#329553 (C++17) No.8030 ミラー・ラビン素数判定法のテスト

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問題	No.8030 ミラー・ラビン素数判定法のテスト
ユーザー	taotao54321
提出日時	2019-03-28 00:49:56
言語	C++17 (gcc 13.3.0 + boost 1.87.0)
結果	AC
実行時間	246 ms / 9,973 ms
コード長	15,856 bytes
コンパイル時間	2,221 ms
コンパイル使用メモリ	197,400 KB
最終ジャッジ日時	2025-01-07 00:34:05
ジャッジサーバーID （参考情報）	judge3 / judge1
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ファイルパターン	結果
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raw source code
/**
 * 
 */

// header {{{
#include <bits/stdc++.h>
using namespace std;

using i8   = int8_t;
using u8   = uint8_t;
using i16  = int16_t;
using u16  = uint16_t;
using i32  = int32_t;
using u32  = uint32_t;
using i64  = int64_t;
using u64  = uint64_t;
#ifdef __SIZEOF_INT128__
using i128 = __int128;
using u128 = unsigned __int128;
#endif

using f32  = float;
using f64  = double;
using f80  = __float80;
using f128 = __float128;
// }}}

template<typename T> constexpr T PROCON_INF();
template<> constexpr i64 PROCON_INF<i64>() { return 1'010'000'000'000'000'000LL; }
template<> constexpr f64 PROCON_INF<f64>() { return 1e100; }

constexpr i64 INF  = PROCON_INF<i64>();
constexpr f64 FINF = PROCON_INF<f64>();

constexpr i64 MOD = 1'000'000'007LL;

constexpr f64 EPS = 1e-12;

constexpr f64 PI = 3.14159265358979323846;

// util {{{
#define FOR(i, start, end) for(i64 i = (start), i##_end=(end); i < i##_end; ++i)
#define REP(i, n) FOR(i, 0, n)

#define ALL(f,c,...) (([&](decltype((c)) cccc) { return (f)(std::begin(cccc), std::end(cccc), ## __VA_ARGS__); })(c))
#define SLICE(f,c,l,r,...) (([&](decltype((c)) cccc, decltype((l)) llll, decltype((r)) rrrr) {\
    auto iiii = llll <= rrrr ? std::begin(cccc)+llll : std::end(cccc);\
    auto jjjj = llll <= rrrr ? std::begin(cccc)+rrrr : std::end(cccc);\
    return (f)(iiii, jjjj, ## __VA_ARGS__);\
})(c,l,r))

#define GENERIC(f) ([](auto&&... args) -> decltype(auto) { return (f)(std::forward<decltype(args)>(args)...); })

template<typename F>
class FixPoint {
public:
    explicit constexpr FixPoint(F&& f) : f_(forward<F>(f)) {}

    template<typename... Args>
    constexpr decltype(auto) operator()(Args&&... args) const {
        return f_(*this, forward<Args>(args)...);
    }

private:
    const F f_;
};

template<typename F>
decltype(auto) FIX(F&& f) {
    return FixPoint<F>(forward<F>(f));
}

template<typename C>
i64 SIZE(const C& c) { return static_cast<i64>(c.size()); }

template<typename T, size_t N>
i64 SIZE(const T (&)[N]) { return static_cast<i64>(N); }

bool is_odd (i64 x) { return x % 2 != 0; }
bool is_even(i64 x) { return x % 2 == 0; }

template<typename T> i64 cmp(T x, T y) { return (y<x) - (x<y); }
template<typename T> i64 sgn(T x) { return cmp(x, T(0)); }

i64 ipow(i64 x, i64 e) {
    assert(e >= 0);
    i64 res = 1;
    REP(_, e) {
        res *= x;
    }
    return res;
}

