#616139 (C++17) No.1094 木登り / Climbing tree

提出ソース
結果

問題	No.1094 木登り / Climbing tree
ユーザー	tkmst201
提出日時	2021-02-11 18:48:59
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	969 ms / 2,000 ms
コード長	14,779 bytes
コンパイル時間	3,421 ms
コンパイル使用メモリ	228,728 KB
実行使用メモリ	36,644 KB
最終ジャッジ日時	2024-11-08 07:16:37
合計ジャッジ時間	19,934 ms
ジャッジサーバーID （参考情報）	judge1 / judge4
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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	2 ms 5,248 KB
testcase_01	AC	749 ms 36,500 KB
testcase_02	AC	138 ms 34,564 KB
testcase_03	AC	77 ms 5,376 KB
testcase_04	AC	163 ms 18,080 KB
testcase_05	AC	366 ms 32,568 KB
testcase_06	AC	237 ms 13,716 KB
testcase_07	AC	749 ms 36,508 KB
testcase_08	AC	669 ms 36,496 KB
testcase_09	AC	683 ms 36,628 KB
testcase_10	AC	687 ms 36,504 KB
testcase_11	AC	704 ms 36,628 KB
testcase_12	AC	969 ms 36,628 KB
testcase_13	AC	649 ms 36,504 KB
testcase_14	AC	677 ms 36,404 KB
testcase_15	AC	128 ms 10,312 KB
testcase_16	AC	223 ms 27,700 KB
testcase_17	AC	167 ms 17,708 KB
testcase_18	AC	147 ms 14,360 KB
testcase_19	AC	197 ms 22,784 KB
testcase_20	AC	719 ms 36,644 KB
testcase_21	AC	175 ms 18,660 KB
testcase_22	AC	679 ms 36,500 KB
testcase_23	AC	664 ms 36,640 KB
testcase_24	AC	611 ms 36,640 KB
testcase_25	AC	616 ms 36,628 KB
testcase_26	AC	607 ms 36,504 KB
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ソースコード

raw source code
#include <bits/stdc++.h>
using namespace std;
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) begin(v),end(v)
template<typename A, typename B> inline bool chmax(A & a, const B & b) { if (a < b) { a = b; return true; } return false; }
template<typename A, typename B> inline bool chmin(A & a, const B & b) { if (a > b) { a = b; return true; } return false; }
using ll = long long;
using pii = pair<int, int>;
constexpr ll INF = 1ll<<30;
constexpr ll longINF = 1ll<<60;
constexpr ll MOD = 1000000007;
constexpr bool debug = false;
//---------------------------------//

struct HeavyLightDecomposition {
	using size_type = std::uint_fast32_t;
	using Graph = std::vector<std::vector<size_type>>;
	
private:
	size_type bf_n; // グラフの頂点数
	
	std::vector<size_type> par_; // [v] := 頂点 v の親の頂点番号(存在しなければ自分自身)
	std::vector<size_type> sub_size_; // [v] := 頂点 v を根とする部分木のサイズ
	std::vector<size_type> depth_; // [v] := 頂点 v の元のグラフでの深さ
	
	std::vector<size_type> tree_id_; // [v] := 頂点 v が属する木の id
	std::vector<size_type> roots_; // [i] := i 番目の木の root
	
	std::vector<size_type> heavy_map_; // [v] := 頂点 v が属する heavy-path id
	std::vector<size_type> head_; // [i] := heavy-path i の最も根に近い頂点番号
	std::vector<size_type> heavy_size_ ; // [i] := heavy-path i に属する頂点の個数
	std::vector<size_type> heavy_depth_; // [i] := heavy-path i から根までに通る light-edge の個数
	
	// euler-tour
	std::vector<size_type> in_; // [v] := 頂点 v の EulerTour 順序(同一 heavy-path 内では連続)
	std::vector<size_type> out_; // [v] := 頂点 v から出るときの EulerTour 順序
	std::vector<size_type> euler_map_; // [i] := EulerTour 順序が i であるような頂点
	
