test/yosupo_factorize.test.cpp

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• Last update: 2026-03-22 19:39:35+09:00
• Problem: https://judge.yosupo.jp/problem/factorize

Depends on

• Miller-Rabin素数判定 (math/prime/miller_rabin.cpp)
• 素因数分解(Pollard Rho) (math/prime/primefactor_ll.cpp)
• 高速入出力(Fast IO) (util/fastio.cpp)

Code

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

#include <algorithm>
#include <cstdint>
#include <numeric>
#include <random>
#include <vector>
using namespace std;
using ll = long long;
using uint = unsigned;
using ull = unsigned long long;

#include <cstdio>
#include <cstring>
#include <string>
#include <type_traits>

#include "../util/fastio.cpp"
#include "../math/prime/primefactor_ll.cpp"

int main() {
    Scanner in;
    Printer out;
    int q;
    in.read(q);
    while (q--) {
        ull a;
        in.read(a);
        auto fac = prime_factor(a);
        out.print((int)fac.size());
        if (fac.empty()) out.println();
        else {
            out.print(' ');
            out.println(fac);
        }
    }
    return 0;
}

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

#include <algorithm>
#include <cstdint>
#include <numeric>
#include <random>
#include <vector>
using namespace std;
using ll = long long;
using uint = unsigned;
using ull = unsigned long long;

#include <cstdio>
#include <cstring>
#include <string>
#include <type_traits>

#line 1 "util/fastio.cpp"
using namespace std;

extern "C" int fileno(FILE *);
extern "C" int isatty(int);

template<class T, class = void>
struct is_fastio_range : false_type {};

template<class T>
struct is_fastio_range<T, void_t<decltype(declval<T &>().begin()), decltype(declval<T &>().end())>> : true_type {};

template<class T, class = void>
struct has_fastio_value : false_type {};

template<class T>
struct has_fastio_value<T, void_t<decltype(declval<const T &>().value())>> : true_type {};

struct FastIoDigitTable {
    char num[40000];

    constexpr FastIoDigitTable() : num() {
        for (int i = 0; i < 10000; ++i) {
            int x = i;
            for (int j = 3; j >= 0; --j) {
                num[i * 4 + j] = char('0' + x % 10);
                x /= 10;
            }
        }
    }
};

struct Scanner {
    static constexpr int BUFSIZE = 1 << 17;
    static constexpr int OFFSET = 64;
    char buf[BUFSIZE + 1];
    int idx, size;
    bool interactive;

    Scanner() : idx(0), size(0), interactive(isatty(fileno(stdin))) {}

    inline void load() {
        int len = size - idx;
        memmove(buf, buf + idx, len);
        if (interactive) {
            if (fgets(buf + len, BUFSIZE + 1 - len, stdin)) size = len + (int)strlen(buf + len);
            else size = len;
        } else {
            size = len + (int)fread(buf + len, 1, BUFSIZE - len, stdin);
        }
        idx = 0;
        buf[size] = 0;
    }

    inline void ensure() {
        if (idx + OFFSET > size) load();
    }

    inline void ensure_interactive() {
        if (idx == size) load();
    }

    inline char skip() {
        if (interactive) {
            ensure_interactive();
            while (buf[idx] && buf[idx] <= ' ') {
                ++idx;
                ensure_interactive();
            }
            return buf[idx++];
        }
        ensure();
        while (buf[idx] && buf[idx] <= ' ') {
            ++idx;
            ensure();
        }
        return buf[idx++];
    }

    template<class T, typename enable_if<is_integral<T>::value, int>::type = 0>
    void read(T &x) {
        if (interactive) {
            char c = skip();
            bool neg = false;
            if constexpr (is_signed<T>::value) {
                if (c == '-') {
                    neg = true;
                    ensure_interactive();
                    c = buf[idx++];
                }
            }
            x = 0;
            while (c >= '0') {
                x = x * 10 + (c & 15);
                ensure_interactive();
                c = buf[idx++];
            }
            if constexpr (is_signed<T>::value) {
                if (neg) x = -x;
            }
            return;
        }
        char c = skip();
        bool neg = false;
        if constexpr (is_signed<T>::value) {
            if (c == '-') {
                neg = true;
                c = buf[idx++];
            }
        }
        x = 0;
        while (c >= '0') {
            x = x * 10 + (c & 15);
            c = buf[idx++];
        }
        if constexpr (is_signed<T>::value) {
            if (neg) x = -x;
        }
    }

