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:heavy_check_mark: number_theory/test/factorize.test.cpp

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/factorize"
#define FAST_IO
#include "../../number_theory/factorize.hpp"
#include "../../template/fastio.hpp"
#include "../../template/template.hpp"

void solve() {
    u64 n;
    rd.read(n);
    V<u64> ps = factorize(n);
    wr.write(LEN(ps));
    for (i64 p : ps) {
        wr.write(' ');
        wr.write(p);
    }
    wr.writeln();
}

int main() {
    i32 t = 1;
    rd.read(t);
    while (t--) {
        solve();
    }
}
#line 1 "number_theory/test/factorize.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/factorize"
#define FAST_IO
#line 2 "number_theory/factorize.hpp"
#include <algorithm>
#include <vector>
#line 2 "template/random.hpp"
#include <chrono>
#include <random>

#if defined(LOCAL) || defined(FIX_SEED)
std::mt19937_64 mt(123456789);
#else
std::mt19937_64 mt(std::chrono::steady_clock::now().time_since_epoch().count());
#endif

template <typename T>
T uniform(T l, T r) {
    return std::uniform_int_distribution<T>(l, r - 1)(mt);
}
template <typename T>
T uniform(T n) {
    return std::uniform_int_distribution<T>(0, n - 1)(mt);
}
#line 2 "number_theory/primality.hpp"

namespace primality {

using u64 = unsigned long long;
using u128 = __uint128_t;

u64 inv_64(u64 n) {
    u64 r = n;
    for (int i = 0; i < 5; ++i) {
        r *= 2 - n * r;
    }
    return r;
}

// n: odd, < 2^{62}
struct Montgomery64 {
    u64 n, mni, p;
    Montgomery64(u64 n) : n(n), mni(-inv_64(n)), p(-1ULL % n + 1) {}
    u64 mulmr(u64 xr, u64 yr) const {
        u128 z = (u128)xr * yr;
        u64 ret = (z + (u128)((u64)z * mni) * n) >> 64;
        if (ret >= n) {
            ret -= n;
        }
        return ret;
    }
    u64 mr(u64 xr) const {
        u64 ret = (xr + (u128)(xr * mni) * n) >> 64;
        if (ret >= n) {
            ret -= n;
        }
        return ret;
    }
    u64 pow(u64 xr, u64 t) const {
        u64 ret = p;
        while (t) {
            if (t & 1) {
                ret = mulmr(ret, xr);
            }
            xr = mulmr(xr, xr);
            t >>= 1;
        }
        return ret;
    }
};

bool is_prime(u64 n) {
    if (n == 2) {
        return true;
    }
    if (n == 1 || n % 2 == 0) {
        return false;
    }
    u64 s = __builtin_ctzll(n - 1);
    u64 d = (n - 1) >> s;
    u64 base[] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022};
    Montgomery64 mont(n);
    u64 fl = n - mont.p;
    for (u64 b : base) {
        b = mont.mr(b);
        if (!b) {
            continue;
        }
        u64 t = mont.pow(b, d);
        if (t == mont.p) {
            continue;
        }
        u64 i = 0;
        for (; i < s; ++i) {
            if (t == fl) {
                break;
            }
            t = mont.mulmr(t, t);
        }
        if (i == s) {
            return false;
        }
    }
    return true;
}

}  // namespace primality

bool is_prime(unsigned long long n) {
    return primality::is_prime(n);
}
#line 2 "number_theory/montgomery_64.hpp"
#include <cassert>

