test/data-structure/lazy-lct/yosupo-Dynamic-Tree-Vertex-Set-Path-Composite.test.cpp

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

Depends on

• Link Cut Tree (library/data-structure/lazy-lct.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/dynamic_tree_vertex_set_path_composite"

#include <iostream>
#include <vector>
#include "../../../library/modint/modint.hpp"
#include "../../../library/data-structure/lazy-lct.hpp"
using namespace std;
using namespace felix;

using mint = modint998244353;

struct S {
	pair<mint, mint> f, g;

	S() : S(1, 0) {}
	S(mint a, mint b) : f(a, b), g(a, b) {}
	S(pair<mint, mint> a, pair<mint, mint> b) : f(a), g(b) {}
};

pair<mint, mint> combine(pair<mint, mint> f, pair<mint, mint> g) { return make_pair(f.first * g.first, f.first * g.second + f.second); }

S e() { return S(); }
S op(S a, S b) { return S(combine(a.f, b.f), combine(b.g, a.g)); }
S reversal(S s) { return S(s.g, s.f); }

using F = bool;

F id() { return false; }
S mapping(F f, S s) { return s; }
F composition(F a, F b) { return false; }

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++) {
		mint x, y;
		cin >> x >> y;
		a[i] = S(x, y);
	}
	lazy_lct<S, e, op, reversal, F, id, mapping, composition> lct(a);
	for(int i = 0; i < n - 1; i++) {
		int u, v;
		cin >> u >> v;
		lct.link(u, v);
	}
	while(q--) {
		int type, x, y;
		cin >> type >> x >> y;
		if(type == 0) {
			int u, v;
			cin >> u >> v;
			lct.cut(x, y);
			lct.link(u, v);
		} else if(type == 1) {
			int z;
			cin >> z;
			lct.set(x, S(y, z));
		} else {
			int z;
			cin >> z;
			auto res = lct.prod(x, y).g;
			cout << res.first * z + res.second << "\n";
		}
	}
	return 0;
}

#line 1 "test/data-structure/lazy-lct/yosupo-Dynamic-Tree-Vertex-Set-Path-Composite.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/dynamic_tree_vertex_set_path_composite"

#include <iostream>
#include <vector>
#line 4 "library/modint/modint.hpp"
#include <algorithm>

#include <cassert>

#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 5 "library/data-structure/lazy-lct.hpp"

namespace felix {

template<class S,
         S (*e)(),
         S (*op)(S, S),
         S (*reversal)(S),
         class F,
         F (*id)(),
         S (*mapping)(F, S),
         F (*composition)(F, F)>
struct lazy_lct {
public:
	struct node_t {
		S val = e(), sum = e();
		F lz = id();
		bool rev = false;
		int sz = 1;
		node_t* l = nullptr;
		node_t* r = nullptr;
		node_t* p = nullptr;

		node_t() {}
		node_t(const S& s) : val(s), sum(s) {}

		bool is_root() const { return p == nullptr || (p->l != this && p->r != this); }
	};

	lazy_lct() : n(0) {}
	explicit lazy_lct(int _n) : lazy_lct(std::vector<S>(_n, e())) {}
	explicit lazy_lct(const std::vector<S>& v) : n(v.size()) {
		a.reserve(n);
		for(int i = 0; i < n; i++) {
			a.emplace_back(v[i]);
		}
	}

	node_t* access(int u) {
		assert(0 <= u && u < n);
		node_t* v = &a[u];
		node_t* last = nullptr;
		for(node_t* p = v; p != nullptr; p = p->p) {
			splay(p);
			p->r = last;
			pull(p);
			last = p;
		}
		splay(v);
		return last;
	}

	void make_root(int u) {
		access(u);
		a[u].rev ^= 1;
		push(&a[u]);
	}

	void link(int u, int v) {
		make_root(v);
		a[v].p = &a[u];
	}

	void cut(int u) {
		access(u);
		if(a[u].l != nullptr) {
			a[u].l->p = nullptr;
			a[u].l = nullptr;
			pull(&a[u]);
		}
	}

	void cut(int u, int v) {
		make_root(u);
		cut(v);
	}

	bool is_connected(int u, int v) {
		if(u == v) {
			return true;
		}
		access(u), access(v);
		return a[u].p != nullptr;
	}

	int get_lca(int u, int v) {
		if(u == v) {
			return u;
		}
		access(u);
		return access(v) - &a[0];
	}

	int get_root(int u) {
		node_t* v = access(u);
		push(v);
		while(v->l != nullptr) {
			v = v->l;
			push(v);
		}
		access(v);
		return v - &a[0];
	}

	void set(int u, const S& s) {
		access(u);
		a[u].val = s;
		pull(&a[u]);
	}

	S get(int u) {
		access(u);
		return a[u].val;
	}

	void apply(int u, int v, const F& f) {
		make_root(u);
		access(v);
		all_apply(&a[v], f);
		push(&a[v]);
	}

