結果

問題 No.2379 Burnside's Theorem
ユーザー gyouzasushi
提出日時 2023-07-14 21:38:11
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 2 ms / 2,000 ms
コード長 3,817 bytes
コンパイル時間 2,318 ms
コンパイル使用メモリ 208,272 KB
最終ジャッジ日時 2025-02-15 13:46:28
ジャッジサーバーID
（参考情報） 		judge3 / judge3
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ファイルパターン 結果
sample AC * 4
other AC * 20
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 #
プレゼンテーションモードにする

#line 1 "main.cpp"
#include <bits/stdc++.h>
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define rrep(i, n) for (int i = (int)(n - 1); i >= 0; i--)
#define all(x) (x).begin(), (x).end()
#define sz(x) int(x.size())
using namespace std;
using ll = long long;
constexpr int INF = 1e9;
constexpr ll LINF = 1e18;
string YesNo(bool cond) {
    return cond ? "Yes" : "No";
}
string YESNO(bool cond) {
    return cond ? "YES" : "NO";
}
template <class T>
bool chmax(T& a, const T& b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}
template <class T>
bool chmin(T& a, const T& b) {
    if (b < a) {
        a = b;
        return true;
    }
    return false;
}
template <typename T, class F>
T bisect(T ok, T ng, const F& f) {
    while (abs(ok - ng) > 1) {
        T mid = min(ok, ng) + (abs(ok - ng) >> 1);
        (f(mid) ? ok : ng) = mid;
    }
    return ok;
}
template <typename T, class F>
T bisect_double(T ok, T ng, const F& f, int iter = 100) {
    while (iter--) {
        T mid = (ok + ng) / 2;
        (f(mid) ? ok : ng) = mid;
    }
    return ok;
}
template <class T>
vector<T> make_vec(size_t a) {
    return vector<T>(a);
}
template <class T, class... Ts>
auto make_vec(size_t a, Ts... ts) {
    return vector<decltype(make_vec<T>(ts...))>(a, make_vec<T>(ts...));
}
template <typename T>
istream& operator>>(istream& is, vector<T>& v) {
    for (int i = 0; i < int(v.size()); i++) {
        is >> v[i];
    }
    return is;
}
template <typename T>
ostream& operator<<(ostream& os, const vector<T>& v) {
    for (int i = 0; i < int(v.size()); i++) {
        os << v[i];
        if (i < sz(v) - 1) os << ' ';
    }
    return os;
}
#line 4 "/Users/gyouzasushi/kyopro/library/math/factorize.hpp"
long long modmul(long long x, long long y, long long mod) {
    using i128 = __int128_t;
    return (long long)(i128(x) * i128(y) % i128(mod));
}
long long modpow(long long a, long long n, long long mod) {
    long long ret = 1;
    while (n > 0) {
        if (n & 1) ret = modmul(ret, a, mod);
        a = modmul(a, a, mod);
        n >>= 1;
    }
    return ret;
}
long long rho(long long n) {
    long long z = 0;
    auto f = [&](long long x) -> long long {
        long long ret = modmul(x, x, n) + z;
        if (ret == n) return 0;
        return ret;
    };
    while (true) {
        long long x = ++z;
        long long y = f(x);
        while (true) {
            long long d = std::gcd(std::abs(x - y), n);
            if (d == n) break;
            if (d > 1) return d;
            x = f(x);
            y = f(f(y));
        }
    }
}
#include <initializer_list>
bool miller_rabin(long long n) {
    if (n == 1) return 0;
    long long d = n - 1, s = 0;
    while (~d & 1) d >>= 1, s++;
    auto check = [&](long long a) -> bool {
        long long x = modpow(a, d, n);
        if (x == 1) return 1;
        long long y = n - 1;
        for (int i = 0; i < s; i++) {
            if (x == y) return true;
            x = modmul(x, x, n);
        }
        return false;
    };
    for (long long a : {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}) {
        if (a >= n) break;
        if (!check(a)) return false;
    }
    return true;
}
#line 59 "/Users/gyouzasushi/kyopro/library/math/factorize.hpp"
std::map<long long, int> factorize(long long n) {
    std::map<long long, int> ret;
    while (~n & 1) n >>= 1, ret[2]++;
    std::queue<long long> q;
    q.push(n);
    while (!q.empty()) {
        long long p = q.front();
        q.pop();
        if (p == 1) continue;
        if (miller_rabin(p)) {
            ret[p]++;
            continue;
        }
        long long d = rho(p);
        q.push(d);
        q.push(p / d);
    }
    return ret;
}
#line 72 "main.cpp"
int main() {
    ll n;
    cin >> n;
    cout << YesNo(sz(factorize(n)) <= 2) << '\n';
}
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