#597739 (C++14) No.3030 ミラー・ラビン素数判定法のテスト

提出ソース
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	pyranine
提出日時	2020-12-27 09:25:02
言語	C++14 (gcc 12.3.0 + boost 1.83.0)
結果	RE
実行時間	-
コード長	11,781 bytes
コンパイル時間	2,277 ms
コンパイル使用メモリ	184,388 KB
実行使用メモリ	5,376 KB
最終ジャッジ日時	2024-04-29 14:46:16
合計ジャッジ時間	3,418 ms
ジャッジサーバーID （参考情報）	judge5 / judge4
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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	2 ms 5,376 KB
testcase_02	AC	1 ms 5,376 KB
testcase_03	AC	2 ms 5,376 KB
testcase_04	RE	-
testcase_05	RE	-
testcase_06	RE	-
testcase_07	RE	-
testcase_08	RE	-
testcase_09	RE	-
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ソースコード

raw source code
#include <bits/stdc++.h>
using namespace std;

namespace inner {

using i32 = int32_t;
using u32 = uint32_t;
using i64 = int64_t;
using u64 = uint64_t;

template <typename T>
T gcd(T a, T b) {
    while (b) swap(a %= b, b);
    return a;
}

uint64_t gcd_impl(uint64_t n, uint64_t m) {
    constexpr uint64_t K = 5;
    for (int i = 0; i < 80; ++i) {
        uint64_t t = n - m;
        uint64_t s = n - m * K;
        bool q = t < m;
        bool p = t < m * K;
        n = q ? m : t;
        m = q ? t : m;
        if (m == 0) return n;
        n = p ? n : s;
    }
    return gcd_impl(m, n % m);
}

uint64_t gcd_pre(uint64_t n, uint64_t m) {
    for (int i = 0; i < 4; ++i) {
        uint64_t t = n - m;
        bool q = t < m;
        n = q ? m : t;
        m = q ? t : m;
        if (m == 0) return n;
    }
    return gcd_impl(n, m);
}

uint64_t gcd_fast(uint64_t n, uint64_t m) {
    return n > m ? gcd_pre(n, m) : gcd_pre(m, n);
}

template <typename T = int32_t>
T inv(T a, T p) {
    T b = p, x = 1, y = 0;
    while (a) {
        T q = b % a;
        swap(a, b /= a);
        swap(x, y -= q * x);
    }
    assert(b == 1);
    return y < 0 ? y + p : y;
}

template <typename T = int32_t, typename U = int64_t>
T modpow(T a, U n, T p) {
    T ret = 1;
    for (; n; n >>= 1, a = U(a) * a % p)
        if (n & 1) ret = U(ret) * a % p;
    return ret;
}

}  // namespace inner

using namespace std;

unsigned long long rng() {
    static unsigned long long x_ = 88172645463325252ULL;
    x_ = x_ ^ (x_ << 7);
    return x_ = x_ ^ (x_ >> 9);
}

struct ArbitraryLazyMontgomeryModInt {
    using mint = ArbitraryLazyMontgomeryModInt;
    using i32 = int32_t;
    using u32 = uint32_t;
    using u64 = uint64_t;

    static u32 mod;
    static u32 r;
    static u32 n2;

    static u32 get_r() {
        u32 ret = mod;
        for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
        return ret;
    }

    static void set_mod(u32 m) {
        assert(m < (1 << 30));
        assert((m & 1) == 1);
        mod = m;
        n2 = -u64(m) % m;
        r = get_r();
        assert(r * mod == 1);
    }

    u32 a;

    ArbitraryLazyMontgomeryModInt() : a(0) {}
    ArbitraryLazyMontgomeryModInt(const int64_t &b) : a(reduce(u64(b % mod + mod) * n2)) {};

    static u32 reduce(const u64 &b) {
        return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
    }

    mint &operator+=(const mint &b) {
        if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
        return *this;
    }

    mint &operator-=(const mint &b) {
        if (i32(a -= b.a) < 0) a += 2 * mod;
        return *this;
    }

    mint &operator*=(const mint &b) {
        a = reduce(u64(a) * b.a);
        return *this;
    }

    mint &operator/=(const mint &b) {
        *this *= b.inverse();
        return *this;
    }

    mint operator+(const mint &b) const { return mint(*this) += b; }
    mint operator-(const mint &b) const { return mint(*this) -= b; }
    mint operator*(const mint &b) const { return mint(*this) *= b; }
    mint operator/(const mint &b) const { return mint(*this) /= b; }
    bool operator==(const mint &b) const {
        return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
    }
    bool operator!=(const mint &b) const {
        return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
    }
    mint operator-() const { return mint() - mint(*this); }