	// heavy-path doubling
	std::vector<std::vector<size_type>> par_dblng_; // [k][i] := heavy-path i から 2^k 回 light-edge を上った先の頂点
	
public:
	HeavyLightDecomposition(const Graph & g, bool use_lca = false) : HeavyLightDecomposition(g, g.size(), use_lca) {}
	HeavyLightDecomposition(const Graph & g, size_type root, bool use_lca) : bf_n(g.size()) {
		par_.resize(bf_size());
		sub_size_.resize(bf_size());
		depth_.resize(bf_size());
		tree_id_.assign(bf_size(), bf_size());
		std::vector<size_type> next(bf_size()); // [v] := 頂点 v と同一 heavy-path 内で v より 1 つ葉側の頂点(存在しなければ自分自身)
		
		for (size_type i = 0; i < bf_size(); ++i) {
			if (tree_id_[i] != bf_size()) continue;
			if (root != bf_size() && i != root) continue;
			
			std::stack<std::pair<size_type, size_type>> stk;
			par_[i] = i;
			depth_[i] = 0;
			tree_id_[i] = roots_.size();
			stk.emplace(i, 0);
			
			while (!stk.empty()) {
				const size_type u = stk.top().first, i = stk.top().second; stk.pop();
				if (i < g[u].size()) {
					stk.emplace(u, i + 1);
					const size_type v = g[u][i];
					if (v == par_[u]) continue;
					par_[v] = u;
					depth_[v] = depth_[u] + 1;
					tree_id_[v] = roots_.size();
					stk.emplace(v, 0);
				}
				else {
					size_type mx = 0;
					next[u] = u;
					sub_size_[u] = 1;
					for (size_type v : g[u]) {
						if (v == par_[u]) continue;
						sub_size_[u] += sub_size_[v];
						if (mx < sub_size_[v]) {
							mx = sub_size_[v];
							next[u] = v;
						}
					}
				}
			}
			roots_.emplace_back(i);
		}
		
		heavy_map_.resize(bf_size());
		in_.resize(bf_size());
		out_.resize(bf_size());
		euler_map_.reserve(bf_size());
		
		for (size_type root : roots_) {
			std::stack<std::pair<size_type, size_type>> stk;
			
			heavy_map_[root] = head_.size();
			head_.emplace_back(root);
			heavy_size_.emplace_back(1);
			heavy_depth_.emplace_back(0);
			stk.emplace(root, 0);
			
			while (!stk.empty()) {
				const size_type u = stk.top().first, i = stk.top().second; stk.pop();
				if (i < g[u].size()) {
					stk.emplace(u, i + 1);
					const size_type v = g[u][i];
					if (v != par_[u] && v != next[u]) {
						heavy_map_[v] = head_.size();
						head_.emplace_back(v);
						heavy_size_.emplace_back(1);
						heavy_depth_.emplace_back(heavy_depth_[heavy_map_[u]] + 1);
						stk.emplace(v, 0);
					}
				}
				if (i == 0) {
					in_[u] = euler_map_.size();
					euler_map_.emplace_back(u);
					const size_type v = next[u];
					if (v != u) {
						heavy_map_[v] = heavy_map_[u];
						++heavy_size_[heavy_map_[u]];
						stk.emplace(v, 0);
					}
				}
				if (i == g[u].size()) out_[u] = euler_map_.size();
			}
		}
		
		if (!use_lca) return;
		size_type max_depth = *std::max_element(begin(heavy_depth_), end(heavy_depth_));
		size_type lglg_n = 0;
		while ((1 << lglg_n) < max_depth) ++lglg_n;
		
		par_dblng_.assign(lglg_n + 1, std::vector<size_type>(af_size()));
		for (size_type i = 0; i < af_size(); ++i) par_dblng_[0][i] = par_[head_[i]];
		for (size_type i = 0; i < lglg_n; ++i) {
			for (size_type j = 0; j < af_size(); ++j) {
				par_dblng_[i + 1][j] = par_dblng_[i][heavy_map_[par_dblng_[i][j]]];
			}
		}
	}
	
	size_type bf_size() const noexcept { return bf_n; }
	size_type af_size() const noexcept { return head_.size(); }
	
	size_type par(size_type v) const { assert(v < bf_size()); return par_[v]; }
	size_type sub_size(size_type v) const { assert(v < bf_size()); return sub_size_[v]; }
	size_type depth(size_type v) const { assert(v < bf_size()); return depth_[v]; }
	
	size_type tree_id(size_type v) const { assert(v < bf_size()); return tree_id_[v]; }
	size_type tree_cnt() const noexcept { return roots_.size(); }
	const std::vector<size_type> & trees() const noexcept { return roots_; }
	
