結果

問題 No.2611 Count 01
コンテスト
ユーザー Aeren
提出日時 2024-01-19 23:11:04
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 204 ms / 6,000 ms
コード長 16,123 bytes
コンパイル時間 2,925 ms
コンパイル使用メモリ 255,100 KB
実行使用メモリ 24,576 KB
最終ジャッジ日時 2024-09-28 05:03:35
合計ジャッジ時間 8,537 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
（要ログイン）
ファイルパターン 結果
sample AC * 3
other AC * 20
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

diff # 

#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<bool HAS_QUERY, bool HAS_UPDATE, class T, class U, class F1, class F2, class F3>
struct segment_tree_base{
#define ifQ if constexpr(HAS_QUERY)
#define ifU if constexpr(HAS_UPDATE)
	int n, size, log;
	vector<T> data;
	vector<U> data_action;
	F1 TT; // monoid operation (always adjacent)
	T T_id; // monoid identity
	F2 UU; // monoid operation (superset, subset)
	U U_id; // monoid identity
	F3 UT; // action of U on T (superset, subset)
	// O(n)
	segment_tree_base(F1 TT, T T_id, F2 UU, U U_id, F3 UT): TT(TT), T_id(T_id), UU(UU), U_id(U_id), UT(UT){ }
	segment_tree_base &operator=(const segment_tree_base &seg){
		n = seg.n;
		size = seg.size;
		log = seg.log;
		data = seg.data;
		data_action = seg.data_action;
	}
	// O(n)
	void build(int n){
		this->n = n;
		size = 1;
		while(size < n) size <<= 1;
		log = __lg(size);
		ifQ data.assign(size << 1, T_id);
		ifU data_action.assign(HAS_QUERY ? size : size << 1, U_id);
	}
	// O(n)
	void build(int n, T x){
		static_assert(HAS_QUERY);
		this->n = n;
		size = 1;
		while(size < n) size <<= 1;
		log = __lg(size);
		data.assign(size << 1, T_id);
		fill(data.begin() + size, data.begin() + size + n, x);
		for(auto i = size - 1; i >= 1; -- i) refresh(i);
		ifU data_action.assign(size, U_id);
	}
	// O(n)
	void build(const vector<T> &a){
		static_assert(HAS_QUERY);
		n = (int)a.size();
		size = 1;
		while(size < n) size <<= 1;
		log = __lg(size);
		data.assign(size << 1, T_id);
		copy(a.begin(), a.end(), data.begin() + size);
		for(auto i = size - 1; i >= 1; -- i) refresh(i);
		ifU data_action.assign(size, U_id);
	}
	// O(n)
	void build_action(int n){
		static_assert(!HAS_QUERY && HAS_UPDATE);
		build(n);
	}
	// O(n)
	void build_action(int n, U f){
		static_assert(!HAS_QUERY && HAS_UPDATE);
		this->n = n;
		size = 1;
		while(size < n) size <<= 1;
		log = __lg(size);
		data_action.assign(size << 1, U_id);
		fill(data_action.begin() + size, data_action.begin() + size + n, f);
	}
	// O(n)
	void build_action(const vector<U> &a){
		static_assert(!HAS_QUERY && HAS_UPDATE);
		n = (int)a.size();
		size = 1;
		while(size < n) size <<= 1;
		log = __lg(size);
		data_action.assign(size << 1, U_id);
		copy(a.begin(), a.end(), data_action.begin() + size);
	}
	// O(1)
	void refresh(int i){
		static_assert(HAS_QUERY);
		data[i] = TT(data[i << 1], data[i << 1 | 1]);
	}
	// O(1)
	void apply(int i, U f){
		static_assert(HAS_UPDATE);
		ifQ data[i] = UT(f, data[i]);
		if(!HAS_QUERY || i < size) data_action[i] = UU(f, data_action[i]);
	}
	// O(1)
	void push(int i){
		static_assert(HAS_UPDATE);
		apply(i << 1, data_action[i]), apply(i << 1 | 1, data_action[i]);
		data_action[i] = U_id;
	}
	// O(log(n)) if HAS_UPDATE, O(1) otherwise.
	T query(int p){
		static_assert(HAS_QUERY);
		assert(0 <= p && p < n);
		p += size;
		ifU for(auto i = log; i >= 1; -- i) push(p >> i);
		return data[p];
	}
	// O(log(n))
	U query_action(int p){
		static_assert(!HAS_QUERY && HAS_UPDATE);
		assert(0 <= p && p < n);
		p += size;
		ifU for(auto i = log; i >= 1; -- i) push(p >> i);
		return data_action[p];
	}
	// O(log(n))
	T query(int l, int r){
		static_assert(HAS_QUERY);
		assert(0 <= l && l <= r && r <= n);
