#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))