#883717 (C++14) No.2369 Some Products

• 問題: No.2369 Some Products
• ユーザー: Kak1_n0_tane
• 提出日時: 2023-06-23 15:47:05
• 言語: C++14 (gcc 12.3.0 + boost 1.83.0)
• 結果: TLE (最新)
  AC
  (最初)
• 実行時間: -
• コード長: 13,309 bytes
• コンパイル時間: 3,886 ms
• コンパイル使用メモリ: 245,076 KB
• 実行使用メモリ: 108,576 KB
• 最終ジャッジ日時: 2024-07-07 08:06:07
• 合計ジャッジ時間: 7,785 ms
• ジャッジサーバーID （参考情報）: judge3 / judge4

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	1 ms; 13,888 KB
testcase_01	AC	2 ms; 6,944 KB
testcase_02	TLE	-
testcase_03	--	-
testcase_04	--	-
testcase_05	--	-
testcase_06	--	-
testcase_07	--	-
testcase_08	--	-
testcase_09	--	-
testcase_10	--	-
testcase_11	--	-
testcase_12	--	-
testcase_13	--	-
testcase_14	--	-

コンパイルメッセージ

main.cpp: In member function 'FormalPowerSeries<T>::F& FormalPowerSeries<T>::multiply_inplace(std::vector<std::pair<int, E> >)':
main.cpp:166:10: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17' [-Wc++17-extensions]
  166 |     auto [d, c] = g.front();
      |          ^
main.cpp:171:18: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17' [-Wc++17-extensions]
  171 |       for (auto &[j, b] : g) {
      |                  ^
main.cpp: In member function 'FormalPowerSeries<T>::F& FormalPowerSeries<T>::divide_inplace(std::vector<std::pair<int, E> >)':
main.cpp:182:10: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17' [-Wc++17-extensions]
  182 |     auto [d, c] = g.front();
      |          ^
main.cpp:187:18: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17' [-Wc++17-extensions]
  187 |       for (auto &[j, b] : g) {
      |                  ^

ソースコード

#include <bits/stdc++.h>
using namespace std;
#include <atcoder/all>
using namespace atcoder;

istream &operator>>(istream &is, modint998244353 &a) { long long v; is >> v; a = v; return is; }
ostream &operator<<(ostream &os, const modint998244353 &a) { return os << a.val(); }
istream &operator>>(istream &is, modint1000000007 &a) { long long v; is >> v; a = v; return is; }
ostream &operator<<(ostream &os, const modint1000000007 &a) { return os << a.val(); }
template<int m> istream &operator>>(istream &is, static_modint<m> &a) { long long v; is >> v; a = v; return is; }
template<int m> istream &operator>>(istream &is, dynamic_modint<m> &a) { long long v; is >> v; a = v; return is; }
template<int m> ostream &operator<<(ostream &os, const static_modint<m> &a) { return os << a.val(); }
template<int m> ostream &operator<<(ostream &os, const dynamic_modint<m> &a) { return os << a.val(); }
#define rep_(i, a_, b_, a, b, ...) for (int i = (a), lim##i = (b); i < lim##i; ++i)
#define rep(i, ...) rep_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
#define drep_(i, a_, b_, a, b, ...) for (int i = (a)-1, lim##i = (b); i >= lim##i; --i)
#define drep(i, ...) drep_(i, __VA_ARGS__, __VA_ARGS__, __VA_ARGS__, 0)
using ll = long long;
template<class T> istream &operator>>(istream &is, vector<T> &v) { for (auto &e : v) is >> e; return is; }
template<class T> ostream &operator<<(ostream &os, const vector<T> &v) { for (auto &e : v) os << e << ' '; return os; }
struct fast_ios { fast_ios(){ cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;

using mint = modint998244353;

template<typename T> struct Factorial {
  int MAX;
  vector<T> fac, finv;
  Factorial(int m = 0) : MAX(m), fac(m+1, 1), finv(m+1, 1) {
    rep(i, 2, MAX+1) fac[i] = fac[i-1] * i;
    finv[MAX] /= fac[MAX];
    drep(i, MAX+1, 3) finv[i-1] = finv[i] * i;
  }
  T binom(int n, int k) {
    if (k < 0 || n < k) return 0;
    return fac[n] * finv[k] * finv[n-k];
  }
  T perm(int n, int k) {
    if (k < 0 || n < k) return 0;
    return fac[n] * finv[n-k];
  }
};
Factorial<mint> fc;



template<class T>
struct FormalPowerSeries : vector<T> {
  using vector<T>::vector;
  using vector<T>::operator=;
  using F = FormalPowerSeries;