// mod: odd, < 2^{63}
template <int id>
struct MontgomeryModInt64 {
    using u64 = unsigned long long;
    using u128 = __uint128_t;

    static u64 inv_64(u64 n) {
        u64 r = n;
        for (int i = 0; i < 5; ++i) {
            r *= 2 - n * r;
        }
        return r;
    }

    static u64 mod, neg_inv, sq;
    static void set_mod(u64 m) {
        assert(m % 2 == 1 && m < (1ULL << 63));
        mod = m;
        neg_inv = -inv_64(m);
        sq = -u128(mod) % mod;
    }
    static u64 get_mod() { return mod; }

    static u64 reduce(u128 xr) {
        u64 ret = (xr + u128(u64(xr) * neg_inv) * mod) >> 64;
        if (ret >= mod) {
            ret -= mod;
        }
        return ret;
    }

    using M = MontgomeryModInt64<id>;

    u64 x;
    MontgomeryModInt64() : x(0) {}
    MontgomeryModInt64(u64 _x) : x(reduce(u128(_x) * sq)) {}

    u64 val() const { return reduce(u128(x)); }

    M &operator+=(M rhs) {
        if ((x += rhs.x) >= mod) {
            x -= mod;
        }
        return *this;
    }
    M &operator-=(M rhs) {
        if ((x -= rhs.x) >= mod) {
            x += mod;
        }
        return *this;
    }
    M &operator*=(M rhs) {
        x = reduce(u128(x) * rhs.x);
        return *this;
    }
    M operator+(M rhs) const { return M(*this) += rhs; }
    M operator-(M rhs) const { return M(*this) -= rhs; }
    M operator*(M rhs) const { return M(*this) *= rhs; }

    M pow(u64 t) const {
        M ret(1);
        M self = *this;
        while (t) {
            if (t & 1) {
                ret *= self;
            }
            self *= self;
            t >>= 1;
        }
        return ret;
    }
    M inv() const {
        assert(x);
        return this->pow(mod - 2);
    }

    M &operator/=(M rhs) {
        *this /= rhs.inv();
        return *this;
    }
    M operator/(M rhs) const { return M(*this) /= rhs; }
};

template <int id> unsigned long long MontgomeryModInt64<id>::mod = 1;
template <int id> unsigned long long MontgomeryModInt64<id>::neg_inv = 1;
template <int id> unsigned long long MontgomeryModInt64<id>::sq = 1;
#line 7 "number_theory/factorize.hpp"

namespace factorize_impl {

unsigned long long bgcd(unsigned long long x, unsigned long long y) {
    if (x == 0) {
        return y;
    }
    if (y == 0) {
        return x;
    }
    int n = __builtin_ctzll(x);
    int m = __builtin_ctzll(y);
    x >>= n;
    y >>= m;
    while (x != y) {
        if (x > y) {
            x = (x - y) >> __builtin_ctzll(x - y);
        } else {
            y = (y - x) >> __builtin_ctzll(y - x);
        }
    }
    return x << (n < m ? n : m);
}

template <typename T>
unsigned long long rho(unsigned long long n, unsigned long long c) {
    T cc(c);
    auto f = [cc](T x) -> T {
        return x * x + cc;
    };
    T y(2);
    T x = y;
    T z = y;
    T p(1);
    unsigned long long g = 1;
    constexpr int M = 128;
    for (int r = 1; g == 1; r *= 2) {
        x = y;
        for (int i = 0; i < r && g == 1; i += M) {
            z = y;
            for (int j = 0; j < r - i && j < M; ++j) {
                y = f(y);
                p *= y - x;
            }
            g = bgcd(p.val(), n);
        }
    }
    if (g == n) {
        do {
            z = f(z);
            g = bgcd((z - x).val(), n);
        } while (g == 1);
    }
    return g;
}

unsigned long long find_factor(unsigned long long n) {
    using M = MontgomeryModInt64<20250127>;
    M::set_mod(n);
    while (true) {
        unsigned long long c = uniform(n);
        unsigned long long g = rho<M>(n, c);
        if (g != n) {
            return g;
        }
    }
    return 0;
}

void factor_inner(unsigned long long n, std::vector<unsigned long long> &ps) {
    if (is_prime(n)) {
        ps.push_back(n);
        return;
    }
    if (n % 2 == 0) {
        ps.push_back(2);
        factor_inner(n / 2, ps);
        return;
    }
    unsigned long long m = find_factor(n);
    factor_inner(m, ps);
    factor_inner(n / m, ps);
}

