#1080916 (C++23) No.2990 Interval XOR

提出ソース
結果

問題	No.2990 Interval XOR
ユーザー	Aeren
提出日時	2025-04-29 13:47:16
言語	C++23 (gcc 13.3.0 + boost 1.87.0)
結果	AC
実行時間	274 ms / 2,000 ms
コード長	17,049 bytes
コンパイル時間	3,977 ms
コンパイル使用メモリ	297,044 KB
実行使用メモリ	13,988 KB
最終ジャッジ日時	2025-04-29 13:47:28
合計ジャッジ時間	11,855 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 * 37
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
// #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 debug_bin(...) 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 constexpr 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 constexpr 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 constexpr 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 constexpr 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(){ }
	constexpr modular_fixed_base(const double &x){ _data = _normalize(llround(x)); }
	constexpr modular_fixed_base(const long double &x){ _data = _normalize(llround(x)); }
	template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> constexpr modular_fixed_base(const T &x){ _data = _normalize(x); }
	template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> static constexpr 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> constexpr operator T() const{ return data(); }
	constexpr modular_fixed_base &operator+=(const modular_fixed_base &otr){ if((_data += otr._data) >= _mod) _data -= _mod; return *this; }
	constexpr 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> constexpr modular_fixed_base &operator+=(const T &otr){ return *this += modular_fixed_base(otr); }
	template<class T, typename enable_if<IS_INTEGRAL(T)>::type* = nullptr> constexpr modular_fixed_base &operator-=(const T &otr){ return *this -= modular_fixed_base(otr); }
	constexpr modular_fixed_base &operator++(){ return *this += 1; }
	constexpr modular_fixed_base &operator--(){ return *this += _mod - 1; }
	constexpr modular_fixed_base operator++(int){ modular_fixed_base result(*this); *this += 1; return result; }
	constexpr modular_fixed_base operator--(int){ modular_fixed_base result(*this); *this += _mod - 1; return result; }
	constexpr modular_fixed_base operator-() const{ return modular_fixed_base(_mod - _data); }
	constexpr 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>
	constexpr 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>
	constexpr 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>
	constexpr 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>
	constexpr modular_fixed_base geometric_sum(T e, modular_fixed_base c = 1) const{
		return modular_fixed_base(*this).inplace_geometric_sum(e, c);
	}
	// Returns the minimum integer e>0 with b^e=*this, if it exists
	// O(sqrt(mod)) applications of hashmap
	constexpr optional<data_t> log(const modular_fixed_base &b) const{
		data_t m = mod(), n = sqrtl(m) + 1, j = 1;
		modular_fixed_base e = 1, f = 1;
		unordered_map<data_t, data_t> A;
		while(j <= n && (f = e *= b) != *this) A[(e * *this).data()] = j ++;
		if(e == *this) return j;
		if(gcd(mod(), e.data()) == gcd(mod(), data())) for(auto i = 2; i < n + 2; ++ i) if(A.count((e *= f).data())) return n * i - A[e.data()];
		return {};
	}
	constexpr optional<modular_fixed_base> inverse() const{
		make_signed_t<data_t> a = data(), m = _mod, u = 0, v = 1;
		if(data() < _INV.size()) return _INV[data()];
		while(a){
			make_signed_t<data_t> t = m / a;
			m -= t * a; swap(a, m);
			u -= t * v; swap(u, v);
		}
		if(m != 1) return {};
		return modular_fixed_base{u};
	}
	modular_fixed_base &operator/=(const modular_fixed_base &otr){
		auto inv_ptr = otr.inverse();
		assert(inv_ptr);
		return *this = *this * *inv_ptr;
	}
#define ARITHMETIC_OP(op, apply_op)\
constexpr 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>\
constexpr 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>\
constexpr 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)\
constexpr 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>\
constexpr 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>\
constexpr 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;
	constexpr data_t data() const{ return _data; }
#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;

constexpr unsigned int mod = (119 << 23) + 1; // 998244353
// constexpr unsigned int mod = 1e9 + 7; // 1000000007
// constexpr unsigned int mod = 1e9 + 9; // 1000000009
// constexpr unsigned long long mod = (unsigned long long)1e18 + 9;
using modular = modular_fixed_base<decay_t<decltype(mod)>, mod>;

constexpr modular operator""_m(const char *x){
	modular res = 0;
	long long buffer = 0;
	long long buffer_width = 1;
	constexpr long long buffer_th = 1'000'000'000'000'000'000LL;
	while(*x){
		#ifdef LOCAL
		assert(isdigit(*x));
		#endif
		buffer = buffer * 10 + (*(x ++) - '0');
		if((buffer_width *= 10) == buffer_th){
			res = buffer_width * res + buffer;
			buffer = 0;
			buffer_width = 1;
		}
	}
	res = buffer_width * res + buffer;
	return res;
}

