algorithm-in-python/math/numberTheory/factor.py

#coding: utf-8
''' mbinary
#######################################################################
# File : factorize.py
# Author: mbinary
# Mail: zhuheqin1@gmail.com
# Blog: https://mbinary.xyz
# Github: https://github.com/mbinary
# Created Time: 2018-12-16  09:36
# Description: factorization, using pollard's rho algorithm and miller-rabin primality test
#######################################################################
'''

from random import randint
from isPrime import isPrime
from gcd import gcd


def factor(n):
    '''pollard's rho algorithm'''
    if n < 1:
        raise Exception('[Error]: {} is less than 1'.format(n))
    if n == 1:
        return []
    if isPrime(n):
        return [n]
    fact = 1
    cycle_size = 2
    x = x_fixed = 2
    c = randint(1, n)
    while fact == 1:
        for i in range(cycle_size):
            if fact > 1:
                break
            x = (x*x+c) % n
            if x == x_fixed:
                c = randint(1, n)
                continue
            fact = gcd(x-x_fixed, n)
        cycle_size *= 2
        x_fixed = x
    return factor(fact)+factor(n//fact)


def fact(n):
    f = 2
    ret = []
    while f*f <= n:
        while not n % f:
            ret.append(f)
            n//f
        f += 1
    if n > 1:
        ret.append(n)
    return ret


if __name__ == '__main__':
    while 1:
        n = int(input('n: '))
        print(factor(n))