結果

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 2023-03-02 21:23:26
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
WA  
実行時間 -
コード長 7,912 bytes
コンパイル時間 2,228 ms
コンパイル使用メモリ 197,520 KB
最終ジャッジ日時 2025-02-11 01:15:28
ジャッジサーバーID
（参考情報） 		judge5 / judge1
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ファイルパターン 結果
other AC * 4 WA * 6
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ソースコード

diff # 

#line 2 "template.hpp"
#include<bits/stdc++.h>
using namespace std;
#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 = vector<vector<int>>;
using P = pair<int, int>;
constexpr int inf = 1e9;
constexpr ll infl = 1e18;
constexpr ld eps = 1e-6;
constexpr long double pi = acos(-1);
constexpr ll MOD = 1e9 + 7;
constexpr ll MOD2 = 998244353;
constexpr int dx[] = { 1,0,-1,0 };
constexpr int dy[] = { 0,1,0,-1 };
template<class T>inline void chmax(T&x,T y){if(x<y)x=y;}
template<class T>inline void chmin(T&x,T y){if(x>y)x=y;}
#line 2 "math/montgomery.hpp"
class 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;
    }
public:
    static void set_mod(const u128& m) {
        assert(m < (i128(1) << 64));
        assert((m & 1) == 1);
        mod = m;
        n2 = -u128(m) % m;
        r = get_r();
        assert(r * mod == 1);
    }

protected:
    i128 a;

public:
    montgomery64() : a(0) {}
    template<typename T>
    montgomery64(const T& b) : a(reduce((u128(b) + mod)* n2)) {};
private:
    template<class T>
    static u64 reduce(const T& b) {
        return (b + u128(u64(b) * u64(-r)) * mod) >> 64;
    }
public:
    template<class T>
    mint& operator=(const T& rhs) {
        return (*this) = mint(rhs);
    }

    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.inv();
        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.val();
    }

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

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

    u64 val() 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;

class ArbitraryModInt {
    using mint = ArbitraryModInt;
    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;
    }
public:
    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);
    }
protected:
    u32 a;
public:
    ArbitraryModInt() : a(0) {}
    ArbitraryModInt(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 = ArbitraryModInt(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 ArbitraryModInt::u32 ArbitraryModInt::mod;
typename ArbitraryModInt::u32 ArbitraryModInt::r;
typename ArbitraryModInt::u32 ArbitraryModInt::n2;
/// @brief Montgomery
///by https://nyaannyaan.github.io/library/modint/modint-montgomery64.hpp,https://nyaannyaan.github.io/library/modint/arbitrary-prime-modint.hpp
#line 3 "main.test.cpp"

namespace fast_prime{
    //fast_is_prime
    using u64 = uint64_t;
    namespace miller_rabin{

        constexpr u64 bases_int[] = {2, 7, 67};
        constexpr u64 bases_long[] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022};

        template<typename mint>
        bool miller_rabin(u64 n, const u64 bases[],const int len){
            if (mint::get_mod() != n){
                mint::set_mod(n);
            }

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

            const mint e1 = 1, e2 = n - 1;

            for (int i = 0; i < len; i++){
                u64 a = bases[i];

                if (n <= a){
                    break;
                }

                u64 t = d;
                mint y = mint(a).pow(t);

                while(t!=n-1&&y!=e1&&y!=e2){
                    y *= y;
                    t <<= 1;
                }

                if (y != e2 && (~t & 1ul)){
                    return false;
                }
            }

            return true;
        }

        bool is_prime(u64 n){
            if (n == 2){
                return true;
            }
            else if (n < 2||(~n & 1)){
                return false;
            }

            if (n < (1ul << 30)){
                return miller_rabin<ArbitraryModInt>(n, bases_int, 3);
            }
            else{
                return miller_rabin<montgomery64>(n, bases_long, 7);
            }
        }
    };
};
using fast_prime::miller_rabin::is_prime;
int main(){
    int n;
    cin >> n;
    while (n--){
        unsigned long long x;
        cin>>x;
        cout << x << ' ';
        if(is_prime(x)){
            cout << "1\n";
        }else{
            cout << "0\n";
        }
    }
}
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