Python：找出一个数的两个质因数。 如何让这段代码更有效率？

Question

My current code:

import math
def factorMe(value):
last = int(math.sqrt(value)+1)
for i in range(2,last):
    if value %i ==0:
        return (i,int(value/i))

My code can meet most test case; But if the input is 603091532958059 then the answer will be (24557917, 24557927); But it will take more than 1 second to finish ( Time limit exceeded );

Any suggestion? Thank you!

Answer 1

To speed up your code you could use Fermat's factorization method , as @PM 2Ring told in comments. Try following code

import math
def factorMe(value):
    last = int(math.sqrt(value)+1)
    # check if value is even
    if value % 2 == 0:
        return (2, int(value / 2))
    # value is odd number
    a = int(math.sqrt(value)) + 1
    b2 = int(a * a - value)
    b = int(math.sqrt(b2))
    while b ** 2 != int(b2):
        a += 1
        b2 = a * a - value
        b = int(math.sqrt(b2))
    return (int(a - math.sqrt(b2)), int(a + math.sqrt(b2)))


v = 603091532958059
%timeit r = factorMe(v)
print(r)

100000 loops, best of 3: 2.15 µs per loop
(24557917, 24557927)