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 w2w2w2w2
提出日時 2021-07-23 05:51:19
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 241 ms / 9,973 ms
コード長 11,343 bytes
コンパイル時間 6,543 ms
コンパイル使用メモリ 311,676 KB
実行使用メモリ 5,248 KB
最終ジャッジ日時 2024-11-16 23:40:00
合計ジャッジ時間 7,856 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge2
このコードへのチャレンジ
（要ログイン）

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 1 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 147 ms
5,248 KB
testcase_05 AC 139 ms
5,248 KB
testcase_06 AC 65 ms
5,248 KB
testcase_07 AC 64 ms
5,248 KB
testcase_08 AC 65 ms
5,248 KB
testcase_09 AC 241 ms
5,248 KB
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 region Macros
#pragma GCC target("avx", "avx2")
#pragma GCC optimize("-O3", "unroll-loops")
#include <bits/stdc++.h>
using namespace std;
#if __has_include(<atcoder/all>)
#include <atcoder/convolution>
#include <atcoder/fenwicktree>
#include <atcoder/lazysegtree>
#include <atcoder/math>
#include <atcoder/maxflow>
#include <atcoder/mincostflow>
#include <atcoder/modint>
#include <atcoder/scc>
#include <atcoder/segtree>
#include <atcoder/string>
#include <atcoder/twosat>
using namespace atcoder;
#endif
using ll= long long;
using ld= long double;
using ull= unsigned long long;
using i128= __int128;
using pll= pair<ll, ll>;
using vi= vector<int>;
using vl= vector<ll>;
using vd= vector<ld>;
using vs= vector<string>;
using vi128= vector<i128>;
using vpll= vector<pll>;
using vvi= vector<vi>;
using vvl= vector<vl>;
using vvd= vector<vd>;
using vvs= vector<vs>;
using vvi128= vector<vi128>;
using vvpll= vector<vpll>;
#if __has_include(<atcoder/modint>)
using mint= modint1000000007;
// using mint = modint998244353;
using vm= vector<mint>;
using vvm= vector<vm>;
#endif
constexpr ll mod= 1e9 + 7;
// constexpr ll mod= 998244353;
#define ALL(x) (x).begin(), (x).end()
#define _overload3(_1, _2, _3, name, ...) name
#define REPBASE(i, a, b) for(ll i= (a), i##_b= (b); i < i##_b; i++)
#define RREPBASE(i, a, b) for(ll i= (a), i##_b= (b); i >= i##_b; i--)
#define LOOP(n) REPBASE(i##__COUNTER__##_##__LINE__, 0, n)
#define REPB(i, n) REPBASE(i, 0, n)
#define REPS(i, n) REPBASE(i, 1, n + 1)
#define RREP(i, n) RREPBASE(i, n - 1, 0)
#define RREPS(i, n) RREPBASE(i, n, 1)
#define REP(...) _overload3(__VA_ARGS__, REPBASE, REPB, LOOP)(__VA_ARGS__)
#define EACH(x, c) for(auto &x : c)
#define PERM(p)   \
    sort(ALL(p)); \
    for(bool(p##c)= 1; (p##c); (p##c)= next_permutation(ALL(p)))
#define eb emplace_back
#define mp make_pair
#define fi first
#define se second
#define likely(x) __builtin_expect(!!(x), 1)
#define unlikely(x) __builtin_expect(!!(x), 0)
template <class T> inline ll SZ(const T &x) { return x.size(); }
ll TOPBIT(const ll &t) { return (t == 0 ? -1 : 63 - __builtin_clzll(t)); }
ll BIT(const ll &n) { return (1LL << n); }
template <class T> inline string YES(const T &n) { return (n ? "YES" : "NO"); }
template <class T> inline string Yes(const T &n) { return (n ? "Yes" : "No"); }
template <class T> inline string yes(const T &n) { return (n ? "yes" : "no"); }
template <class T> inline void UNIQUE(T &v) {
    v.erase(unique(ALL(v)), v.end());
}
template <class T, class U> inline ll LB(const T &v, const U &x) {
    return distance(v.begin(), lower_bound(ALL(v), x));
}
template <class T, class U> inline ll UB(const T &v, const U &x) {
    return distance(v.begin(), upper_bound(ALL(v), x));
}
template <class T> inline bool chmax(T &a, const T &b) {
    if(a < b) {
        a= b;
        return 1;
    }
    return 0;
}
template <class T> inline bool chmin(T &a, const T &b) {
    if(b < a) {
        a= b;
        return 1;
    }
    return 0;
}
const vpll dx4{{1, 0}, {0, 1}, {-1, 0}, {0, -1}};
const vpll dx8{{1, 0},  {1, 1},   {0, 1},  {-1, 1},
               {-1, 0}, {-1, -1}, {0, -1}, {1, -1}};
#define VEC(name, size, ...)        \
    vector<__VA_ARGS__> name(size); \
    IN(name)
#define VV(name, h, w, ...)                                        \
