python用二分法求平方根_使用二分法（BisectionMethod）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

验证一下。

>>> sqrtBI(2,0.000001)

>>> 1.41421365738

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。

>>> sqrtBI(0.25,0.000001)

>>> 0.25

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

验证一下：

>>> sqrtBI(0.25,0.000001)

>>> 0.5

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