結果

問題 No.3030 ミラー・ラビン素数判定法のテスト
ユーザー nonamaenonamae
提出日時 2022-07-19 15:31:39
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
WA  
実行時間 -
コード長 11,230 bytes
コンパイル時間 3,190 ms
コンパイル使用メモリ 217,480 KB
実行使用メモリ 4,384 KB
最終ジャッジ日時 2023-09-14 10:59:13
合計ジャッジ時間 4,148 ms
ジャッジサーバーID
（参考情報） 		judge11 / judge15
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
4,380 KB
testcase_01 AC 2 ms
4,376 KB
testcase_02 AC 1 ms
4,376 KB
testcase_03 AC 1 ms
4,380 KB
testcase_04 WA -
testcase_05 WA -
testcase_06 WA -
testcase_07 WA -
testcase_08 WA -
testcase_09 WA -
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ソースコード

diff # 

#pragma region opt
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma endregion opt

#include <bits/stdc++.h>

#pragma region type
using i8 = std::int8_t; using i16 = std::int16_t; using i32 = std::int32_t; using i64 = std::int64_t; using u8 = std::uint8_t; using u16 = std::uint16_t; using u32 = std::uint32_t; using u64 = std::uint64_t;
using i128 = __int128_t; using u128 = __uint128_t;
using f32 = float; using f64 = double; using f80 = long double;

template<typename T> using vec = std::vector<T>;
template<typename T> using vvec = std::vector<std::vector<T>>;
template<typename T> using vvvec = std::vector<std::vector<std::vector<T>>>;
template<typename T> using pvec = std::pair<std::vector<T>, std::vector<T>>;
#pragma endregion type

#pragma region MACRO for
#define FOR(i,a,b) for(int i=(a), i##_len=(b); i<i##_len; ++i)
#define REP(i,n) for(int i=0, i##_len=(n); i<i##_len; ++i)
#define LOOP(n) for(int _=0; _<(n); ++_)
#pragma endregion MACRO for

#pragma region MACRO container
#define ALL(obj) (obj).begin(),(obj).end()
#define SZ(obj) (static_cast<int>((obj).size()))
#pragma endregion MACRO container

#pragma region MACRO bits
#define POPCNT32(a) __builtin_popcount((a))
#define POPCNT64(a) __builtin_popcountll((a))
#define CTZ32(a) __builtin_ctz((a))
#define CLZ32(a) __builtin_clz((a))
#define CTZ64(a) __builtin_ctzll((a))
#define CLZ64(a) __builtin_clzll((a))
#define HAS_SINGLE_BIT32(a) (__builtin_popcount((a)) == (1))
#define HAS_SINGLE_BIT64(a) (__builtin_popcountll((a)) == (1))
#define MSB32(a) ((31) - __builtin_clz((a)))
#define MSB64(a) ((63) - __builtin_clzll((a)))
#define BIT_WIDTH32(a) ((a) ? ((32) - __builtin_clz((a))) : (0))
#define BIT_WIDTH64(a) ((a) ? ((64) - __builtin_clzll((a))) : (0))
#define LSBit(a) ((a) & (-(a)))
#define CLSBit(a) ((a) & ((a) - (1)))
#define BIT_CEIL32(a) ((!(a)) ? (1) : ((POPCNT32(a)) == (1) ? ((1u) << ((31) - CLZ32((a)))) : ((1u) << ((32) - CLZ32(a)))))
#define BIT_CEIL64(a) ((!(a)) ? (1) : ((POPCNT64(a)) == (1) ? ((1ull) << ((63) - CLZ64((a)))) : ((1ull) << ((64) - CLZ64(a)))))
#define BIT_FLOOR32(a) ((!(a)) ? (0) : ((1u) << ((31) - CLZ32((a)))))
#define BIT_FLOOR64(a) ((!(a)) ? (0) : ((1ull) << ((63) - CLZ64((a)))))
#define _ROTL32(x, s) (((x) << ((s) % (32))) | (((x) >> ((32) - ((s) % (32))))))
#define _ROTR32(x, s) (((x) >> ((s) % (32))) | (((x) << ((32) - ((s) % (32))))))
#define ROTL32(x, s) (((s) == (0)) ? (x) : ((((i64)(s)) < (0)) ? (_ROTR32((x), -(s))) : (_ROTL32((x), (s)))))
#define ROTR32(x, s) (((s) == (0)) ? (x) : ((((i64)(s)) < (0)) ? (_ROTL32((x), -(s))) : (_ROTR32((x), (s)))))
#define _ROTL64(x, s) (((x) << ((s) % (64))) | (((x) >> ((64) - ((s) % (64))))))
#define _ROTR64(x, s) (((x) >> ((s) % (64))) | (((x) << ((64) - ((s) % (64))))))
#define ROTL64(x, s) (((s) == (0)) ? (x) : ((((i128)(s)) < (0)) ? (_ROTR64((x), -(s))) : (_ROTL64((x), (s)))))
#define ROTR64(x, s) (((s) == (0)) ? (x) : ((((i128)(s)) < (0)) ? (_ROTL64((x), -(s))) : (_ROTR64((x), (s)))))
#pragma endregion MACRO bits

