一种是二分查找的使用
二分法，在很多排序，查找等问题中经常使用
def squareRootBi(x, epsilon):
"""Assume x >= 0 and epsilon > 0
Return y s.t. y*y is within epsilon of x"""
#假设x>=0且ε>0，返回y，使得y*y在x的ε内
assert x >= 0, 'x必须为非负数，而不是' + str(x)
assert epsilon > 0, 'ε必须为正数，而不是' + str(epsilon)
low = 0
high = x
#high = max(x,1)
guess = (low + high)/2.0
ctr = 1
while abs(guess**2 - x) > epsilon and ctr <= 100:
#print 'low:', low, 'high:', high, 'guess:', guess
if guess**2 < x:
low = guess
else:
high = guess
guess = (low + high)/2.0
ctr += 1
assert ctr <=100, '循环计数次数超出范围'
print 'Bi方法，循环数', ctr, '估值', guess
return guess
另外一种，是求切点的值的思路，使用了牛顿迭代法
def squareRootNR(x, epsilon):
"""Assume x >= 0 and epsilon > 0
Return y s.t. y*y is within epsilon of x"""
#假设x>=0且ε>0，返回y，使得y*y在x的ε内
assert x >= 0, 'x必须为非负数，而不是' + str(x)
assert epsilon > 0, 'ε必须为正数，而不是' + str(epsilon)
x = float(x)
guess = x/2.0
#guess = 0.001
diff = guess**2 -x
ctr = 1
while abs(diff) > epsilon and ctr <= 100:
#print '差值:', diff, '猜想值:', guess
guess = guess - diff/(2.0*guess)
diff = guess**2 - x
ctr += 1
assert ctr <=100, '循环计数次数超出范围'
print 'NR方法，循环数', ctr, '估值', guess
return guess
