#857842 (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: 2023-04-08 10:13:24
• 言語: C++23 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 37 ms / 9,973 ms
• コード長: 10,802 bytes
• コンパイル時間: 2,773 ms
• コンパイル使用メモリ: 247,956 KB
• 実行使用メモリ: 5,248 KB
• 最終ジャッジ日時: 2024-10-03 06:00:37
• 合計ジャッジ時間: 3,769 ms
• ジャッジサーバーID （参考情報）: judge1 / judge5

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	1 ms; 5,248 KB
testcase_03	AC	2 ms; 5,248 KB
testcase_04	AC	24 ms; 5,248 KB
testcase_05	AC	24 ms; 5,248 KB
testcase_06	AC	15 ms; 5,248 KB
testcase_07	AC	15 ms; 5,248 KB
testcase_08	AC	14 ms; 5,248 KB
testcase_09	AC	37 ms; 5,248 KB

ソースコード

#line 1 "test/yuki/No-3030.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/3030"
#line 2 "template.hpp"
#include<bits/stdc++.h>
#define rep(i, N) for (int i = 0; i < (N); i++)
#define all(x) (x).begin(),(x).end()
#define popcount(x) __builtin_popcount(x)
using i128=__int128_t;
using ll = long long;
using ld = long double;
using graph = std::vector<std::vector<int>>;
using P = std::pair<int, int>;
constexpr int inf = 1e9;
constexpr ll infl = 1e18;
constexpr ld eps = 1e-6;
const long double pi = acos(-1);
constexpr uint64_t MOD = 1e9 + 7;
constexpr uint64_t MOD2 = 998244353;
constexpr int dx[] = { 1,0,-1,0 };
constexpr int dy[] = { 0,1,0,-1 };
template<class T>constexpr inline void chmax(T&x,T y){if(x<y)x=y;}
template<class T>constexpr inline void chmin(T&x,T y){if(x>y)x=y;}
#line 2 "internal/barrett.hpp"
namespace internal {
	///@brief barrett reduction
	class barrett {
		using u32 = uint32_t;
		using u64 = uint64_t;

		u64 m;
		u64 im;
	public:
		explicit barrett() = default;
		explicit barrett(u64 m_) :m(m_), im((u64)(long double)static_cast<u64>(-1) / m_ + 1) {}

		u64 get_mod() const { return m; }
		u64 reduce(int64_t a)const{
        	if (a < 0) return m - reduce(-a);
            u64 q = ((__uint128_t)a * im) >> 64;
            a -= m * q;
            if (a >= m) a -= m;
            return a;
        }
		u64 mul(u64 a, u64 b) const {
			if (a == 0 || b == 0) {
				return 0;
			}
			u64 z = a;
			z *= b;
			u64 x = (u64)(((__uint128_t)(z)*im) >> 64);

			u32 v = (u32)(z - x * m);

			if (v >= m)v += m;
			return v;
		}
	};
}
#line 4 "internal/montgomery.hpp"
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 MontgomeryReduction
    template<typename T,typename LargeT>
    class MontgomeryReduction64 {
        static constexpr int lg = std::numeric_limits<T>::digits;
        T mod, r, r2, minv;
        T calc_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:
        MontgomeryReduction64() = default;
        constexpr T get_mod() { return mod; }
        constexpr int get_lg() { return lg; }


        void set_mod(const T& m) {
            assert(m > 0);
            assert(m & 1);

            mod = m;

            r = (-static_cast<T>(mod)) % mod;
            r2 = (-static_cast<LargeT>(mod)) % mod;
            minv = calc_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 mult(T x, T y) {
            return reduce(static_cast<LargeT>(x) * y);
        }
    };
};
#line 6 "math/dynamic_modint.hpp"
template <int id = -1> class barrett_modint {
    using u32 = uint32_t;
    using u64 = uint64_t;

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

    static br brt;
    static u32 mod;
    u32 v;  // value
  public:
    static void set_mod(u32 mod_) {
        brt = br(mod_);
        mod = mod_;
    }

  public:
    explicit constexpr barrett_modint() : v(0) {
        assert(mod);
    }  // modが決定済みである必要がある
    explicit constexpr barrett_modint(i64 v_) : v(brt.reduce(v_)) {
        assert(mod);
    }

    u32 val() const { return v; }
    static u32 get_mod() { return mod; }
    using mint = barrett_modint<id>;

    // operators
    constexpr mint& operator=(i64 r) {
        v = brt.reduce(r);
        return (*this);
    }
    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) const { return mint(*this) += r; }
    constexpr mint operator-(const mint& r) const { return mint(*this) -= r; }
    constexpr mint operator*(const mint& r) const { return mint(*this) *= r; }

    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; }

    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 = 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;
    }
    inline 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/=(i64 r) { return (*this) /= mint(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; }
};
template <int id> typename barrett_modint<id>::u32 barrett_modint<id>::mod;
template <int id> typename barrett_modint<id>::br barrett_modint<id>::brt;

template <typename T = uint32_t, typename LargeT = uint64_t, int id = -1>
class dynamic_modint {
    static T mod;
    static internal::MontgomeryReduction64<T, LargeT> mr;

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

    static T get_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, LargeT, 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.mult(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; }
};
template <typename T, typename LargeT, int id>
T dynamic_modint<T, LargeT, id>::mod;
template <typename T, typename LargeT, int id>
internal::MontgomeryReduction64<T, LargeT> dynamic_modint<T, LargeT, id>::mr;

/// @brief dynamic modint(動的modint)
/// @docs docs/math/dynamic_modint.md
#line 3 "math/miller.hpp"
namespace library {
    namespace miller {
        using i128 = __int128_t;
        using u128 = __uint128_t;
        using u64 = uint64_t;
        using u32 = uint32_t;

        template<typename mint>
        bool inline miller_rabin(u64 n, const u64 bases[], int length) {
            u64 d = n - 1;

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

            u64 rev = n - 1;
            if (mint::get_mod() != n) {
                mint::set_mod(n);
            }
            for (int i = 0; i < length; i++) {
                u64 a = bases[i];

                if (n <= a) {
                    return true;
                }
                u64 t = d;
                mint y = mint(a).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;
        }


        constexpr u64 bases_int[3] = { 2, 7, 61 };  // intだと、2,7,61で十分
        constexpr u64 bases_ll[7] = { 2, 325, 9375, 28178, 450775, 9780504, 1795265022 };
        constexpr bool is_prime(u64 n) {
            if (n < 2) {
                return false;
            }
            else if (n == 2) {
                return true;
            }
            else if (~n & 1) {
                return false;
            }
            if (n < (1ul << 31)) {
                return miller_rabin<barrett_modint<-1>>(n, bases_int, 3);
            }
            else {
                return miller_rabin<dynamic_modint<u64,u128,-1>>(n, bases_ll, 7);
            }
        }
    };
};
///@brief MillerRabinの素数判定
#line 4 "test/yuki/No-3030.test.cpp"

using namespace std;
int main(){
    int n;
    scanf("%d", &n);
    for (int i = 0; i < n; i++){
        uint64_t xi;
        scanf("%lld", &xi);
        printf("%lld ", xi);
        if (library::miller::is_prime(xi)) {
            puts("1");
        } else {
            puts("0");
        }
    }
}