}

std::vector<unsigned long long> factorize(unsigned long long n) {
    if (n <= 1) {
        return std::vector<unsigned long long>();
    }
    std::vector<unsigned long long> ps;
    factorize_impl::factor_inner(n, ps);
    std::sort(ps.begin(), ps.end());
    return ps;
}
#line 1 "template/fastio.hpp"
#include <cstdio>
#include <cstring>
#include <type_traits>
#include <utility>

// unable to read INT_MIN (int), LLONG_MIN (long long)
class Reader {
    FILE *fp;
    static constexpr int BUF = 1 << 18;
    char buf[BUF];
    char *pl, *pr;

    void reread() {
        int wd = pr - pl;
        std::memcpy(buf, pl, wd);
        pl = buf;
        pr = buf + wd;
        pr += std::fread(pr, 1, BUF - wd, fp);
    }

    char skip() {
        char ch = *pl++;
        while (ch <= ' ') {
            ch = *pl++;
        }
        return ch;
    }

    template <typename T>
    void read_unsigned(T &x) {
        if (pr - pl < 64) {
            reread();
        }
        x = 0;
        char ch = skip();
        while ('0' <= ch) {
            x = 10 * x + (0xf & ch);
            ch = *pl++;
        }
    }
    template <typename T>
    void read_signed(T &x) {
        if (pr - pl < 64) {
            reread();
        }
        x = 0;
        bool neg = false;
        char ch = skip();
        if (ch == '-') {
            ch = *pl++;
            neg = true;
        }
        while ('0' <= ch) {
            x = 10 * x + (0xf & ch);
            ch = *pl++;
        }
        if (neg) {
            x = -x;
        }
    }

    void read_single(int &x) { read_signed(x); }
    void read_single(unsigned &x) { read_unsigned(x); }
    void read_single(long &x) { read_signed(x); }
    void read_single(unsigned long &x) { read_signed(x); }
    void read_single(long long &x) { read_signed(x); }
    void read_single(unsigned long long &x) { read_unsigned(x); }

public:
    Reader(FILE *fp) : fp(fp), pl(buf), pr(buf) { reread(); }

    void read() {}
    template <typename Head, typename... Tail>
    void read(Head &head, Tail &...tail) {
        read_single(head);
        read(tail...);
    }
};

struct NumberToString {
    char buf[10000][4];
    constexpr NumberToString() : buf() {
        for (int i = 0; i < 10000; ++i) {
            int n = i;
            for (int j = 3; j >= 0; --j) {
                buf[i][j] = '0' + n % 10;
                n /= 10;
            }
        }
    }
} constexpr number_to_string_precalc;

class Writer {
    FILE *fp;
    static constexpr int BUF = 1 << 18;
    char buf[BUF];
    char *ptr;

    void write_u32(unsigned x) {
        if ((buf + BUF - ptr) < 32) {
            flush();
        }
        static char sml[12];
        int t = 8;
        while (x >= 10000) {
            unsigned n = x % 10000;
            x /= 10000;
            std::memcpy(sml + t, number_to_string_precalc.buf[n], 4);
            t -= 4;
        }
        if (x >= 1000) {
            std::memcpy(ptr, number_to_string_precalc.buf[x], 4);
            ptr += 4;
        } else if (x >= 100) {
            std::memcpy(ptr, number_to_string_precalc.buf[x] + 1, 3);
            ptr += 3;
        } else if (x >= 10) {
            unsigned q = (x * 103) >> 10;
            *ptr++ = q | '0';
            *ptr++ = (x - 10 * q) | '0';
        } else {
            *ptr++ = '0' | x;
        }
        std::memcpy(ptr, sml + (t + 4), 8 - t);
        ptr += 8 - t;
    }