    template<class T, typename enable_if<!is_integral<T>::value && !is_fastio_range<T>::value && !is_same<typename decay<T>::type, string>::value && has_fastio_value<T>::value, int>::type = 0>
    void read(T &x) {
        long long v;
        read(v);
        x = T(v);
    }

    template<class Head, class Next, class... Tail>
    void read(Head &head, Next &next, Tail &...tail) {
        read(head);
        read(next, tail...);
    }

    template<class T, class U>
    void read(pair<T, U> &p) {
        read(p.first, p.second);
    }

    template<class T, typename enable_if<is_fastio_range<T>::value && !is_same<typename decay<T>::type, string>::value, int>::type = 0>
    void read(T &a) {
        for (auto &x : a) read(x);
    }

    void read(char &c) {
        c = skip();
    }

    void read(string &s) {
        s.clear();
        if (interactive) {
            ensure_interactive();
            while (buf[idx] && buf[idx] <= ' ') {
                ++idx;
                ensure_interactive();
            }
            while (true) {
                int start = idx;
                while (idx < size && buf[idx] > ' ') ++idx;
                s.append(buf + start, idx - start);
                if (idx < size) break;
                load();
                if (size == 0) break;
            }
            if (idx < size) ++idx;
            return;
        }
        ensure();
        while (buf[idx] && buf[idx] <= ' ') {
            ++idx;
            ensure();
        }
        while (true) {
            int start = idx;
            while (idx < size && buf[idx] > ' ') ++idx;
            s.append(buf + start, idx - start);
            if (idx < size) break;
            load();
        }
        if (idx < size) ++idx;
    }
};

struct Printer {
    static constexpr int BUFSIZE = 1 << 17;
    static constexpr int OFFSET = 64;
    char buf[BUFSIZE];
    int idx;
    bool interactive;
    inline static constexpr FastIoDigitTable table{};

    Printer() : idx(0), interactive(isatty(fileno(stdout))) {}
    ~Printer() { flush(); }

    inline void flush() {
        if (idx) {
            fwrite(buf, 1, idx, stdout);
            idx = 0;
        }
    }

    inline void pc(char c) {
        if (idx > BUFSIZE - OFFSET) flush();
        buf[idx++] = c;
        if (interactive && c == '\n') flush();
    }

    inline void print_range(const char *s, size_t n) {
        size_t pos = 0;
        while (pos < n) {
            if (idx == BUFSIZE) flush();
            size_t chunk = min(n - pos, (size_t)(BUFSIZE - idx));
            memcpy(buf + idx, s + pos, chunk);
            idx += (int)chunk;
            pos += chunk;
        }
    }

    void print(const char *s) {
        print_range(s, strlen(s));
    }

    void print(const string &s) {
        print_range(s.data(), s.size());
    }

    void print(char c) {
        pc(c);
    }

    void print(bool b) {
        pc(char('0' + (b ? 1 : 0)));
    }

    template<class T, typename enable_if<is_integral<T>::value && !is_same<T, bool>::value, int>::type = 0>
    void print(T x) {
        if (idx > BUFSIZE - 100) flush();
        using U = typename make_unsigned<T>::type;
        U y;
        if constexpr (is_signed<T>::value) {
            if (x < 0) {
                buf[idx++] = '-';
                y = U(0) - static_cast<U>(x);
            } else {
                y = static_cast<U>(x);
            }
        } else {
            y = x;
        }
        if (y == 0) {
            buf[idx++] = '0';
            return;
        }
        static constexpr int TMP_SIZE = sizeof(U) * 10 / 4;
        char tmp[TMP_SIZE];
        int pos = TMP_SIZE;
        while (y >= 10000) {
            pos -= 4;
            memcpy(tmp + pos, table.num + (y % 10000) * 4, 4);
            y /= 10000;
        }
        if (y >= 1000) {
            memcpy(buf + idx, table.num + (y << 2), 4);
            idx += 4;
        } else if (y >= 100) {
            memcpy(buf + idx, table.num + (y << 2) + 1, 3);
            idx += 3;
        } else if (y >= 10) {
            unsigned q = (unsigned(y) * 205) >> 11;
            buf[idx] = char('0' + q);
            buf[idx + 1] = char('0' + (unsigned(y) - q * 10));
            idx += 2;
        } else {
            buf[idx++] = char('0' + y);
        }
        memcpy(buf + idx, tmp + pos, TMP_SIZE - pos);
        idx += TMP_SIZE - pos;
    }

