結果

問題 No.1138 No Bingo!
ユーザー Mister
提出日時 2020-08-18 08:44:03
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 660 ms / 3,000 ms
コード長 5,792 bytes
コンパイル時間 1,177 ms
コンパイル使用メモリ 82,460 KB
最終ジャッジ日時 2025-01-13 02:53:15
ジャッジサーバーID
（参考情報） 		judge3 / judge5
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ファイルパターン 結果
other AC * 30
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ソースコード

diff #
raw source code 

#include <iostream>
#include <vector>

template <int MOD>
struct ModInt {
    using lint = long long;
    int val;

    // constructor
    ModInt(lint v = 0) : val(v % MOD) {
        if (val < 0) val += MOD;
    };

    // unary operator
    ModInt operator+() const { return ModInt(val); }
    ModInt operator-() const { return ModInt(MOD - val); }
    ModInt inv() const { return this->pow(MOD - 2); }

    // arithmetic
    ModInt operator+(const ModInt& x) const { return ModInt(*this) += x; }
    ModInt operator-(const ModInt& x) const { return ModInt(*this) -= x; }
    ModInt operator*(const ModInt& x) const { return ModInt(*this) *= x; }
    ModInt operator/(const ModInt& x) const { return ModInt(*this) /= x; }
    ModInt pow(lint n) const {
        auto x = ModInt(1);
        auto b = *this;
        while (n > 0) {
            if (n & 1) x *= b;
            n >>= 1;
            b *= b;
        }
        return x;
    }

    // compound assignment
    ModInt& operator+=(const ModInt& x) {
        if ((val += x.val) >= MOD) val -= MOD;
        return *this;
    }
    ModInt& operator-=(const ModInt& x) {
        if ((val -= x.val) < 0) val += MOD;
        return *this;
    }
    ModInt& operator*=(const ModInt& x) {
        val = lint(val) * x.val % MOD;
        return *this;
    }
    ModInt& operator/=(const ModInt& x) { return *this *= x.inv(); }

    // compare
    bool operator==(const ModInt& b) const { return val == b.val; }
    bool operator!=(const ModInt& b) const { return val != b.val; }
    bool operator<(const ModInt& b) const { return val < b.val; }
    bool operator<=(const ModInt& b) const { return val <= b.val; }
    bool operator>(const ModInt& b) const { return val > b.val; }
    bool operator>=(const ModInt& b) const { return val >= b.val; }

    // I/O
    friend std::istream& operator>>(std::istream& is, ModInt& x) noexcept {
        lint v;
        is >> v;
        x = v;
        return is;
    }
    friend std::ostream& operator<<(std::ostream& os, const ModInt& x) noexcept { return os << x.val; }
};

template <int MOD, int Root>
struct NumberTheoreticalTransform {
    using mint = ModInt<MOD>;
    using mints = std::vector<mint>;

    std::vector<mint> zetas;

    explicit NumberTheoreticalTransform() {
        int exp = MOD - 1;
        while (true) {
            mint zeta = mint(Root).pow(exp);
            zetas.push_back(zeta);
            if (exp % 2 != 0) break;
            exp /= 2;
        }
    }

    void bitrev(mints& f) const {
        int n = f.size();

        for (int i = 0; i < n; ++i) {
            int ti = i, ni = 0;
            for (int k = 0; (1 << k) < n; ++k) {
                int b = (ti & 1);
                ti >>= 1;
                ni <<= 1;
                ni += b;
            }

            if (i < ni) {
                std::swap(f[i], f[ni]);
            }
        }
    }

    void udft(mints& f, bool isinv) const {
        if (f.size() <= 1) return;

        int l = 1;
        int k = 1 << l;
        int n = f.size();

        while (k <= n) {
            mint zeta = zetas[l];
            if (isinv) zeta = zeta.inv();

            for (int r = 0; r < n / k; ++r) {
                mint zetapow = 1;

                for (int j = 0; j < k / 2; ++j) {
                    int b = r * k + j;
                    mint t = zetapow * f[b + k / 2];

                    f[b + k / 2] = f[b] - t;
                    f[b] = f[b] + t;

                    zetapow *= zeta;
                }
            }

            ++l;
            k <<= 1;
        }
    }

    void dft(mints& f, bool isinv) const {
        bitrev(f);
        udft(f, isinv);
    }

    mints ntt(mints f, mints g) const {
        int fdeg = f.size(),
            gdeg = g.size();

        int k = 0;
        while ((1 << k) < fdeg + gdeg) ++k;

        int n = (1 << k);
        f.resize(n, mint(0));
        g.resize(n, mint(0));

        dft(f, false);
        dft(g, false);

        mints h(n);
        for (int i = 0; i < n; ++i) h[i] = f[i] * g[i];

        dft(h, true);
        h.resize(fdeg + gdeg - 1);
        for (auto& x : h) x /= n;
        return h;
    }
};

template <class T>
struct Combination {
    int max_n;
    std::vector<T> f, invf;

    explicit Combination(int n)
        : max_n(n), f(n + 1), invf(n + 1) {
        f[0] = 1;
        for (int i = 1; i <= n; ++i) {
            f[i] = f[i - 1] * i;
        }

        invf[max_n] = f[max_n].inv();
        for (int i = max_n - 1; i >= 0; --i) {
            invf[i] = invf[i + 1] * (i + 1);
        }
    }

    T fact(int n) const { return n < 0 ? T(0) : f[n]; }
    T invfact(int n) const { return n < 0 ? T(0) : invf[n]; }
    T perm(int a, int b) const {
        return a < b || b < 0 ? T(0) : f[a] * invf[a - b];
    }
    T binom(int a, int b) const {
        return a < b || b < 0 ? T(0) : f[a] * invf[a - b] * invf[b];
    }
};

constexpr int MOD = 998244353;
using mint = ModInt<MOD>;
const Combination<mint> C(200000);
const NumberTheoreticalTransform<MOD, 3> NTT;

std::vector<mint> pow(std::vector<mint> xs,
                      int n) {
    std::vector<mint> ret{1};
    while (n > 0) {
        if (n & 1) ret = NTT.ntt(ret, xs);
        n >>= 1;
        xs = NTT.ntt(xs, xs);
    }
    return ret;
}

void solve() {
    int n;
    std::cin >> n;

    std::vector<mint> bs{1, 4, 2};
    bs = pow(bs, n / 2);
    if (n % 2 == 1) bs = NTT.ntt(bs, {1, 1});

    mint ans = C.fact(n);
    for (int k = 0; k <= n; ++k) {
        ans -= mint(-1).pow(k) * C.binom(n, k) * C.fact(n - k) * 2;
    }
    for (int k = 0; k <= n; ++k) {
        ans += mint(-1).pow(k) * bs[k] * C.fact(n - k);
    }

    std::cout << ans << "\n";
}

int main() {
    std::cin.tie(nullptr);
    std::ios::sync_with_stdio(false);

    solve();

    return 0;
}
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