#895144 (C++23) No.8030 ミラー・ラビン素数判定法のテスト

• 問題: No.8030 ミラー・ラビン素数判定法のテスト
• ユーザー: AC2K
• 提出日時: 2023-07-25 10:17:48
• 言語: C++23 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 36 ms / 9,973 ms
• コード長: 15,007 bytes
• コンパイル時間: 955 ms
• コンパイル使用メモリ: 84,828 KB
• 実行使用メモリ: 5,248 KB
• 最終ジャッジ日時: 2024-10-02 04:43:50
• 合計ジャッジ時間: 1,759 ms
• ジャッジサーバーID （参考情報）: judge2 / judge1

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 5,248 KB
testcase_01	AC	2 ms; 5,248 KB
testcase_02	AC	2 ms; 5,248 KB
testcase_03	AC	2 ms; 5,248 KB
testcase_04	AC	26 ms; 5,248 KB
testcase_05	AC	23 ms; 5,248 KB
testcase_06	AC	12 ms; 5,248 KB
testcase_07	AC	12 ms; 5,248 KB
testcase_08	AC	12 ms; 5,248 KB
testcase_09	AC	36 ms; 5,248 KB

ソースコード

#line 1 "test/yuki/No3030.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/3030"
#include <iostream>
#line 2 "src/math/dynamic_modint.hpp"
#include <cassert>
#line 2 "src/internal/barrett.hpp"
#include <cstdint>
namespace kyopro {
namespace internal {

/**
 * @brief Barrett Reduction
 */
class barrett {
    using u32 = uint32_t;
    using u64 = uint64_t;
    using u128 = __uint128_t;

    u32 m;
    u64 im;

public:
    constexpr explicit barrett() : m(0), im(0) {}
    constexpr explicit barrett(u32 m)
        : m(m), im(static_cast<u64>(-1) / m + 1) {}

    constexpr u32 get_mod() const { return m; }
    constexpr u32 reduce(u32 a) const { return mul(1, a); }
    constexpr u32 mul(u32 a, u32 b) const {
        u64 z = (u64)a * b;
        u64 x = (u64)(((u128)(z)*im) >> 64);
        u64 y = x * m;
        return (u32)(z - y + (z < y ? m : 0));
    }
};
};  // namespace internal
};  // namespace kyopro

/**
 * @ref
 * https://github.com/atcoder/ac-library/blob/master/atcoder/internal_math.hpp
 */
#line 3 "src/internal/montgomery.hpp"
#include <limits>
#include <numeric>
#line 5 "src/internal/type_traits.hpp"
#include <typeinfo>
namespace kyopro {
namespace internal {
/*
 * @ref https://qiita.com/kazatsuyu/items/f8c3b304e7f8b35263d8
 */
template <typename... Args> struct first_enabled {};

template <typename T, typename... Args>
struct first_enabled<std::enable_if<true, T>, Args...> {
    using type = T;
};
template <typename T, typename... Args>
struct first_enabled<std::enable_if<false, T>, Args...>
    : first_enabled<Args...> {};
template <typename T, typename... Args> struct first_enabled<T, Args...> {
    using type = T;
};

template <typename... Args>
using first_enabled_t = typename first_enabled<Args...>::type;

template <int dgt> struct int_least {
    static_assert(dgt <= 128);
    using type = first_enabled_t<std::enable_if<dgt <= 8, __int8_t>,
                                 std::enable_if<dgt <= 16, __int16_t>,
                                 std::enable_if<dgt <= 32, __int32_t>,
                                 std::enable_if<dgt <= 64, __int64_t>,
                                 std::enable_if<dgt <= 128, __int128_t> >;
};
template <int dgt> struct uint_least {
    static_assert(dgt <= 128);
    using type = first_enabled_t<std::enable_if<dgt <= 8, __uint8_t>,
                                 std::enable_if<dgt <= 16, __uint16_t>,
                                 std::enable_if<dgt <= 32, __uint32_t>,
                                 std::enable_if<dgt <= 64, __uint64_t>,
                                 std::enable_if<dgt <= 128, __uint128_t> >;
};

template <int dgt> using int_least_t = typename int_least<dgt>::type;
template <int dgt> using uint_least_t = typename uint_least<dgt>::type;

template <typename T>
using double_size_uint_t = uint_least_t<2 * std::numeric_limits<T>::digits>;

template <typename T>
using double_size_int_t = int_least_t<2 * std::numeric_limits<T>::digits>;
};  // namespace internal
};  // namespace kyopro
#line 6 "src/internal/montgomery.hpp"
namespace kyopro {
namespace internal {
using u32 = uint32_t;
using u64 = uint64_t;
using i32 = int32_t;
using i64 = int64_t;
using u128 = __uint128_t;
using i128 = __int128_t;

