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#define PROBLEM "https://judge.yosupo.jp/problem/lca" #include "../../tree/lowest_common_ancestor.hpp" #include <iostream> #include "../../graph/base.hpp" int main() { int n, q; std::cin >> n >> q; ebi::Graph<int> g(n); g.read_parents(0); ebi::lowest_common_ancestor lca(g); while (q--) { int u, v; std::cin >> u >> v; std::cout << lca.lca(u, v) << '\n'; } }
#line 1 "test/tree/lowest_common_ancestor.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/lca" #line 2 "tree/lowest_common_ancestor.hpp" #include <vector> #line 2 "data_structure/sparse_table.hpp" #line 4 "data_structure/sparse_table.hpp" /* reference: https://scrapbox.io/data-structures/Sparse_Table */ namespace ebi { template <class Band, Band (*op)(Band, Band)> struct sparse_table { public: sparse_table() = default; sparse_table(const std::vector<Band> &a) : n(a.size()) { table = std::vector(std::__lg(n) + 1, std::vector<Band>(n)); for (int i = 0; i < n; i++) { table[0][i] = a[i]; } for (int k = 1; (1 << k) <= n; k++) { for (int i = 0; i + (1 << k) <= n; i++) { table[k][i] = op(table[k - 1][i], table[k - 1][i + (1 << (k - 1))]); } } } void build(const std::vector<Band> &a) { n = (int)a.size(); table = std::vector(std::__lg(n) + 1, std::vector<Band>(n)); for (int i = 0; i < n; i++) { table[0][i] = a[i]; } for (int k = 1; (1 << k) <= n; k++) { for (int i = 0; i + (1 << k) <= n; i++) { table[k][i] = op(table[k - 1][i], table[k - 1][i + (1 << (k - 1))]); } } } // [l, r) Band fold(int l, int r) { int k = std::__lg(r - l); return op(table[k][l], table[k][r - (1 << k)]); } private: int n; std::vector<std::vector<Band>> table; }; } // namespace ebi #line 2 "graph/base.hpp" #include <cassert> #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 7 "tree/lowest_common_ancestor.hpp" namespace ebi { namespace internal_lca { std::pair<int, int> op(std::pair<int, int> a, std::pair<int, int> b) { return a.second < b.second ? a : b; } } // namespace internal_lca template <class T> struct lowest_common_ancestor { public: lowest_common_ancestor(const Graph<T> &gh, int root = 0) : n(gh.size()), id(n), dist(n, 0) { auto dfs = [&](auto &&self, int v, int par = -1, T d = 0) -> void { id[v] = int(vs.size()); vs.emplace_back(v, d); for (const auto &e : gh[v]) if (e.to != par) { dist[e.to] = dist[v] + e.cost; self(self, e.to, v, d + 1); vs.emplace_back(v, d); } }; dfs(dfs, root); st.build(vs); } int lca(int u, int v) { int l = id[u], r = id[v]; if (r < l) std::swap(l, r); return st.fold(l, r + 1).first; } T distance(int u, int v) { int w = lca(u, v); return dist[u] + dist[v] - 2 * dist[w]; } private: int n; std::vector<int> id; std::vector<T> dist; std::vector<std::pair<int, int>> vs; sparse_table<std::pair<int, int>, internal_lca::op> st; }; } // namespace ebi #line 4 "test/tree/lowest_common_ancestor.test.cpp" #line 6 "test/tree/lowest_common_ancestor.test.cpp" #line 8 "test/tree/lowest_common_ancestor.test.cpp" int main() { int n, q; std::cin >> n >> q; ebi::Graph<int> g(n); g.read_parents(0); ebi::lowest_common_ancestor lca(g); while (q--) { int u, v; std::cin >> u >> v; std::cout << lca.lca(u, v) << '\n'; } }