有以下代码：

# Problem 1.

def square_root_for(a, x0, max_iter = 10, tol=1e-14):  
    
    """ (number, integer, number) -> float

    Return an estimate of the square root of a number using the Heron's method.
        
    >>> square_root_for(5, 5)
    Iteration | Estimate         | Relative Change
    -------------------------------------------------
    1         | 3.00000000000000 | 0.4000000000000000
    2         | 2.33333333333333 | 0.2222222222222222
    3         | 2.23809523809524 | 0.0408163265306123
    4         | 2.23606889564336 | 0.0009053870529653
    5         | 2.23606797749998 | 0.0000004106060359
    6         | 2.23606797749979 | 0.0000000000000842
    7         | 2.23606797749979 | 0.0000000000000000
    2.23606797749979
    """
    
    x = [x0]
    x.append(a/x0)
  
    print('Iteration | Estimate         | Relative Change')
    print('-------------------------------------------------')
         
    
    for i in range(1,max_iter):
       
        change = (abs(x[i] - x[i-1]) / x[i-1])
        if change > tol:
            x.append(1/2 * (x[i] + (a / x[i])))
        else:
            break
        print('{}         | {:.14f} | {:.16f}'.format(i, x[i], change))
    return(x[i])

        
        
    
           
# Don't change or delete the 5 lines of code below.
a = 5
max_iter = 100
tol = 1e-15
x_final = square_root_for(a, a, max_iter, tol)
print('Final estimate using square_root_for is {0}'.format(x_final))

# Problem 2.

def square_root_while(a, x0, tol=1e-14):
    """ (number, number, number) -> float

    Return an estimate of the square root of a number using the Heron's method.
        
    >>> square_root_while(5, 5)
    Iteration | Estimate         | Relative Change
    -------------------------------------------------
    1         | 3.00000000000000 | 0.4000000000000000
    2         | 2.33333333333333 | 0.2222222222222222
    3         | 2.23809523809524 | 0.0408163265306123
    4         | 2.23606889564336 | 0.0009053870529653
    5         | 2.23606797749998 | 0.0000004106060359
    6         | 2.23606797749979 | 0.0000000000000842
    7         | 2.23606797749979 | 0.0000000000000000
    2.23606797749979
    """
    
    x = [x0]
    x.append(a/x0)
  
    print('Iteration | Estimate         | Relative Change')
    print('-------------------------------------------------')
    
    i = 1
    while i < max_iter + 1:
        change = (abs(x[i] - x[i-1]) / x[i-1])
        if change > tol:
            x.append(1/2 * (x[i] + (a / x[i])))

        else:
            break
        print('{}         | {:.14f} | {:.16f}'.format(i, x[i], change))
        i += 1
        
    return x[i]

        

# Don't change or delete the 4 lines of code below.
a = 5
tol = 1e-15
x_final = square_root_while(a, a, tol)
print('Final estimate using square_root_while is {0}'.format(x_final))

问题是我的输出不正确。正确的输出（如文档字符串中所示）将是：

Iteration | Estimate         | Relative Change
    -------------------------------------------------
    1         | 3.00000000000000 | 0.4000000000000000
    2         | 2.33333333333333 | 0.2222222222222222
    3         | 2.23809523809524 | 0.0408163265306123
    4         | 2.23606889564336 | 0.0009053870529653
    5         | 2.23606797749998 | 0.0000004106060359
    6         | 2.23606797749979 | 0.0000000000000842
    7         | 2.23606797749979 | 0.0000000000000000
    2.23606797749979

我的输出是：

Iteration | Estimate         | Relative Change
    -------------------------------------------------
    1         | 1.00000000000000 | 0.8000000000000000
    2         | 3.00000000000000 | 2.0000000000000000
    3         | 2.33333333333333 | 0.2222222222222222
    4         | 2.23809523809524 | 0.0408163265306123
    5         | 2.23606889564336 | 0.0009053870529653
    6         | 2.23606797749998 | 0.0000004106060359
    7         | 2.23606797749979 | 0.0000000000000842
    2.23606797749979

问题出在前两行输出中，但我不知道我做错了什么。也许这与数学有关？一个学生问我的老师一个类似的问题，她说“当你做第一个追加时，它与其他追加有点不同。数学。” 我不确定这是否有帮助。任何提示将不胜感激我非常卡住。

标签： pythonloopsmath

解决方案

一般来说，如果你发现自己猜测代码行的顺序，你应该尝试重写代码——现在，你应该明白每一行的含义，看下面：

def square_root_for(a, first_guess, max_iter=10, tol=1e-14):
    print('Iteration | Estimate         | Relative Change')
    print('-------------------------------------------------')

    # put a and the first guess in a list
    guesses = [a, first_guess]
    # loop for a maximum of max_iter times
    for i in range(1, max_iter):
        # add a new guess to the end of the list
        guesses.append(1 / 2 * (guesses[i] + (a / guesses[i])))
        # compute the relative change between the last guess [-1] and the one before [-2]
        change = abs(guesses[-1] - guesses[-2]) / guesses[-2]
        print('{}         | {:.14f} | {:.16f}'.format(i, guesses[-1], change))
        # stop if the change is at or below tol
        if change <= tol:
            break
    # return the last guess in the list as the result
    return guesses[-1]

这将返回相同的正确结果，但请注意每行执行某项操作实际上更容易理解，因为它更从字面上描述了自己。你几乎不需要评论。

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