    void write_u64(unsigned long long x) {
        if ((buf + BUF - ptr) < 32) {
            flush();
        }
        if (x >= 10000000000000000) {
            unsigned long long z = x % 100000000;
            x /= 100000000;
            unsigned long long y = x % 100000000;
            x /= 100000000;
            if (x >= 1000) {
                std::memcpy(ptr, number_to_string_precalc.buf[x], 4);
                ptr += 4;
            } else if (x >= 100) {
                std::memcpy(ptr, number_to_string_precalc.buf[x] + 1, 3);
                ptr += 3;
            } else if (x >= 10) {
                unsigned q = (x * 103) >> 10;
                *ptr++ = q | '0';
                *ptr++ = (x - 10 * q) | '0';
            } else {
                *ptr++ = '0' | x;
            }
            std::memcpy(ptr, number_to_string_precalc.buf[y / 10000], 4);
            std::memcpy(ptr + 4, number_to_string_precalc.buf[y % 10000], 4);
            std::memcpy(ptr + 8, number_to_string_precalc.buf[z / 10000], 4);
            std::memcpy(ptr + 12, number_to_string_precalc.buf[z % 10000], 4);
            ptr += 16;
        } else {
            static char sml[12];
            int t = 8;
            while (x >= 10000) {
                unsigned long long n = x % 10000;
                x /= 10000;
                std::memcpy(sml + t, number_to_string_precalc.buf[n], 4);
                t -= 4;
            }
            if (x >= 1000) {
                std::memcpy(ptr, number_to_string_precalc.buf[x], 4);
                ptr += 4;
            } else if (x >= 100) {
                std::memcpy(ptr, number_to_string_precalc.buf[x] + 1, 3);
                ptr += 3;
            } else if (x >= 10) {
                unsigned q = (x * 103) >> 10;
                *ptr++ = q | '0';
                *ptr++ = (x - 10 * q) | '0';
            } else {
                *ptr++ = '0' | x;
            }
            std::memcpy(ptr, sml + (t + 4), 8 - t);
            ptr += 8 - t;
        }
    }

    void write_char(char c) {
        if (ptr == buf + BUF) {
            flush();
        }
        *ptr++ = c;
    }

    template <typename T>
    void write_unsigned(T x) {
        if constexpr (std::is_same_v<T, unsigned long long> ||
                      std::is_same_v<T, unsigned long>) {
            write_u64(x);
        } else {
            write_u32(x);
        }
    }

    template <typename T>
    void write_signed(T x) {
        std::make_unsigned_t<T> y = x;
        if (x < 0) {
            write_char('-');
            y = -y;
        }
        write_unsigned(y);
    }
    
    void write_string(const std::string &s) {
        for (char c : s) {
            write_char(c);
        }
    }

    void write_single(int x) { write_signed(x); }
    void write_single(unsigned x) { write_unsigned(x); }
    void write_single(long x) { write_signed(x); }
    void write_single(unsigned long x) { write_unsigned(x); }
    void write_single(long long x) { write_signed(x); }
    void write_single(unsigned long long x) { write_unsigned(x); }
    void write_single(char c) { write_char(c); }
    void write_single(const std::string &s) { write_string(s); }

public:
    Writer(FILE *fp) : fp(fp), ptr(buf) {}
    ~Writer() { flush(); }

    void flush() {
        std::fwrite(buf, 1, ptr - buf, fp);
        ptr = buf;
    }

    void write() {}
    template <typename Head, typename... Tail>
    void write(Head &&head, Tail &&...tail) {
        write_single(head);
        if (sizeof...(Tail)) {
            write_char(' ');
        }
        write(std::forward<Tail>(tail)...);
    }

    template <typename... T>
    void writeln(T &&...t) {
        write(std::forward<T>(t)...);
        write_char('\n');
    }
};

