#587153 (C++14) No.1302 Random Tree Score

• 問題: No.1302 Random Tree Score
• ユーザー: masayoshi361
• 提出日時: 2020-11-30 08:41:17
• 言語: C++14 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 826 ms / 3,000 ms
• コード長: 16,838 bytes
• コンパイル時間: 2,873 ms
• コンパイル使用メモリ: 191,980 KB
• 実行使用メモリ: 10,768 KB
• 最終ジャッジ日時: 2024-09-13 02:14:24
• 合計ジャッジ時間: 9,627 ms
• ジャッジサーバーID （参考情報）: judge4 / judge3

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 6,812 KB
testcase_01	AC	2 ms; 6,944 KB
testcase_02	AC	150 ms; 6,940 KB
testcase_03	AC	359 ms; 7,152 KB
testcase_04	AC	142 ms; 6,944 KB
testcase_05	AC	826 ms; 10,000 KB
testcase_06	AC	678 ms; 10,168 KB
testcase_07	AC	139 ms; 6,940 KB
testcase_08	AC	400 ms; 7,480 KB
testcase_09	AC	647 ms; 10,768 KB
testcase_10	AC	679 ms; 8,912 KB
testcase_11	AC	128 ms; 6,940 KB
testcase_12	AC	767 ms; 9,908 KB
testcase_13	AC	2 ms; 6,940 KB
testcase_14	AC	657 ms; 10,388 KB
testcase_15	AC	744 ms; 10,512 KB
testcase_16	AC	2 ms; 6,940 KB

ソースコード

#line 1 "verify/FPS.power.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/1302"
#line 1 "library/template/template.cpp"
/* #region header */

#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
using namespace std;
// types
using ll = long long;
using ull = unsigned long long;
using ld = long double;
typedef pair<ll, ll> Pl;
typedef pair<int, int> Pi;
typedef vector<ll> vl;
typedef vector<int> vi;
typedef vector<char> vc;
template <typename T>
using mat = vector<vector<T>>;
typedef vector<vector<int>> vvi;
typedef vector<vector<long long>> vvl;
typedef vector<vector<char>> vvc;
// abreviations
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define rep_(i, a_, b_, a, b, ...) for (ll i = (a), max_i = (b); i < max_i; i++)
#define rep(i, ...) rep_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
#define rrep_(i, a_, b_, a, b, ...) \
    for (ll i = (b - 1), min_i = (a); i >= min_i; i--)
#define rrep(i, ...) rrep_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
#define srep(i, a, b, c) for (ll i = (a), max_i = (b); i < max_i; i += c)
#define SZ(x) ((int)(x).size())
#define pb(x) push_back(x)
#define eb(x) emplace_back(x)
#define mp make_pair
//入出力
#define print(x) cout << x << endl
template <class T>
ostream& operator<<(ostream& os, const vector<T>& v) {
    for (auto& e : v) cout << e << " ";
    cout << endl;
    return os;
}
void scan(int& a) { cin >> a; }
void scan(long long& a) { cin >> a; }
void scan(char& a) { cin >> a; }
void scan(double& a) { cin >> a; }
void scan(string& a) { cin >> a; }
template <class T>
void scan(vector<T>& a) {
    for (auto& i : a) scan(i);
}
#define vsum(x) accumulate(all(x), 0LL)
#define vmax(a) *max_element(all(a))
#define vmin(a) *min_element(all(a))
#define lb(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define ub(c, x) distance((c).begin(), upper_bound(all(c), (x)))
// functions
// gcd(0, x) fails.
ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }
template <class T>
bool chmax(T& a, const T& b) {
    if (a < b) {
        a = b;
        return 1;
    }
    return 0;
}
template <class T>
bool chmin(T& a, const T& b) {
    if (b < a) {
        a = b;
        return 1;
    }
    return 0;
}
template <typename T>
T mypow(T x, ll n) {
    T ret = 1;
    while (n > 0) {
        if (n & 1) (ret *= x);
        (x *= x);
        n >>= 1;
    }
    return ret;
}
ll modpow(ll x, ll n, const ll mod) {
    ll ret = 1;
    while (n > 0) {
        if (n & 1) (ret *= x);
        (x *= x);
        n >>= 1;
        x %= mod;
        ret %= mod;
    }
    return ret;
}