    template<class T, typename enable_if<!is_integral<T>::value && !is_fastio_range<T>::value && !is_same<typename decay<T>::type, string>::value && has_fastio_value<T>::value, int>::type = 0>
    void print(const T &x) {
        print(x.value());
    }

    template<class T, typename enable_if<is_fastio_range<T>::value && !is_same<typename decay<T>::type, string>::value, int>::type = 0>
    void print(const T &a) {
        bool first = true;
        for (auto &&x : a) {
            if (!first) pc(' ');
            first = false;
            print(x);
        }
    }

    template<class T>
    void println(const T &x) {
        print(x);
        pc('\n');
    }

    template<class Head, class... Tail>
    void println(const Head &head, const Tail &...tail) {
        print(head);
        ((pc(' '), print(tail)), ...);
        pc('\n');
    }

    void println() {
        pc('\n');
    }
};

template<class T>
Scanner &operator>>(Scanner &in, T &x) {
    in.read(x);
    return in;
}

template<class T>
Printer &operator<<(Printer &out, const T &x) {
    out.print(x);
    return out;
}

/**
 * @brief 高速入出力(Fast IO)
 */
#line 1 "math/prime/miller_rabin.cpp"
using u128 = __uint128_t;

struct mod64 {
    unsigned long long n;
    static unsigned long long mod, inv, r2;
    mod64() : n(0) {}
    mod64(unsigned long long x) : n(init(x)) {}
    static unsigned long long init(unsigned long long w) {
        return reduce(u128(w) * r2);
    }
    static void set_mod(unsigned long long m) {
        mod = inv = m;
        for (int i = 0; i < 5; ++i) inv *= 2 - inv * m;
        r2 = -u128(m) % m;
    }
    static unsigned long long reduce(u128 x) {
        unsigned long long y =
            static_cast<unsigned long long>(x >> 64)
            - static_cast<unsigned long long>((u128(static_cast<unsigned long long>(x) * inv) * mod) >> 64);
        return (long long)y < 0 ? y + mod : y;
    }
    mod64& operator*=(mod64 x) {
        n = reduce(u128(n) * x.n);
        return *this;
    }
    mod64 operator*(mod64 x) const {
        return mod64(*this) *= x;
    }
    mod64& operator+=(mod64 x) {
        n += x.n - mod;
        if((long long)n < 0) n += mod;
        return *this;
    }
    mod64 operator+(mod64 x) const {
        return mod64(*this) += x;
    }
    unsigned long long val() const {
        return reduce(n);
    }
};

unsigned long long mod64::mod, mod64::inv, mod64::r2;

bool suspect(unsigned long long a, unsigned long long s, unsigned long long d, unsigned long long n){
    if(mod64::mod != n) mod64::set_mod(n);
    mod64 x(1), xx(a), one(1), minusone(n - 1);
    while(d > 0){
        if(d & 1) x *= xx;
        xx *= xx;
        d >>= 1;
    }
    if (x.n == one.n) return true;
    for (unsigned long long r = 0; r < s; ++r) {
        if(x.n == minusone.n) return true;
        x *= x;
    }
    return false;
}

template<class T>
bool miller_rabin(T m){
    unsigned long long n = m;
    if (n <= 1 || (n > 2 && n % 2 == 0)) return false;
    if (n == 2 || n == 3 || n == 5 || n == 7) return true;
    if (n % 3 == 0 || n % 5 == 0 || n % 7 == 0) return false;
    unsigned long long d = n - 1, s = 0;
    while (!(d & 1)) { ++s; d >>= 1; }
    static constexpr unsigned long long small[] = {2, 7, 61};
    static constexpr unsigned long long large[] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022};
    if(n < 4759123141ULL) {
        for (auto p : small) {
            if(p >= n) break;
            if(!suspect(p, s, d, n)) return false;
        }
    } else {
        for (auto p : large) {
            if(p >= n) break;
            if(!suspect(p, s, d, n)) return false;
        }
    }
    return true;
}

