Factor
(math/factor.hpp)

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• Last update: 2022-12-02 07:43:56+00:00
• Include: #include "math/factor.hpp"

Source: KACTL

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• test/factor.test.cpp

Code

#ifndef FACTOR_HPP
#define FACTOR_HPP

#include <algorithm>
#include <numeric>
#include <vector>

unsigned long long modmul(unsigned long long a, unsigned long long b,
                          unsigned long long M) {
    long long ret =
        a * b - M * static_cast<unsigned long long>(1.L / M * a * b);
    return ret + M * (ret < 0) - M * (ret >= static_cast<long long>(M));
}

unsigned long long modpow(unsigned long long b, unsigned long long e,
                          unsigned long long mod) {
    unsigned long long ans = 1;
    for (; e; b = modmul(b, b, mod), e /= 2) {
        if (e & 1) {
            ans = modmul(ans, b, mod);
        }
    }
    return ans;
}

bool is_prime(unsigned long long n) {
    if (n < 2 || n % 6 % 4 != 1) {
        return (n | 1) == 3;
    }
    unsigned long long A[] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022},
                       s = __builtin_ctzll(n - 1), d = n >> s;
    for (unsigned long long a : A) {
        unsigned long long p = modpow(a % n, d, n), i = s;
        while (p != 1 && p != n - 1 && a % n && i--) {
            p = modmul(p, p, n);
        }
        if (p != n - 1 && i != s) {
            return 0;
        }
    }
    return 1;
}

unsigned long long pollard(unsigned long long n) {
    auto f = [n](unsigned long long x) { return modmul(x, x, n) + 1; };
    unsigned long long x = 0, y = 0, t = 30, prd = 2, i = 1, q;
    while (t++ % 40 || std::gcd(prd, n) == 1) {
        if (x == y) {
            x = ++i, y = f(x);
        }
        if ((q = modmul(prd, std::max(x, y) - std::min(x, y), n))) {
            prd = q;
        }
        x = f(x), y = f(f(y));
    }
    return std::gcd(prd, n);
}

std::vector<unsigned long long> factor(unsigned long long n) {
    if (n == 1) {
        return {};
    }
    if (is_prime(n)) {
        return {n};
    }
    unsigned long long x = pollard(n);
    auto l = factor(x), r = factor(n / x);
    l.insert(l.end(), r.begin(), r.end());
    return l;
}

unsigned long long euler_phi(unsigned long long n) {
    auto f = factor(n);
    std::sort(f.begin(), f.end());
    f.erase(std::unique(f.begin(), f.end()), f.end());
    for (auto p : f) {
        n -= n / p;
    }
    return n;
}

#endif // FACTOR_HPP

#line 1 "math/factor.hpp"



#include <algorithm>
#include <numeric>
#include <vector>

unsigned long long modmul(unsigned long long a, unsigned long long b,
                          unsigned long long M) {
    long long ret =
        a * b - M * static_cast<unsigned long long>(1.L / M * a * b);
    return ret + M * (ret < 0) - M * (ret >= static_cast<long long>(M));
}

unsigned long long modpow(unsigned long long b, unsigned long long e,
                          unsigned long long mod) {
    unsigned long long ans = 1;
    for (; e; b = modmul(b, b, mod), e /= 2) {
        if (e & 1) {
            ans = modmul(ans, b, mod);
        }
    }
    return ans;
}

bool is_prime(unsigned long long n) {
    if (n < 2 || n % 6 % 4 != 1) {
        return (n | 1) == 3;
    }
    unsigned long long A[] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022},
                       s = __builtin_ctzll(n - 1), d = n >> s;
    for (unsigned long long a : A) {
        unsigned long long p = modpow(a % n, d, n), i = s;
        while (p != 1 && p != n - 1 && a % n && i--) {
            p = modmul(p, p, n);
        }
        if (p != n - 1 && i != s) {
            return 0;
        }
    }
    return 1;
}

unsigned long long pollard(unsigned long long n) {
    auto f = [n](unsigned long long x) { return modmul(x, x, n) + 1; };
    unsigned long long x = 0, y = 0, t = 30, prd = 2, i = 1, q;
    while (t++ % 40 || std::gcd(prd, n) == 1) {
        if (x == y) {
            x = ++i, y = f(x);
        }
        if ((q = modmul(prd, std::max(x, y) - std::min(x, y), n))) {
            prd = q;
        }
        x = f(x), y = f(f(y));
    }
    return std::gcd(prd, n);
}

std::vector<unsigned long long> factor(unsigned long long n) {
    if (n == 1) {
        return {};
    }
    if (is_prime(n)) {
        return {n};
    }
    unsigned long long x = pollard(n);
    auto l = factor(x), r = factor(n / x);
    l.insert(l.end(), r.begin(), r.end());
    return l;
}

unsigned long long euler_phi(unsigned long long n) {
    auto f = factor(n);
    std::sort(f.begin(), f.end());
    f.erase(std::unique(f.begin(), f.end()), f.end());
    for (auto p : f) {
        n -= n / p;
    }
    return n;
}

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