# (p-1)-алгоритм полларда, реализация _rho_minus_1_pollard из интернета
import time
from math import gcd
from utils import is_prime

def primes(B):
    primes_list = []
    is_prime = [True] * (B + 1)
    is_prime[0] = is_prime[1] = False
    for p in range(2, B + 1):
        if is_prime[p]:
            primes_list.append(p)
            for i in range(p * p, B + 1, p):
                is_prime[i] = False
    return primes_list

def _rho_minus_1_pollard(n, 
                         B_start=100, 
                         B_step=10, B_max=1000000000000):
    B = B_start
    while B <= B_max:
        a = 2
        for p in primes(B):
            pp = 1
            while pp * p <= B:
                pp *= p
            a = pow(a, pp, n)
            g = gcd(a - 1, n)
            if 1 < g < n:
                return g, B
        B *= B_step
    return None, B_max

def rho_minus_1_pollard(n):
    factors, stack = [], [n]
    while stack:
        current = stack.pop()
        if current == 1: continue
        if is_prime(current):
            factors.append(current)
            continue

        divisor, _ = _rho_minus_1_pollard(current)
        if divisor is None:
            factors.append(current)
            continue

        stack.append(divisor)
        stack.append(current // divisor)

    return sorted(factors)

if __name__ == '__main__':
    start_time = time.time()

    N1 = 13611197472111783959
    N2 = 1191515026104746183243378937330489098579
    N3 = 74048093444435937986114388960912781233885985702403356033834092312625704192350369

    number = N2

    factors = rho_minus_1_pollard(number)
    print(f"Факторизация числа {number}: {factors}")

    elapsed_time = time.time() - start_time
    print(f"Общее время работы программы: {elapsed_time} секунд.")