Reader rd(stdin);
Writer wr(stdout);
#line 2 "template/template.hpp"
#include <bits/stdc++.h>
#define OVERRIDE(a, b, c, d, ...) d
#define REP2(i, n) for (i32 i = 0; i < (i32)(n); ++i)
#define REP3(i, m, n) for (i32 i = (i32)(m); i < (i32)(n); ++i)
#define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)
#define PER2(i, n) for (i32 i = (i32)(n)-1; i >= 0; --i)
#define PER3(i, m, n) for (i32 i = (i32)(n)-1; i >= (i32)(m); --i)
#define PER(...) OVERRIDE(__VA_ARGS__, PER3, PER2)(__VA_ARGS__)
#define ALL(x) begin(x), end(x)
#define LEN(x) (i32)(x.size())
using namespace std;
using u32 = unsigned int;
using u64 = unsigned long long;
using i32 = signed int;
using i64 = signed long long;
using f64 = double;
using f80 = long double;
using pi = pair<i32, i32>;
using pl = pair<i64, i64>;
template <typename T>
using V = vector<T>;
template <typename T>
using VV = V<V<T>>;
template <typename T>
using VVV = V<V<V<T>>>;
template <typename T>
using VVVV = V<V<V<V<T>>>>;
template <typename T>
using PQR = priority_queue<T, V<T>, greater<T>>;
template <typename T>
bool chmin(T &x, const T &y) {
    if (x > y) {
        x = y;
        return true;
    }
    return false;
}
template <typename T>
bool chmax(T &x, const T &y) {
    if (x < y) {
        x = y;
        return true;
    }
    return false;
}
template <typename T>
i32 lob(const V<T> &arr, const T &v) {
    return (i32)(lower_bound(ALL(arr), v) - arr.begin());
}
template <typename T>
i32 upb(const V<T> &arr, const T &v) {
    return (i32)(upper_bound(ALL(arr), v) - arr.begin());
}
template <typename T>
V<i32> argsort(const V<T> &arr) {
    V<i32> ret(arr.size());
    iota(ALL(ret), 0);
    sort(ALL(ret), [&](i32 i, i32 j) -> bool {
        if (arr[i] == arr[j]) {
            return i < j;
        } else {
            return arr[i] < arr[j];
        }
    });
    return ret;
}
#ifdef INT128
using u128 = __uint128_t;
using i128 = __int128_t;
#endif
[[maybe_unused]] constexpr i32 INF = 1000000100;
[[maybe_unused]] constexpr i64 INF64 = 3000000000000000100;
struct SetUpIO {
    SetUpIO() {
#ifdef FAST_IO
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
#endif
        cout << fixed << setprecision(15);
    }
} set_up_io;
void scan(char &x) { cin >> x; }
void scan(u32 &x) { cin >> x; }
void scan(u64 &x) { cin >> x; }
void scan(i32 &x) { cin >> x; }
void scan(i64 &x) { cin >> x; }
void scan(f64 &x) { cin >> x; }
void scan(string &x) { cin >> x; }
template <typename T>
void scan(V<T> &x) {
    for (T &ele : x) {
        scan(ele);
    }
}
void read() {}
template <typename Head, typename... Tail>
void read(Head &head, Tail &...tail) {
    scan(head);
    read(tail...);
}
#define CHAR(...)     \
    char __VA_ARGS__; \
    read(__VA_ARGS__);
#define U32(...)     \
    u32 __VA_ARGS__; \
    read(__VA_ARGS__);
#define U64(...)     \
    u64 __VA_ARGS__; \
    read(__VA_ARGS__);
#define I32(...)     \
    i32 __VA_ARGS__; \
    read(__VA_ARGS__);
#define I64(...)     \
    i64 __VA_ARGS__; \
    read(__VA_ARGS__);
#define F64(...)     \
    f64 __VA_ARGS__; \
    read(__VA_ARGS__);
#define STR(...)        \
    string __VA_ARGS__; \
    read(__VA_ARGS__);
#define VEC(type, name, size) \
    V<type> name(size);       \
    read(name);
#define VVEC(type, name, size1, size2)    \
    VV<type> name(size1, V<type>(size2)); \
    read(name);
#line 6 "number_theory/test/factorize.test.cpp"

void solve() {
    u64 n;
    rd.read(n);
    V<u64> ps = factorize(n);
    wr.write(LEN(ps));
    for (i64 p : ps) {
        wr.write(' ');
        wr.write(p);
    }
    wr.writeln();
}

int main() {
    i32 t = 1;
    rd.read(t);
    while (t--) {
        solve();
    }
}
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