#951654 (C++23) No.2633 Subsequence Combination Score

提出ソース
結果

問題	No.2633 Subsequence Combination Score
ユーザー	Aeren
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
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 * 38
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

raw source code
// #pragma GCC optimize("O3,unroll-loops")
#include <bits/stdc++.h>
// #include <x86intrin.h>
using namespace std;
#if __cplusplus >= 202002L
using namespace numbers;
#endif

template<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 prime
	static 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_OP
	friend istream &operator>>(istream &in, modular_fixed_base &number){
		long long x;
		in >> x;
		number.data = modular_fixed_base::_normalize(x);
		return in;
	}
#define _SHOW_FRACTION
	friend 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 << ")";
	#endif
		return 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 modular
template<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;
}

/*

*/
yukicoder

結果

ソースコード