#pragma region util
template<class T> inline bool chmax(T& a,T b){ if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a,T b){ if (a > b) { a = b; return 1; } return 0; }
#pragma endregion util

#pragma region IO
// -2147483648 ～ 2147483647 (> 10 ^ 9)
i32 in_i32(void) {
    i32 c, x = 0, f = 1;
    while (c = getchar_unlocked(), c < 48 || c > 57) if (c == 45) f = -f;
    while (47 < c && c < 58) {
        x = x * 10 + c - 48;
        c = getchar_unlocked();
    }
    return f * x;
}
static inline void out_i32_inner(i32 x) {
    if (x >= 10) out_i32_inner(x / 10);
    putchar_unlocked(x - x / 10 * 10 + 48);
}
void out_i32(i32 x) {
    if (x < 0) {
        putchar_unlocked('-');
        x = -x;
    }
    out_i32_inner(x);
}
// -9223372036854775808 ～ 9223372036854775807 (> 10 ^ 18)
i64 in_i64(void) {
    i64 c, x = 0, f = 1;
    while (c = getchar_unlocked(), c < 48 || c > 57) if (c == 45) f = -f;
    while (47 < c && c < 58) {
        x = x * 10 + c - 48;
        c = getchar_unlocked();
    }
    return f * x;
}
static inline void out_i64_inner(i64 x) {
    if (x >= 10) out_i64_inner(x / 10);
    putchar_unlocked(x - x / 10 * 10 + 48);
}
void out_i64(i64 x) {
    if (x < 0) {
        putchar_unlocked('-');
        x = -x;
    }
    out_i64_inner(x);
}
// 0 ～ 4294967295 (> 10 ^ 9)
u32 in_u32(void) {
    u32 c, x = 0;
    while (c = getchar_unlocked(), c < 48 || c > 57);
    while (47 < c && c < 58) {
        x = x * 10 + c - 48;
        c = getchar_unlocked();
    }
    return x;
}
void out_u32(u32 x) {
    if (x >= 10) out_u32(x / 10);
    putchar_unlocked(x - x / 10 * 10 + 48);
}
// 0 ～ 18446744073709551615 (> 10 ^ 19)
u64 in_u64(void) {
    u64 c, x = 0;
    while (c = getchar_unlocked(), c < 48 || c > 57);
    while (47 < c && c < 58) {
        x = x * 10 + c - 48;
        c = getchar_unlocked();
    }
    return x;
}
void out_u64(u64 x) {
    if (x >= 10) out_u64(x / 10);
    putchar_unlocked(x - x / 10 * 10 + 48);
}
void NL(void) { putchar_unlocked('\n'); }
void SP(void) { putchar_unlocked(' '); }
#pragma endregion IO

#pragma region jacobi
int jacobi_symbol(i64 a, u64 n) {
    u64 t;
    int j = 1;
    while (a) {
        if (a < 0) {
            a = -a;
            if ((n & 3) == 3) j = -j;
        }
        int s = __builtin_ctzll(a);
        a >>= s;
        if (((n & 7) == 3 || (n & 7) == 5) && (s & 1)) j = -j;
        if ((a & n & 3) == 3) j = -j;
        t = a, a = n, n = t;
        a %= n;
        if (u64(a) > n / 2) a -= n;
    }
    return n == 1 ? j : 0;
}
#pragma endregion jacobi

#pragma region m64

struct Runtime_m64 {

private:
    using m64 = u64;

public:
    inline static m64 one, r2, n, md;
    
    m64 x;

    static void set_mod(u64 m) {
        md = m;
        one = u64(-1ull) % m + 1;
        r2 = u128(i128(-1)) % m + 1;
        u64 nn = m;
        for (int _ = 0; _ < 5; ++_) nn *= 2 - nn * m;
        n = nn;
    }

    static m64 reduce(u128 a) {
        u64 y = (u64(a >> 64)) - (u64((u128(u64(a) * n) * md) >> 64));
        return i64(y) < 0 ? y + md : y;
    }

    Runtime_m64() : x(0) { }
    Runtime_m64(u64 x) : x(reduce(u128(x) * r2)) { }
    Runtime_m64(u64 x, bool is_montgomery) : x(is_montgomery ? x : reduce(u128(x) * r2)) { }
    
    u64 get_val() const {
        return reduce(u128(x));
    }
    u64 get_raw() const {
        return x;
    }

