結果

問題 No.2264 Gear Coloring
ユーザー 🍮かんプリン🍮かんプリン
提出日時 2023-04-08 23:21:51
言語 C++14
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 67 ms / 2,000 ms
コード長 6,187 bytes
コンパイル時間 2,435 ms
コンパイル使用メモリ 179,024 KB
実行使用メモリ 6,944 KB
最終ジャッジ日時 2024-04-14 19:08:43
合計ジャッジ時間 3,098 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge4
このコードへのチャレンジ
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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 2 ms
6,816 KB
testcase_01 AC 2 ms
6,816 KB
testcase_02 AC 2 ms
6,944 KB
testcase_03 AC 2 ms
6,944 KB
testcase_04 AC 1 ms
6,944 KB
testcase_05 AC 2 ms
6,944 KB
testcase_06 AC 2 ms
6,944 KB
testcase_07 AC 2 ms
6,940 KB
testcase_08 AC 2 ms
6,944 KB
testcase_09 AC 2 ms
6,940 KB
testcase_10 AC 2 ms
6,944 KB
testcase_11 AC 2 ms
6,944 KB
testcase_12 AC 2 ms
6,944 KB
testcase_13 AC 2 ms
6,940 KB
testcase_14 AC 11 ms
6,940 KB
testcase_15 AC 3 ms
6,944 KB
testcase_16 AC 67 ms
6,944 KB
testcase_17 AC 3 ms
6,940 KB
testcase_18 AC 3 ms
6,944 KB
testcase_19 AC 5 ms
6,940 KB
testcase_20 AC 3 ms
6,944 KB
testcase_21 AC 2 ms
6,944 KB
権限があれば一括ダウンロードができます
コンパイルメッセージ
main.cpp: In function 'int main()':
main.cpp:214:15: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17' [-Wc++17-extensions]
  214 |     for (auto [p,e] : v) {
      |               ^

ソースコード

diff # 

/**
 *   @FileName	a.cpp
 *   @Author	kanpurin
 *   @Created	2023.04.08 23:21:45
**/

#include "bits/stdc++.h" 
using namespace std; 
typedef long long ll;


template< int MOD >
struct mint {
public:
    unsigned int x;
    mint() : x(0) {}
    mint(long long v) {
        long long w = (long long)(v % (long long)(MOD));
        if (w < 0) w += MOD;
        x = (unsigned int)(w);
    }
    mint(std::string &s) {
        unsigned int z = 0;
        for (int i = 0; i < s.size(); i++) {
            z *= 10;
            z += s[i] - '0';
            z %= MOD;
        }
        x = z;
    }
    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }
    mint& operator+=(const mint &a) {
        if ((x += a.x) >= MOD) x -= MOD;
        return *this;
    }
    mint& operator-=(const mint &a) {
        if ((x -= a.x) >= MOD) x += MOD;
        return *this;
    }
    mint& operator*=(const mint &a) {
        unsigned long long z = x;
        z *= a.x;
        x = (unsigned int)(z % MOD);
        return *this;
    }
    mint& operator/=(const mint &a) {return *this = *this * a.inv(); }
    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs.x == rhs.x;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs.x != rhs.x;
    }
    friend std::ostream& operator<<(std::ostream &os, const mint &n) {
        return os << n.x;
    }
    friend std::istream &operator>>(std::istream &is, mint &n) {
        unsigned int x;
        is >> x;
        n = mint(x);
        return is;
    }
    mint inv() const {
        assert(x);
        return pow(MOD-2);
    }
    mint pow(long long n) const {        
        assert(0 <= n);
        mint p = *this, r = 1;
        while (n) {
            if (n & 1) r *= p;
            p *= p;
            n >>= 1;
        }
        return r;
    }
    