	size_type heavy_map(size_type v) const { assert(v < bf_size()); return heavy_map_[v]; }
	size_type head(size_type k) const { assert(k < af_size()); return head_[k]; }
	size_type heavy_size(size_type k) const { assert(k < af_size()); return heavy_size_[k]; }
	size_type heavy_depth(size_type k) const { assert(k < af_size()); return heavy_depth_[k]; }
	
	size_type in(size_type v) const { assert(v < bf_size()); return in_[v]; }
	size_type out(size_type v) const { assert(v < bf_size()); return out_[v]; }
	size_type euler_map(size_type k) const { assert(k < bf_size()); return euler_map_[k]; }
	
	const std::vector<std::vector<size_type>> & par_dblng() const {
		assert(!par_dblng_.empty());
		return par_dblng_;
	}
	
	std::pair<size_type, size_type> get_lca_path(size_type x, size_type y) const {
		assert(!par_dblng_.empty());
		assert(x < bf_size());
		assert(y < bf_size());
		assert(tree_id_[x] == tree_id_[y]);
		if (heavy_map_[x] == heavy_map_[y]) return {x, y};
		
		bool isswap = heavy_depth_[heavy_map_[x]] < heavy_depth_[heavy_map_[y]];
		if (isswap) std::swap(x, y);
		
		const size_type diff = heavy_depth_[heavy_map_[x]] - heavy_depth_[heavy_map_[y]];
		for (size_type i = par_dblng_.size(); i > 0; --i) {
			if (diff >> (i - 1) & 1) x = par_dblng_[i - 1][heavy_map_[x]];
		}
		if (heavy_map_[x] == heavy_map_[y]) return isswap ? std::make_pair(y, x) : std::make_pair(x, y);
		
		for (size_type i = par_dblng_.size(); i > 0; --i) {
			const size_type p1 = par_dblng_[i - 1][heavy_map_[x]], p2 = par_dblng_[i - 1][heavy_map_[y]];
			if (heavy_map_[p1] != heavy_map_[p2]) x = p1, y = p2;
		}
		x = par_dblng_[0][heavy_map_[x]];
		y = par_dblng_[0][heavy_map_[y]];
		return isswap ? std::make_pair(y, x) : std::make_pair(x, y);
	}
	
	size_type get_lca(size_type x, size_type y) {
		assert(!par_dblng_.empty());
		assert(x < bf_size());
		assert(y < bf_size());
		std::pair<size_type, size_type> res = get_lca_path(x, y);
		return in_[res.first] < in_[res.second] ? res.first : res.second;
	}
};

template<class HLD, typename T, template<typename> class SEG>
struct HeavyLightDecomposition_Query {
	using value_type = T;
	using const_reference = const value_type &;
	using seg_type = SEG<value_type>;
	using hld_type = HLD;
	using size_type = std::uint_fast32_t;
	using Graph = typename hld_type::Graph;
	using F = std::function<value_type(const_reference, const_reference)>;
	
private:
	value_type id_elem;
	F f;
	hld_type hld;
	seg_type seg, rseg;
	bool value_on_vertex;
	
public:
	HeavyLightDecomposition_Query(const Graph & g, const value_type & id_elem, const F & f, bool value_on_vertex)
		: HeavyLightDecomposition_Query(g, g.size(), id_elem, f, value_on_vertex) {}
	
	HeavyLightDecomposition_Query(const Graph & g, size_type root, const value_type & id_elem, const F & f, bool value_on_vertex)
		: id_elem(id_elem), f(f), hld(g, root, false), value_on_vertex(value_on_vertex) {
		seg = seg_type{ hld.bf_size(), id_elem, f };
		rseg = seg_type{ hld.bf_size(), id_elem, f };
	}
	
	template<typename U>
	HeavyLightDecomposition_Query(const Graph & g, const std::vector<U> & v, const value_type & id_elem, const F & f)
		: HeavyLightDecomposition_Query(g, g.size(), v, id_elem, f) {}
	
	template<typename U>
	HeavyLightDecomposition_Query(const Graph & g, size_type root, const std::vector<U> & v, const value_type & id_elem, const F & f)
		: id_elem(id_elem), f(f), hld(g, root, false), value_on_vertex(true) {
		std::vector<value_type> init(hld.bf_size());
		for (size_type i = 0; i < hld.bf_size(); ++i) init[i] = v[hld.euler_map(i)];
		seg = seg_type{ init, id_elem, f };
		
