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