    mint sqrt() const {
        if (this->x < 2) return *this;
        if (this->pow((MOD-1)>>1).x != 1) return mint(0);
        mint b = 1, one = 1;
        while (b.pow((MOD-1) >> 1) == 1) b += one;
        long long m = MOD-1, e = 0;
        while (m % 2 == 0) m >>= 1, e += 1;
        mint x = this->pow((m - 1) >> 1);
        mint y = (*this) * x * x;
        x *= (*this);
        mint z = b.pow(m);
        while (y.x != 1) {
            int j = 0;
            mint t = y;
            while (t != one) j += 1, t *= t;
            z = z.pow(1LL << (e-j-1));
            x *= z; z *= z; y *= z; e = j;
        }
        return x;
    }
};

constexpr int MOD = 998244353;

bool isprime(long long N) {
    if (N <= 1) return false;
    if (N == 2) return true;
    if (N % 2 == 0) return false;

    auto modpow = [](__int128_t a, long long n, long long mo) {
        __int128_t r = 1;
        a %= mo;
        while (n) r = r * ((n % 2) ? a : 1) % mo, a = a * a % mo, n >>= 1;
        return r;
    };

    std::vector<long long> A = {2, 325, 9375, 28178, 450775,
                           9780504, 1795265022};
    long long s = 0, d = N - 1;
    while (d % 2 == 0) d >>= 1, s++;

    for (long long a : A) {
        if (a % N == 0) return true;
        long long j, r = modpow(a, d, N);
        if (r == 1) continue;
        for (j = 0; j < s; j++) {
            if (r == N - 1) break;
            r = __int128_t(r) * r % N;
        }
        if (j == s) return false;
    }
    return true;
}

long long PollardRho(long long N) {
    if (N % 2 == 0) return 2;
    long long m = 1LL<<(70-__builtin_clrsbll(N))/8;
    for (long long c = 1; c < N; c++) {
        auto f = [&](long long x) { return ((__int128_t)x*x+c)%N; };
        long long x,y,g,q,r,k,ys;
        y = k = 0;
        g = q = r = 1;
        while (g == 1) {
            x = y;
            while(k < 3*r/4) {
                y = f(y);
                k += 1;
            }
            while(k < r && g == 1) {
                ys = y;
                for (int _ = 0; _ < min(m,r-k); _++) {
                    y = f(y);
                    q = (__int128_t)q*abs(x-y)%N;
                }
                g = __gcd(q,N);
                k += m;
            }
            k = r;
            r <<= 1;
        }
        if (g == N) {
            g = 1;
            y = ys;
            while(g == 1) {
                y = f(y);
                g = __gcd(abs(x-y),N);
            }
        }
        if (g == N) continue;
        if (isprime(g)) return g;
        else if (isprime(N/g)) return N/g;
        else return PollardRho(g);
    }
    return -1; 
}

vector<pair<long long,int>> prime_factorization(long long N) {
    vector<pair<long long,int>> res;
    while(!isprime(N) && N > 1) {
        long long p = PollardRho(N);
        int cnt = 0;
        while(N%p==0) {
            N /= p;
            cnt++;
        }
        res.push_back({p,cnt});
    }
    if (N > 1) res.push_back({N,1});
    sort(res.begin(), res.end());
    return res;
}

int main() {
    int n,m;cin >> n >> m;
    vector<int> a(n);
    int L = 1;
    for (int i = 0; i < n; i++) {
        cin >> a[i];
        L = (ll)L * a[i] / __gcd(a[i],L);
    }
    auto v = prime_factorization(L);
    vector<int> divisor,euler;
    divisor.push_back(1);
    euler.push_back(1);
    for (auto [p,e] : v) {
        int sz = divisor.size();
        for (int i = 0; i < e; i++) {
            for (int j = sz*i; j < sz*(i+1); j++) {
                divisor.push_back(divisor[j]*p);
                euler.push_back(euler[j]*(p-!i));
            }
        }
    }
    mint<MOD> ans = 0;
    for (int i = 0; i < euler.size(); i++) {
        int d = L/divisor[i];
        ll total = 0;
        for (int j = 0; j < n; j++) {
            total += __gcd(d,a[j]);
        }
        ans += mint<MOD>(m).pow(total)*euler[i];
    }
    cout << ans/L << endl;
    return 0;
}
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