/**
 * @brief Montgomery Reduction
 */
template <typename T> class Montgomery {
    static constexpr int lg = std::numeric_limits<T>::digits;
    using LargeT = internal::double_size_uint_t<T>;
    T mod, r, r2, minv;
    T inv() {
        T t = 0, res = 0;
        for (int i = 0; i < lg; ++i) {
            if (~t & 1) {
                t += mod;
                res += static_cast<T>(1) << i;
            }
            t >>= 1;
        }
        return res;
    }

public:
    Montgomery() = default;
    constexpr T get_mod() { return mod; }

    void set_mod(T m) {
        assert(m);
        assert(m & 1);

        mod = m;

        r = (-static_cast<T>(mod)) % mod;
        r2 = (-static_cast<LargeT>(mod)) % mod;
        minv = inv();
    }

    T reduce(LargeT x) const {
        u64 res =
            (x + static_cast<LargeT>(static_cast<T>(x) * minv) * mod) >> lg;

        if (res >= mod) res -= mod;
        return res;
    }

    T generate(LargeT x) { return reduce(x * r2); }

    T mul(T x, T y) { return reduce((LargeT)x * y); }
};
};  // namespace internal
};  // namespace kyopro
#line 6 "src/math/dynamic_modint.hpp"
namespace kyopro {
template <int id = -1> class barrett_modint {
    using mint = barrett_modint<id>;
    using u32 = uint32_t;
    using u64 = uint64_t;

    using i32 = int32_t;
    using i64 = int64_t;
    using br = internal::barrett;

    static br brt;
    u32 v;

public:
    static void set_mod(u32 mod_) { brt = br(mod_); }

public:
    explicit constexpr barrett_modint() : v(0) { assert(mod()); }
    explicit constexpr barrett_modint(i64 v_) : v() {
        assert(mod());
        if (v_ < 0) v_ = (i64)mod() - v_;
        v = brt.reduce(v_);
    }

    u32 val() const { return v; }
    static u32 mod() { return brt.get_mod(); }
    static mint raw(u32 v) {
        mint x;
        x.v = v;
        return x;
    }

    constexpr mint& operator++() {
        ++v;
        if (v == mod()) v = 0;
        return (*this);
    }
    constexpr mint& operator--() {
        if (v == 0) v = mod();
        --v;
        return (*this);
    }
    constexpr mint operator++(int) {
        mint res(*this);
        ++(*this);
        return res;
    }
    constexpr mint operator--(int) {
        mint res(*this);
        --(*this);
        return res;
    }

    constexpr mint& operator+=(const mint& r) {
        v += r.v;
        if (v >= mod()) v -= mod();
        return (*this);
    }
    constexpr mint& operator-=(const mint& r) {
        v += mod() - r.v;
        if (v >= mod()) {
            v -= mod();
        }

        return (*this);
    }
    constexpr mint& operator*=(const mint& r) {
        v = brt.mul(v, r.v);
        return (*this);
    }
    constexpr mint& operator/=(const mint& r) { return (*this) *= r.inv(); }

