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。

二分法求平方根(Python实现)-LMLPHP


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。

二分法求平方根(Python实现)-LMLPHP

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:

二分法求平方根(Python实现)-LMLPHP


如果不知道怎样去调用自定义的方法(模块),可参考http://www.cnblogs.com/memory4young/p/python-import-module.html

05-16 06:58