uint64_t my_rand(void) {
    static uint64_t x = 88172645463325252ULL;
    x = x ^ (x << 13);
    x = x ^ (x >> 7);
    return x = x ^ (x << 17);
}
int popcnt(ull x) { return __builtin_popcountll(x); }
template <typename T>
vector<int> IOTA(vector<T> a) {
    int n = a.size();
    vector<int> id(n);
    iota(all(id), 0);
    sort(all(id), [&](int i, int j) { return a[i] < a[j]; });
    return id;
}
struct Timer {
    clock_t start_time;
    void start() { start_time = clock(); }
    int lap() {
        // return x ms.
        return (clock() - start_time) * 1000 / CLOCKS_PER_SEC;
    }
};
/* #endregion*/
// constant
#define inf 1000000000ll
#define INF 4000000004000000000LL
#define endl '\n'
const long double eps = 0.000000000000001;
const long double PI = 3.141592653589793;
#line 3 "verify/FPS.power.test.cpp"
// library
#line 1 "library/convolution/NTT.cpp"
template <typename Mint>
struct NTT {
    vector<Mint> dw, idw;
    int max_base;
    Mint root;

    NTT() {
        const unsigned Mod = Mint::get_mod();
        assert(Mod >= 3 && Mod % 2 == 1);
        auto tmp = Mod - 1;
        max_base = 0;
        while (tmp % 2 == 0) tmp >>= 1, max_base++;
        root = 2;
        while (root.pow((Mod - 1) >> 1) == 1) root += 1;
        assert(root.pow(Mod - 1) == 1);
        dw.resize(max_base);
        idw.resize(max_base);
        for (int i = 0; i < max_base; i++) {
            dw[i] = -root.pow((Mod - 1) >> (i + 2));
            idw[i] = Mint(1) / dw[i];
        }
    }

    void ntt(vector<Mint>& a) {
        const int n = (int)a.size();
        assert((n & (n - 1)) == 0);
        assert(__builtin_ctz(n) <= max_base);
        for (int m = n; m >>= 1;) {
            Mint w = 1;
            for (int s = 0, k = 0; s < n; s += 2 * m) {
                for (int i = s, j = s + m; i < s + m; ++i, ++j) {
                    auto x = a[i], y = a[j] * w;
                    a[i] = x + y, a[j] = x - y;
                }
                w *= dw[__builtin_ctz(++k)];
            }
        }
    }

    void intt(vector<Mint>& a, bool f = true) {
        const int n = (int)a.size();
        assert((n & (n - 1)) == 0);
        assert(__builtin_ctz(n) <= max_base);
        for (int m = 1; m < n; m *= 2) {
            Mint w = 1;
            for (int s = 0, k = 0; s < n; s += 2 * m) {
                for (int i = s, j = s + m; i < s + m; ++i, ++j) {
                    auto x = a[i], y = a[j];
                    a[i] = x + y, a[j] = (x - y) * w;
                }
                w *= idw[__builtin_ctz(++k)];
            }
        }
        if (f) {
            Mint inv_sz = Mint(1) / n;
            for (int i = 0; i < n; i++) a[i] *= inv_sz;
        }
    }

    vector<Mint> multiply(vector<Mint> a, vector<Mint> b) {
        int need = a.size() + b.size() - 1;
        int nbase = 1;
        while ((1 << nbase) < need) nbase++;
        int sz = 1 << nbase;
        a.resize(sz, 0);
        b.resize(sz, 0);
        ntt(a);
        ntt(b);
        Mint inv_sz = Mint(1) / sz;
        for (int i = 0; i < sz; i++) a[i] *= b[i] * inv_sz;
        intt(a, false);
        a.resize(need);
        return a;
    }
};
#line 1 "library/math/FormalPowerSeries.cpp"
template <typename T>
struct FormalPowerSeries : vector<T> {
    using vector<T>::vector;
    using P = FormalPowerSeries;

    using MULT = function<P(P, P)>;

    static MULT& get_mult() {
        static MULT mult = nullptr;
        return mult;
    }

    static void set_fft(MULT f) { get_mult() = f; }

    // 末尾の0を消す
    void shrink() {
        while (this->size() && this->back() == T(0)) this->pop_back();
    }

    P operator+(const P& r) const { return P(*this) += r; }

    P operator+(const T& v) const { return P(*this) += v; }

    P operator-(const P& r) const { return P(*this) -= r; }

    P operator-(const T& v) const { return P(*this) -= v; }

    P operator*(const P& r) const { return P(*this) *= r; }

    P operator*(const T& v) const { return P(*this) *= v; }

    P operator/(const P& r) const { return P(*this) /= r; }

    P operator%(const P& r) const { return P(*this) %= r; }

    P& operator+=(const P& r) {
        if (r.size() > this->size()) this->resize(r.size());
        for (int i = 0; i < r.size(); i++) (*this)[i] += r[i];
        return *this;
    }

