test/data-structure/lazy-segtree/yosupo-Range-Affine-Range-Sum.test.cpp

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• Last update: 2023-07-31 16:36:45+08:00
• Problem: https://judge.yosupo.jp/problem/range_affine_range_sum

Depends on

• library/data-structure/lazy-segtree.hpp
• library/data-structure/segtree.hpp
• library/math/inv-gcd.hpp
• library/math/safe-mod.hpp
• library/misc/type-traits.hpp
• library/modint/modint.hpp

Code

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

#include <iostream>

#include <vector>

#include "../../../library/data-structure/lazy-segtree.hpp"

#include "../../../library/modint/modint.hpp"

using namespace std;
using namespace felix;

using mint = modint998244353;

struct S {
	mint sum;
	int size = 0;

	S() {}
	S(mint a, int b = 1) : sum(a), size(b) {}
};

S e() { return S(); }

S op(S a, S b) {
	a.sum += b.sum;
	a.size += b.size;
	return a;
}

struct F {
	mint a, b;
	bool bad = true;

	F() {}
	F(mint x, mint y) : a(x), b(y), bad(false) {}
};

F id() { return F(); }

S mapping(F f, S s) {
	if(f.bad || s.size == 0) {
		return s;
	}
	s.sum = f.a * s.sum + f.b * s.size;
	return s;
}

F composition(F f, F g) {
	if(f.bad || g.bad) {
		return f.bad ? g : f;
	}
	return F(f.a * g.a, f.a * g.b + f.b);
}

int main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	int n, q;
	cin >> n >> q;
	vector<S> a(n);
	for(int i = 0; i < n; i++) {
		cin >> a[i].sum;
		a[i].size = 1;
	}
	lazy_segtree<S, e, op, F, id, mapping, composition> seg(a);
	while(q--) {
		int type, l, r;
		cin >> type >> l >> r;
		if(type == 0) {
			mint a, b;
			cin >> a >> b;
			seg.apply(l, r, F(a, b));
		} else {
			cout << seg.prod(l, r).sum << "\n";
		}
	}
	return 0;
}

#line 1 "test/data-structure/lazy-segtree/yosupo-Range-Affine-Range-Sum.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/range_affine_range_sum"

#include <iostream>

#include <vector>

#line 3 "library/data-structure/lazy-segtree.hpp"
#include <algorithm>
#include <functional>
#include <cassert>
#line 6 "library/data-structure/segtree.hpp"

namespace felix {

template<class S, S (*e)(), S (*op)(S, S)>
struct segtree {
public:
    segtree() {}
    explicit segtree(int _n) : segtree(std::vector<S>(_n, e())) {}
    explicit segtree(const std::vector<S>& a): n(a.size()) {
        log = std::__lg(2 * n - 1);
        size = 1 << log;
        d.resize(size * 2, e());
        for(int i = 0; i < n; ++i) {
            d[size + i] = a[i];
        }
        for(int i = size - 1; i >= 1; i--) {
            update(i);
        }
    }
    
    void set(int p, S val) {
        assert(0 <= p && p < n);
        p += size;
        d[p] = val;
        for(int i = 1; i <= log; ++i) {
            update(p >> i);
        }
    }

    S get(int p) const {
        assert(0 <= p && p < n);
        return d[p + size];
    }

    S operator[](int p) const { return get(p); }
    
    S prod(int l, int r) const {
        assert(0 <= l && l <= r && r <= n);
        S sml = e(), smr = e();
        for(l += size, r += size; l < r; l >>= 1, r >>= 1) {
            if(l & 1) {
                sml = op(sml, d[l++]);
            }
            if(r & 1) {
                smr = op(d[--r], smr);
            }
        }
        return op(sml, smr);
    }

