結果

問題 No.1302 Random Tree Score
ユーザー Kite_kuma
提出日時 2020-11-09 12:22:21
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 753 ms / 3,000 ms
コード長 4,102 bytes
コンパイル時間 1,703 ms
コンパイル使用メモリ 176,092 KB
実行使用メモリ 9,304 KB
最終ジャッジ日時 2024-07-22 16:00:26
合計ジャッジ時間 8,212 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 14
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

/*  author:  Kite_kuma
    created: 2020.11.09 12:08:40 */
// #ifdef LOCAL
// #define _GLIBCXX_DEBUG
// #endif
#include <bits/stdc++.h>
using namespace std;
const int mod = 998244353;
const int root = 3;
unsigned int add(const unsigned int x, const unsigned int y) { return (x + y < mod) ? x + y : x + y - mod; }
unsigned int sub(const unsigned int x, const unsigned int y) { return (x >= y) ? (x - y) : (mod - y + x); }
unsigned int mul(const unsigned int x, const unsigned int y) { return (unsigned long long)x * y % mod; }
unsigned int mod_pow(unsigned int x, unsigned int n) {
    unsigned int res = 1;
    while(n > 0) {
        if(n & 1) {
            res = mul(res, x);
        }
        x = mul(x, x);
        n >>= 1;
    }
    return res;
}
unsigned int inverse(const unsigned int x) { return mod_pow(x, mod - 2); }
void ntt(vector<int> &a, const bool rev = false) {
    unsigned int i, j, k, l, p, q, r, s;
    const unsigned int size = a.size();
    if(size == 1) return;
    vector<int> b(size);
    r = rev ? (mod - 1 - (mod - 1) / size) : (mod - 1) / size;
    s = mod_pow(root, r);
    vector<unsigned int> kp(size / 2 + 1, 1);
    for(i = 0; i < size / 2; ++i) kp[i + 1] = mul(kp[i], s);
    for(i = 1, l = size / 2; i < size; i <<= 1, l >>= 1) {
        for(j = 0, r = 0; j < l; ++j, r += i) {
            for(k = 0, s = kp[i * j]; k < i; ++k) {
                p = a[k + r], q = a[k + r + size / 2];
                b[k + 2 * r] = add(p, q);
                b[k + 2 * r + i] = mul(sub(p, q), s);
            }
        }
        swap(a, b);
    }
    if(rev) {
        s = inverse(size);
        for(i = 0; i < size; i++) {
            a[i] = mul(a[i], s);
        }
    }
}
vector<int> convolute(const vector<int> &a, const vector<int> &b) {
    const int size = (int)a.size() + (int)b.size() - 1;
    int t = 1;
    while(t < size) {
        t <<= 1;
    }
    vector<int> A(t, 0), B(t, 0);
    for(int i = 0; i < (int)a.size(); i++) {
        A[i] = a[i];
    }
    for(int i = 0; i < (int)b.size(); i++) {
        B[i] = b[i];
    }
    ntt(A), ntt(B);
    for(int i = 0; i < t; i++) {
        A[i] = mul(A[i], B[i]);
    }
    ntt(A, true);
    A.resize(size);
    return A;
}
#pragma region modint
template <int mod>
struct ModInt {
    int x;
    ModInt() : x(0) {}
    ModInt(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
    ModInt &operator+=(const ModInt &p) {
        if((x += p.x) >= mod) x -= mod;
        return *this;
    }
    ModInt &operator-=(const ModInt &p) {
        if((x += mod - p.x) >= mod) x -= mod;
        return *this;
    }
    ModInt &operator*=(const ModInt &p) {
        x = (int)(1LL * x * p.x % mod);
        return *this;
    }
    ModInt &operator/=(const ModInt &p) {
        *this *= p.inverse();
        return *this;
    }
    ModInt operator-() const { return ModInt(-x); }
    ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
    ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
    ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
    ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
    bool operator==(const ModInt &p) const { return x == p.x; }
    bool operator!=(const ModInt &p) const { return x != p.x; }
    ModInt inverse() const {
        int a = x, b = mod, u = 1, v = 0, t;
        while(b > 0) {
            t = a / b;
            swap(a -= t * b, b);
            swap(u -= t * v, v);
        }
        return ModInt(u);
    }
    ModInt pow(long long n) const {
        ModInt ret(1), mul(x);
        while(n > 0) {
            if(n & 1) ret *= mul;
            mul *= mul;
            n >>= 1;
        }
        return ret;
    }
    friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; }
    friend istream &operator>>(istream &is, ModInt &a) {
        long long t;
        is >> t;
        a = ModInt<mod>(t);
        return (is);
    }
    static int get_mod() { return mod; }
};
using mint = ModInt<mod>;
#pragma endregion
int main() {
    int n;
    cin >> n;
    vector<mint> fac(n + 2);
    fac[0] = 1;
    for(int i = 0; i < n + 1; i++) {
        fac[i + 1] = fac[i] * (i + 1);
    }
    vector<int> fx(n - 1);
    for(int i = 0; i < n - 1; i++) {
        fx[i] = ((mint)(i + 1) / fac[i]).x;
    }
    int k = n;
    vector<int> res = {1};
    while(k) {
        if(k & 1) {
            res = convolute(res, fx);
            if(res.size() >= n) res.resize(n - 1);
        }
        fx = convolute(fx, fx);
        if(fx.size() >= n) fx.resize(n - 1);
        k >>= 1;
    }
    res.resize(n - 1);
    cout << fac[n - 2] * res[n - 2] / mod_pow(n, n - 2) << endl;
    
    return 0;
}
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