#980677 (C++23) No.2754 Cumulate and Drop

提出ソース
結果

問題	No.2754 Cumulate and Drop
ユーザー	Aeren
提出日時	2024-05-10 22:14:27
言語	C++23 (gcc 13.3.0 + boost 1.87.0)
結果	AC
実行時間	34 ms / 2,000 ms
コード長	10,938 bytes
コンパイル時間	3,149 ms
コンパイル使用メモリ	251,496 KB
実行使用メモリ	8,704 KB
最終ジャッジ日時	2024-12-20 05:54:35
合計ジャッジ時間	4,757 ms
ジャッジサーバーID （参考情報）	judge2 / judge3
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 * 17
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 || e == 1) return *this;
		if(data == mod() - 1) return e % 2 ? *this : *this = -*this;
		if(e < 0) *this = 1 / *this, e = -e;
		if(e == 1) return *this;
		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_UNSIGNED
};
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{
#ifdef LOCAL
	#define ASSERT(c) assert(c)
#else
	#define ASSERT(c) 42
#endif
	// 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);
	}
	// Multinomial Coefficient
	T mC(int n, const vector<int> &a) const{
		ASSERT((int)a.size() >= 2 && accumulate(a.begin(), a.end(), 0) == n);
		ASSERT(0 <= min(n, *min_element(a.begin(), a.end())) && max(n, *max_element(a.begin(), a.end())) <= SZ);
		T res = fact[n];
		for(auto x: a) res *= invfact[x];
		return res;
	}
	// Multinomial Coefficient
	template<class... U, typename enable_if<(is_integral_v<U> && ...)>::type* = nullptr>
	T mC(int n, U... pack){
		ASSERT(sizeof...(pack) >= 2 && (... + pack) == n);
		return (fact[n] * ... * invfact[pack]);
	}
	// 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, k) : k <= n + m ? C(n + k, k) - C(n + k, k - m - 1) : T();
	}
#undef ASSERT
};

int main(){
	cin.tie(0)->sync_with_stdio(0);
	cin.exceptions(ios::badbit | ios::failbit);
	int n;
	cin >> n;
	vector<modular> a(n);
	copy_n(istream_iterator<modular>(cin), n, a.begin());
	if(n == 1){
		cout << a[0] << "\n";
		return 0;
	}
	combinatorics<modular> C(n << 1);
	modular res = 0;
	for(auto i = 0; i < n; ++ i){
		res += a[i] * C.Catalan(n - 1 - i, n - 2, min(i, n - 2));
	}
	cout << res << "\n";
	return 0;
}

/*
(1,0,0,0,0), (0,1,0,0,0), (0,0,1,0,0), (0,0,0,1,0), (0,0,0,0,1)
             (1,1,0,0,0), (1,1,1,0,0), (1,1,1,1,0), (1,1,1,1,1)
                          (2,2,1,0,0), (3,3,2,1,0), (4,4,3,2,1)
                                       (5,5,3,1,0), (9,9,6,3,1)
*/
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