結果

問題 No.235 めぐるはめぐる (5)
ユーザー noshi_botnoshi_bot
提出日時 2018-06-16 18:50:09
言語 C++14
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 737 ms / 10,000 ms
コード長 9,057 bytes
コンパイル時間 864 ms
コンパイル使用メモリ 77,760 KB
実行使用メモリ 20,112 KB
最終ジャッジ日時 2024-06-30 16:23:40
合計ジャッジ時間 4,181 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge2
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 737 ms
20,108 KB
testcase_01 AC 380 ms
20,088 KB
testcase_02 AC 601 ms
20,112 KB
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ソースコード

diff # 

#define NDEBUG
#include <cassert>
#include <cstddef>
#include <memory>
#include <utility>
#include <vector>

template <class ValueMonoid, class OperatorMonoid, class Modifier>
class link_cut_tree {
public:
	using value_structure = ValueMonoid;
	using value_type = typename value_structure::value_type;
	using operator_structure = OperatorMonoid;
	using operator_type = typename operator_structure::value_type;
	using modifier_type = Modifier;
	using size_type = ::std::size_t;

private:
	class node_type {
	public:
		node_type *left, *right, *parent;
		typename link_cut_tree::value_type value, sum;
		typename link_cut_tree::operator_type lazy;
		bool reversed; // reverse->lazy
		node_type(value_type &&v, operator_type &&o)
			: value(::std::move(v)), sum(value), lazy(::std::move(o)), reversed(0) {
		}
	};

	using pointer = node_type *;
	using const_pointer = const node_type *;

	::std::vector<node_type> nodes;
	size_type size_;
	value_structure vf;
	operator_structure of;
	modifier_type mf;

	pointer nil() noexcept { return nodes.data(); }
	void reverse(const pointer ptr) {
		ptr->lazy = of.reverse(ptr->lazy);
		ptr->reversed ^= 1;
	}
	void push(const pointer ptr) {
		if (ptr->reversed) {
			ptr->reversed = 0;
			ptr->value = vf.reverse(ptr->value);
			::std::swap(ptr->left, ptr->right);
			reverse(ptr->left);
			reverse(ptr->right);
		}
		ptr->left->lazy = of(ptr->left->lazy, ptr->lazy);
		ptr->right->lazy = of(ptr->right->lazy, ptr->lazy);
		ptr->value = mf(ptr->value, ptr->lazy);
		ptr->lazy = of.identity();
	}
	void propagate(pointer ptr) {
		pointer prev = nullptr;
		while (ptr != nil()) {
			::std::swap(ptr->parent, prev);
			::std::swap(ptr, prev);
		}
		while (prev) {
			push(prev);
			::std::swap(prev->parent, ptr);
			::std::swap(prev, ptr);
		}
		nil()->sum = vf.identity();
		nil()->lazy = of.identity();
		nil()->reversed = 0;
	}
	value_type reflect(const const_pointer ptr) {
		return mf(ptr->reversed ? vf.reverse(ptr->sum) : ptr->sum, ptr->lazy);
	}
	void calc(const pointer ptr) {
		ptr->sum = vf(vf(reflect(ptr->left), ptr->value), reflect(ptr->right));
	}
	static void set_l(const pointer ptr, const pointer ch) {
		ptr->left = ch;
		ch->parent = ptr;
	}
	static void set_r(const pointer ptr, const pointer ch) {
		ptr->right = ch;
		ch->parent = ptr;
	}
	void rotate_l(const pointer ptr, const pointer ch) {
		set_r(ptr, ch->left);
		calc(ptr);
		set_l(ch, ptr);
	}
	void rotate_r(const pointer ptr, const pointer ch) {
		set_l(ptr, ch->right);
		calc(ptr);
		set_r(ch, ptr);
	}
	void splay(const pointer ptr) {
		for (pointer x, y = ptr;;) {
			x = ptr->parent;
			if (x->left == y) {
				y = x->parent;
				ptr->parent = y->parent;
				if (y->left == x)
					rotate_r(y, x), rotate_r(x, ptr);
				else if (y->right == x)
					rotate_l(y, ptr), rotate_r(x, ptr);
				else
					return ptr->parent = y, rotate_r(x, ptr);
			}
			else if (x->right == y) {
				y = x->parent;
				ptr->parent = y->parent;
				if (y->right == x)
					rotate_l(y, x), rotate_l(x, ptr);
				else if (y->left == x)
					rotate_r(y, ptr), rotate_l(x, ptr);
				else
					return ptr->parent = y, rotate_l(x, ptr);
			}
			else {
				return;
			}
		}
	}
	void expose(const pointer ptr) {
		propagate(ptr);
		pointer x = ptr, prev = nil();
		while (x != nil()) {
			splay(x);
			x->right = prev;
			calc(x);
			prev = x;
			x = x->parent;
		}
		splay(ptr);
		calc(ptr);
	}
	void reroot(const pointer ptr) {
		expose(ptr);
		reverse(ptr);
	}
	pointer get_ptr(const size_type i) noexcept { return nodes.data() + 1 + i; }

public:
	link_cut_tree() : link_cut_tree(0) {}
	explicit link_cut_tree(const size_type size,
		const value_structure &x = value_structure(),
		const operator_structure &y = operator_structure(),
		const modifier_type &z = modifier_type())
		: size_(size), vf(x), of(y), mf(z) {
		nodes.reserve(size_ + 1);
		nodes.emplace_back(vf.identity(), of.identity());
		const pointer n = nil();
		n->left = n->right = n->parent = n;
		nodes.resize(size_ + 1, nodes.front());
	}

	bool empty() const noexcept { return !size_; }
	size_type size() const noexcept { return size_; }