  F operator-() const {
    F res(*this);
    for (auto &e : res) e = -e;
    return res;
  }
  F &operator*=(const T &g) {
    for (auto &e : *this) e *= g;
    return *this;
  }
  F &operator/=(const T &g) {
    assert(g != T(0));
    *this *= g.inv();
    return *this;
  }
  F &operator+=(const F &g) {
    int n = this->size(), m = g.size();
    rep(i, min(n, m)) (*this)[i] += g[i];
    return *this;
  }
  F &operator-=(const F &g) {
    int n = this->size(), m = g.size();
    rep(i, min(n, m)) (*this)[i] -= g[i];
    return *this;
  }
  F &operator<<=(const int d) {
    int n = this->size();
    if (d >= n) *this = F(n);
    this->insert(this->begin(), d, 0);
    this->resize(n);
    return *this;
  }
  F &operator>>=(const int d) {
    int n = this->size();
    this->erase(this->begin(), this->begin() + min(n, d));
    this->resize(n);
    return *this;
  }

  // O(n log n)
  F inv(int d = -1) const {
    int n = this->size();
    assert(n != 0 && (*this)[0] != 0);
    if (d == -1) d = n;
    assert(d >= 0);
    F res{(*this)[0].inv()};
    for (int m = 1; m < d; m *= 2) {
      F f(this->begin(), this->begin() + min(n, 2*m));
      F g(res);
      f.resize(2*m), internal::butterfly(f);
      g.resize(2*m), internal::butterfly(g);
      rep(i, 2*m) f[i] *= g[i];
      internal::butterfly_inv(f);
      f.erase(f.begin(), f.begin() + m);
      f.resize(2*m), internal::butterfly(f);
      rep(i, 2*m) f[i] *= g[i];
      internal::butterfly_inv(f);
      T iz = T(2*m).inv(); iz *= -iz;
      rep(i, m) f[i] *= iz;
      res.insert(res.end(), f.begin(), f.begin() + m);
    }
    res.resize(d);
    return res;
  }

  // fast: FMT-friendly modulus only
  // O(n log n)
  F &multiply_inplace(const F &g, int d = -1) {
    int n = this->size();
    if (d == -1) d = n;
    assert(d >= 0);
    *this = convolution(move(*this), g);
    this->resize(d);
    return *this;
  }
  F multiply(const F &g, const int d = -1) const { return F(*this).multiply_inplace(g, d); }
  // O(n log n)
  F &divide_inplace(const F &g, int d = -1) {
    int n = this->size();
    if (d == -1) d = n;
    assert(d >= 0);
    *this = convolution(move(*this), g.inv(d));
    this->resize(d);
    return *this;
  }
  F divide(const F &g, const int d = -1) const { return F(*this).divide_inplace(g, d); }

  // // naive
  // // O(n^2)
  // F &multiply_inplace(const F &g) {
  //   int n = this->size(), m = g.size();
  //   drep(i, n) {
  //     (*this)[i] *= g[0];
  //     rep(j, 1, min(i+1, m)) (*this)[i] += (*this)[i-j] * g[j];
  //   }
  //   return *this;
  // }
  // F multiply(const F &g) const { return F(*this).multiply_inplace(g); }
  // // O(n^2)
  // F &divide_inplace(const F &g) {
  //   assert(g[0] != T(0));
  //   T ig0 = g[0].inv();
  //   int n = this->size(), m = g.size();
  //   rep(i, n) {
  //     rep(j, 1, min(i+1, m)) (*this)[i] -= (*this)[i-j] * g[j];
  //     (*this)[i] *= ig0;
  //   }
  //   return *this;
  // }
  // F divide(const F &g) const { return F(*this).divide_inplace(g); }

  // sparse
  // O(nk)
  F &multiply_inplace(vector<pair<int, T>> g) {
    int n = this->size();
    auto [d, c] = g.front();
    if (d == 0) g.erase(g.begin());
    else c = 0;
    drep(i, n) {
      (*this)[i] *= c;
      for (auto &[j, b] : g) {
        if (j > i) break;
        (*this)[i] += (*this)[i-j] * b;
      }
    }
    return *this;
  }
  F multiply(const vector<pair<int, T>> &g) const { return F(*this).multiply_inplace(g); }
  // O(nk)
  F &divide_inplace(vector<pair<int, T>> g) {
    int n = this->size();
    auto [d, c] = g.front();
    assert(d == 0 && c != T(0));
    T ic = c.inv();
    g.erase(g.begin());
    rep(i, n) {
      for (auto &[j, b] : g) {
        if (j > i) break;
        (*this)[i] -= (*this)[i-j] * b;
      }
      (*this)[i] *= ic;
    }
    return *this;
  }
  F divide(const vector<pair<int, T>> &g) const { return F(*this).divide_inplace(g); }

