test/math/factor.test.cpp

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• Last update: 2025-09-17 00:10:14+09:00
• Problem: https://judge.yosupo.jp/problem/factorize

Depends on

• Factor (math/factor.hpp)

Code

#define PROBLEM "https://judge.yosupo.jp/problem/factorize"

#include "math/factor.hpp"
#include <bits/stdc++.h>

int main() {
    std::cin.tie(0)->sync_with_stdio(0);
    int Q;
    std::cin >> Q;
    for (auto i = 0; i < Q; ++i) {
        unsigned long long a;
        std::cin >> a;
        auto f = factor(a);
        std::sort(f.begin(), f.end());
        std::cout << f.size() << ' ';
        std::copy(f.begin(), f.end(),
                  std::ostream_iterator<unsigned long long>(std::cout, " "));
        std::cout << '\n';
    }
}

#line 1 "test/math/factor.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/factorize"

#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 * (unsigned long long)(1.L / (long double)M * (long double)a * (long double)b);
    return ret + M * (ret < 0) - M * (ret >= (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) {
    unsigned long long x = 0, y = 0, t = 30, prd = 2, i = 1, q;
    auto f = [&](unsigned long long a) { return modmul(a, a, n) + i; };
    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};
    }
    auto 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;
}


#line 4 "test/math/factor.test.cpp"
#include <bits/stdc++.h>

int main() {
    std::cin.tie(0)->sync_with_stdio(0);
    int Q;
    std::cin >> Q;
    for (auto i = 0; i < Q; ++i) {
        unsigned long long a;
        std::cin >> a;
        auto f = factor(a);
        std::sort(f.begin(), f.end());
        std::cout << f.size() << ' ';
        std::copy(f.begin(), f.end(),
                  std::ostream_iterator<unsigned long long>(std::cout, " "));
        std::cout << '\n';
    }
}

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