// Haskell の divMod と同じ
pair<i64,i64> divmod(i64 a, i64 b) {
    i64 q = a / b;
    i64 r = a % b;
    if((b>0 && r<0) || (b<0 && r>0)) {
        --q;
        r += b;
    }
    return {q,r};
}

i64 div_ceil(i64 a, i64 b) {
    i64 q = a / b;
    i64 r = a % b;
    if((b>0 && r>0) || (b<0 && r<0))
        ++q;
    return q;
}

i64 div_floor(i64 a, i64 b) {
    return divmod(a,b).first;
}

i64 modulo(i64 a, i64 b) {
    return divmod(a,b).second;
}

bool feq(f64 x, f64 y, f64 eps=EPS) {
    return fabs(x-y) < eps;
}

template<typename T, typename U>
bool chmax(T& xmax, const U& x) {
    if(xmax < x) {
        xmax = x;
        return true;
    }
    return false;
}

template<typename T, typename U>
bool chmin(T& xmin, const U& x) {
    if(x < xmin) {
        xmin = x;
        return true;
    }
    return false;
}

template<typename ForwardIt, typename T, typename Comp=less<>>
ForwardIt bsearch_find(ForwardIt first, ForwardIt last, const T& x, Comp comp={}) {
    auto it = lower_bound(first, last, x, comp);
    if(it == last || comp(x,*it)) return last;
    return it;
}

// x 未満の最後の要素
template<typename BidiIt, typename T, typename Comp=less<>>
BidiIt bsearch_lt(BidiIt first, BidiIt last, const T& x, Comp comp={}) {
    auto it = lower_bound(first, last, x, comp);
    if(it == first) return last;
    return prev(it);
}

// x 以下の最後の要素
template<typename BidiIt, typename T, typename Comp=less<>>
BidiIt bsearch_le(BidiIt first, BidiIt last, const T& x, Comp comp={}) {
    auto it = upper_bound(first, last, x, comp);
    if(it == first) return last;
    return prev(it);
}

// x より大きい最初の要素
template<typename BidiIt, typename T, typename Comp=less<>>
BidiIt bsearch_gt(BidiIt first, BidiIt last, const T& x, Comp comp={}) {
    return upper_bound(first, last, x, comp);
}

// x 以上の最初の要素
template<typename BidiIt, typename T, typename Comp=less<>>
BidiIt bsearch_ge(BidiIt first, BidiIt last, const T& x, Comp comp={}) {
    return lower_bound(first, last, x, comp);
}

template<typename InputIt>
auto SUM(InputIt first, InputIt last) {
    using T = typename iterator_traits<InputIt>::value_type;
    return accumulate(first, last, T());
}

template<typename ForwardIt, typename UnaryOperation>
ForwardIt transform_self(ForwardIt first, ForwardIt last, UnaryOperation op) {
    return transform(first, last, first, op);
}

template<typename C>
void UNIQ(C& c) {
    c.erase(ALL(unique,c), end(c));
}

template<typename T, typename F>
enable_if_t<rank<T>::value==0> ARRAY_FOREACH(T& e, F f) {
    f(e);
}

template<typename Array, typename F>
enable_if_t<rank<Array>::value!=0> ARRAY_FOREACH(Array& ary, F f) {
    for(auto& e : ary)
        ARRAY_FOREACH(e, f);
}

template<typename Array, typename U>
enable_if_t<rank<Array>::value!=0> ARRAY_FILL(Array& ary, const U& v) {
    ARRAY_FOREACH(ary, [&v](auto& e) { e = v; });
}

template<typename BinaryFunc, typename UnaryFunc>
auto ON(BinaryFunc bf, UnaryFunc uf) {
    return [bf,uf](const auto& x, const auto& y) {
        return bf(uf(x), uf(y));
    };
}

template<typename F>
auto LT_ON(F f) { return ON(less<>(), f); }

template<typename F>
auto GT_ON(F f) { return ON(greater<>(), f); }

struct IDENTITY {
    template<typename T>
    constexpr T&& operator()(T&& x) const noexcept {
        return forward<T>(x);
    }
};