  // multiply and divide (1 + cz^d)
  // O(n)
  void multiply_inplace(const int d, const T c) { 
    int n = this->size();
    if (c == T(1)) drep(i, n-d) (*this)[i+d] += (*this)[i];
    else if (c == T(-1)) drep(i, n-d) (*this)[i+d] -= (*this)[i];
    else drep(i, n-d) (*this)[i+d] += (*this)[i] * c;
  }
  // O(n)
  void divide_inplace(const int d, const T c) {
    int n = this->size();
    if (c == T(1)) rep(i, n-d) (*this)[i+d] -= (*this)[i];
    else if (c == T(-1)) rep(i, n-d) (*this)[i+d] += (*this)[i];
    else rep(i, n-d) (*this)[i+d] -= (*this)[i] * c;
  }

  // O(n)
  T eval(const T &a) const {
    T x(1), res(0);
    for (auto e : *this) res += e * x, x *= a;
    return res;
  }

  // O(n)
  F &integral_inplace() {
    int n = this->size();
    assert(n > 0);
    if (n == 1) return *this = F{0};
    this->insert(this->begin(), 0);
    this->pop_back();
    vector<T> inv(n);
    inv[1] = 1;
    int p = T::mod();
    rep(i, 2, n) inv[i] = - inv[p%i] * (p/i);
    rep(i, 2, n) (*this)[i] *= inv[i];
    return *this;
  }
  F integral() const { return F(*this).integral_inplace(); }

  // O(n)
  F &derivative_inplace() {
    int n = this->size();
    assert(n > 0);
    rep(i, 2, n) (*this)[i] *= i;
    this->erase(this->begin());
    this->push_back(0);
    return *this;
  }
  F derivative() const { return F(*this).derivative_inplace(); }

  // O(n log n)
  F &log_inplace(int d = -1) {
    int n = this->size();
    assert(n > 0 && (*this)[0] == 1);
    if (d == -1) d = n;
    assert(d >= 0);
    if (d < n) this->resize(d);
    F f_inv = this->inv();
    this->derivative_inplace();
    this->multiply_inplace(f_inv);
    this->integral_inplace();
    return *this;
  }
  F log(const int d = -1) const { return F(*this).log_inplace(d); }

  // O(n log n)
  // https://arxiv.org/abs/1301.5804 (Figure 1, right)
  F &exp_inplace(int d = -1) {
    int n = this->size();
    assert(n > 0 && (*this)[0] == 0);
    if (d == -1) d = n;
    assert(d >= 0);
    F g{1}, g_fft{1, 1};
    (*this)[0] = 1;
    this->resize(d);
    F h_drv(this->derivative());
    for (int m = 2; m < d; m *= 2) {
      // prepare
      F f_fft(this->begin(), this->begin() + m);
      f_fft.resize(2*m), internal::butterfly(f_fft);

      // Step 2.a'
      {
        F _g(m);
        rep(i, m) _g[i] = f_fft[i] * g_fft[i];
        internal::butterfly_inv(_g);
        _g.erase(_g.begin(), _g.begin() + m/2);
        _g.resize(m), internal::butterfly(_g);
        rep(i, m) _g[i] *= g_fft[i];
        internal::butterfly_inv(_g);
        _g.resize(m/2);
        _g /= T(-m) * m;
        g.insert(g.end(), _g.begin(), _g.begin() + m/2);
      }

      // Step 2.b'--d'
      F t(this->begin(), this->begin() + m);
      t.derivative_inplace();
      {
        // Step 2.b'
        F r{h_drv.begin(), h_drv.begin() + m-1};
        // Step 2.c'
        r.resize(m); internal::butterfly(r);
        rep(i, m) r[i] *= f_fft[i];
        internal::butterfly_inv(r);
        r /= -m;
        // Step 2.d'
        t += r;
        t.insert(t.begin(), t.back()); t.pop_back();
      }

