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 satashun
提出日時 2022-02-27 20:43:57
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 268 ms / 9,973 ms
コード長 5,813 bytes
コンパイル時間 2,200 ms
コンパイル使用メモリ 199,608 KB
最終ジャッジ日時 2025-01-28 03:44:41
ジャッジサーバーID
（参考情報） 		judge2 / judge5
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ファイルパターン 結果
other AC * 10
権限があれば一括ダウンロードができます

ソースコード

diff # 

//#pragma GCC optimize("Ofast")
//#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>

#include <atcoder/modint>
using namespace std;
using namespace atcoder;

using ll = long long;
using ull = unsigned long long;
using pii = pair<int, int>;
using Mint = modint998244353;

template <class T>
using V = vector<T>;
template <class T>
using VV = V<V<T>>;

template <class T>
V<T> make_vec(size_t a) {
    return V<T>(a);
}

template <class T, class... Ts>
auto make_vec(size_t a, Ts... ts) {
    return V<decltype(make_vec<T>(ts...))>(a, make_vec<T>(ts...));
}

#define pb push_back
#define eb emplace_back
#define mp make_pair
#define fi first
#define se second
#define rep(i, n) rep2(i, 0, n)
#define rep2(i, m, n) for (int i = m; i < (n); i++)
#define per(i, b) per2(i, 0, b)
#define per2(i, a, b) for (int i = int(b) - 1; i >= int(a); i--)
#define ALL(c) (c).begin(), (c).end()
#define SZ(x) ((int)(x).size())

constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); }

template <class T, class U>
void chmin(T& t, const U& u) {
    if (t > u) t = u;
}
template <class T, class U>
void chmax(T& t, const U& u) {
    if (t < u) t = u;
}

template <class T>
void mkuni(vector<T>& v) {
    sort(ALL(v));
    v.erase(unique(ALL(v)), end(v));
}

template <class T>
vector<int> sort_by(const vector<T>& v) {
    vector<int> res(v.size());
    iota(res.begin(), res.end(), 0);
    sort(res.begin(), res.end(), [&](int i, int j) { return v[i] < v[j]; });
    return res;
}

template <class T, class U>
istream& operator>>(istream& is, pair<T, U>& p) {
    is >> p.first >> p.second;
    return is;
}

template <class T, class U>
ostream& operator<<(ostream& os, const pair<T, U>& p) {
    os << "(" << p.first << "," << p.second << ")";
    return os;
}

template <class T>
istream& operator>>(istream& is, vector<T>& v) {
    for (auto& x : v) {
        is >> x;
    }
    return is;
}

template <class T>
ostream& operator<<(ostream& os, const vector<T>& v) {
    os << "{";
    rep(i, v.size()) {
        if (i) os << ",";
        os << v[i];
    }
    os << "}";
    return os;
}

template <class T>
auto operator<<(ostream& os, T t) ->
    typename std::enable_if_t<internal::is_modint<T>::value, ostream&> {
    os << t.val();
    return os;
}

#ifdef LOCAL
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
    cerr << " " << H;
    debug_out(T...);
}
#define debug(...) \
    cerr << __LINE__ << " [" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#define dump(x) cerr << __LINE__ << " " << #x << " = " << (x) << endl
#else
#define debug(...) (void(0))
#define dump(x) (void(0))
#endif

template <class T>
void scan(vector<T>& v, T offset = T(0)) {
    for (auto& x : v) {
        cin >> x;
        x += offset;
    }
}

template <class T>
void print(T x, int suc = 1) {
    cout << x;
    if (suc == 1)
        cout << "\n";
    else if (suc == 2)
        cout << " ";
}

template <class T>
void print(const vector<T>& v, int suc = 1) {
    for (int i = 0; i < v.size(); ++i)
        print(v[i], i == int(v.size()) - 1 ? suc : 2);
}

struct prepare_io {
    prepare_io() {
        cin.tie(nullptr);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(10);
    }
} prep_io;

template <class T>
T powmod(T x, ll k, T m) {
    x %= m;
    T res(1);
    while (k) {
        if (k & 1) {
            res = res * x % m;
        }
        k >>= 1;
        x = x * x % m;
    }
    return res;
}

// O(sqrt(x))
bool is_prime(ll x) {
    if (x <= 1) return false;
    for (ll i = 2; i * i <= x; ++i) {
        if (x % i == 0) return false;
    }
    return true;
}

// see : https://joisino.hatenablog.com/entry/2017/08/03/210000
// test : https://yukicoder.me/problems/no/3030
// ref : http://miller-rabin.appspot.com/
// check if n is prime
// n < 4,759,123,141 -> always correct
// O(k log^3 n)
bool miller_rabin(ll n) {
    static const vector<ll> v = {2, 7, 61};
    // static const vector<ll> v = {2, 325, 9375, 28178, 450775, 9780504,
    // 1795265022};
    if (n < 2) {
        return false;
    }
    ll d = n - 1;
    ll s = 0;
    while (d % 2 == 0) {
        d /= 2;
        s++;
    }
    for (auto a : v) {
        if (a == n) {
            return true;
        }
        if (powmod(a, d, n) != 1) {
            bool ok = true;
            for (ll r = 0; r < s; r++) {
                if (powmod(a, d * (1LL << r), n) == n - 1) {
                    ok = false;
                    break;
                }
            }
            if (ok) return false;
        }
    }
    return true;
}

using R = __int128_t;
using ull = unsigned long long;
bool miller_rabin_big(ull n) {
    static const vector<R> v = {2,      325,     9375,      28178,
                                450775, 9780504, 1795265022};

    if (n < 2) {
        return false;
    } else if (n == 2) {
        return true;
    } else if (n % 2 == 0) {
        return false;
    }

    ull d = n - 1;
    ll s = 0;
    while (d % 2 == 0) {
        d /= 2;
        s++;
    }
    for (auto a : v) {
        if (a % n == 0) continue;
        auto x = powmod(a, d, R(n));
        if (x == 1 || x == n - 1) continue;

        for (R r = 0; r < s; r++) {
            auto y = x * x % n;
            if (y == 1) {
                if (x != 1 && x != n - 1) {
                    return false;
                } else {
                    x = 1;
                    break;
                }
            }
            x = y;
        }
        if (x != 1) return false;
    }
    return true;
}

int main() {
    int q;
    cin >> q;
    while (q--) {
        ll x;
        cin >> x;
        cout << x << ' ';
        if (miller_rabin_big(x)) {
            print("1");
        } else {
            print("0");
        }
    }
    return 0;
}
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