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 2022-07-15 19:34:04
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 87 ms / 9,973 ms
コード長 3,982 bytes
コンパイル時間 2,115 ms
コンパイル使用メモリ 201,500 KB
実行使用メモリ 5,248 KB
最終ジャッジ日時 2024-11-16 23:48:11
合計ジャッジ時間 2,928 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge2
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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
5,248 KB
testcase_01 AC 1 ms
5,248 KB
testcase_02 AC 2 ms
5,248 KB
testcase_03 AC 2 ms
5,248 KB
testcase_04 AC 48 ms
5,248 KB
testcase_05 AC 46 ms
5,248 KB
testcase_06 AC 14 ms
5,248 KB
testcase_07 AC 14 ms
5,248 KB
testcase_08 AC 15 ms
5,248 KB
testcase_09 AC 87 ms
5,248 KB
権限があれば一括ダウンロードができます
コンパイルメッセージ
main.cpp: In member function 'RuntimeMontgomeryModint64 RuntimeMontgomeryModint64::operator<<(u64) const':
main.cpp:83:97: warning: no return statement in function returning non-void [-Wreturn-type]
   83 |     RuntimeMontgomeryModint64 operator<<(u64 y) const { RuntimeMontgomeryModint64(*this) <<= y; }
      |                                                                                                 ^
main.cpp: In member function 'RuntimeMontgomeryModint64 RuntimeMontgomeryModint64::operator>>(u64) const':
main.cpp:84:97: warning: no return statement in function returning non-void [-Wreturn-type]
   84 |     RuntimeMontgomeryModint64 operator>>(u64 y) const { RuntimeMontgomeryModint64(*this) >>= y; }
      |                                                                                                 ^

ソースコード

diff # 

#include <bits/stdc++.h>

using i32 = std::int32_t;
using i64 = std::int64_t;
using u32 = std::uint32_t;
using u64 = std::uint64_t;
using i128 = __int128_t;
using u128 = __uint128_t;

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;
}

struct RuntimeMontgomeryModint64 {

private:
    using m64 = u64;

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

    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;
    }

    RuntimeMontgomeryModint64() : x(0) { }
    RuntimeMontgomeryModint64(u64 x) : x(reduce(u128(x) * r2)) { }
    u64 val() const {
        return reduce(u128(x));
    }

    m64 x;

    RuntimeMontgomeryModint64 &operator+=(RuntimeMontgomeryModint64 y) {
        x += y.x - md;
        if (i64(x) < 0) x += md;
        return *this;
    }
    RuntimeMontgomeryModint64 &operator-=(RuntimeMontgomeryModint64 y) {
        if (i64(x -= y.x) < 0) x += 2 * md;
        return *this;
    }
    RuntimeMontgomeryModint64 &operator*=(RuntimeMontgomeryModint64 y) {
        x = reduce(u128(x) * y.x);
        return *this;
    }
    RuntimeMontgomeryModint64 &operator<<=(u64 y) {
        x <<= y;
        return *this;
    }
    RuntimeMontgomeryModint64 &operator>>=(u64 y) {
        x >>= y;
        return *this;
    }
    RuntimeMontgomeryModint64 operator+(RuntimeMontgomeryModint64 y) const { return RuntimeMontgomeryModint64(*this) += y; }
    RuntimeMontgomeryModint64 operator-(RuntimeMontgomeryModint64 y) const { return RuntimeMontgomeryModint64(*this) -= y; }
    RuntimeMontgomeryModint64 operator*(RuntimeMontgomeryModint64 y) const { return RuntimeMontgomeryModint64(*this) *= y; }
    RuntimeMontgomeryModint64 operator<<(u64 y) const { RuntimeMontgomeryModint64(*this) <<= y; }
    RuntimeMontgomeryModint64 operator>>(u64 y) const { RuntimeMontgomeryModint64(*this) >>= y; }
    bool operator==(RuntimeMontgomeryModint64 y) const { return (x >= md ? x - md : x) == (y.x >= md ? y.x - md : y.x); }
    bool operator!=(RuntimeMontgomeryModint64 y) const { return not operator==(y); }
    RuntimeMontgomeryModint64 pow(u64 k) {
        RuntimeMontgomeryModint64 y = 1, z = *this;
        for ( ; k; k >>= 1, z *= z) if (k & 1) y *= z;
        return y;
    }
    RuntimeMontgomeryModint64 inv() {
        return (*this).pow(md - 2);
    }
};

static u64 lcg_state = 14534622846793005ull;
u32 lcg_rand(u32 l, u32 r) {
    lcg_state = 6364136223846793005ULL * lcg_state + 1442695040888963407ULL;
    return l + (u32)((double)(r - l) * (double)(lcg_state >> 32) / 4294967296.0);
}

int solovay_strassen_primality_test(u64 n) {
    if (n <= 1) return 0;
    if (n <= 3) return 1;
    if (!(n & 1)) return 0;
    RuntimeMontgomeryModint64::set_mod(n);
    RuntimeMontgomeryModint64 a{1};
    RuntimeMontgomeryModint64 b{n - 1};
    for (int _ = 0; _ < 15; ++_) {
        u32 ra = lcg_rand(2u, ((n - 1) > ((1ull << 32) - 1)) ? 1u << 31 : n - 1);
        int x = jacobi_symbol(i64(ra), n);
        RuntimeMontgomeryModint64 y = (x == -1) ? b : ((x == 0) ? RuntimeMontgomeryModint64{0} : a);
        RuntimeMontgomeryModint64 A{ra};
        if (y == 0 || y != A.pow((n - 1) / 2)) return 0;
    }
    return 1;
}

int main() {

    u64 Q; scanf("%lu", &Q);
    while (Q--) {
        u64 x; scanf("%lu", &x);
        printf("%lu %d\n", x, solovay_strassen_primality_test(x));
    }
}
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