    P& operator+=(const T& r) {
        if (this->empty()) this->resize(1);
        (*this)[0] += r;
        return *this;
    }

    P& operator-=(const P& r) {
        if (r.size() > this->size()) this->resize(r.size());
        for (int i = 0; i < r.size(); i++) (*this)[i] -= r[i];
        shrink();
        return *this;
    }

    P& operator-=(const T& r) {
        if (this->empty()) this->resize(1);
        (*this)[0] -= r;
        shrink();
        return *this;
    }

    P& operator*=(const T& v) {
        const int n = (int)this->size();
        for (int k = 0; k < n; k++) (*this)[k] *= v;
        return *this;
    }

    P& operator*=(const P& r) {
        if (this->empty() || r.empty()) {
            this->clear();
            return *this;
        }
        assert(get_mult() != nullptr);
        return *this = get_mult()(*this, r);
    }

    P& operator%=(const P& r) { return *this -= *this / r * r; }

    P operator-() const {
        P ret(this->size());
        for (int i = 0; i < this->size(); i++) ret[i] = -(*this)[i];
        return ret;
    }

    P& operator/=(const P& r) {
        if (this->size() < r.size()) {
            this->clear();
            return *this;
        }
        int n = this->size() - r.size() + 1;
        return *this = (rev().pre(n) * r.rev().inv(n)).pre(n).rev(n);
    }

    P pre(int sz) const {
        return P(begin(*this), begin(*this) + min((int)this->size(), sz));
    }

    // f/x^sz
    P operator>>(int sz) const {
        if (this->size() <= sz) return {};
        P ret(*this);
        ret.erase(ret.begin(), ret.begin() + sz);
        return ret;
    }

    // f*x^sz
    P operator<<(int sz) const {
        P ret(*this);
        ret.insert(ret.begin(), sz, T(0));
        return ret;
    }

    // 反転
    P rev(int deg = -1) const {
        P ret(*this);
        if (deg != -1) ret.resize(deg, T(0));
        reverse(begin(ret), end(ret));
        return ret;
    }

    //微分
    P diff() const {
        const int n = (int)this->size();
        P ret(max(0, n - 1));
        for (int i = 1; i < n; i++) ret[i - 1] = (*this)[i] * T(i);
        return ret;
    }

    // 積分
    P integral() const {
        const int n = (int)this->size();
        P ret(n + 1);
        ret[0] = T(0);
        for (int i = 0; i < n; i++) ret[i + 1] = (*this)[i] / T(i + 1);
        return ret;
    }

    // 1/fのdeg項
    // F(0) must not be 0
    P inv(int deg = -1) const {
        assert(((*this)[0]) != T(0));
        const int n = (int)this->size();
        if (deg == -1) deg = n;
        P ret({T(1) / (*this)[0]});
        for (int i = 1; i < deg; i <<= 1) {
            ret = (ret + ret - ret * ret * pre(i << 1)).pre(i << 1);
        }
        return ret.pre(deg);
    }

    // F(0) must be 1
    P log(int deg = -1) const {
        assert((*this)[0] == 1);
        const int n = (int)this->size();
        if (deg == -1) deg = n;
        return (this->diff() * this->inv(deg)).pre(deg - 1).integral();
    }

    P sqrt(int deg = -1) const {
        const int n = (int)this->size();
        if (deg == -1) deg = n;

        if ((*this)[0] == T(0)) {
            for (int i = 1; i < n; i++) {
                if ((*this)[i] != T(0)) {
                    if (i & 1) return {};
                    if (deg - i / 2 <= 0) break;
                    auto ret = (*this >> i).sqrt(deg - i / 2) << (i / 2);
                    if (ret.size() < deg) ret.resize(deg, T(0));
                    return ret;
                }
            }
            return P(deg, 0);
        }

        P ret({T(1)});
        T inv2 = T(1) / T(2);
        for (int i = 1; i < deg; i <<= 1) {
            ret = (ret + pre(i << 1) * ret.inv(i << 1)) * inv2;
        }
        return ret.pre(deg);
    }

    // F(0) must be 0
    P exp(int deg = -1) const {
        assert((*this)[0] == T(0));
        const int n = (int)this->size();
        if (deg == -1) deg = n;
        P ret({T(1)});
        for (int i = 1; i < deg; i <<= 1) {
            ret = (ret * (pre(i << 1) + T(1) - ret.log(i << 1))).pre(i << 1);
        }
        return ret.pre(deg);
    }