    mint pow(u64 n) const {
        mint ret(1), mul(*this);
        while (n > 0) {
            if (n & 1) ret *= mul;
            mul *= mul;
            n >>= 1;
        }
        return ret;
    }

    friend ostream &operator<<(ostream &os, const mint &b) {
        return os << b.get();
    }

    friend istream &operator>>(istream &is, mint &b) {
        int64_t t;
        is >> t;
        b = ArbitraryLazyMontgomeryModInt(t);
        return (is);
    }

    mint inverse() const { return pow(mod - 2); }

    u32 get() const {
        u32 ret = reduce(a);
        return ret >= mod ? ret - mod : ret;
    }

    static u32 get_mod() { return mod; }
};
typename ArbitraryLazyMontgomeryModInt::u32 ArbitraryLazyMontgomeryModInt::mod;
typename ArbitraryLazyMontgomeryModInt::u32 ArbitraryLazyMontgomeryModInt::r;
typename ArbitraryLazyMontgomeryModInt::u32 ArbitraryLazyMontgomeryModInt::n2;

struct montgomery64 {
    using mint = montgomery64;
    using i64 = int64_t;
    using u64 = uint64_t;
    using u128 = __uint128_t;

    static u64 mod;
    static u64 r;
    static u64 n2;

    static u64 get_r() {
        u64 ret = mod;
        for (i64 i = 0; i < 5; ++i) ret *= 2 - mod * ret;
        return ret;
    }

    static void set_mod(u64 m) {
        assert(m < (1LL << 62));
        assert((m & 1) == 1);
        mod = m;
        n2 = -u128(m) % m;
        r = get_r();
        assert(r * mod == 1);
    }

    u64 a;

    montgomery64() : a(0) {}
    montgomery64(const int64_t &b) : a(reduce((u128(b) + mod) * n2)){};

    static u64 reduce(const u128 &b) {
        return (b + u128(u64(b) * u64(-r)) * mod) >> 64;
    }

    mint &operator+=(const mint &b) {
        if (i64(a += b.a - 2 * mod) < 0) a += 2 * mod;
        return *this;
    }

    mint &operator-=(const mint &b) {
        if (i64(a -= b.a) < 0) a += 2 * mod;
        return *this;
    }

    mint &operator*=(const mint &b) {
        a = reduce(u128(a) * b.a);
        return *this;
    }

    mint &operator/=(const mint &b) {
        *this *= b.inverse();
        return *this;
    }

    mint operator+(const mint &b) const { return mint(*this) += b; }
    mint operator-(const mint &b) const { return mint(*this) -= b; }
    mint operator*(const mint &b) const { return mint(*this) *= b; }
    mint operator/(const mint &b) const { return mint(*this) /= b; }
    bool operator==(const mint &b) const {
        return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
    }
    bool operator!=(const mint &b) const {
        return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
    }
    mint operator-() const { return mint() - mint(*this); }

    mint pow(u128 n) const {
        mint ret(1), mul(*this);
        while (n > 0) {
            if (n & 1) ret *= mul;
            mul *= mul;
            n >>= 1;
        }
        return ret;
    }

    friend ostream &operator<<(ostream &os, const mint &b) {
        return os << b.get();
    }

    friend istream &operator>>(istream &is, mint &b) {
        int64_t t;
        is >> t;
        b = montgomery64(t);
        return (is);
    }

    mint inverse() const { return pow(mod - 2); }

    u64 get() const {
        u64 ret = reduce(a);
        return ret >= mod ? ret - mod : ret;
    }

    static u64 get_mod() { return mod; }
};
typename montgomery64::u64 montgomery64::mod, montgomery64::r, montgomery64::n2;

namespace fast_factorize {
using u64 = uint64_t;

template <typename mint>
bool miller_rabin(u64 n, vector<u64> as) {
    if (mint::get_mod() != n) mint::set_mod(n);
    u64 d = n - 1;
    while (~d & 1) d >>= 1;
    mint e{1}, rev{int64_t(n - 1)};
    for (u64 a : as) {
        if (n <= a) break;
        u64 t = d;
        mint y = mint(a).pow(t);
        while (t != n - 1 && y != e && y != rev) {
            y *= y;
            t *= 2;
        }
        if (y != rev && t % 2 == 0) return false;
    }
    return true;
}

bool is_prime(u64 n) {
    if (~n & 1) return n == 2;
    if (n <= 1) return false;
    if (n < (1LL << 30))
        return miller_rabin<ArbitraryLazyMontgomeryModInt>(n, {2, 7, 61});
    else
        return miller_rabin<montgomery64>(n, {2, 325, 9375, 28178, 450775, 9780504, 1795265022});
}