char digit_chr(i64 n) {
    return static_cast<char>('0' + n);
}

i64 digit_ord(char c) {
    return c - '0';
}

char lower_chr(i64 n) {
    return static_cast<char>('a' + n);
}

i64 lower_ord(char c) {
    return c - 'a';
}

char upper_chr(i64 n) {
    return static_cast<char>('A' + n);
}

i64 upper_ord(char c) {
    return c - 'A';
}

// 出力は operator<< を直接使わず、このテンプレート経由で行う
// 提出用出力とデバッグ用出力を分けるため
template<typename T>
struct Formatter {
    static ostream& write_str(ostream& out, const T& x)  { return out << x; }
    static ostream& write_repr(ostream& out, const T& x) { return out << x; }
};

template<typename T>
ostream& WRITE_STR(ostream& out, const T& x) {
    return Formatter<T>::write_str(out, x);
}

template<typename T>
ostream& WRITE_REPR(ostream& out, const T& x) {
    return Formatter<T>::write_repr(out, x);
}

template<typename InputIt>
ostream& WRITE_JOIN_STR(ostream& out, InputIt first, InputIt last, const string& sep) {
    while(first != last) {
        WRITE_STR(out, *first++);
        if(first != last)
            out << sep;
    }
    return out;
}

template<typename InputIt>
ostream& WRITE_JOIN_REPR(ostream& out, InputIt first, InputIt last, const string& sep) {
    while(first != last) {
        WRITE_REPR(out, *first++);
        if(first != last)
            out << sep;
    }
    return out;
}

template<typename InputIt>
ostream& WRITE_RANGE_STR(ostream& out, InputIt first, InputIt last) {
    return WRITE_JOIN_STR(out, first, last, " ");
}

template<typename InputIt>
ostream& WRITE_RANGE_REPR(ostream& out, InputIt first, InputIt last) {
    out << "[";
    WRITE_JOIN_REPR(out, first, last, ", ");
    out << "]";
    return out;
}

template<typename T>
void FROM_STR(const string& s, T& x) {
    istringstream in(s);
    in >> x;
}

template<typename T>
string TO_STR(const T& x) {
    ostringstream out;
    WRITE_STR(out, x);
    return out.str();
}

template<typename T>
string TO_REPR(const T& x) {
    ostringstream out;
    WRITE_REPR(out, x);
    return out.str();
}

template<typename InputIt>
string RANGE_TO_STR(InputIt first, InputIt last) {
    ostringstream out;
    WRITE_RANGE_STR(out, first, last);
    return out.str();
}

template<typename InputIt>
string RANGE_TO_REPR(InputIt first, InputIt last) {
    ostringstream out;
    WRITE_RANGE_REPR(out, first, last);
    return out.str();
}

template<typename InputIt>
string JOIN(InputIt first, InputIt last, const string& sep) {
    ostringstream out;
    WRITE_JOIN_STR(out, first, last, sep);
    return out.str();
}

template<>
struct Formatter<i64> {
    static ostream& write_str(ostream& out, i64 x) {
        return out << x;
    }
    static ostream& write_repr(ostream& out, i64 x) {
        if(x == INF) return out << "INF";
        if(x == -INF) return out << "-INF";
        return out << x;
    }
};

template<>
struct Formatter<f64> {
    static ostream& write_str(ostream& out, f64 x) {
        return out << x;
    }
    static ostream& write_repr(ostream& out, f64 x) {
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wfloat-equal"
        if(x == FINF) return out << "FINF";
        if(x == -FINF) return out << "-FINF";
#pragma GCC diagnostic pop
        return out << x;
    }
};

template<typename T>
struct Formatter<vector<T>> {
    static ostream& write_str(ostream& out, const vector<T>& v) {
        return WRITE_RANGE_STR(out, begin(v), end(v));
    }
    static ostream& write_repr(ostream& out, const vector<T>& v) {
        out << "vector";
        return WRITE_RANGE_REPR(out, begin(v), end(v));
    }
};