    S all_prod() const { return d[1]; }

    template<bool (*f)(S)> int max_right(int l) {
        return max_right(l, [](S x) { return f(x); });
    }

    template<class F> int max_right(int l, F f) {
        assert(0 <= l && l <= n);
        assert(f(e()));
        if(l == n) {
            return n;
        }
        l += size;
        S sm = e();
        do {
            while(~l & 1) {
                l >>= 1;
            }
            if(!f(op(sm, d[l]))) {
                while(l < size) {
                    push(l);
                    l <<= 1;
                    if(f(op(sm, d[l]))) {
                        sm = op(sm, d[l++]);
                    }
                }
                return l - size;
            }
            sm = op(sm, d[l++]);
        } while((l & -l) != l);
        return n;
    }

    template<bool (*f)(S)> int min_left(int r) {
        return min_left(r, [](S x) { return f(x); });
    }

    template<class F> int min_left(int r, F f) {
        assert(0 <= r && r <= n);
        assert(f(e()));
        if(r == 0) {
            return 0;
        }
        r += size;
        S sm = e();
        do {
            r--;
            while(r > 1 && (r & 1)) {
                r >>= 1;
            }
            if(!f(op(d[r], sm))) {
                while(r < size) {
                    push(r);
                    r = 2 * r + 1;
                    if(f(op(d[r], sm))) {
                        sm = op(d[r--], sm);
                    }
                }
                return r + 1 - size;
            }
            sm = op(d[r], sm);
        } while((r & -r) != r);
        return 0;
    }
    
protected:
    int n, size, log;
    std::vector<S> d;

    void update(int v) {
        d[v] = op(d[2 * v], d[2 * v + 1]);
    }

    virtual void push(int p) {}
};

} // namespace felix
#line 7 "library/data-structure/lazy-segtree.hpp"

namespace felix {

template<class S,
         S (*e)(),
         S (*op)(S, S),
         class F,
         F (*id)(),
         S (*mapping)(F, S),
         F (*composition)(F, F)>
struct lazy_segtree : public segtree<S, e, op> {
	using base = segtree<S, e, op>;

public:
	lazy_segtree() {}
	explicit lazy_segtree(int _n) : lazy_segtree(std::vector<S>(_n, e())) {}
	explicit lazy_segtree(const std::vector<S>& v) : base(v), lz(size, id()) {}

	void set(int p, S x) {
		push_down(p);
		base::set(p, x);
	}

	S get(int p) {
		push_down(p);
		return base::get(p);
	}

	S operator[](int p) { return get(p); }

	S prod(int l, int r) {
		if(l == r) {
			return e();
		}
		push_down(l, r);
		return base::prod(l, r);
	}

	void apply(int p, F f) {
		assert(0 <= p && p < n);
		push_down(p);
		base::set(p, mapping(f, d[p]));
	}

	void apply(int l, int r, F f) {
		assert(0 <= l && l <= r && r <= n);
		if(l == r) {
			return;
		}
		push_down(l, r);
		l += size, r += size;
		{
			int l2 = l, r2 = r;
			while(l < r) {
				if(l & 1) {
					all_apply(l++, f);
				}
				if(r & 1) {
					all_apply(--r, f);
				}
				l >>= 1, r >>= 1;
			}
			l = l2, r = r2;
		}
		for(int i = 1; i <= log; i++) {
			if(((l >> i) << i) != l) {
				update(l >> i);
			}
			if(((r >> i) << i) != r) {
				update((r - 1) >> i);
			}
		}
	}

	template<bool (*g)(S)> int max_right(int l) {
		return max_right(l, [](S x) { return g(x); });
	}

	template<class G> int max_right(int l, G g) {
		assert(0 <= l && l <= n);
		assert(g(e()));
		if(l == n) {
			return n;
		}
		push_down(l);
		return base::max_right(l, g);
	}

	template<bool (*g)(S)> int min_left(int r) {
		return min_left(r, [](S x) { return g(x); });
	}

	template<class G> int min_left(int r, G g) {
		assert(0 <= r && r <= n);
		assert(g(e()));
		if(r == 0) {
			return 0;
		}
		push_down(r - 1);
		return base::min_left(r, g);
	}

protected:
	using base::n, base::log, base::size, base::d;
	using base::update;

	std::vector<F> lz;