      // Step 2.e'
      if (2*m < d) {
        t.resize(2*m); internal::butterfly(t); 
        g_fft = g; g_fft.resize(2*m); internal::butterfly(g_fft);
        rep(i, 2*m) t[i] *= g_fft[i];
        internal::butterfly_inv(t);
        t.resize(m);
        t /= 2*m;
      }
      else { // この場合分けをしても数パーセントしか速くならない
        F g1(g.begin() + m/2, g.end());
        F s1(t.begin() + m/2, t.end());
        t.resize(m/2);
        g1.resize(m), internal::butterfly(g1);
        t.resize(m),  internal::butterfly(t);
        s1.resize(m), internal::butterfly(s1);
        rep(i, m) s1[i] = g_fft[i] * s1[i] + g1[i] * t[i];
        rep(i, m) t[i] *= g_fft[i];
        internal::butterfly_inv(t);
        internal::butterfly_inv(s1);
        rep(i, m/2) t[i+m/2] += s1[i];
        t /= m;
      }
      
      // Step 2.f'
      F v(this->begin() + m, this->begin() + min<int>(d, 2*m)); v.resize(m);
      t.insert(t.begin(), m-1, 0); t.push_back(0);
      t.integral_inplace();
      rep(i, m) v[i] -= t[m+i];

      // Step 2.g'
      v.resize(2*m); internal::butterfly(v);
      rep(i, 2*m) v[i] *= f_fft[i];
      internal::butterfly_inv(v);
      v.resize(m);
      v /= 2*m;

      // Step 2.h'
      rep(i, min(d-m, m)) (*this)[m+i] = v[i];
    }
    return *this;
  }
  F exp(const int d = -1) const { return F(*this).exp_inplace(d); }

  // O(n log n)
  F &pow_inplace(const ll k, int d = -1) {
    int n = this->size();
    if (d == -1) d = n;
    assert(d >= 0 && k >= 0);
    if (d == 0) return *this = F(0);
    if (k == 0) {
      *this = F(d);
      (*this)[0] = 1;
      return *this;
    }
    int l = 0;
    while (l < n && (*this)[l] == 0) ++l;
    if (l == n || l > (d-1)/k) return *this = F(d);
    T c{(*this)[l]};
    this->erase(this->begin(), this->begin() + l);
    *this /= c;
    this->log_inplace(d - l*k);
    *this *= k;
    this->exp_inplace();
    *this *= c.pow(k);
    this->insert(this->begin(), l*k, 0);
    return *this;
  }
  F pow(const ll k, const int d = -1) const { return F(*this).pow_inplace(k, d); }

  // O(n log n)
  F &shift_inplace(const T c) {
    int n = this->size();
    fc = Factorial<T>(n);
    rep(i, n) (*this)[i] *= fc.fac[i];
    reverse(this->begin(), this->end());
    F g(n);
    T cp = 1;
    rep(i, n) g[i] = cp * fc.finv[i], cp *= c;
    this->multiply_inplace(g, n);
    reverse(this->begin(), this->end());
    rep(i, n) (*this)[i] *= fc.finv[i];
    return *this;
  }
  F shift(const T c) const { return F(*this).shift_inplace(c); }

  F operator*(const T &g) const { return F(*this) *= g; }
  F operator/(const T &g) const { return F(*this) /= g; }
  F operator+(const F &g) const { return F(*this) += g; }
  F operator-(const F &g) const { return F(*this) -= g; }
  F operator<<(const int d) const { return F(*this) <<= d; }
  F operator>>(const int d) const { return F(*this) >>= d; }
};

using fps = FormalPowerSeries<mint>;



int main(){
    // FILE *out = freopen("out1.txt", "w", stdout);
    int N;
    cin >> N;
    vector<ll> P(N);
    rep(i,N) cin >> P[i];

    // func[B][X] := 1以上B以下の整数からX個選び、積の総和
    vector<vector<mint>> func(N+1, vector<mint>(N+1, 0));
    rep(x,N+1){
        if(x==0) continue;
        rep(b,N){
            if(x==1){
                func[b+1][1] = func[b][1] + P[b];
            }
            else{
                func[b+1][x] = func[b][x] + P[b]*func[b][x-1];
            }
        }
    }
    /*
    rep(i,N+1){
        rep(j,N+1){
            cout << func[i][j] << (j==N?'\n':' ');
        }
    }
    */

    int Q;
    cin >> Q;

    while(Q--){
        ll A, B, X;
        cin >> A >> B >> X;
        fps keisuu(X+1);
        keisuu[0] = 1;
        rep(i,X) keisuu[i+1] = func[A-1][i+1];
        fps answer(X+1);
        answer[0] = 1;
        rep(i,X) answer[i+1] = func[B][i+1];
        /*
        cout << keisuu << '\n';
        cout << answer << '\n';
        */
        fps func_abi(X+1);
        func_abi = convolution(answer, keisuu.inv());
        cout << func_abi[X] << endl; 
    }
}