    vector<vector<__VA_ARGS__>> name((h), vector<__VA_ARGS__>(w)); \
    IN(name)
#define LL(...)     \
    ll __VA_ARGS__; \
    IN(__VA_ARGS__)
#define STR(...)        \
    string __VA_ARGS__; \
    IN(__VA_ARGS__)
#define LD(...)     \
    ld __VA_ARGS__; \
    IN(__VA_ARGS__)
#define I128(...)     \
    i128 __VA_ARGS__; \
    IN(__VA_ARGS__)
void _scan() {}
template <class T, class S> void _scan(pair<T, S> &p) {
    _scan(p.fi), _scan(p.se);
}
template <class T> void _scan(T &a) { cin >> a; }
void IN() {}
template <class Head, class... Tail> void IN(Head &head, Tail &...tail) {
    _scan(head);
    IN(tail...);
}
#if __has_include(<atcoder/modint>)
inline ostream &operator<<(ostream &stream, const mint &m) {
    stream << m.val();
    return stream;
}
#endif
template <class T> inline istream &operator>>(istream &stream, vector<T> &v) {
    EACH(x, v)
    stream >> x;
    return stream;
}
template <class T>
inline ostream &operator<<(ostream &stream, const vector<T> &v) {
    ll sz= SZ(v);
    REP(i, sz) { stream << v[i] << (i == sz - 1 ? "" : " "); }
    return stream;
}
template <class T>
inline ostream &operator<<(ostream &stream, const vector<vector<T>> &v) {
    ll sz= SZ(v);
    REP(i, sz) { stream << v[i] << (i == sz - 1 ? "" : "\n"); }
    return stream;
}
template <class T, class U>
inline istream &operator>>(istream &stream, pair<T, U> &p) {
    stream >> p.fi >> p.se;
    return stream;
}
template <class T, class U>
inline ostream &operator<<(ostream &stream, const pair<T, U> &p) {
    stream << p.fi << " " << p.se;
    return stream;
}
template <class T, class U>
inline pair<T, U> operator+(pair<T, U> p, const pair<T, U> &q) {
    p+= q;
    return p;
}
template <class T, class U>
inline pair<T, U> &operator+=(pair<T, U> &p, const pair<T, U> &q) {
    p.fi+= q.fi;
    p.se+= q.se;
    return p;
}
template <class T, class U>
inline pair<T, U> operator-(pair<T, U> p, const pair<T, U> &q) {
    p-= q;
    return p;
}
template <class T, class U>
inline pair<T, U> &operator-=(pair<T, U> &p, const pair<T, U> &q) {
    p.fi-= q.fi;
    p.se-= q.se;
    return p;
}
template <class T, class U> inline pair<T, U> operator+(const pair<T, U> &p) {
    return p;
}
template <class T, class U> inline pair<T, U> operator-(const pair<T, U> &p) {
    return mp(-p.fi, -p.se);
}
inline i128 parse(string &s) {
    reverse(ALL(s));
    i128 ret= 0;
    bool minus= 0;
    if(*(s.rbegin()) == '-') {
        minus= 1;
        s.pop_back();
    }
    while(!s.empty()) {
        if('0' <= *(s.rbegin()) && *(s.rbegin()) <= '9') {
            ret= ret * 10 + *(s.rbegin()) - '0';
            s.pop_back();
        } else {
            break;
        }
    }
    reverse(ALL(s));
    if(minus) ret*= -1;
    return ret;
}
inline string to_string(i128 val) {
    string ret= "";
    bool minus= 0;
    if(val < 0) {
        minus= 1;
        val*= -1;
    }
    do {
        int digit= val % 10;
        ret+= to_string(digit);
        val/= 10;
    } while(val != 0);
    if(minus) ret+= "-";
    reverse(ALL(ret));
    return ret;
}
inline istream &operator>>(istream &stream, i128 &val) {
    string str;
    stream >> str;
    val= parse(str);
    while(!str.empty()) {
        stream.putback(*(str.rbegin()));
        str.pop_back();
    }
    return stream;
}
inline ostream &operator<<(ostream &stream, const i128 &val) {
    stream << to_string(val);
    return stream;
}
inline void print() { cout << "\n"; }
template <class Head, class... Tail>
inline void print(const Head &H, const Tail &...T) {
    cout << H;
    (cout << ... << (cout << " ", T));
    cout << endl;
}
inline void debug_out() { cout << "\n"; }
template <class Head, class... Tail>
inline void debug_out(const Head &H, const Tail &...T) {
    cout << H;
    (cout << ... << (cout << " ", T));
    cout << endl;
}
#ifdef _DEBUG
#define debug(...) debug_out(__VA_ARGS__)
#else
#define debug(...)
#endif
#pragma endregion