	bool connected(const size_type v, const size_type u) {
		assert(v < size());
		assert(u < size());
		expose(get_ptr(v));
		expose(get_ptr(u));
		return nodes[v + 1].parent != nil() || v == u;
	}
	value_type fold(const size_type v, const size_type u) {
		assert(v < size());
		assert(u < size());
		assert(connected(v, u));
		reroot(get_ptr(v));
		expose(get_ptr(u));
		return nodes[u + 1].sum;
	}

	void link(const size_type parent, const size_type child) {
		assert(parent < size());
		assert(child < size());
		assert(!connected(parent, child));
		reroot(get_ptr(child));
		nodes[child + 1].parent = get_ptr(parent);
	}
	void cut(const size_type v) {
		assert(v < size());
		expose(get_ptr(v));
		nodes[v + 1].left->parent = nil();
		nodes[v + 1].left = nil();
		nodes[v + 1].sum = nodes[v + 1].value;
	}
	void update(const size_type v, const size_type u, const operator_type &data) {
		assert(v < size());
		assert(u < size());
		assert(connected(v, u));
		reroot(get_ptr(v));
		expose(get_ptr(u));
		nodes[u + 1].lazy = data;
	}
	template <class F> void update(const size_type v, const F &f) {
		assert(v < size());
		expose(get_ptr(v));
		nodes[v + 1].value = f(nodes[v + 1].value);
		calc(get_ptr(v));
	}
};

template <class V, class O, class M>
link_cut_tree<V, O, M> make_lctree(const ::std::size_t size, const V &v,
	const O &o, const M &m) {
	return link_cut_tree<V, O, M>(size, v, o, m);
}

#include <cstdint>

template <::std::uint_fast32_t MODULO> class modint {
	using uint32 = ::std::uint_fast32_t;
	using uint64 = ::std::uint_fast64_t;

public:
	using value_type = uint32;
	uint32 a;
	modint() : a(0) {}
	modint(const uint32 x) : a(x) {}
	modint operator+(const modint &o) const {
		return a + o.a < MODULO ? modint(a + o.a) : modint(a + o.a - MODULO);
	}
	modint operator-(const modint &o) const {
		return modint(a < o.a ? a + MODULO - o.a : a - o.a);
	}
	modint operator*(const modint &o) const {
		return modint(static_cast<uint64>(a) * o.a % MODULO);
	}
	modint operator/(const modint &o) const {
		return modint(static_cast<uint64>(a) * ~o % MODULO);
	}
	modint &operator+=(const modint &o) { return *this = *this + o; }
	modint &operator-=(const modint &o) { return *this = *this - o; }
	modint &operator*=(const modint &o) { return *this = *this * o; }
	modint &operator/=(const modint &o) { return *this = *this / o; }
	modint operator~() const { return pow(MODULO - 2); }
	modint operator-() const { return a ? modint(MODULO - a) : modint(); }
	modint operator++() { return a == MODULO - 1 ? a = 0 : ++a, *this; }
	modint operator--() { return a ? --a : a = MODULO - 1, *this; }
	bool operator==(const modint &o) const { return a == o.a; }
	bool operator!=(const modint &o) const { return a != o.a; }
	bool operator<(const modint &o) const { return a < o.a; }
	bool operator<=(const modint &o) const { return a <= o.a; }
	bool operator>(const modint &o) const { return a > o.a; }
	bool operator>=(const modint &o) const { return a >= o.a; }
	explicit operator bool() const { return a; }
	explicit operator uint32() const { return a; }
	modint pow(uint32 x) const {
		uint64 t = a, u = 1;
		while (x) {
			if (x & 1)
				u = u * t % MODULO;
			t = (t * t) % MODULO;
			x >>= 1;
		}
		return modint(u);
	}
};

#include <algorithm>
#include <cstddef>
#include <limits>
#include <utility>

template <class T, class S = ::std::size_t> class sum_monoid {
public:
	using size_type = S;
	using value_type = ::std::pair<T, size_type>;
	value_type operator()(const value_type &x, const value_type &y) const {
		return value_type(x.first + y.first, x.second + y.second);
	}
	value_type identity() const { return value_type(T(0), S(0)); }
	value_type reverse(const value_type &x) const { return x; }
};

template <class T> class plus_monoid {
public:
	using value_type = T;
	value_type operator()(const value_type &x, const value_type &y) const {
		return x + y;
	}
	value_type identity() const { return value_type(0); }
	value_type reverse(const value_type &x) const { return x; }
};

template <class P, class T> class sum_plus {
public:
	P operator()(const P &x, const T &y) const {
		return P(x.first + y * x.second, x.second);
	}
};

#include <cstdio>
#include <vector>

int main() {
	using uint = unsigned int;
	using mint = modint<1000000007>;
	using pm = std::pair<mint, mint>;
	uint n;
	scanf("%u", &n);
	auto T = make_lctree(n,
		sum_monoid<mint, mint>(),
		plus_monoid<mint>(),
		sum_plus<pm, mint>());
	std::vector<mint> s(n), c(n);
	for (auto &e : s)
		scanf("%u", &e.a);
	for (auto &e : c)
		scanf("%u", &e.a);
	for (uint i = 0;i < n;++i)
		T.update(i, [&](const pm &x) {return pm(s[i], c[i]);});
	while (--n) {
		uint a, b;
		scanf("%u%u", &a, &b);
		--a;--b;
		T.link(a, b);
	}
	uint q;
	scanf("%u", &q);
	while (q--) {
		uint t, x, y;
		mint z;
		scanf("%u%u%u", &t, &x, &y);
		--x;--y;
		if (t) {
			printf("%u\n", T.fold(x, y).first.a);
		}
		else {
			scanf("%u", &z.a);
			T.update(x, y, mint(z));
		}
	}
	return 0;
}
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