#1047662 (C++23) No.3044 よくあるカエルさん

提出ソース
結果

問題	No.3044 よくあるカエルさん
ユーザー	Aeren
提出日時	2025-02-28 22:57:15
言語	C++23 (gcc 13.3.0 + boost 1.87.0)
結果	AC
実行時間	3 ms / 2,000 ms
コード長	11,136 bytes
コンパイル時間	3,888 ms
コンパイル使用メモリ	283,200 KB
実行使用メモリ	8,232 KB
最終ジャッジ日時	2025-02-28 22:57:20
合計ジャッジ時間	4,988 ms
ジャッジサーバーID （参考情報）	judge3 / judge2
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 * 1
other	AC * 20
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ソースコード

raw source code
// #include <bits/allocator.h> // Temp fix for gcc13 global pragma
// #pragma GCC target("avx2,bmi2,popcnt,lzcnt")
// #pragma GCC optimize("O3,unroll-loops")
#include <bits/stdc++.h>
// #include <x86intrin.h>
using namespace std;
#if __cplusplus >= 202002L
using namespace numbers;
#endif
#ifdef LOCAL
	#include "Debug.h"
#else
	#define debug_endl() 42
	#define debug(...) 42
	#define debug2(...) 42
	#define debugbin(...) 42
#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(1 <= _mod && _mod < data_t(1) << 8 * sizeof(data_t) - 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;
	}
	template<class T>
	static vector<modular_fixed_base> precalc_geometric_sum(T base, int SZ){
		vector<modular_fixed_base> res(SZ + 1);
		for(auto i = 1; i <= SZ; ++ i) res[i] = res[i - 1] * base + 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);
	}
	// c + c * x + ... + c * x^{e-1}
	template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>
	modular_fixed_base &inplace_geometric_sum(T e, modular_fixed_base c = 1){
		if(e == 0) return *this = {};
		if(data == 0) return *this = {};
		if(data == 1) return *this = c * e;
		if(e == 1) return *this = c;
		if(data == mod() - 1) return *this = c * abs(e % 2);
		modular_fixed_base res = 0;
		if(e < 0) return *this = geometric_sum(-e + 1, -*this) - 1;
		if(e == 1) return *this = c * *this;
		for(; e; c *= 1 + *this, *this *= *this, e >>= 1) if(e & 1) res += c, c *= *this;
		return *this = res;
	}
	// c + c * x + ... + c * x^{e-1}
	template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr>
	modular_fixed_base geometric_sum(T e, modular_fixed_base c = 1) const{
		return modular_fixed_base(*this).inplace_geometric_sum(e, c);
	}
	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;
	}
	friend ostream &operator<<(ostream &out, const modular_fixed_base &number){
		out << number.data;
#ifdef LOCAL
		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 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>;
modular operator""_m(const char *x){ return stoll(x); }

// Store the linear recurrence relation of form \sum_{t<=i<t+n} coef[i]*init[i] = init[t+n]
// T must be of modular type
// Requires modular
template<class T>
struct linear_recurrence_solver{
	int n;
	vector<T> init, coef;
	linear_recurrence_solver(const vector<T> &init, const vector<T> &coef): n((int)coef.size()), init(init), coef(coef){
		assert(coef.size() == init.size());
	}
	// Berlekamp Massey Algorithm
	// Find a minimum linear recurrence relation
	// O(len(s) * (n + log(mod)))
	linear_recurrence_solver(const vector<T> &s){
		int sz = (int)s.size();
		vector<T> b = {-1};
		coef = {-1};
		T y = 1;
		for(auto t = 1; t <= sz; ++ t){
			int l = (int)coef.size(), m = (int)b.size();
			T x = 0;
			for(auto i = 0; i < l; ++ i) x += coef[i] * s[t - l + i];
			b.push_back(0);
			++ m;
			if(x == 0) continue;
			T freq = x / y;
			if(l < m){
				auto tmp = coef;
				coef.insert(coef.begin(), m - l, 0);
				for(auto i = 0; i < m; ++ i) coef[m - 1 - i] -= freq * b[m - 1 - i];
				b = tmp;
				y = x;
			}
			else for(auto i = 0; i < m; ++ i) coef[l - 1 - i] -= freq * b[m - 1 - i];
		}
		coef.pop_back();
		n = (int)coef.size();
		init = vector<T>(s.begin(), s.begin() + n);
	}
	// O(n^2 * log(i))
	template<class U>
	vector<T> get_coef(U i) const{
		assert(0 <= i);
		if(n == 0) return vector<T>(n + 1);
		auto merge = [&](const vector<T> &a, const vector<T> &b){
			vector<T> res(2 * n + 1);
			for(auto i = 0; i <= n; ++ i) for(auto j = 0; j <= n; ++ j) res[i + j] += a[i] * b[j];
			for(auto i = n << 1; i >= n; -- i) for(auto j = 0; j < n; ++ j) res[i - 1 - j] += res[i] * coef[n - 1 - j];
			res.resize(n + 1);
			res[n] = 0;
			return res;
		};
		vector<T> power(n + 1), base(n + 1);
		for(power[0] = base[1] = 1; i; i >>= 1, base = merge(base, base)) if(i & 1) power = merge(power, base);
		T res = 0;
		return power;
	}
	// O(n^2 * log(i))
	template<class U>
	T operator[](U i) const{
		assert(0 <= i);
		if(n == 0) return 0;
		auto power = get_coef(i);
		T res = 0;
		for(auto i = 0; i < n; ++ i) res += power[i] * init[i];
		return res;
	}
};

int main(){
	cin.tie(0)->sync_with_stdio(0);
	cin.exceptions(ios::badbit | ios::failbit);
	int n, t, k, l;
	cin >> n >> t >> k >> l;
	modular p = (k - 1) / 6_m, q = (l - k) / 6_m, r = 1 - p - q;
	vector<modular> init(t), coef(t);
	init[1] = 1;
	for(auto x = 2; x < t; ++ x){
		init[x] = init[x - 1] * p + init[x - 2] * q;
	}
	coef[0] = r;
	coef[t - 2] = q;
	coef[t - 1] = p;
	cout << linear_recurrence_solver(init, coef)[n] << "\n";
	return 0;
}

/*

*/
yukicoder

結果

ソースコード
