Test/SegmentTree.fold.test.cpp

• View this file on GitHub
• Last update: 2021-06-05 13:56:14+09:00
• Problem: https://judge.yosupo.jp/problem/point_set_range_composite

Depends on

• セグメント木 (DataStructure/SegmentTree.hpp)
• ModInt 構造体 (Mathematics/ModInt.hpp)

Code

#define PROBLEM "https://judge.yosupo.jp/problem/point_set_range_composite"

#include "DataStructure/SegmentTree.hpp"
#include "Mathematics/ModInt.hpp"

#include <cstdio>

int main() {
	int N, Q;
	scanf("%d %d", &N, &Q);
	
	using mint = ModInt<998244353>;
	using pmm = std::pair<mint, mint>;
	
	SegmentTree<pmm> seg(N, pmm(1, 0), [](const pmm & a, const pmm & b) -> pmm {
		return {a.first * b.first, b.first * a.second + b.second};
	});
	
	for (int i = 0; i < N; ++i) {
		int a, b;
		scanf("%d %d", &a, &b);
		seg.set(i, {a, b});
	}
	
	while (Q--) {
		int q, a, b, c;
		scanf("%d %d %d %d", &q, &a, &b, &c);
		if (q == 0) {
			seg.set(a, {b, c});
		}
		else {
			pmm v = seg.fold(a, b);
			mint ans = v.first * c + v.second;
			printf("%d\n", ans.val());
		}
	}
}

#line 1 "Test/SegmentTree.fold.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/point_set_range_composite"

#line 1 "DataStructure/SegmentTree.hpp"



#include <vector>
#include <algorithm>
#include <cassert>
#include <functional>

/**
 * @brief https://tkmst201.github.io/Library/DataStructure/SegmentTree.hpp
 */
template<typename T>
struct SegmentTree {
	using value_type = T;
	using const_reference = const value_type &;
	using F = std::function<value_type (const_reference, const_reference)>;
	using size_type = std::size_t;
	
private:
	size_type n, n_;
	value_type id_elem;
	F f;
	std::vector<value_type> node;
	
public:
	SegmentTree() = default;
	
	SegmentTree(size_type n, const_reference id_elem, const F & f)
		: n(n), id_elem(id_elem), f(f) {
		n_ = 1;
		while (n_ < n) n_ <<= 1;
		node.assign(2 * n_, id_elem);
	}
	
	SegmentTree(const std::vector<value_type> & v, const_reference id_elem, const F & f)
		: SegmentTree(v.size(), id_elem, f) {
		for (size_type i = 0; i < v.size(); ++i) node[i + n_] = v[i];
		for (size_type i = n_ - 1; i > 0; --i) node[i] = f(node[i << 1], node[i << 1 | 1]);
	}
	
	size_type size() const noexcept {
		return n;
	}
	
	void set(size_type i, const_reference x) noexcept {
		assert(i < size());
		node[i += n_] = x;
		while (i > 1) {
			i >>= 1;
			node[i] = f(node[i << 1], node[i << 1 | 1]);
		}
	}
	
	const_reference get(size_type i) const noexcept {
		assert(i < size());
		return node[i + n_];
	}
	
	value_type fold(size_type l, size_type r) const noexcept {
		assert(l <= r);
		assert(r <= size());
		value_type lv = id_elem, rv = id_elem;
		for (l += n_, r += n_; l < r; l >>= 1, r >>= 1) {
			if (l & 1) lv = f(lv, node[l++]);
			if (r & 1) rv = f(node[r - 1], rv);
		}
		return f(lv, rv);
	}
	
	value_type fold_all() const noexcept {
		return node[1];
	}
	
	size_type max_right(size_type l, std::function<bool (const_reference)> g) const noexcept {
		assert(l <= size());
		assert(g(id_elem));
		if (l == size()) return size();
		l += n_;
		value_type sum = id_elem;
		while (true) {
			while (~l & 1) l >>= 1;
			const value_type nex_sum = f(sum, node[l]);
			if (g(nex_sum)) { sum = nex_sum; ++l; }
			else break;
			if ((l & -l) == l) return size();
		}
		while (l < n_) {
			const value_type nex_sum = f(sum, node[l << 1]);
			l <<= 1;
			if (g(nex_sum)) { sum = nex_sum; l |= 1; }
		}
		return l - n_;
	}
	
	size_type min_left(size_type r, std::function<bool (const_reference)> g) const noexcept {
		assert(r <= size());
		assert(g(id_elem));
		if (r == 0) return 0;
		r += n_;
		value_type sum = id_elem;
		while (true) {
			--r;
			while (r > 1 && (r & 1)) r >>= 1;
			const value_type nex_sum = f(node[r], sum);
			if (g(nex_sum)) sum = nex_sum;
			else break;
			if ((r & -r) == r) return 0;
		}
		while (r < n_) {
			const value_type nex_sum = f(node[r << 1 | 1], sum);
			r <<= 1;
			if (!g(nex_sum)) r |= 1;
			else sum = nex_sum;
		}
		return r + 1 - n_;
	}
};


