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#include "tree/level_ancestor.hpp"
根付き木のLevel Ancestorを構築 $O(N)$ / クエリ $O(\log N)$
頂点uの根方向に $k$ だけ上った頂点を返す。 $O(\log N)$
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#pragma once #include <algorithm> #include <cassert> #include <vector> #include "../graph/base.hpp" namespace ebi { template <class T> struct level_ancestor { private: int n; std::vector<int> in; std::vector<int> inv_in; std::vector<int> depths; std::vector<std::vector<int>> s; public: level_ancestor(const Graph<T> &gh, int root = 0) : n(gh.size()), in(n), inv_in(n), depths(n) { int cnt = 0; int max = 0; auto dfs = [&](auto &&self, int v, int par = -1) -> void { inv_in[cnt] = v; in[v] = cnt++; max = std::max(max, depths[v]); for (auto e : gh[v]) if (e.to != par) { depths[e.to] = depths[v] + 1; self(self, e.to, v); } }; dfs(dfs, root); s.resize(max + 1); for (int i = 0; i < n; i++) { int u = inv_in[i]; s[depths[u]].emplace_back(i); } } int query(int u, int k) const { int m = depths[u] - k; assert(m >= 0); return inv_in[*std::prev( std::upper_bound(s[m].begin(), s[m].end(), in[u]))]; } int depth(int u) const { return depths[u]; } }; } // namespace ebi
#line 2 "tree/level_ancestor.hpp" #include <algorithm> #include <cassert> #include <vector> #line 2 "graph/base.hpp" #line 4 "graph/base.hpp" #include <iostream> #include <ranges> #line 7 "graph/base.hpp" #line 2 "data_structure/simple_csr.hpp" #line 4 "data_structure/simple_csr.hpp" #include <utility> #line 6 "data_structure/simple_csr.hpp" namespace ebi { template <class E> struct simple_csr { simple_csr() = default; simple_csr(int n, const std::vector<std::pair<int, E>>& elements) : start(n + 1, 0), elist(elements.size()) { for (auto e : elements) { start[e.first + 1]++; } for (auto i : std::views::iota(0, n)) { start[i + 1] += start[i]; } auto counter = start; for (auto [i, e] : elements) { elist[counter[i]++] = e; } } simple_csr(const std::vector<std::vector<E>>& es) : start(es.size() + 1, 0) { int n = es.size(); for (auto i : std::views::iota(0, n)) { start[i + 1] = (int)es[i].size() + start[i]; } elist.resize(start.back()); for (auto i : std::views::iota(0, n)) { std::copy(es[i].begin(), es[i].end(), elist.begin() + start[i]); } } int size() const { return (int)start.size() - 1; } const auto operator[](int i) const { return std::ranges::subrange(elist.begin() + start[i], elist.begin() + start[i + 1]); } auto operator[](int i) { return std::ranges::subrange(elist.begin() + start[i], elist.begin() + start[i + 1]); } const auto operator()(int i, int l, int r) const { return std::ranges::subrange(elist.begin() + start[i] + l, elist.begin() + start[i + 1] + r); } auto operator()(int i, int l, int r) { return std::ranges::subrange(elist.begin() + start[i] + l, elist.begin() + start[i + 1] + r); } private: std::vector<int> start; std::vector<E> elist; }; } // namespace ebi #line 9 "graph/base.hpp" namespace ebi { template <class T> struct Edge { int from, to; T cost; int id; }; template <class E> struct Graph { using cost_type = E; using edge_type = Edge<cost_type>; Graph(int n_) : n(n_) {} Graph() = default; void add_edge(int u, int v, cost_type c) { buff.emplace_back(u, edge_type{u, v, c, m}); edges.emplace_back(edge_type{u, v, c, m++}); } void add_undirected_edge(int u, int v, cost_type c) { buff.emplace_back(u, edge_type{u, v, c, m}); buff.emplace_back(v, edge_type{v, u, c, m}); edges.emplace_back(edge_type{u, v, c, m}); m++; } void read_tree(int offset = 1, bool is_weighted = false) { read_graph(n - 1, offset, false, is_weighted); } void read_parents(int offset = 1) { for (auto i : std::views::iota(1, n)) { int p; std::cin >> p; p -= offset; add_undirected_edge(p, i, 1); } build(); } void read_graph(int e, int offset = 1, bool is_directed = false, bool is_weighted = false) { for (int i = 0; i < e; i++) { int u, v; std::cin >> u >> v; u -= offset; v -= offset; if (is_weighted) { cost_type c; std::cin >> c; if (is_directed) { add_edge(u, v, c); } else { add_undirected_edge(u, v, c); } } else { if (is_directed) { add_edge(u, v, 1); } else { add_undirected_edge(u, v, 1); } } } build(); } void build() { assert(!prepared); csr = simple_csr<edge_type>(n, buff); buff.clear(); prepared = true; } int size() const { return n; } int node_number() const { return n; } int edge_number() const { return m; } edge_type get_edge(int i) const { return edges[i]; } std::vector<edge_type> get_edges() const { return edges; } const auto operator[](int i) const { return csr[i]; } auto operator[](int i) { return csr[i]; } private: int n, m = 0; std::vector<std::pair<int,edge_type>> buff; std::vector<edge_type> edges; simple_csr<edge_type> csr; bool prepared = false; }; } // namespace ebi #line 8 "tree/level_ancestor.hpp" namespace ebi { template <class T> struct level_ancestor { private: int n; std::vector<int> in; std::vector<int> inv_in; std::vector<int> depths; std::vector<std::vector<int>> s; public: level_ancestor(const Graph<T> &gh, int root = 0) : n(gh.size()), in(n), inv_in(n), depths(n) { int cnt = 0; int max = 0; auto dfs = [&](auto &&self, int v, int par = -1) -> void { inv_in[cnt] = v; in[v] = cnt++; max = std::max(max, depths[v]); for (auto e : gh[v]) if (e.to != par) { depths[e.to] = depths[v] + 1; self(self, e.to, v); } }; dfs(dfs, root); s.resize(max + 1); for (int i = 0; i < n; i++) { int u = inv_in[i]; s[depths[u]].emplace_back(i); } } int query(int u, int k) const { int m = depths[u] - k; assert(m >= 0); return inv_in[*std::prev( std::upper_bound(s[m].begin(), s[m].end(), in[u]))]; } int depth(int u) const { return depths[u]; } }; } // namespace ebi