	virtual void all_apply(int k, F f) {
		d[k] = mapping(f, d[k]);
		if(k < size) {
			lz[k] = composition(f, lz[k]);
		}
	}

	void push(int k) override {
		all_apply(2 * k, lz[k]);
		all_apply(2 * k + 1, lz[k]);
		lz[k] = id();
	}

	void push_down(int p) {
		p += size;
		for(int i = log; i >= 1; i--) {
			push(p >> i);
		}
	}

	void push_down(int l, int r) {
		l += size, r += size;
		for(int i = log; i >= 1; i--) {
			if(((l >> i) << i) != l) {
				push(l >> i);
			}
			if(((r >> i) << i) != r) {
				push((r - 1) >> i);
			}
		}
	}
};

} // namespace felix
#line 6 "library/modint/modint.hpp"
#include <type_traits>

#line 3 "library/misc/type-traits.hpp"
#include <numeric>

#line 5 "library/misc/type-traits.hpp"

namespace felix {

namespace internal {

#ifndef _MSC_VER
template<class T> using is_signed_int128 = typename std::conditional<std::is_same<T, __int128_t>::value || std::is_same<T, __int128>::value, std::true_type, std::false_type>::type;
template<class T> using is_unsigned_int128 = typename std::conditional<std::is_same<T, __uint128_t>::value || std::is_same<T, unsigned __int128>::value, std::true_type, std::false_type>::type;
template<class T> using make_unsigned_int128 = typename std::conditional<std::is_same<T, __int128_t>::value, __uint128_t, unsigned __int128>;
template<class T> using is_integral = typename std::conditional<std::is_integral<T>::value || is_signed_int128<T>::value || is_unsigned_int128<T>::value, std::true_type, std::false_type>::type;
template<class T> using is_signed_int = typename std::conditional<(is_integral<T>::value && std::is_signed<T>::value) || is_signed_int128<T>::value, std::true_type, std::false_type>::type;
template<class T> using is_unsigned_int = typename std::conditional<(is_integral<T>::value && std::is_unsigned<T>::value) || is_unsigned_int128<T>::value, std::true_type, std::false_type>::type;
template<class T> using to_unsigned = typename std::conditional<is_signed_int128<T>::value, make_unsigned_int128<T>, typename std::conditional<std::is_signed<T>::value, std::make_unsigned<T>, std::common_type<T>>::type>::type;
#else
template<class T> using is_integral = typename std::is_integral<T>;
template<class T> using is_signed_int = typename std::conditional<is_integral<T>::value && std::is_signed<T>::value, std::true_type, std::false_type>::type;
template<class T> using is_unsigned_int = typename std::conditional<is_integral<T>::value && std::is_unsigned<T>::value, std::true_type, std::false_type>::type;
template<class T> using to_unsigned = typename std::conditional<is_signed_int<T>::value, std::make_unsigned<T>, std::common_type<T>>::type;
#endif

template<class T> using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template<class T> using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template<class T> using to_unsigned_t = typename to_unsigned<T>::type;

template<class T> struct safely_multipliable {};
template<> struct safely_multipliable<short> { using type = int; };
template<> struct safely_multipliable<unsigned short> { using type = unsigned int; };
template<> struct safely_multipliable<int> { using type = long long; };
template<> struct safely_multipliable<unsigned int> { using type = unsigned long long; };
template<> struct safely_multipliable<long long> { using type = __int128; };
template<> struct safely_multipliable<unsigned long long> { using type = __uint128_t; };

template<class T> using safely_multipliable_t = typename safely_multipliable<T>::type;

}  // namespace internal


}  // namespace felix

#line 2 "library/math/safe-mod.hpp"

namespace felix {

namespace internal {

template<class T>
constexpr T safe_mod(T x, T m) {
	x %= m;
	if(x < 0) {
		x += m;
	}
	return x;
}

