結果
問題 | No.2633 Subsequence Combination Score |
ユーザー |
|
提出日時 | 2024-02-16 23:21:15 |
言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 263 ms / 2,000 ms |
コード長 | 16,251 bytes |
コンパイル時間 | 3,451 ms |
コンパイル使用メモリ | 264,624 KB |
実行使用メモリ | 10,604 KB |
最終ジャッジ日時 | 2024-09-28 22:04:32 |
合計ジャッジ時間 | 15,480 ms |
ジャッジサーバーID (参考情報) |
judge1 / judge5 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 38 |
ソースコード
// #pragma GCC optimize("O3,unroll-loops")#include <bits/stdc++.h>// #include <x86intrin.h>using namespace std;#if __cplusplus >= 202002Lusing namespace numbers;#endiftemplate<class data_t, data_t _mod>struct modular_fixed_base{#define IS_INTEGRAL(T) (is_integral_v<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>)#define IS_UNSIGNED(T) (is_unsigned_v<T> || is_same_v<T, __uint128_t>)static_assert(IS_UNSIGNED(data_t));static_assert(_mod >= 1);static constexpr bool VARIATE_MOD_FLAG = false;static constexpr data_t mod(){return _mod;}template<class T>static vector<modular_fixed_base> precalc_power(T base, int SZ){vector<modular_fixed_base> res(SZ + 1, 1);for(auto i = 1; i <= SZ; ++ i) res[i] = res[i - 1] * base;return res;}static vector<modular_fixed_base> _INV;static void precalc_inverse(int SZ){if(_INV.empty()) _INV.assign(2, 1);for(auto x = _INV.size(); x <= SZ; ++ x) _INV.push_back(_mod / x * -_INV[_mod % x]);}// _mod must be a primestatic modular_fixed_base _primitive_root;static modular_fixed_base primitive_root(){if(_primitive_root) return _primitive_root;if(_mod == 2) return _primitive_root = 1;if(_mod == 998244353) return _primitive_root = 3;data_t divs[20] = {};divs[0] = 2;int cnt = 1;data_t x = (_mod - 1) / 2;while(x % 2 == 0) x /= 2;for(auto i = 3; 1LL * i * i <= x; i += 2){if(x % i == 0){divs[cnt ++] = i;while(x % i == 0) x /= i;}}if(x > 1) divs[cnt ++] = x;for(auto g = 2; ; ++ g){bool ok = true;for(auto i = 0; i < cnt; ++ i){if((modular_fixed_base(g).power((_mod - 1) / divs[i])) == 1){ok = false;break;}}if(ok) return _primitive_root = g;}}constexpr modular_fixed_base(){ }modular_fixed_base(const double &x){ data = _normalize(llround(x)); }modular_fixed_base(const long double &x){ data = _normalize(llround(x)); }template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> modular_fixed_base(const T &x){ data = _normalize(x); }template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> static data_t _normalize(const T &x){int sign = x >= 0 ? 1 : -1;data_t v = _mod <= sign * x ? sign * x % _mod : sign * x;if(sign == -1 && v) v = _mod - v;return v;}template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> operator T() const{ return data; }modular_fixed_base &operator+=(const modular_fixed_base &otr){ if((data += otr.data) >= _mod) data -= _mod; return *this; }modular_fixed_base &operator-=(const modular_fixed_base &otr){ if((data += _mod - otr.data) >= _mod) data -= _mod; return *this; }template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> modular_fixed_base &operator+=(const T &otr){ return *this +=modular_fixed_base(otr); }template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> modular_fixed_base &operator-=(const T &otr){ return *this -=modular_fixed_base(otr); }modular_fixed_base &operator++(){ return *this += 1; }modular_fixed_base &operator--(){ return *this += _mod - 1; }modular_fixed_base operator++(int){ modular_fixed_base result(*this); *this += 1; return result; }modular_fixed_base operator--(int){ modular_fixed_base result(*this); *this += _mod - 1; return result; }modular_fixed_base operator-() const{ return modular_fixed_base(_mod - data); }modular_fixed_base &operator*=(const modular_fixed_base &rhs){if constexpr(is_same_v<data_t, unsigned int>) data = (unsigned long long)data * rhs.data % _mod;else if constexpr(is_same_v<data_t, unsigned long long>){long long res = data * rhs.data - _mod * (unsigned long long)(1.L / _mod * data * rhs.data);data = res + _mod * (res < 0) - _mod * (res >= (long long)_mod);}else data = _normalize(data * rhs.data);return *this;}template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>modular_fixed_base &inplace_power(T e){if(e == 0) return *this = 1;if(data == 0) return *this = {};if(data == 1) return *this;if(data == mod() - 1) return e % 2 ? *this : *this = -*this;if(e < 0) *this = 1 / *this, e = -e;modular_fixed_base res = 1;for(; e; *this *= *this, e >>= 1) if(e & 1) res *= *this;return *this = res;}template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>modular_fixed_base power(T e) const{return modular_fixed_base(*this).inplace_power(e);}modular_fixed_base &operator/=(const modular_fixed_base &otr){make_signed_t<data_t> a = otr.data, m = _mod, u = 0, v = 1;if(a < _INV.size()) return *this *= _INV[a];while(a){make_signed_t<data_t> t = m / a;m -= t * a; swap(a, m);u -= t * v; swap(u, v);}assert(m == 1);return *this *= u;}#define ARITHMETIC_OP(op, apply_op)\modular_fixed_base operator op(const modular_fixed_base &x) const{ return modular_fixed_base(*this) apply_op x; }\template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>\modular_fixed_base operator op(const T &x) const{ return modular_fixed_base(*this) apply_op modular_fixed_base(x); }\template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>\friend modular_fixed_base operator op(const T &x, const modular_fixed_base &y){ return modular_fixed_base(x) apply_op y; }ARITHMETIC_OP(+, +=) ARITHMETIC_OP(-, -=) ARITHMETIC_OP(*, *=) ARITHMETIC_OP(/, /=)#undef ARITHMETIC_OP#define COMPARE_OP(op)\bool operator op(const modular_fixed_base &x) const{ return data op x.data; }\template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>\bool operator op(const T &x) const{ return data op modular_fixed_base(x).data; }\template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>\friend bool operator op(const T &x, const modular_fixed_base &y){ return modular_fixed_base(x).data op y.data; }COMPARE_OP(==) COMPARE_OP(!=) COMPARE_OP(<) COMPARE_OP(<=) COMPARE_OP(>) COMPARE_OP(>=)#undef COMPARE_OPfriend istream &operator>>(istream &in, modular_fixed_base &number){long long x;in >> x;number.data = modular_fixed_base::_normalize(x);return in;}#define _SHOW_FRACTIONfriend ostream &operator<<(ostream &out, const modular_fixed_base &number){out << number.data;#if defined(LOCAL) && defined(_SHOW_FRACTION)cerr << "(";for(auto d = 1; ; ++ d){if((number * d).data <= 1000000){cerr << (number * d).data;if(d != 1) cerr << "/" << d;break;}else if((-number * d).data <= 1000000){cerr << "-" << (-number * d).data;if(d != 1) cerr << "/" << d;break;}}cerr << ")";#endifreturn out;}data_t data = 0;#undef _SHOW_FRACTION#undef IS_INTEGRAL#undef IS_SIGNED};template<class data_t, data_t _mod> vector<modular_fixed_base<data_t, _mod>> modular_fixed_base<data_t, _mod>::_INV;template<class data_t, data_t _mod> modular_fixed_base<data_t, _mod> modular_fixed_base<data_t, _mod>::_primitive_root;const unsigned int mod = (119 << 23) + 1; // 998244353// const unsigned int mod = 1e9 + 7; // 1000000007// const unsigned int mod = 1e9 + 9; // 1000000009// const unsigned long long mod = (unsigned long long)1e18 + 9;using modular = modular_fixed_base<decay_t<decltype(mod)>, mod>;template<class T>struct combinatorics{// O(n)static vector<T> precalc_fact(int n){vector<T> f(n + 1, 1);for(auto i = 1; i <= n; ++ i) f[i] = f[i - 1] * i;return f;}// O(n * m)static vector<vector<T>> precalc_C(int n, int m){vector<vector<T>> c(n + 1, vector<T>(m + 1));for(auto i = 0; i <= n; ++ i) for(auto j = 0; j <= min(i, m); ++ j) c[i][j] = i && j ? c[i - 1][j - 1] + c[i - 1][j] : T(1);return c;}int SZ = 0;vector<T> inv, fact, invfact;combinatorics(){ }// O(SZ)combinatorics(int SZ): SZ(SZ), inv(SZ + 1, 1), fact(SZ + 1, 1), invfact(SZ + 1, 1){for(auto i = 1; i <= SZ; ++ i) fact[i] = fact[i - 