二分法求平方根（Python实现）

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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

验证一下。

上面的方法，如果 X<1 ，就会有问题。因为 X （X<1）的平方根不在 [0, x] 的范围内。例如，0.25，它的平方根——0.5 不在 [0, 0.25] 的区间内。

那如何求0.25的平方根呢？

只要略微改动上面的代码即可。注意6行和7行的代码。

 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

再检验一下：