template<class T, class _transform_1D>
struct fast_fourier_transform_multidimensional_wrapper_base{
	static vector<T> buffer1, buffer2;
	// Assumes that n is a power of _transform_1D::length
	// O(n * log(n))
	static void transform(int n, T *p, bool invert = false){
		#ifdef LOCAL
		int power = 1;
		while(power < n) power *= _transform_1D::length;
		assert(power == n);
		#endif
		if(!invert){
			for(auto len = 1; len < n; len *= _transform_1D::length)
				for(auto i = 0; i < n; i += _transform_1D::length * len)
					for(auto j = 0; j < len; ++ j) _transform_1D::transform(p + i + j, len);
		}
		else{
			for(auto len = 1; len < n; len *= _transform_1D::length)
				for(auto i = 0; i < n; i += _transform_1D::length * len)
					for(auto j = 0; j < len; ++ j) _transform_1D::inverse_transform(p + i + j, len);
			T inv = 1 / _transform_1D::coefficient(n);
			if(inv != T{1}) for(auto i = 0; i < n; ++ i) p[i] *= inv;
		}
	}
	// O(n * log(n))
	static void transform(vector<T> &p, bool invert = false){
		transform((int)p.size(), p.data(), invert);
	}
	// O(n * log(n))
	static vector<T> convolve(const vector<T> &p, const vector<T> &q){
		int n = (int)p.size();
		assert((int)q.size() == n);
		buffer1.resize(n, 0);
		copy(p.begin(), p.end(), buffer1.begin());
		transform(buffer1);
		buffer2.resize(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() + n);
	}
	// Destroy p and q
	// Store the result on p
	// O(n * log(n))
	static void inplace_convolve(int n, T *p, T *q){
		transform(n, p), transform(n, q);
		for(auto i = 0; i < n; ++ i) p[i] *= q[i];
		transform(n, p, true);
	}
	// Destroy p and q
	// Store the result on p
	// O(n * log(n))
	static void inplace_square(int n, T *p){
		transform(n, p);
		for(auto i = 0; i < n; ++ i) p[i] *= p[i];
		transform(n, p, true);
	}
};
template<class T, class U>
vector<T> fast_fourier_transform_multidimensional_wrapper_base<T, U>::buffer1;
template<class T, class U>
vector<T> fast_fourier_transform_multidimensional_wrapper_base<T, U>::buffer2;

template<class T>
struct _transform_1D_bitwise_xor{
	static constexpr int length = 2;
	static void transform(T *a, int len){
		tie(a[0], a[len]) = tuple{
			a[0] + a[len],
			a[0] - a[len],
		};
	}
	static void inverse_transform(T *a, int len){
		tie(a[0], a[len]) = tuple{
			a[0] + a[len],
			a[0] - a[len],
		};
	}
	// inverse_transform(transform(p)) = coefficient(len(p)) * p
	static T coefficient(int n){
		return n;
	}
};
template<class T>
struct _transform_1D_bitwise_and{
	static constexpr int length = 2;
	static void transform(T *a, int len){
		a[0] += a[len];
	}
	static void inverse_transform(T *a, int len){
		a[0] -= a[len];
	}
	// inverse_transform(transform(p)) = coefficient(len(p)) * p
	static T coefficient(int n){
		return 1;
	}
};
template<class T>
struct _transform_1D_bitwise_or{
	static constexpr int length = 2;
	static void transform(T *a, int len){
		a[len] += a[0];
	}
	static void inverse_transform(T *a, int len){
		a[len] -= a[0];
	}
	// inverse_transform(transform(p)) = coefficient(len(p)) * p
	static T coefficient(int n){
		return 1;
	}
};
template<class T>
struct _transform_1D_tritwise_addition_modular{
	static_assert(T::mod() % 3 == 1);
	static constexpr int length = 3;
	static const T root;
	static const T root_sq;
	static void transform(T *a, int len){
		tie(a[0], a[len], a[len << 1]) = tuple{
			a[0] + a[len] + a[len << 1],
			a[0] + root * a[len] + root_sq * a[len << 1],
			a[0] + root_sq * a[len] + root * a[len << 1]
		};
	}
	static void inverse_transform(T *a, int len){
		tie(a[0], a[len], a[len << 1]) = tuple{
			a[0] + a[len] + a[len << 1],
			a[0] + root_sq * a[len] + root * a[len << 1],
			a[0] + root * a[len] + root_sq * a[len << 1]
		};
	}
	// inverse_transform(transform(p)) = coefficient(len(p)) * p
	static T coefficient(int n){
		return n;
	}
};
template<class T>
const T _transform_1D_tritwise_addition_modular<T>::root = T::primitive_root().power((T::mod() - 1) / 3);
template<class T>
const T _transform_1D_tritwise_addition_modular<T>::root_sq = root * root;

