#include "tree/auxiliary-tree.hpp"
#pragma once #include <algorithm> #include <utility> #include <vector> using namespace std; #include "heavy-light-decomposition.hpp" template <typename G> struct AuxiliaryTree { G g; HeavyLightDecomposition<G> hld; AuxiliaryTree(const G& _g, int root = 0) : g(_g), hld(g, root) {} // ps : 頂点集合 // 返り値 : (aux tree, aux tree の頂点と g の頂点の対応表) // aux tree は 親->子 の向きの辺のみ含まれる // ps が空の場合は空のグラフを返す pair<vector<vector<int>>, vector<int>> get(vector<int> ps) { if (ps.empty()) return {}; auto comp = [&](int i, int j) { return hld.down[i] < hld.down[j]; }; sort(begin(ps), end(ps), comp); for (int i = 0, ie = ps.size(); i + 1 < ie; i++) { ps.push_back(hld.lca(ps[i], ps[i + 1])); } sort(begin(ps), end(ps), comp); ps.erase(unique(begin(ps), end(ps)), end(ps)); vector<vector<int>> aux(ps.size()); vector<int> rs; rs.push_back(0); for (int i = 1; i < (int)ps.size(); i++) { int l = hld.lca(ps[rs.back()], ps[i]); while (ps[rs.back()] != l) rs.pop_back(); aux[rs.back()].push_back(i); rs.push_back(i); } return make_pair(aux, ps); } }; /** * @brief Auxiliary Tree */
#line 2 "tree/auxiliary-tree.hpp" #include <algorithm> #include <utility> #include <vector> using namespace std; #line 2 "tree/heavy-light-decomposition.hpp" #line 2 "graph/graph-template.hpp" template <typename T> struct edge { int src, to; T cost; edge(int _to, T _cost) : src(-1), to(_to), cost(_cost) {} edge(int _src, int _to, T _cost) : src(_src), to(_to), cost(_cost) {} edge &operator=(const int &x) { to = x; return *this; } operator int() const { return to; } }; template <typename T> using Edges = vector<edge<T>>; template <typename T> using WeightedGraph = vector<Edges<T>>; using UnweightedGraph = vector<vector<int>>; // Input of (Unweighted) Graph UnweightedGraph graph(int N, int M = -1, bool is_directed = false, bool is_1origin = true) { UnweightedGraph g(N); if (M == -1) M = N - 1; for (int _ = 0; _ < M; _++) { int x, y; cin >> x >> y; if (is_1origin) x--, y--; g[x].push_back(y); if (!is_directed) g[y].push_back(x); } return g; } // Input of Weighted Graph template <typename T> WeightedGraph<T> wgraph(int N, int M = -1, bool is_directed = false, bool is_1origin = true) { WeightedGraph<T> g(N); if (M == -1) M = N - 1; for (int _ = 0; _ < M; _++) { int x, y; cin >> x >> y; T c; cin >> c; if (is_1origin) x--, y--; g[x].emplace_back(x, y, c); if (!is_directed) g[y].emplace_back(y, x, c); } return g; } // Input of Edges template <typename T> Edges<T> esgraph([[maybe_unused]] int N, int M, int is_weighted = true, bool is_1origin = true) { Edges<T> es; for (int _ = 0; _ < M; _++) { int x, y; cin >> x >> y; T c; if (is_weighted) cin >> c; else c = 1; if (is_1origin) x--, y--; es.emplace_back(x, y, c); } return es; } // Input of Adjacency Matrix template <typename T> vector<vector<T>> adjgraph(int N, int M, T INF, int is_weighted = true, bool is_directed = false, bool is_1origin = true) { vector<vector<T>> d(N, vector<T>(N, INF)); for (int _ = 0; _ < M; _++) { int x, y; cin >> x >> y; T c; if (is_weighted) cin >> c; else c = 1; if (is_1origin) x--, y--; d[x][y] = c; if (!is_directed) d[y][x] = c; } return d; } /** * @brief グラフテンプレート * @docs docs/graph/graph-template.md */ #line 4 "tree/heavy-light-decomposition.hpp" template <typename G> struct HeavyLightDecomposition { private: void