結果
問題 | No.2369 Some Products |
ユーザー |
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提出日時 | 2023-06-25 14:48:14 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
TLE
(最新)
AC
(最初)
|
実行時間 | - |
コード長 | 14,612 bytes |
コンパイル時間 | 4,820 ms |
コンパイル使用メモリ | 268,144 KB |
最終ジャッジ日時 | 2025-02-15 02:13:20 |
ジャッジサーバーID (参考情報) |
judge5 / judge3 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 1 |
other | AC * 11 TLE * 3 |
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 ÷_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 ÷_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 ÷_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) {// prepareF 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;for(int i=0;i<Q;i++){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] << '\n';}}