	S prod(int u, int v) {
		make_root(u);
		access(v);
		return a[v].sum;
	}

private:
	int n;
	std::vector<node_t> a;

	void rotate(node_t* v) {
		auto attach = [&](node_t* p, bool side, node_t* c) {
			(side ? p->r : p->l) = c;
			pull(p);
			if(c != nullptr) {
				c->p = p;
			}
		};
		node_t* p = v->p;
		node_t* g = p->p;
		bool is_right = (p->r == v);
		bool is_root = p->is_root();
		attach(p, is_right, (is_right ? v->l : v->r));
		attach(v, !is_right, p);
		if(!is_root) {
			attach(g, (g->r == p), v);
		} else {
			v->p = g;
		}
	}

	void splay(node_t* v) {
		push(v);
		while(!v->is_root()) {
			auto p = v->p;
			auto g = p->p;
			if(!p->is_root()) {
				push(g);
			}
			push(p), push(v);
			if(!p->is_root()) {
				rotate((g->r == p) == (p->r == v) ? p : v);
			}
			rotate(v);
		}
	}

	void all_apply(node_t* v, F f) {
		v->val = mapping(f, v->val);
		v->sum = mapping(f, v->sum);
		v->lz = composition(f, v->lz);
	}

	void push(node_t* v) {
		if(v->lz != id()) {
			if(v->l != nullptr) {
				all_apply(v->l, v->lz);
			}
			if(v->r != nullptr) {
				all_apply(v->r, v->lz);
			}
			v->lz = id();
		}
		if(v->rev) {
			std::swap(v->l, v->r);
			if(v->l != nullptr) {
				v->l->rev ^= 1;
			}
			if(v->r != nullptr) {
				v->r->rev ^= 1;
			}
			v->sum = reversal(v->sum);
			v->rev = false;
		}
	}

	void pull(node_t* v) {
		v->sz = 1;
		v->sum = v->val;
		if(v->l != nullptr) {
			push(v->l);
			v->sum = op(v->l->sum, v->sum);
			v->sz += v->l->sz;
		}
		if(v->r != nullptr) {
			push(v->r);
			v->sum = op(v->sum, v->r->sum);
			v->sz += v->r->sz;
		}
	}
};

} // namespace felix

#line 7 "test/data-structure/lazy-lct/yosupo-Dynamic-Tree-Vertex-Set-Path-Composite.test.cpp"
using namespace std;
using namespace felix;

using mint = modint998244353;

struct S {
	pair<mint, mint> f, g;

	S() : S(1, 0) {}
	S(mint a, mint b) : f(a, b), g(a, b) {}
	S(pair<mint, mint> a, pair<mint, mint> b) : f(a), g(b) {}
};

pair<mint, mint> combine(pair<mint, mint> f, pair<mint, mint> g) { return make_pair(f.first * g.first, f.first * g.second + f.second); }

S e() { return S(); }
S op(S a, S b) { return S(combine(a.f, b.f), combine(b.g, a.g)); }
S reversal(S s) { return S(s.g, s.f); }

using F = bool;

F id() { return false; }
S mapping(F f, S s) { return s; }
F composition(F a, F b) { return false; }

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++) {
		mint x, y;
		cin >> x >> y;
		a[i] = S(x, y);
	}
	lazy_lct<S, e, op, reversal, F, id, mapping, composition> lct(a);
	for(int i = 0; i < n - 1; i++) {
		int u, v;
		cin >> u >> v;
		lct.link(u, v);
	}
	while(q--) {
		int type, x, y;
		cin >> type >> x >> y;
		if(type == 0) {
			int u, v;
			cin >> u >> v;
			lct.cut(x, y);
			lct.link(u, v);
		} else if(type == 1) {
			int z;
			cin >> z;
			lct.set(x, S(y, z));
		} else {
			int z;
			cin >> z;
			auto res = lct.prod(x, y).g;
			cout << res.first * z + res.second << "\n";
		}
	}
	return 0;
}

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