    Runtime_m64 &operator+=(Runtime_m64 y) {
        x += y.x - md;
        if (i64(x) < 0) x += md;
        return *this;
    }
    Runtime_m64 &operator-=(Runtime_m64 y) {
        if (i64(x -= y.x) < 0) x += 2 * md;
        return *this;
    }
    Runtime_m64 &operator*=(Runtime_m64 y) {
        x = reduce(u128(x) * y.x);
        return *this;
    }
    Runtime_m64 &operator/=(Runtime_m64 y) {
        return *this *= y.inv();
    }
    Runtime_m64 &operator<<=(u64 y) {
        x <<= y;
        return *this;
    }
    Runtime_m64 &operator>>=(u64 y) {
        x >>= y;
        return *this;
    }
    Runtime_m64 operator+(Runtime_m64 y) const { return Runtime_m64(*this) += y; }
    Runtime_m64 operator-(Runtime_m64 y) const { return Runtime_m64(*this) -= y; }
    Runtime_m64 operator*(Runtime_m64 y) const { return Runtime_m64(*this) *= y; }
    Runtime_m64 operator/(Runtime_m64 y) const { return Runtime_m64(*this) /= y; }
    Runtime_m64 operator-() const { return Runtime_m64() - Runtime_m64(*this); }
    Runtime_m64 operator<<(u64 y) const { return Runtime_m64(*this) <<= y; }
    Runtime_m64 operator>>(u64 y) const { return Runtime_m64(*this) >>= y; }
    bool operator==(Runtime_m64 y) const { return (x >= md ? x - md : x) == (y.x >= md ? y.x - md : y.x); }
    bool operator!=(Runtime_m64 y) const { return not operator==(y); }
    bool operator<(const Runtime_m64& other) {
        return (*this).get_val() < other.get_val();
    }
    bool operator<=(const Runtime_m64& other) {
        return (*this).get_val() <= other.get_val();
    }
    bool operator>(const Runtime_m64& other) {
        return (*this).get_val() > other.get_val();
    }
    bool operator>=(const Runtime_m64& other) {
        return (*this).get_val() >= other.get_val();
    }
    Runtime_m64 pow(u64 k) {
        Runtime_m64 y = 1, z = *this;
        for ( ; k; k >>= 1, z *= z) if (k & 1) y *= z;
        return y;
    }
    Runtime_m64 inv() {
        return (*this).pow(md - 2);
    }
};

#pragma endregion m64

#pragma region Baillie_PSW primality test

bool is_prime(u64 n) {
    {
        if (n == 2 || n == 3 || n == 5 || n == 7) return true;
        if (n % 2 == 0 || n % 3 == 0 || n % 5 == 0 || n % 7 == 0) return false;
        if (n < 121) return n > 1;
    }
    using mint = Runtime_m64;
    mint::set_mod(n);
    {
        u64 d = (n - 1) << __builtin_clzll(n - 1);
        mint a(2);
        if (a.get_raw() >= n) {
            mint aa(a.get_raw() - n, true);
            a = aa;
        }
        for (d <<= 1; d; d <<= 1) {
            a *= a;
            if (d >> 63) a <<= 1;
            if (a.get_raw() >= n) {
                mint aa(a.get_raw() - n, true);
                a = aa;
            }
        }
        if (a != mint(1)) {
            u64 x = (n - 1) & -(n - 1);
            mint m = mint(n - 1);
            for (x >>= 1; a != m; x >>= 1) {
                if (x == 0) return false;
                a *= a;
            }
        }
    }
    {
        u32 k = round(sqrtl(n));
        if (k * k == n) return false;
    }
    {
        i64 D = 5;
        for (int i = 0; jacobi_symbol(D, n) != -1 && i < 64; i++) {
            if (i & 1) D -= 2;
            else D += 2;
            D = -D;
        }
        mint Q(D < 0 ? (1 - D) / 4 % n : n - (D - 1) / 4 % n);
        mint u(1);
        mint v(1);
        mint Qn = Q;
        D %= (i64)n;
        mint D_mint(D < 0 ? n + D : D);
        u64 k = (n + 1) << __builtin_clzll(n + 1);
        for (k <<= 1; k; k <<= 1) {
            u *= v;
            v = v * v - (Qn + Qn);
            Qn *= Qn;
            if (k >> 63) {
                mint uu = u + v;
                if (uu.get_raw() & 1) {
                    mint uuu(uu.get_raw() + n, true);
                    uu = uuu;
                }
                uu >>= 1;
                v += D_mint * u;
                if (v.get_raw() & 1) {
                    mint vv(v.get_raw() + n, true);
                    v = vv;
                }
                v >>= 1;
                u = uu;
                Qn *= Q;
            }
        }
        if (u.get_raw() == 0 || v.get_raw() == 0) return true;
        u64 x = (n + 1) & ~n;
        for (x >>= 1; x; x >>= 1) {
            u *= v;
            v = v * v - (Qn + Qn);
            if (v.get_raw() == 0) return true;
            Qn *= Qn;
        }
    }
    return false;
}

#pragma endregion Baillie_PSW primality test

void Main() {
    // your source here
    
    int i = in_i32();
    u64 x;
    LOOP(i) {
        x = in_u64();
        out_u64(x); SP(); out_u64(is_prime(x) ? 1 : 0);
        NL();
    }
    return;
}

int main() {
    
    std::ios_base::sync_with_stdio(false);
    std::cin.tie(nullptr);
    std::cout.tie(nullptr);
    std::cout << std::fixed << std::setprecision(13);
    std::cerr << std::fixed << std::setprecision(3);

    Main();
}
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