1] * i;invfact[SZ] = 1 / fact[SZ];for(auto i = SZ - 1; i >= 0; -- i){invfact[i] = invfact[i + 1] * (i + 1);inv[i + 1] = invfact[i + 1] * fact[i];}}// O(1)T C(int n, int k) const{assert(0 <= min(n, k) && max(n, k) <= SZ);return n >= k ? fact[n] * invfact[k] * invfact[n - k] : T{0};}// O(1)T P(int n, int k) const{assert(0 <= min(n, k) && max(n, k) <= SZ);return n >= k ? fact[n] * invfact[n - k] : T{0};}// O(1)T H(int n, int k) const{assert(0 <= min(n, k));if(n == 0) return 0;return C(n + k - 1, k);}// O(min(k, n - k))T naive_C(long long n, long long k) const{assert(0 <= min(n, k));if(n < k) return 0;T res = 1;k = min(k, n - k);assert(k <= SZ);for(auto i = n; i > n - k; -- i) res *= i;return res * invfact[k];}// O(k)T naive_P(long long n, int k) const{assert(0 <= min<long long>(n, k));if(n < k) return 0;T res = 1;for(auto i = n; i > n - k; -- i) res *= i;return res;}// O(k)T naive_H(long long n, int k) const{assert(0 <= min<long long>(n, k));return naive_C(n + k - 1, k);}// O(1)bool parity_C(long long n, long long k) const{assert(0 <= min(n, k));return n >= k ? (n & k) == k : false;}// Number of ways to place n '('s and k ')'s starting with m copies of '(' such that in each prefix, number of '(' is equal or greater than ')'// Catalan(n, n, 0): n-th catalan number// Catalan(s, s+k-1, k-1): sum of products of k catalan numbers where the index of product sums up to s.// O(1)T Catalan(int n, int k, int m = 0) const{assert(0 <= min({n, k, m}));return k <= m ? C(n + k, n) : k <= n + m ? C(n + k, n) - C(n + k, k - m - 1) : T();}};// T must be of modular type// mod must be a prime// Requires modulartemplate<class T>struct number_theoric_transform_wrapper{// i \in [2^k, 2^{k+1}) holds w_{2^k+1}^{i-2^k}static vector<T> root, buffer1, buffer2;static void adjust_root(int n){if(root.empty()) root = {1, 1};for(auto k = (int)root.size(); k < n; k <<= 1){root.resize(n, 1);T w = T::primitive_root().power((T::mod() - 1) / (k << 1));for(auto i = k; i < k << 1; ++ i) root[i] = i & 1 ? root[i >> 1] * w : root[i >> 1];}}// n must be a power of two// p must have next n memories allocated// O(n * log(n))static void transform(int n, T *p, bool invert = false){assert(n && __builtin_popcount(n) == 1 && (T::mod() - 1) % n == 0);for(auto i = 1, j = 0; i < n; ++ i){int bit = n >> 1;for(; j & bit; bit >>= 1) j ^= bit;j ^= bit;if(i < j) swap(p[i], p[j]);}adjust_root(n);for(auto len = 1; len < n; len <<= 1) for(auto i = 0; i < n; i += len << 1) for(auto j = 0; j < len; ++ j){T x = p[i + j], y = p[len + i + j] * root[len + j];p[i + j] = x + y, p[len + i + j] = x - y;}if(invert){reverse(p + 1, p + n);T inv_n = T(1) / n;for(auto i = 0; i < n; ++ i) p[i] *= inv_n;}}static void transform(vector<T> &p, bool invert = false){transform((int)p.size(), p.data(), invert);}// Double the length of the ntt array// n must be a power of two// p must have next 2n memories allocated// O(n * log(n))static void double_up(int n, T *p){assert(n && __builtin_popcount(n) == 1 && (T().mod() - 1) % (n << 1) == 0);buffer1.resize(n << 1);for(auto i = 0; i < n; ++ i) buffer1[i << 1] = p[i];transform(n, p, true);adjust_root(n << 1);for(auto i = 0; i < n; ++ i) p[i] *= root[n | i];transform(n, p);for(auto i = 0; i < n; ++ i) buffer1[i << 1 | 1] = p[i];copy(buffer1.begin(), buffer1.begin() + 2 * n, p);}static void double_up(vector<T> &p){int n = (int)p.size();p.resize(n << 1);double_up(n, p.data());}// O(n * m)static vector<T> convolute_naive(const vector<T> &p, const vector<T> &q){vector<T> res(max((int)p.size() + (int)q.size() - 1, 0));for(auto i = 0; i < (int)p.size(); ++ i) for(auto j = 0; j < (int)q.size(); ++ j) res[i + j] += p[i] * q[j];return res;}// O((n + m) * log(n + m))static vector<T> convolute(const vector<T> &p, const vector<T> &q){if(min(p.size(), q.size()) < 55) return convolute_naive(p, q);int m = (int)p.size() + (int)q.size() - 1, n = 1 << __lg(m) + 