		if(l == r) return T_id;
		l += size, r += size;
		ifU for(auto i = log; i >= 1; -- i){
			if(l >> i << i != l) push(l >> i);
			if(r >> i << i != r) push(r - 1 >> i);
		}
		T res_left = T_id, res_right = T_id;
		for(; l < r; l >>= 1, r >>= 1){
			if(l & 1) res_left = TT(res_left, data[l ++]);
			if(r & 1) res_right = TT(data[-- r], res_right);
		}
		return TT(res_left, res_right);
	}
	// O(1)
	T query_all() const{
		static_assert(HAS_QUERY);
		return data[1];
	}
	// O(n)
	vector<T> to_array(){
		static_assert(HAS_QUERY);
		ifU for(auto i = 1; i < size; ++ i) push(i);
		return vector<T>(data.begin() + size, data.begin() + size + n);
	}
	// O(n)
	vector<U> to_array_of_updates(){
		static_assert(!HAS_QUERY && HAS_UPDATE);
		for(auto i = 1; i < size; ++ i) push(i);
		return vector<U>(data_action.begin() + size, data_action.begin() + size + n);
	}
	// O(log(n))
	void set(int p, T x){
		static_assert(HAS_QUERY);
		assert(0 <= p && p < n);
		p += size;
		ifU for(auto i = log; i >= 1; -- i) push(p >> i);
		data[p] = x;
		for(auto i = 1; i <= log; ++ i) refresh(p >> i);
	}
	// O(log(n))
	void set_action(int p, U f){
		static_assert(!HAS_QUERY && HAS_UPDATE);
		assert(0 <= p && p < n);
		p += size;
		for(auto i = log; i >= 1; -- i) push(p >> i);
		data_action[p] = f;
	}
	// O(log(n))
	void update(int p, U f){
		static_assert(HAS_UPDATE);
		assert(0 <= p && p < n);
		p += size;
		for(auto i = log; i >= 1; -- i) push(p >> i);
		ifQ{
			data[p] = UT(f, data[p]);
			for(auto i = 1; i <= log; ++ i) refresh(p >> i);
		}
		else data_action[p] = UU(f, data_action[p]);
	}
	// O(log(n))
	void update(int l, int r, U f){
		static_assert(HAS_UPDATE);
		assert(0 <= l && l <= r && r <= n);
		if(l == r) return;
		l += size, r += size;
		for(auto i = log; i >= 1; -- i){
			if(l >> i << i != l) push(l >> i);
			if(r >> i << i != r) push(r - 1 >> i);
		}
		int l2 = l, r2 = r;
		for(; l < r; l >>= 1, r >>= 1){
			if(l & 1) apply(l ++, f);
			if(r & 1) apply(-- r, f);
		}
		l = l2, r = r2;
		ifQ for(auto i = 1; i <= log; ++ i){
			if(l >> i << i != l) refresh(l >> i);
			if(r >> i << i != r) refresh(r - 1 >> i);
		}
	}
	// pred(sum[l, r)) is T, T, ..., T, F, F, ..., F
	// Returns max r with T
	// O(log(n))
	int max_pref(int l, auto pred){
		static_assert(HAS_QUERY);
		assert(0 <= l && l <= n && pred(T_id));
		if(l == n) return n;
		l += size;
		ifU for(auto i = log; i >= 1; -- i) push(l >> i);
		T sum = T_id;
		do{
			while(~l & 1) l >>= 1;
			if(!pred(TT(sum, data[l]))){
				while(l < size){
					ifU push(l);
					l = l << 1;
					if(pred(TT(sum, data[l]))) sum = TT(sum, data[l ++]);
				}
				return l - size;
			}
			sum = TT(sum, data[l]);
			++ l;
		}while((l & -l) != l);
		return n;
	}
	// pred(sum[l, r)) is F, F, ..., F, T, T, ..., T
	// Returns min l with T
	// O(log(n))
	int min_suff(int r, auto pred){
		static_assert(HAS_QUERY);
		assert(0 <= r && r <= n && pred(T_id));
		if(r == 0) return 0;
		r += size;
		ifU for(auto i = log; i >= 1; -- i) push(r - 1 >> i);
		T sum = T_id;
		do{
			-- r;
			while(r > 1 && r & 1) r >>= 1;
			if(!pred(TT(data[r], sum))){
				while(r < size){
					ifU push(r);
					r = r << 1 | 1;
					if(pred(TT(data[r], sum))) sum = TT(data[r --], sum);
				}
				return r + 1 - size;
			}
			sum = TT(data[r], sum);
		}while((r & -r) != r);
		return 0;
	}
	template<class output_stream>
	friend output_stream &operator<<(output_stream &out, segment_tree_base<HAS_QUERY, HAS_UPDATE, T, U, F1, F2, F3> seg){
		out << "{";
		for(auto i = 0; i < seg.n; ++ i){
			ifQ out << seg.query(i);
			else out << seg.query_action(i);
			if(i != seg.n - 1) out << ", ";
		}
		return out << '}';
	}
};

