使用二分法（Bisection Method）求平方根。

使用二分法（Bisection Method）求平方根。

def sqrtBI(x, epsilon):
    assert x>0, 'X must be non-nagtive, not ' + str(x)
    assert epsilon > 0, 'epsilon must be postive, not ' + str(epsilon)
  
    low = 0
    high = x
    guess = (low + high)/2.0
    counter = 1
    while (abs(guess ** 2 - x) > epsilon) and (counter <= 100):
        if guess ** 2 < x:
            low = guess
        else :
            high = guess
        guess = (low + high)/2.0
        counter += 1
    return guess

   

驗證一下。

>>> sqrtBI(2,0.000001)

>>> 1.41421365738

上面的方法，如果 X

>>> sqrtBI(0.25,0.000001)

>>> 0.25

那如何求0.25的平方根呢？

只要稍微改動上面的程式碼即可。注意6行和7行的程式碼。

def sqrtBI(x, epsilon):
    assert x>0, 'X must be non-nagtive, not ' + str(x)
    assert epsilon > 0, 'epsilon must be postive, not ' + str(epsilon)
  
    low = 0
    high = max(x, 1.0)
    ## high = x
    guess = (low + high)/2.0
    counter = 1
    while (abs(guess ** 2 - x) > epsilon) and (counter <= 100):
        if guess ** 2 < x:
            low = guess
        else :
            high = guess
        guess = (low + high)/2.0
        counter += 1
    return guess

   

驗證一下：

>>> sqrtBI(0.25,0.000001)

>>> 0.25,0.000001)

>> 0.55

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