/**
 * @brief Miller-Rabin素数判定
 */
#line 2 "math/prime/primefactor_ll.cpp"

template<typename T>
struct ExactDiv {
    T t, i, val;
    ExactDiv() {}
    ExactDiv(T n) : t(T(-1) / n), i(mul_inv(n)) , val(n) {};
    T mul_inv(T n) {
        T x = n;
        for (int i = 0; i < 5; ++i) x *= 2 - n * x;
        return x;
    }
    bool divide(T n) const {
        if(val == 2) return !(n & 1);
        return n * this->i <= this->t;
    }
};

vector<ExactDiv<ull>> get_prime(int n){
    if(n <= 1) return vector<ExactDiv<ull>>();
    vector<bool> is_prime(n+1, true);
    vector<ExactDiv<ull>> prime;
    is_prime[0] = is_prime[1] = false;
    for (int i = 2; i <= n; ++i) {
        if(is_prime[i]) prime.emplace_back(i);
        for (auto &&j : prime){
            ull v = (ull)i * j.val;
            if(v > (ull)n) break;
            is_prime[v] = false;
            if(j.divide(i)) break;
        }
    }
    return prime;
}
const auto primes = get_prime(50000);

mt19937_64 rng(0x8a5cd789635d2dffULL);

template<class T>
T pollard_rho2(T n) {
    ull nn = n;
    if ((nn & 1) == 0) return 2;
    uniform_int_distribution<ull> ra(1, nn - 1);
    mod64::set_mod(nn);
    while(true){
        ull c_ = ra(rng), g = 1, r = 1, m = 500;
        while(c_ == nn - 2) c_ = ra(rng);
        mod64 y(ra(rng)), xx(0), c(c_), ys(0), q(1);
        while(g == 1){
            xx.n = y.n;
            for (ull i = 0; i < r; ++i) {
                y *= y; y += c;
            }
            ull k = 0; g = 1;
            while(k < r && g == 1){
                ull lim = min(m, r - k);
                for (ull i = 0; i < lim; ++i) {
                    ys.n = y.n;
                    y *= y; y += c;
                    ull xxx = xx.val(), yyy = y.val();
                    q *= mod64(xxx > yyy ? xxx - yyy : yyy - xxx);
                }
                g = gcd<ull>(q.val(), nn);
                k += m;
            }
            r *= 2;
        }
        if(g == nn) g = 1;
        while (g == 1){
            ys *= ys; ys += c;
            ull xxx = xx.val(), yyy = ys.val();
            g = gcd<ull>(xxx > yyy ? xxx - yyy : yyy - xxx, nn);
        }
        if (g != nn && miller_rabin(g)) return (T)g;
    }
}

template<class T>
void prime_factor_impl(T n, vector<T> &res, bool trial){
    if(trial) {
        for (auto &&i : primes) {
            while (i.divide(n)){
                res.emplace_back(i.val);
                n /= i.val;
            }
        }
    }
    if(n == 1) return;
    if(miller_rabin(n)) {
        res.emplace_back(n);
        return;
    }
    T x = pollard_rho2(n);
    prime_factor_impl(x, res, false);
    prime_factor_impl(n / x, res, false);
}

template<class T>
vector<T> prime_factor(T n){
    vector<T> res;
    prime_factor_impl(n, res, true);
    sort(res.begin(),res.end());
    return res;
}

/**
 * @brief 素因数分解(Pollard Rho)
 */
#line 20 "test/yosupo_factorize.test.cpp"

int main() {
    Scanner in;
    Printer out;
    int q;
    in.read(q);
    while (q--) {
        ull a;
        in.read(a);
        auto fac = prime_factor(a);
        out.print((int)fac.size());
        if (fac.empty()) out.println();
        else {
            out.print(' ');
            out.println(fac);
        }
    }
    return 0;
}

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