} // namespace internal


} // namespace felix
#line 3 "library/math/inv-gcd.hpp"

namespace felix {

namespace internal {

template<class T>
constexpr std::pair<T, T> inv_gcd(T a, T b) {
	a = safe_mod(a, b);
	if(a == 0) {
		return {b, 0};
	}
	T s = b, t = a;
	T m0 = 0, m1 = 1;
	while(t) {
		T u = s / t;
		s -= t * u;
		m0 -= m1 * u;
		auto tmp = s;
		s = t;
		t = tmp;
		tmp = m0;
		m0 = m1;
		m1 = tmp;
	}
	if(m0 < 0) {
		m0 += b / s;
	}
	return {s, m0};
}

} // namespace internal


} // namespace felix

#line 9 "library/modint/modint.hpp"

namespace felix {

template<int id>
struct modint {
public:
	static constexpr int mod() { return (id > 0 ? id : md); }
 	
	static constexpr void set_mod(int m) {
		if(id > 0 || md == m) {
			return;
		}
		md = m;
		fact.resize(1);
		inv_fact.resize(1);
		invs.resize(1);
	}

	static constexpr void prepare(int n) {
		int sz = (int) fact.size();
		if(sz == mod()) {
			return;
		}
		n = 1 << std::__lg(2 * n - 1);
		if(n < sz) {
			return;
		}
		if(n < (sz - 1) * 2) {
			n = std::min((sz - 1) * 2, mod() - 1);
		}
		fact.resize(n + 1);
		inv_fact.resize(n + 1);
		invs.resize(n + 1);
		for(int i = sz; i <= n; i++) {
			fact[i] = fact[i - 1] * i;
		}
		auto eg = internal::inv_gcd(fact.back().val(), mod());
		assert(eg.first == 1);
		inv_fact[n] = eg.second;
		for(int i = n - 1; i >= sz; i--) {
			inv_fact[i] = inv_fact[i + 1] * (i + 1);
		}
		for(int i = n; i >= sz; i--) {
			invs[i] = inv_fact[i] * fact[i - 1];
		}
	}
 
	constexpr modint() : v(0) {} 
	template<class T, internal::is_signed_int_t<T>* = nullptr> constexpr modint(T x) : v(x >= 0 ? x % mod() : x % mod() + mod()) {}
	template<class T, internal::is_unsigned_int_t<T>* = nullptr> constexpr modint(T x) : v(x % mod()) {}
 
	constexpr int val() const { return v; }

	constexpr modint inv() const {
		if(id > 0 && v < std::min(mod() >> 1, 1 << 18)) {
			prepare(v);
			return invs[v];
		} else {
			auto eg = internal::inv_gcd(v, mod());
			assert(eg.first == 1);
			return eg.second;
		}
	}
 
	constexpr modint& operator+=(const modint& rhs) & {
		v += rhs.v;
		if(v >= mod()) {
			v -= mod();
		}
		return *this;
	}
 
	constexpr modint& operator-=(const modint& rhs) & {
		v -= rhs.v;
		if(v < 0) {
			v += mod();
		}
		return *this;
	}

	constexpr modint& operator*=(const modint& rhs) & {
		v = 1LL * v * rhs.v % mod();
		return *this;
	}

	constexpr modint& operator/=(const modint& rhs) & {
		return *this *= rhs.inv();
	}

	friend constexpr modint operator+(modint lhs, modint rhs) { return lhs += rhs; }
	friend constexpr modint operator-(modint lhs, modint rhs) { return lhs -= rhs; }
	friend constexpr modint operator*(modint lhs, modint rhs) { return lhs *= rhs; }
	friend constexpr modint operator/(modint lhs, modint rhs) { return lhs /= rhs; }

	constexpr modint operator+() const { return *this; }
	constexpr modint operator-() const { return modint() - *this; } 
	constexpr bool operator==(const modint& rhs) const { return v == rhs.v; } 
	constexpr bool operator!=(const modint& rhs) const { return v != rhs.v; }

	constexpr modint pow(long long p) const {
		modint a(*this), res(1);
		if(p < 0) {
			a = a.inv();
			p = -p;
		}
		while(p) {
			if(p & 1) {
				res *= a;
			}
			a *= a;
			p >>= 1;
		}
		return res;
	}