1;buffer1.assign(n, 0);copy(p.begin(), p.end(), buffer1.begin());transform(buffer1);buffer2.assign(n, 0);copy(q.begin(), q.end(), buffer2.begin());transform(buffer2);for(auto i = 0; i < n; ++ i) buffer1[i] *= buffer2[i];transform(buffer1, true);return vector<T>(buffer1.begin(), buffer1.begin() + m);}// O((n + m) * log(n + m))static vector<T> square(const vector<T> &p){if((int)p.size() < 40) return convolute_naive(p, p);int m = 2 * (int)p.size() - 1, n = 1 << __lg(m) + 1;buffer1.assign(n, 0);copy(p.begin(), p.end(), buffer1.begin());transform(buffer1);for(auto i = 0; i < n; ++ i) buffer1[i] *= buffer1[i];transform(buffer1, true);return vector<T>(buffer1.begin(), buffer1.begin() + m);}// O((n + m) * log(n + m))static vector<T> arbitrarily_convolute(const vector<T> &p, const vector<T> &q){using modular0 = modular_fixed_base<unsigned int, 1045430273>;using modular1 = modular_fixed_base<unsigned int, 1051721729>;using modular2 = modular_fixed_base<unsigned int, 1053818881>;using ntt0 = number_theoric_transform_wrapper<modular0>;using ntt1 = number_theoric_transform_wrapper<modular1>;using ntt2 = number_theoric_transform_wrapper<modular2>;vector<modular0> p0((int)p.size()), q0((int)q.size());for(auto i = 0; i < (int)p.size(); ++ i) p0[i] = p[i].data;for(auto i = 0; i < (int)q.size(); ++ i) q0[i] = q[i].data;auto xy0 = ntt0::convolute(p0, q0);vector<modular1> p1((int)p.size()), q1((int)q.size());for(auto i = 0; i < (int)p.size(); ++ i) p1[i] = p[i].data;for(auto i = 0; i < (int)q.size(); ++ i) q1[i] = q[i].data;auto xy1 = ntt1::convolute(p1, q1);vector<modular2> p2((int)p.size()), q2((int)q.size());for(auto i = 0; i < (int)p.size(); ++ i) p2[i] = p[i].data;for(auto i = 0; i < (int)q.size(); ++ i) q2[i] = q[i].data;auto xy2 = ntt2::convolute(p2, q2);static const modular1 r01 = 1 / modular1(modular0::mod());static const modular2 r02 = 1 / modular2(modular0::mod());static const modular2 r12 = 1 / modular2(modular1::mod());static const modular2 r02r12 = r02 * r12;static const T w1 = modular0::mod();static const T w2 = w1 * modular1::mod();int n = (int)p.size() + (int)q.size() - 1;vector<T> res(n);for(auto i = 0; i < n; ++ i){using ull = unsigned long long;ull a = xy0[i].data;ull b = (xy1[i].data + modular1::mod() - a) * r01.data % modular1::mod();ull c = ((xy2[i].data + modular2::mod() - a) * r02r12.data + (modular2::mod() - b) * r12.data) % modular2::mod();res[i] = xy0[i].data + w1 * b + w2 * c;}return res;}};template<class T> vector<T> number_theoric_transform_wrapper<T>::root;template<class T> vector<T> number_theoric_transform_wrapper<T>::buffer1;template<class T> vector<T> number_theoric_transform_wrapper<T>::buffer2;using ntt = number_theoric_transform_wrapper<modular>;template<class F>struct y_combinator_result{F f;template<class T> explicit y_combinator_result(T &&f): f(forward<T>(f)){ }template<class ...Args> decltype(auto) operator()(Args &&...args){ return f(ref(*this), forward<Args>(args)...); }};template<class F>decltype(auto) y_combinator(F &&f){return y_combinator_result<decay_t<F>>(forward<F>(f));}int main(){cin.tie(0)->sync_with_stdio(0);cin.exceptions(ios::badbit | ios::failbit);const int mx = 1e5;combinatorics<modular> C(mx);int n;cin >> n;vector<int> cnt(mx + 1);for(auto i = 0; i < n; ++ i){int x;cin >> x;++ cnt[x];}auto power = modular::precalc_power(2, n);vector<modular> f(mx + 1);y_combinator([&](auto self, int l, int r)->void{if(r - l == 1){f[l] = (f[l] + C.invfact[l]) * (power[cnt[l]] - 1);return;}int m = l + r >> 1;self(l, m);vector<modular> p(f.begin() + l, f.begin() + m);vector<modular> q(r - l);for(auto i = 1; i < r - l; ++ i){q[i] = C.invfact[i];}p = ntt::convolute(p, q);for(auto i = m; i < r; ++ i){if(i - l < (int)p.size()){f[i] += p[i - l];}}self(m, r);})(0, mx + 1);modular res = 0;for(auto x = 0; x <= mx; ++ x){res += C.fact[x] * f[x];}cout << res << "\n";return 0;}/**/