		for (size_type i = 0; i < hld.af_size(); ++i) {
			const size_type fidx = hld.in(hld.head(i));
			std::reverse(begin(init) + fidx, begin(init) + fidx + hld.heavy_size(i));
		}
		rseg = seg_type{ init, id_elem, f };
	}
	
	const hld_type & get_hld() const {
		return hld;
	}
	
	void set(size_type v, const_reference x) {
		assert(value_on_vertex);
		assert(v < hld.bf_size());
		set_(v, x);
	}
	
	value_type get(size_type v) const {
		assert(value_on_vertex);
		assert(v < hld.bf_size());
		return get_(v);
	}
	
	void set(size_type u, size_type v, const_reference x) {
		assert(!value_on_vertex);
		assert(u < hld.bf_size());
		assert(v < hld.bf_size());
		assert(hld.par(u) == v || hld.par(v) == u);
		set_(hld.par(u) == v ? u : v, x);
	}
	
	value_type get(size_type u, size_type v) const {
		assert(!value_on_vertex);
		assert(u < hld.bf_size());
		assert(v < hld.bf_size());
		assert(hld.par(u) == v || hld.par(v) == u);
		return get_(hld.par(u) == v ? u : v);
	}
	
private:
	void set_(size_type v, const_reference x) {
		seg.set(hld.in(v), x);
		rseg.set(reverse_idx(v), x);
	}
	
	value_type get_(size_type v) const {
		return seg.get(hld.in(v));
	}
	
public:
	value_type fold(size_type u, size_type v) const {
		assert(u < hld.bf_size());
		assert(v < hld.bf_size());
		assert(hld.tree_id(u) == hld.tree_id(v));
		value_type lv = id_elem, rv = id_elem;
		
		while (hld.heavy_map(u) != hld.heavy_map(v)) {
			if (hld.heavy_depth(hld.heavy_map(u)) >= hld.heavy_depth(hld.heavy_map(v))) {
				const size_type head = hld.head(hld.heavy_map(u));
				lv = f(lv, rseg.fold(reverse_idx(u), reverse_idx(head) + 1));
				u = hld.par(head);
			}
			if (hld.heavy_map(u) == hld.heavy_map(v)) break;
			if (hld.heavy_depth(hld.heavy_map(u)) <= hld.heavy_depth(hld.heavy_map(v))) {
				const size_type head = hld.head(hld.heavy_map(v));
				rv = f(seg.fold(hld.in(head), hld.in(v) + 1), rv);
				v = hld.par(head);
			}
		}
		
		const size_type id = hld.heavy_map(u);
		if (hld.in(u) < hld.in(v)) rv = f(seg.fold(hld.in(u) + !value_on_vertex, hld.in(v) + 1), rv);
		else lv = f(lv, rseg.fold(reverse_idx(u), reverse_idx(v) + value_on_vertex));
		return f(lv, rv);
	}
	
	value_type subtree_sum(size_type v) const {
		return seg.fold(hld.in(v), hld.out(v));
	}
	
private:
	size_type reverse_idx(size_type v) const {
		const size_type id = hld.heavy_map(v);
		return (hld.in(hld.head(id)) << 1) + hld.heavy_size(id) - hld.in(v) - 1;
	}
};

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.resize(2 * n_, id_elem);
	}
	
	SegmentTree(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) {
		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 {
		assert(i < size());
		return node[i + n_];
	}
	
	value_type fold(size_type l, size_type r) const {
		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);
	}
	
	const_reference fold_all() const {
		return node[1];
	}
	
	size_type max_right(size_type l, std::function<bool(const_reference)> g) const {
		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 {
		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_;
	}
};

int main() {
	int N;
	cin >> N;
	vector<int> A(N), B(N), C(N);
	HeavyLightDecomposition::Graph g(N);
	REP(i, N - 1) {
		scanf("%d %d %d", &A[i], &B[i], &C[i]);
		--A[i]; --B[i];
		g[A[i]].emplace_back(B[i]);
		g[B[i]].emplace_back(A[i]);
	}
	
	HeavyLightDecomposition_Query<HeavyLightDecomposition, int, SegmentTree> hld(g, 0, [](int a, int b) { return a + b; }, false);
	REP(i, N - 1) hld.set(A[i], B[i], C[i]);
	
	int Q;
	cin >> Q;
	while (Q--) {
		int s, t;
		scanf("%d %d", &s, &t);
		--s; --t;
		printf("%d\n", hld.fold(s, t));
	}
}
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結果

テストケース

ソースコード