    P pow(int64_t k, int deg = -1) const {
        const int n = (int)this->size();
        if (deg == -1) deg = n;
        for (int i = 0; i < n; i++) {
            if ((*this)[i] != T(0)) {
                T rev = T(1) / (*this)[i];
                P C(*this * rev);
                P D(n - i);
                for (int j = i; j < n; j++) D[j - i] = C[j];
                D = (D.log() * k).exp() * (*this)[i].pow(k);
                P E(deg);
                if (i * k > deg) return E;
                auto S = i * k;
                for (int j = 0; j + S < deg && j < D.size(); j++)
                    E[j + S] = D[j];
                return E;
            }
        }
        return *this;
    }

    //代入
    T eval(T x) const {
        T r = 0, w = 1;
        for (auto& v : *this) {
            r += w * v;
            w *= x;
        }
        return r;
    }
};

// NTT<mint> ntt;
// FPS mult_ntt(const FPS::P& a, const FPS::P& b) {
//     auto ret = ntt.multiply(a, b);
//     return FPS::P(ret.begin(), ret.end());
// }
// FPS mult(const FPS::P& a, const FPS::P& b) {
//     FPS c(a.size() + b.size() - 1);
//     rep(i, a.size()) rep(j, b.size()) { c[i + j] += a[i] * b[j]; }
//     return c;
// }
#line 1 "library/math/combination.cpp"
/**
 * @brief Combination(P, C, H, Stirling number, Bell number)
 * @docs docs/Combination.md
 */
template <typename T>
struct Combination {
    vector<T> _fact, _rfact, _inv;

    Combination(int sz) : _fact(sz + 1), _rfact(sz + 1), _inv(sz + 1) {
        _fact[0] = _rfact[sz] = _inv[0] = 1;
        for (int i = 1; i <= sz; i++) _fact[i] = _fact[i - 1] * i;
        _rfact[sz] /= _fact[sz];
        for (int i = sz - 1; i >= 0; i--) _rfact[i] = _rfact[i + 1] * (i + 1);
        for (int i = 1; i <= sz; i++) _inv[i] = _rfact[i] * _fact[i - 1];
    }

    inline T fact(int k) const { return _fact[k]; }

    inline T rfact(int k) const { return _rfact[k]; }

    inline T inv(int k) const { return _inv[k]; }

    T P(int n, int r) const {
        if (r < 0 || n < r) return 0;
        return fact(n) * rfact(n - r);
    }

    T C(int p, int q) const {
        if (q < 0 || p < q) return 0;
        return fact(p) * rfact(q) * rfact(p - q);
    }

    T H(int n, int r) const {
        if (n < 0 || r < 0) return (0);
        return r == 0 ? 1 : C(n + r - 1, r);
    }

    // O(klog(n))
    // n個の区別できる玉をk個のグループに分割する場合の数（グループのサイズは1以上）
    T Stirling(int n, int k) {
        T res = 0;
        rep(i, k + 1) {
            res += (T)((k - i) % 2 ? -1 : 1) * C(k, i) * mypow<T>(i, n);
        }
        return res / _fact[k];
    }

    // O(klog(n))
    // n個の区別できる玉をk個のグループに分割する場合の数（グループのサイズは0以上）
    // もしくは、k個以下の玉の一個以上入ったグループに分けると考えてもいい
    T Bell(int n, int k) {
        if (n < k) k = n;
        vector<T> sm(k + 1);
        sm[0] = 1;
        rep(j, 1, k + 1) { sm[j] = sm[j - 1] + (T)(j % 2 ? -1 : 1) / _fact[j]; }
        T res = 0;
        rep(i, k + 1) { res += mypow<T>(i, n) / _fact[i] * sm[k - i]; }
        return res;
    }
};
#line 1 "library/mod/modint.cpp"
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(int64_t 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; }

    inline int get() { return x; }
};
#line 8 "verify/FPS.power.test.cpp"
using mint = modint<998244353>;
using FPS = FormalPowerSeries<mint>;
NTT<mint> ntt;
FPS mult_ntt(const FPS::P& a, const FPS::P& b) {
    auto ret = ntt.multiply(a, b);
    return FPS::P(ret.begin(), ret.end());
}
// FPS::set_fft(mult_ntt); in main
int main() {
    FPS::set_fft(mult_ntt);
    int n;
    cin >> n;
    Combination<mint> comb(n);
    FPS f(n + 1), g(1);
    g[0] = 1;
    rep(i, n + 1) { f[i] = (mint)(i + 1) / comb.fact(i); }
    int tmp = n;
    while (tmp) {
        if (tmp & 1) g *= f;
        f *= f;
        tmp >>= 1;
        f.resize(n + 1);
        g.resize(n + 1);
    }
    print(g[n - 2] * comb.fact(n - 2) / mypow<mint>(n, n - 2));
}