template <typename mint, typename T>
T pollard_rho(T n) {
    if (~n & 1) return 2;
    if (is_prime(n)) return n;
    if (mint::get_mod() != n) mint::set_mod(n);
    mint R, one = 1;
    auto f = [&](mint x) { return x * x + R; };
    auto rnd = [&]() { return rng() % (n - 2) + 2; };
    while (1) {
        mint x, y, ys, q = one;
        R = rnd(), y = rnd();
        T g = 1;
        constexpr int m = 128;
        for (int r = 1; g == 1; r <<= 1) {
            x = y;
            for (int i = 0; i < r; ++i) y = f(y);
            for (int k = 0; g == 1 && k < r; k += m) {
                ys = y;
                for (int i = 0; i < m && i < r - k; ++i) q *= x - (y = f(y));
                g = inner::gcd_fast(q.get(), n);
            }
        }
        if (g == n) do {
            g = inner::gcd_fast((x - (ys = f(ys))).get(), n);
        } while (g == 1);
        if (g != n) return g;
    }
    exit(1);
}

vector<u64> inner_factorize(u64 n) {
    if (n <= 1) return {};
    u64 p;
    if (n <= (1LL << 30))
        p = pollard_rho<ArbitraryLazyMontgomeryModInt>(n);
    else
        p = pollard_rho<montgomery64>(n);
    if (p == n) return {p};
    auto l = inner_factorize(p);
    auto r = inner_factorize(n / p);
    copy(begin(r), end(r), back_inserter(l));
    return l;
}

vector<u64> factorize(u64 n) {
    auto ret = inner_factorize(n);
    sort(begin(ret), end(ret));
    return ret;
}

}  // namespace fast_factorize
using fast_factorize::factorize;
using fast_factorize::is_prime;

namespace fastio {
static constexpr int SZ = 1 << 17;
char ibuf[SZ], obuf[SZ];
int pil = 0, pir = 0, por = 0;

struct Pre {
    char num[40000];
    constexpr Pre() : num() {
        for (int i = 0; i < 10000; i++) {
            int n = i;
            for (int j = 3; j >= 0; j--) {
                num[i * 4 + j] = n % 10 + '0';
                n /= 10;
            }
        }
    }
} constexpr pre;

inline void load() {
    memcpy(ibuf, ibuf + pil, pir - pil);
    pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
    pil = 0;
}

inline void flush() {
    fwrite(obuf, 1, por, stdout);
    por = 0;
}

inline void rd(char& c) { c = ibuf[pil++]; }
template <typename T>
inline void rd(T& x) {
    if (pil + 32 > pir) load();
    char c;
    do {
        c = ibuf[pil++];
    }
    while (c < '-');
    bool minus = 0;
    if (c == '-') {
        minus = 1;
        c = ibuf[pil++];
    }
    x = 0;
    while (c >= '0') {
        x = x * 10 + (c & 15);
        c = ibuf[pil++];
    }
    if (minus) x = -x;
}
inline void rd() {}
template <typename Head, typename... Tail>
inline void rd(Head& head, Tail&... tail) {
    rd(head);
    rd(tail...);
}

inline void wt(char c) { obuf[por++] = c; }
template <typename T>
inline void wt(T x) {
    if (por > SZ - 32) flush();
    if (!x) {
        obuf[por++] = '0';
        return;
    }
    if (x < 0) {
        obuf[por++] = '-';
        x = -x;
    }
    int i = 12;
    char buf[16];
    while (x >= 10000) {
        memcpy(buf + i, pre.num + (x % 10000) * 4, 4);
        x /= 10000;
        i -= 4;
    }
    if (x < 100) {
        if (x < 10) {
            wt(char('0' + char(x)));
        }
        else {
            uint32_t q = (uint32_t(x) * 205) >> 11;
            uint32_t r = uint32_t(x) - q * 10;
            obuf[por + 0] = '0' + q;
            obuf[por + 1] = '0' + r;
            por += 2;
        }
    }
    else {
        if (x < 1000) {
            memcpy(obuf + por, pre.num + (x << 2) + 1, 3);
            por += 3;
        }
        else {
            memcpy(obuf + por, pre.num + (x << 2), 4);
            por += 4;
        }
    }
    memcpy(obuf + por, buf + i + 4, 12 - i);
    por += 12 - i;
}

inline void wt() {}
template <typename Head, typename... Tail>
inline void wt(Head head, Tail... tail) {
    wt(head);
    wt(tail...);
}
template <typename T>
inline void wtn(T x) {
    wt(x, '\n');
}

struct Dummy {
    Dummy() { atexit(flush); }
} dummy;

}  // namespace fastio
using fastio::rd;
using fastio::wt;
using fastio::wtn;

int main() {
    int t;
    rd(t);
    while (t--) {
        int64_t n;
        rd(n);
        auto ret = is_prime(n);
        wt(n, ' ', (int)ret, '\n');
    }
}
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結果

テストケース

ソースコード
