Project Euler Problem 3 - Largest prime factor

The prime factors of 13195 are 5, 7, 13 and 29.

What is the largest prime factor of the number 600851475143 ?

首先将给定n不断除以2，然后可只考虑奇因子

求出小于sqrt(n)的最大的n的奇因子，然后递归求解

Python代码：

from math import sqrt
from math import trunc
from time import clock

nb = 600851475143

def g(n):
    """ n is odd """ 
    a = trunc(sqrt(n))
    if(a % 2 == 0):
        a -= 1
    while(n % a != 0):
        a -= 2
    if(a == 1):
        return n
    b = g(n/a)
    if(b >= a):
        return b
    return max(g(a), b)
    
def f(n):
    while(n % 2 == 0):
        n /= 2
    if(n == 1):
        return 2
    return g(n)

t = 10
s = clock()
for i in range(t):
    r = f(nb)
e = clock()
print r, (e-s)/t    # 0.06

复杂度？