// Supports query
template<class T, class F>
auto make_Q_segment_tree(F TT, T T_id){
	using U = int;
	auto _UU = [&](U, U)->U{ return U{}; };
	auto _UT = [&](U, T)->T{ return T{}; };
	return segment_tree_base<true, false, T, U, F, decltype(_UU), decltype(_UT)>(TT, T_id, _UU, U{}, _UT);
}
// Supports update
template<class U, class F>
auto make_U_segment_tree(F UU, U U_id){
	using T = int;
	auto _TT = [&](T, T)->T{ return T{}; };
	auto _UT = [&](U, T)->T{ return T{}; };
	return segment_tree_base<false, true, T, U, decltype(_TT), F, decltype(_UT)>(_TT, T{}, UU, U_id, _UT);
}
// Supports query and update
template<class T, class U, class F1, class F2, class F3>
auto make_QU_segment_tree(F1 TT, T T_id, F2 UU, U U_id, F3 UT){
	return segment_tree_base<true, true, T, U, F1, F2, F3>(TT, T_id, UU, U_id, UT);
}

int main(){
	cin.tie(0)->sync_with_stdio(0);
	cin.exceptions(ios::badbit | ios::failbit);
	int n, qn;
	string s;
	cin >> n >> qn >> s;
	using T = array<modular, 8>;
	// sum of ij where si != sj
	// sum of i where si != sj
	// sum of j where si != sj
	// sum of 1 where si != sj
	
	// sum of i where si = 0
	// sum of 1 where si = 0

	// sum of i where si = 1
	// sum of 1 where si = 1
	auto TT = [&](T x, T y)->T{
		return {
			x[0] + y[0] + x[4] * y[6] + x[6] * y[4],
			x[1] + y[1] + x[4] * y[7] + x[6] * y[5],
			x[2] + y[2] + x[5] * y[6] + x[7] * y[4],
			x[3] + y[3] + x[5] * y[7] + x[7] * y[5],
			x[4] + y[4],
			x[5] + y[5],
			x[6] + y[6],
			x[7] + y[7]
		};
	};
	T T_id{};
	auto gen = [&](int i, char c)->T{
		return {
			0,
			0,
			0,
			0,
			i * (c == '0'),
			1 * (c == '0'),
			i * (c == '1'),
			1 * (c == '1')
		};
	};
	vector<T> init(n);
	for(auto i = 0; i < n; ++ i){
		init[i] = gen(i, s[i]);
	}
	auto seg = make_Q_segment_tree(TT, T_id);
	seg.build(init);
	for(auto qi = 0; qi < qn; ++ qi){
		int type;
		cin >> type;
		if(type == 1){
			int p;
			cin >> p, -- p;
			s[p] ^= '0' ^ '1';
			seg.set(p, gen(p, s[p]));
		}
		else{
			int l, r;
			cin >> l >> r, -- l;
			auto q = seg.query(l, r);
			cout << -q[0] + (l - 1) * q[2] + r * q[1] - 1LL * (l - 1) * r * q[3] << "\n";
		}
	}
	return 0;
}

/*

*/
0