dfs_sz(int cur) { size[cur] = 1; for (auto& dst : g[cur]) { if (dst == par[cur]) { if (g[cur].size() >= 2 && int(dst) == int(g[cur][0])) swap(g[cur][0], g[cur][1]); else continue; } depth[dst] = depth[cur] + 1; par[dst] = cur; dfs_sz(dst); size[cur] += size[dst]; if (size[dst] > size[g[cur][0]]) { swap(dst, g[cur][0]); } } } void dfs_hld(int cur) { down[cur] = id++; for (auto dst : g[cur]) { if (dst == par[cur]) continue; nxt[dst] = (int(dst) == int(g[cur][0]) ? nxt[cur] : int(dst)); dfs_hld(dst); } up[cur] = id; } // [u, v) vector<pair<int, int>> ascend(int u, int v) const { vector<pair<int, int>> res; while (nxt[u] != nxt[v]) { res.emplace_back(down[u], down[nxt[u]]); u = par[nxt[u]]; } if (u != v) res.emplace_back(down[u], down[v] + 1); return res; } // (u, v] vector<pair<int, int>> descend(int u, int v) const { if (u == v) return {}; if (nxt[u] == nxt[v]) return {{down[u] + 1, down[v]}}; auto res = descend(u, par[nxt[v]]); res.emplace_back(down[nxt[v]], down[v]); return res; } public: G& g; int root, id; vector<int> size, depth, down, up, nxt, par; HeavyLightDecomposition(G& _g, int _root = 0) : g(_g), root(_root), id(0), size(g.size(), 0), depth(g.size(), 0), down(g.size(), -1), up(g.size(), -1), nxt(g.size(), root), par(g.size(), root) { dfs_sz(root); dfs_hld(root); } pair<int, int> idx(int i) const { return make_pair(down[i], up[i]); } template <typename F> void path_query(int u, int v, bool vertex, const F& f) { int l = lca(u, v); for (auto&& [a, b] : ascend(u, l)) { int s = a + 1, t = b; s > t ? f(t, s) : f(s, t); } if (vertex) f(down[l], down[l] + 1); for (auto&& [a, b] : descend(l, v)) { int s = a, t = b + 1; s > t ? f(t, s) : f(s, t); } } template <typename F> void path_noncommutative_query(int u, int v, bool vertex, const F& f) { int l = lca(u, v); for (auto&& [a, b] : ascend(u, l)) f(a + 1, b); if (vertex) f(down[l], down[l] + 1); for (auto&& [a, b] : descend(l, v)) f(a, b + 1); } template <typename F> void subtree_query(int u, bool vertex, const F& f) { f(down[u] + int(!vertex), up[u]); } int lca(int a, int b) { while (nxt[a] != nxt[b]) { if (down[a] < down[b]) swap(a, b); a = par[nxt[a]]; } return depth[a] < depth[b] ? a : b; } int dist(int a, int b) { return depth[a] + depth[b] - depth[lca(a, b)] * 2; } }; /** * @brief Heavy Light Decomposition(重軽分解) * @docs docs/tree/heavy-light-decomposition.md */ #line 9 "tree/auxiliary-tree.hpp" template <typename G> struct AuxiliaryTree { G g; HeavyLightDecomposition<G> hld; AuxiliaryTree(const G& _g, int root = 0) : g(_g), hld(g, root) {} // ps : 頂点集合 // 返り値 : (aux tree, aux tree の頂点と g の頂点の対応表) // aux tree は 親->子 の向きの辺のみ含まれる // ps が空の場合は空のグラフを返す pair<vector<vector<int>>, vector<int>> get(vector<int> ps) { if (ps.empty()) return {}; auto comp = [&](int i, int j) { return hld.down[i] < hld.down[j]; }; sort(begin(ps), end(ps), comp); for (int i = 0, ie = ps.size(); i + 1 < ie; i++) { ps.push_back(hld.lca(ps[i], ps[i + 1])); } sort(begin(ps), end(ps), comp); ps.erase(unique(begin(ps), end(ps)), end(ps)); vector<vector<int>> aux(ps.size()); vector<int> rs; rs.push_back(0); for (int i = 1; i < (int)ps.size(); i++) { int l = hld.lca(ps[rs.back()], ps[i]); while (ps[rs.back()] != l) rs.pop_back(); aux[rs.back()].push_back(i); rs.push_back(i); } return make_pair(aux, ps); } }; /** * @brief Auxiliary Tree */