	constexpr bool has_sqrt() const {
		if(mod() == 2 || v == 0) {
			return true;
		}
		if(pow((mod() - 1) / 2).val() != 1) {
			return false;
		}
		return true;
	}

	constexpr modint sqrt() const {
		if(mod() == 2 || v < 2) {
			return *this;
		}
		assert(pow((mod() - 1) / 2).val() == 1);
		modint b = 1;
		while(b.pow((mod() - 1) >> 1).val() == 1) {
			b += 1;
		}
		int m = mod() - 1, e = __builtin_ctz(m);
		m >>= e;
		modint x = modint(*this).pow((m - 1) >> 1);
		modint y = modint(*this) * x * x;
		x *= v;
		modint z = b.pow(m);
		while(y.val() != 1) {
			int j = 0;
			modint t = y;
			while(t.val() != 1) {
				t *= t;
				j++;
			}
			z = z.pow(1LL << (e - j - 1));
			x *= z, z *= z, y *= z;
			e = j;
		}
		return x;
	}

	friend std::istream& operator>>(std::istream& in, modint& num) {
		long long x;
		in >> x;
		num = modint<id>(x);
		return in;
	}
	
	friend std::ostream& operator<<(std::ostream& out, const modint& num) {
		return out << num.val();
	}

public:
	static std::vector<modint> fact, inv_fact, invs;
 
private:
	int v;
	static int md;
};

template<int id> int modint<id>::md = 998244353;
template<int id> std::vector<modint<id>> modint<id>::fact = {1};
template<int id> std::vector<modint<id>> modint<id>::inv_fact = {1};
template<int id> std::vector<modint<id>> modint<id>::invs = {0};

using modint998244353 = modint<998244353>;
using modint1000000007 = modint<1000000007>;

namespace internal {

template<class T> struct is_modint : public std::false_type {};
template<int id> struct is_modint<modint<id>> : public std::true_type {};

template<class T, class ENABLE = void> struct is_static_modint : public std::false_type {};
template<int id> struct is_static_modint<modint<id>, std::enable_if_t<(id > 0)>> : public std::true_type {};
template<class T> using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;

template<class T, class ENABLE = void> struct is_dynamic_modint : public std::false_type {};
template<int id> struct is_dynamic_modint<modint<id>, std::enable_if_t<(id <= 0)>> : public std::true_type {};
template<class T> using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;

} // namespace internal


} // namespace felix

#line 7 "test/data-structure/lazy-segtree/yosupo-Range-Affine-Range-Sum.test.cpp"
using namespace std;
using namespace felix;

using mint = modint998244353;

struct S {
	mint sum;
	int size = 0;

	S() {}
	S(mint a, int b = 1) : sum(a), size(b) {}
};

S e() { return S(); }

S op(S a, S b) {
	a.sum += b.sum;
	a.size += b.size;
	return a;
}

struct F {
	mint a, b;
	bool bad = true;

	F() {}
	F(mint x, mint y) : a(x), b(y), bad(false) {}
};

F id() { return F(); }

S mapping(F f, S s) {
	if(f.bad || s.size == 0) {
		return s;
	}
	s.sum = f.a * s.sum + f.b * s.size;
	return s;
}

F composition(F f, F g) {
	if(f.bad || g.bad) {
		return f.bad ? g : f;
	}
	return F(f.a * g.a, f.a * g.b + f.b);
}

int main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	int n, q;
	cin >> n >> q;
	vector<S> a(n);
	for(int i = 0; i < n; i++) {
		cin >> a[i].sum;
		a[i].size = 1;
	}
	lazy_segtree<S, e, op, F, id, mapping, composition> seg(a);
	while(q--) {
		int type, l, r;
		cin >> type >> l >> r;
		if(type == 0) {
			mint a, b;
			cin >> a >> b;
			seg.apply(l, r, F(a, b));
		} else {
			cout << seg.prod(l, r).sum << "\n";
		}
	}
	return 0;
}

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