template<typename T1, typename T2>
struct Formatter<pair<T1,T2>> {
    static ostream& write_str(ostream& out, const pair<T1,T2>& p) {
        WRITE_STR(out, p.first);
        out << ' ';
        WRITE_STR(out, p.second);
        return out;
    }
    static ostream& write_repr(ostream& out, const pair<T1,T2>& p) {
        out << "(";
        WRITE_REPR(out, p.first);
        out << ",";
        WRITE_REPR(out, p.second);
        out << ")";
        return out;
    }
};

template<typename... TS>
struct Formatter<tuple<TS...>> {
    template<size_t I=0, enable_if_t<I == sizeof...(TS), nullptr_t> = nullptr>
    static ostream& write_str_impl(ostream& out, const tuple<TS...>&) {
        return out;
    }
    template<size_t I=0, enable_if_t<I < sizeof...(TS), nullptr_t> = nullptr>
    static ostream& write_str_impl(ostream& out, const tuple<TS...>& t) {
        if(I != 0) out << ' ';
        WRITE_STR(out, get<I>(t));
        return write_str_impl<I+1>(out, t);
    }

    template<size_t I=0, enable_if_t<I == sizeof...(TS), nullptr_t> = nullptr>
    static ostream& write_repr_impl(ostream& out, const tuple<TS...>&) {
        if(sizeof...(TS) == 0) out << "(";
        return out << ")";
    }
    template<size_t I=0, enable_if_t<I < sizeof...(TS), nullptr_t> = nullptr>
    static ostream& write_repr_impl(ostream& out, const tuple<TS...>& t) {
        if(I == 0)
            out << "(";
        else
            out << ",";
        WRITE_REPR(out, get<I>(t));
        return write_repr_impl<I+1>(out, t);
    }

    static ostream& write_str(ostream& out, const tuple<TS...>& t) {
        return write_str_impl(out, t);
    }
    static ostream& write_repr(ostream& out, const tuple<TS...>& t) {
        return write_repr_impl(out, t);
    }
};

template<typename T>
void RD(T& x) {
    cin >> x;
#ifdef PROCON_LOCAL
    assert(cin);
#endif
}

template<typename T>
void RD(vector<T>& v, i64 n) {
    v.reserve(n);
    REP(_, n) {
        T e; RD(e);
        v.emplace_back(e);
    }
}

void PRINT() {}

template<typename T, typename... TS>
void PRINT(const T& x, const TS& ...args) {
    WRITE_STR(cout, x);
    if(sizeof...(args)) {
        cout << ' ';
        PRINT(args...);
    }
}

template<typename... TS>
void PRINTLN(const TS& ...args) {
    PRINT(args...);
    cout << '\n';
}

[[noreturn]] void EXIT() {
#ifdef PROCON_LOCAL
    cerr.flush();
#endif
    cout.flush();
    _Exit(0);
}

template<typename T>
void DBG_IMPL(i64 line, const char* expr, const T& value) {
#ifdef PROCON_LOCAL
    cerr << "[L " << line << "]: ";
    cerr << expr << " = ";
    WRITE_REPR(cerr, value);
    cerr << "\n";
#endif
}

template<typename T, size_t N>
void DBG_ARRAY_IMPL(i64 line, const char* expr, const T (&ary)[N]) {
#ifdef PROCON_LOCAL
    cerr << "[L " << line << "]: ";
    cerr << expr << " = ";
    WRITE_RANGE_REPR(cerr, begin(ary), end(ary));
    cerr << "\n";
#endif
}

template<typename InputIt>
void DBG_RANGE_IMPL(i64 line, const char* expr1, const char* expr2, InputIt first, InputIt last) {
#ifdef PROCON_LOCAL
    cerr << "[L " << line << "]: ";
    cerr << expr1 << "," << expr2 << " = ";
    WRITE_RANGE_REPR(cerr, first, last);
    cerr << "\n";
#endif
}