template<class T>
using bitwise_xor_transform = fast_fourier_transform_multidimensional_wrapper_base<T, _transform_1D_bitwise_xor<T>>;
template<class T>
using bitwise_and_transform = fast_fourier_transform_multidimensional_wrapper_base<T, _transform_1D_bitwise_and<T>>;
template<class T>
using bitwise_or_transform = fast_fourier_transform_multidimensional_wrapper_base<T, _transform_1D_bitwise_or<T>>;
template<class T>
using tritwise_addition_transform = fast_fourier_transform_multidimensional_wrapper_base<T, _transform_1D_tritwise_addition_modular<T>>;
template<class T>
using fwht = bitwise_xor_transform<T>;

int main(){
	cin.tie(0)->sync_with_stdio(0);
	cin.exceptions(ios::badbit | ios::failbit);
	auto power = modular::precalc_power(2, 1 << 18);
	int n, m;
	cin >> m >> n;
	vector<array<int, 2>> inter(n);
	vector<modular> f(1 << m);
	f[0] = 1;
	for(auto &[l, r]: inter){
		cin >> l >> r, ++ r;
		f[0] *= r - l;
	}
	vector<array<modular, 2>> coef;
	for(auto lsb = 0; lsb < m; ++ lsb){
		int base_exponent = 0;
		coef.assign(1 << m - lsb - 1, array{1_m, 0_m});
		for(auto [l, r]: inter){
			int l_start = l >> lsb + 1 << lsb + 1;
			int r_start = r >> lsb + 1 << lsb + 1;
			int l_mid = l >> lsb << lsb;
			int r_mid = r >> lsb << lsb;
			modular l_coef = (l_start == l_mid ? 1 : -1) * (2 * l_mid - l_start - l);
			modular r_coef = (r_start == r_mid ? -1 : 1) * (2 * r_mid - r_start - r);
			l >>= lsb + 1, r >>= lsb + 1;
			r %= 1 << m - lsb - 1;
			base_exponent ^= l;
			r ^= l;
			coef[r] = {coef[r][0] * l_coef + coef[r][1] * r_coef, coef[r][0] * r_coef + coef[r][1] * l_coef};
		}
		for(auto i = 0; i < 1 << m - lsb - 1; ++ i){
			coef[i] = {
				coef[i][0] + coef[i][1],
				coef[i][0] - coef[i][1],
			};
		}
		for(auto len = 1; len < 1 << m - lsb - 1; len <<= 1){
			for(auto i = 0; i < 1 << m - lsb - 1; i += len << 1){
				for(auto j = i; j < i + len; ++ j){
					tie(coef[j], coef[j + len]) = tuple{
						array{coef[j][0] * coef[j + len][0], coef[j][1] * coef[j + len][1]},
						array{coef[j][0] * coef[j + len][1], coef[j][1] * coef[j + len][0]}
					};
				}
			}
		}
		for(auto k = 1 << lsb; k < 1 << m; k += 1 << lsb + 1){
			f[k] = coef[k >> lsb + 1][0] * (__builtin_popcount(k >> lsb + 1 & base_exponent) & 1 ? -1 : 1);
		}
	}
	fwht<modular>::transform(f, true);
	ranges::copy(f, ostream_iterator<modular>(cout, "\n"));
	return 0;
}

/*
(1+X+X^2)(X+X^2+X^3)

sign(a,b) = (-1)^popcount(a & b)
[X^k]T(f) = \sum_{i=0~2^m-1} sign(k,i) * f_i
p[i] = X^0 + ... + X^{i-1}
f[i] = p[r[i]] - p[l[i]]
T(f[i]) = T(p[r[i]]) - T(p[l[i]])

Let b = lsb(k)
[X^k]T(p[r])
= sign(k/2^{b+1},r/2^{b+1}) * \sum_{i=r/2^{b+1}*2^{b+1} ~ r-1} sign(2^b,i)
= [X^{k/2^{b+1}}] T((\sum_{i=r/2^{b+1}*2^{b+1} ~ r-1} sign(2^b,i)) * X^{r/2^{b+1}})
*/
yukicoder

結果

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