/* safe_mod */
/* O(1) */
constexpr ll safe_mod(ll x, const ll &m= mod) {
    x%= m;
    if(x < 0) x+= m;
    return x;
}

/* modpow */
/* O(logN) */
/* requirement : safe_mod */
constexpr ll modpow(ll a, ll b, ll m= mod) {
    ll res= 1;
    for(a= safe_mod(a, m); b; a= i128(a) * a % m, b>>= 1) {
        if(b & 1) res= i128(res) * a % m;
    }
    return res % m;
}

/* Miller-Rabin primality test */
/* requirement : safe_mod, modpow */
/* O(logN) */
bool miller_rabin(const ll &n) {
    if(n <= 1) return 0;
    if(n <= BIT(31)) {
        if(n == 2 || n == 7 || n == 61) return 1;
        if(n % 2 == 0) return 0;
        vl bases= {2, 7, 61};
        ll d= n - 1;
        while(d % 2 == 0) d/= 2;
        for(ll a : bases) {
            if(n <= a) break;
            ll t= d;
            a= modpow(a, d, n);
            while(t != n - 1 && a != 1 && a != n - 1) {
                a= a * a % n;
                t<<= 1;
            }
            if(a != n - 1 && t % 2 == 0) {
                return 0;
            }
        }
        return 1;
    } else {
        vl bases= {2, 325, 9375, 28178, 450775, 9780504, 1795265022};
        if(n % 2 == 0) return 0;
        ll d= n - 1;
        while(d % 2 == 0) d/= 2;
        for(ll a : bases) {
            ll t= d;
            a= modpow(a, d, n);
            while(t != n - 1 && a != 1 && a != n - 1) {
                a= i128(a) * a % n;
                t<<= 1;
            }
            if(a != n - 1 && t % 2 == 0) return 0;
        }
        return 1;
    }
}

vl prime_factor(ll n) {
    vl ret= {};
    while(~n & 1) {
        ret.eb(2);
        n/= 2;
    }
    while(n % 3 == 0) {
        ret.eb(3);
        n/= 3;
    }
    while(n % 5 == 0) {
        ret.eb(5);
        n/= 5;
    }
    for(ll i= 0; i < 100; i+= 30) {
        vl ps= {1, 7, 11, 13, 17, 19, 23, 29};
        REP(l, 8) {
            if(i + l == 0) continue;
            while(n % (i + ps[l]) == 0) {
                ret.eb(i + ps[l]);
                n/= i + ps[l];
            }
        }
    }
    if(n == 1) {
        return ret;
    } else if(miller_rabin(n)) {
        ret.eb(n);
        return ret;
    } else {
        queue<ll> que;
        que.emplace(n);
        while(!que.empty()) {
            // 非自明な約数を探す
            ll a= que.front();
            que.pop();
            ll m= 128;
            for(ll c= 1;; ++c) {
                ll g= 1;
                i128 y= 2, x, q= 1, ys;
                for(ll r= 1; g == 1; r<<= 1) {
                    x= y;
                    REP(i, r) y= (y * y + c) % a;
                    for(ll k= 0; k < r && g == 1; k+= m) {
                        ys= y;
                        REP(min(m, r - k)) {
                            y= (y * y + c) % a;
                            q*= x - y;
                            q%= a;
                        }
                        q= abs((ll)q);
                        g= gcd((ll)q, a);
                        debug(c, r, k, q, g, a);
                    }
                }
                if(g == a) {
                    g= 1;
                    while(g == 1) {
                        ys= (ys * ys + c) % a;
                        g= gcd(abs(ll(x - ys)), a);
                        debug(g, ys);
                    }
                }
                if(g < a) {
                    if(miller_rabin(g)) {
                        ret.eb(g);
                    } else {
                        que.emplace(g);
                    }
                    if(miller_rabin(a / g)) {
                        ret.eb(a / g);
                    } else {
                        que.emplace(a / g);
                    }
                    break;
                }
            }
        }
        sort(ALL(ret));
        return ret;
    }
}

signed main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(12);
    LL(Q);
    REP(Q) {
        LL(A);
        print(A, miller_rabin(A));
    }
    // print(miller_rabin(3896644057));
    // REP(Q) {
    //     LL(A);
    //     vl fact= prime_factor(A);
    //     print(SZ(fact),fact);
    // }
}
0