#define DBG(expr) DBG_IMPL(__LINE__, #expr, (expr))
#define DBG_ARRAY(expr) DBG_ARRAY_IMPL(__LINE__, #expr, (expr))
#define DBG_RANGE(first,last) DBG_RANGE_IMPL(__LINE__, #first, #last, (first), (last))

#define PAIR  make_pair
#define TUPLE make_tuple
// }}}

// init {{{
struct ProconInit {
    static constexpr int IOS_PREC = 15;
    static constexpr bool AUTOFLUSH = false;

    ProconInit() {
        cin.tie(nullptr);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(IOS_PREC);
#ifdef PROCON_LOCAL
        cerr << fixed << setprecision(IOS_PREC);
#endif
        if(AUTOFLUSH)
            cout << unitbuf;
    }
} PROCON_INIT;
// }}}

//--------------------------------------------------------------------

// Miller-Rabin 法
//
// 参考: http://miller-rabin.appspot.com/
bool is_prime_u32(u32 n) {
    static constexpr u32 AS[] {
         2,
         7,
        61,
    };

    static const auto mulmod32 = [](u32 a, u32 b, u32 m) -> u32 {
        u64 res = a;
        res *= b;
        res %= m;
        return static_cast<u32>(res);
    };

    static const auto powmod32 = [](u32 a, u32 b, u32 m) -> u32 {
        u32 res = 1;
        while(b > 0) {
            if(b & 1)
                res = mulmod32(res, a, m);
            a = mulmod32(a, a, m);
            b >>= 1;
        }
        return res;
    };

    if(n <= 1)     return false;
    if(n == 2)     return true;
    if(n % 2 == 0) return false;

    u32 d = n-1;
    u32 s = __builtin_ctz(d);
    d >>= s;

    for(u32 a : AS) {
        if(a >= n) a %= n;
        if(a == 0) continue;

        u32 x = powmod32(a, d, n);
        if(x == 1 || x == n-1) continue;

        u32 r;
        for(r = 1; r < s; ++r) {
            x = mulmod32(x, x, n);
            if(x == 1)   return false;
            if(x == n-1) break;
        }
        if(r == s) return false;
    }

    return true;
}

bool is_prime_u64(u64 n) {
    static constexpr u64 AS[] {
                 2,
               325,
              9375,
             28178,
            450775,
           9780504,
        1795265022,
    };

    static const auto mulmod64 = [](u64 a, u64 b, u64 m) -> u64 {
        u128 res = a;
        res *= b;
        res %= m;
        return static_cast<u64>(res);
    };

    static const auto powmod64 = [](u64 a, u64 b, u64 m) -> u64 {
        u64 res = 1;
        while(b > 0) {
            if(b & 1)
                res = mulmod64(res, a, m);
            a = mulmod64(a, a, m);
            b >>= 1;
        }
        return res;
    };

    if(n <= numeric_limits<u32>::max()) return is_prime_u32(static_cast<u32>(n));
    if(n % 2 == 0) return false;

    u64 d = n-1;
    u64 s = __builtin_ctzll(d);
    d >>= s;

    for(u64 a : AS) {
        if(a >= n) a %= n;
        if(a == 0) continue;

        u64 x = powmod64(a, d, n);
        if(x == 1 || x == n-1) continue;

        u64 r;
        for(r = 1; r < s; ++r) {
            x = mulmod64(x, x, n);
            if(x == 1)   return false;
            if(x == n-1) break;
        }
        if(r == s) return false;
    }

    return true;
}

void solve() {
    i64 N; RD(N);

    REP(_, N) {
        u64 X; RD(X);
        bool ans = is_prime_u64(X);
        PRINTLN(X, ans);
    }
}

signed main() {
    

    solve();

    EXIT();
}
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結果

ソースコード
