CP-codes/Math/pollard_rho.cpp at master · hemant2132/CP-codes · GitHub

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/*
    -> Pollard's Rho Algorithm for fast integer factorization
    -> works in O(n^(1/4))
    -> ref: 1. https://cp-algorithms.com/algebra/factorization.html
            2. http://morris821028.github.io/2015/07/11/uva-11476/ (for implementation)
    -> tested on SPOJ/FACT0 (15 digits)
*/

int pollardRho(int n, int c) {
    int x = 2, y = 2, i = 1, k = 2, d;
    while (1) {
        x = (mulmod(x, x, n) + c);
        if (x >= n)
            x -= n;

        d = __gcd(x - y, n);
        if (d > 1)
            return d;

        if (++i == k)
            y = x, k <<= 1;
    }

    return n;
}

void trialDivision(int n, vi &factors) {
    for (int i = 2; i * i <= n; ++i) {
        while (n % i == 0) {
            factors.pb(i);
            n /= i;
        }
    }

    if (n > 1)
        factors.pb(n);
}

void factorize(int n, vi &factors) {
    if (n == 1)
        return;

    if (n < inf) {
        trialDivision(n, factors);
        return;
    }

    if (millerRabin(n)) {
        factors.pb(n);
        return;
    }

    int d = n;
    for (int i = 2; d == n; ++i)
        d = pollardRho(n, i);

    factorize(d, factors);
    factorize(n / d, factors);
}