    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }

    constexpr mint& operator+=(i64 r) { return (*this) += mint(r); }
    constexpr mint& operator-=(i64 r) { return (*this) -= mint(r); }
    constexpr mint& operator*=(i64 r) { return (*this) *= mint(r); }

    friend mint operator+(i64 l, const mint& r) { return mint(l) += r; }
    friend mint operator+(const mint& l, i64 r) { return mint(l) += r; }
    friend mint operator-(i64 l, const mint& r) { return mint(l) -= r; }
    friend mint operator-(const mint& l, i64 r) { return mint(l) -= r; }
    friend mint operator*(i64 l, const mint& r) { return mint(l) *= r; }
    friend mint operator*(const mint& l, i64 r) { return mint(l) *= r; }

    constexpr mint operator+() const { return *this; }
    constexpr mint operator-() const { return mint() - *this; }
    friend std::ostream& operator<<(std::ostream& os, const mint& mt) {
        os << mt.val();
        return os;
    }
    friend std::istream& operator>>(std::istream& is, mint& mt) {
        i64 v_;
        is >> v_;
        mt = mint(v_);
        return is;
    }
    template <typename T> mint pow(T e) const {
        mint res(1), base(*this);

        while (e) {
            if (e & 1) {
                res *= base;
            }
            e >>= 1;
            base *= base;
        }
        return res;
    }
    constexpr mint inv() const { return pow(mod() - 2); }
};
};  // namespace kyopro
template <int id>
typename kyopro::barrett_modint<id>::br kyopro::barrett_modint<id>::brt;

namespace kyopro {
template <typename T, int id = -1> class dynamic_modint {
    using LargeT = internal::double_size_uint_t<T>;
    static T _mod;
    static internal::Montgomery<T> mr;

public:
    static void set_mod(T mod_) {
        mr.set_mod(mod_);
        _mod = mod_;
    }

    static T mod() { return _mod; }

private:
    T v;

public:
    dynamic_modint(T v_ = 0) {
        assert(_mod);
        v = mr.generate(v_);
    }
    T val() const { return mr.reduce(v); }

    using mint = dynamic_modint<T, id>;
    mint& operator+=(const mint& r) {
        v += r.v;
        if (v >= mr.get_mod()) {
            v -= mr.get_mod();
        }

        return (*this);
    }

    mint& operator-=(const mint& r) {
        v += mr.get_mod() - r.v;
        if (v >= mr.get_mod) {
            v -= mr.get_mod();
        }

        return (*this);
    }

    mint& operator*=(const mint& r) {
        v = mr.mul(v, r.v);
        return (*this);
    }

    mint operator+(const mint& r) { return mint(*this) += r; }
    mint operator-(const mint& r) { return mint(*this) -= r; }
    mint operator*(const mint& r) { return mint(*this) *= r; }

    mint& operator=(const T& v_) {
        (*this) = mint(v_);
        return (*this);
    }

    friend std::ostream& operator<<(std::ostream& os, const mint& mt) {
        os << mt.val();
        return os;
    }
    friend std::istream& operator>>(std::istream& is, mint& mt) {
        T v_;
        is >> v_;
        mt = v_;
        return is;
    }
    template <typename P> mint pow(P e) const {
        assert(e >= 0);
        mint res(1), base(*this);

        while (e) {
            if (e & 1) {
                res *= base;
            }
            e >>= 1;
            base *= base;
        }
        return res;
    }
    mint inv() const { return pow(mod() - 2); }

    mint& operator/=(const mint& r) { return (*this) *= r.inv(); }
    mint operator/(const mint& r) const { return mint(*this) *= r.inv(); }
    mint& operator/=(T r) { return (*this) /= mint(r); }
    friend mint operator/(const mint& l, T r) { return mint(l) /= r; }
    friend mint operator/(T l, const mint& r) { return mint(l) /= r; }
};
};  // namespace kyopro
template <typename T, int id> T kyopro::dynamic_modint<T, id>::_mod;
template <typename T, int id>
kyopro::internal::Montgomery<T> kyopro::dynamic_modint<T, id>::mr;

/**
 * @brief 動的modint
 * @docs docs/math/dynamic_modint.md
 */
#line 3 "src/math/miller.hpp"
namespace kyopro {