#line 1 "Mathematics/ModInt.hpp"



#line 5 "Mathematics/ModInt.hpp"
#include <iostream>
#include <cstdint>

/**
 * @brief https://tkmst201.github.io/Library/Mathematics/ModInt.hpp
 */
template<int M>
struct ModInt {
	static_assert(M > 0);
	
	using value_type = int;
	using calc_type = std::int_fast64_t;
	
private:
	value_type val_;
	
public:
	constexpr ModInt(calc_type val = 0) : val_(val % M + (val >= 0 ? 0 : M)) {}
	constexpr value_type val() const noexcept { return val_; }
	constexpr static decltype(M) mod() noexcept { return M; }
	
	explicit constexpr operator bool() const noexcept { return val_; }
	constexpr bool operator !() const noexcept { return !static_cast<bool>(*this); }
	constexpr ModInt operator +() const noexcept { return *this; }
	constexpr ModInt operator -() const noexcept { return ModInt(val_ == 0 ? 0 : M - val_); }
	constexpr ModInt operator ++(int) noexcept { ModInt res = *this; ++*this; return res; }
	constexpr ModInt operator --(int) noexcept { ModInt res = *this; --*this; return res; }
	constexpr ModInt & operator ++() noexcept { val_ = val_ + 1 == M ? 0 : val_ + 1; return *this; }
	constexpr ModInt & operator --() noexcept { val_ = val_ == 0 ? M - 1 : val_ - 1; return *this; }
	constexpr ModInt & operator +=(const ModInt & rhs) noexcept { val_ += val_ < M - rhs.val_ ? rhs.val_ : rhs.val_ - M; return *this; }
	constexpr ModInt & operator -=(const ModInt & rhs) noexcept { val_ += val_ >= rhs.val_ ? -rhs.val_ : M - rhs.val_; return *this; }
	constexpr ModInt & operator *=(const ModInt & rhs) noexcept { val_ = static_cast<calc_type>(val_) * rhs.val_ % M; return *this; }
	constexpr ModInt & operator /=(const ModInt & rhs) noexcept { return *this *= rhs.inv(); }
	friend constexpr ModInt operator +(const ModInt & lhs, const ModInt & rhs) noexcept { return ModInt(lhs) += rhs; }
	friend constexpr ModInt operator -(const ModInt & lhs, const ModInt & rhs) noexcept { return ModInt(lhs) -= rhs; }
	friend constexpr ModInt operator *(const ModInt & lhs, const ModInt & rhs) noexcept { return ModInt(lhs) *= rhs; }
	friend constexpr ModInt operator /(const ModInt & lhs, const ModInt & rhs) noexcept { return ModInt(lhs) /= rhs; }
	friend constexpr bool operator ==(const ModInt & lhs, const ModInt & rhs) noexcept { return lhs.val_ == rhs.val_; }
	friend constexpr bool operator !=(const ModInt & lhs, const ModInt & rhs) noexcept { return !(lhs == rhs); }
	friend std::ostream & operator <<(std::ostream & os, const ModInt & rhs) { return os << rhs.val_; }
	friend std::istream & operator >>(std::istream & is, ModInt & rhs) { calc_type x; is >> x; rhs = ModInt(x); return is; }
	
	constexpr ModInt pow(calc_type n) const noexcept {
		ModInt res = 1, x = val_;
		if (n < 0) { x = x.inv(); n = -n; }
		while (n) { if (n & 1) res *= x; x *= x; n >>= 1; }
		return res;
	}
	
	constexpr ModInt inv() const noexcept {
		value_type a = val_, a1 = 1, b = M, b1 = 0;
		while (b > 0) {
			const value_type q = a / b;
			value_type tmp = a - q * b; a = b; b = tmp;
			tmp = a1 - q * b1; a1 = b1; b1 = tmp;
		}
		assert(a == 1);
		if (a1 < 0) a1 += M;
		return a1;
	}
};


#line 5 "Test/SegmentTree.fold.test.cpp"

#include <cstdio>

int main() {
	int N, Q;
	scanf("%d %d", &N, &Q);
	
	using mint = ModInt<998244353>;
	using pmm = std::pair<mint, mint>;
	
	SegmentTree<pmm> seg(N, pmm(1, 0), [](const pmm & a, const pmm & b) -> pmm {
		return {a.first * b.first, b.first * a.second + b.second};
	});
	
	for (int i = 0; i < N; ++i) {
		int a, b;
		scanf("%d %d", &a, &b);
		seg.set(i, {a, b});
	}
	
	while (Q--) {
		int q, a, b, c;
		scanf("%d %d %d %d", &q, &a, &b, &c);
		if (q == 0) {
			seg.set(a, {b, c});
		}
		else {
			pmm v = seg.fold(a, b);
			mint ans = v.first * c + v.second;
			printf("%d\n", ans.val());
		}
	}
}

Back to top page