/**
 * @brief MillerRabin素数判定法
 */
class miller {
    using i128 = __int128_t;
    using u128 = __uint128_t;
    using u64 = uint64_t;
    using u32 = uint32_t;

    template <typename T, typename mint, const int bases[], int length>
    static constexpr bool miller_rabin(T n) {
        T d = n - 1;

        while (~d & 1) {
            d >>= 1;
        }

        const T rev = n - 1;
        if (mint::mod() != n) {
            mint::set_mod(n);
        }
        for (int i = 0; i < length; ++i) {
            if (n <= bases[i]) {
                return true;
            }
            T t = d;
            mint y = mint(bases[i]).pow(t);

            while (t != n - 1 && y.val() != 1 && y.val() != rev) {
                y *= y;
                t <<= 1;
            }

            if (y.val() != rev && (~t & 1)) return false;
        }
        return true;
    }
    // 底
    static constexpr int bases_int[3] = {2, 7, 61};
    static constexpr int bases_ll[7] = {2,      325,     9375,      28178,
                                        450775, 9780504, 1795265022};

public:
    template <typename T> static constexpr bool is_prime(T n) {
        if (n < 2) {
            return false;
        } else if (n == 2) {
            return true;
        } else if (~n & 1) {
            return false;
        };
        if (std::numeric_limits<T>::digits < 32 || n <= 1 << 30) {
            return miller_rabin<T, dynamic_modint<std::make_unsigned_t<T>>,
                                bases_int, 3>(n);
        } else {
            return miller_rabin<T, dynamic_modint<std::make_unsigned_t<T>>,
                                bases_ll, 7>(n);
        }
        return false;
    }
};
};  // namespace kyopro

/**
 * @docs docs/math/miller.md
 */
#line 2 "src/stream.hpp"
#include <ctype.h>
#include <stdio.h>
#include <string>
namespace kyopro {
/**
 * 文字を1個読み込む
 */
inline char readchar() {
    char c = getchar_unlocked();
    while (isspace(c)) c = getchar_unlocked();
    return c;
}
/**
 *  整数の入出力
 */
template <typename T> constexpr inline void readint(T& a) {
    a = 0;
    bool is_negative = false;
    char c = getchar_unlocked();
    while (isspace(c)) {
        c = getchar_unlocked();
    }
    if (c == '-') is_negative = true, c = getchar_unlocked();
    while (isdigit(c)) {
        a = 10 * a + (c - '0');
        c = getchar_unlocked();
    }
    if (is_negative) a *= -1;
}
template <typename Head, typename... Tail>
constexpr inline void readint(Head& head, Tail&... tail) {
    readint(head);
    readint(tail...);
}

template <typename T> void write_int(T a) {
    if (!a) {
        putchar_unlocked('0');
        putchar_unlocked('\n');
        return;
    }
    if (a < 0) putchar_unlocked('-'), a *= -1;
    char s[37];
    int now = 37;
    while (a) {
        s[--now] = (char)'0' + a % 10;
        a /= 10;
    }
    while (now < 37) putchar_unlocked(s[now++]);
}
template <typename T> constexpr inline void putint(T a) {
    if (!a) {
        putchar_unlocked('0');
        putchar_unlocked('\n');
        return;
    }
    if (a < 0) putchar_unlocked('-'), a *= -1;
    char s[37];
    int now = 37;
    while (a) {
        s[--now] = (char)'0' + a % 10;
        a /= 10;
    }
    while (now < 37) putchar_unlocked(s[now++]);
    putchar_unlocked('\n');
}
template <typename Head, typename... Tail>
constexpr inline void putint(Head head, Tail... tail) {
    putint(head);
    putint(tail...);
}

/**
 * 文字列の入出力
 */

inline void readstr(std::string& str) {
    char c = getchar_unlocked();
    while (isspace(c)) c = getchar_unlocked();
    while (!isspace(c)) {
        str += c;
        c = getchar_unlocked();
    }
}

inline void readstr(std::string& str,std::string& tail...) {
    readstr(str);
    readstr(tail);
}
inline void putstr(const std::string& str) {
    for (auto c : str) {
        putchar_unlocked(c);
    }
    putchar_unlocked('\n');
}
inline void putstr(const std::string& str, const std::string& tail...) {
    putstr(str);
    putstr(tail);
}
};  // namespace kyopro

/**
 * @brief fastIO
 */
#line 5 "test/yuki/No3030.test.cpp"
int main() {
    int n;
    scanf("%d", &n);
    for (int i = 0; i < n; ++i) {
        long long x;
        kyopro::readint(x);
        kyopro::write_int(x);
        putchar_unlocked(' ');
        putchar_unlocked(kyopro::miller::is_prime(x)?'1':'0');
        putchar_unlocked('\n');
    }
}