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#include "graph/tree/centroid-decomposition.hpp"
#pragma once #include "../graph-template.hpp" /** * @brief Centroid-Decomosition(重心分解) */ template< typename T > struct CentroidDecomposition : Graph< T > { public: using Graph< T >::Graph; using Graph< T >::g; Graph< int > tree; int build(int t = 0) { sub.assign(g.size(), 0); v.assign(g.size(), 0); tree = Graph< int >(g.size()); return build_dfs(0); } explicit CentroidDecomposition(const Graph< T > &g) : Graph< T >(g) {} private: vector< int > sub; vector< int > v; inline int build_dfs(int idx, int par) { sub[idx] = 1; for(auto &to : g[idx]) { if(to == par || v[to]) continue; sub[idx] += build_dfs(to, idx); } return sub[idx]; } inline int search_centroid(int idx, int par, const int mid) { for(auto &to : g[idx]) { if(to == par || v[to]) continue; if(sub[to] > mid) return search_centroid(to, idx, mid); } return idx; } inline int build_dfs(int idx) { int centroid = search_centroid(idx, -1, build_dfs(idx, -1) / 2); v[centroid] = true; for(auto &to : g[centroid]) { if(!v[to]) tree.add_directed_edge(centroid, build_dfs(to)); } v[centroid] = false; return centroid; } };
#line 2 "graph/tree/centroid-decomposition.hpp" #line 2 "graph/graph-template.hpp" /** * @brief Graph Template(グラフテンプレート) */ template< typename T = int > struct Edge { int from, to; T cost; int idx; Edge() = default; Edge(int from, int to, T cost = 1, int idx = -1) : from(from), to(to), cost(cost), idx(idx) {} operator int() const { return to; } }; template< typename T = int > struct Graph { vector< vector< Edge< T > > > g; int es; Graph() = default; explicit Graph(int n) : g(n), es(0) {} size_t size() const { return g.size(); } void add_directed_edge(int from, int to, T cost = 1) { g[from].emplace_back(from, to, cost, es++); } void add_edge(int from, int to, T cost = 1) { g[from].emplace_back(from, to, cost, es); g[to].emplace_back(to, from, cost, es++); } void read(int M, int padding = -1, bool weighted = false, bool directed = false) { for(int i = 0; i < M; i++) { int a, b; cin >> a >> b; a += padding; b += padding; T c = T(1); if(weighted) cin >> c; if(directed) add_directed_edge(a, b, c); else add_edge(a, b, c); } } inline vector< Edge< T > > &operator[](const int &k) { return g[k]; } inline const vector< Edge< T > > &operator[](const int &k) const { return g[k]; } }; template< typename T = int > using Edges = vector< Edge< T > >; #line 4 "graph/tree/centroid-decomposition.hpp" /** * @brief Centroid-Decomosition(重心分解) */ template< typename T > struct CentroidDecomposition : Graph< T > { public: using Graph< T >::Graph; using Graph< T >::g; Graph< int > tree; int build(int t = 0) { sub.assign(g.size(), 0); v.assign(g.size(), 0); tree = Graph< int >(g.size()); return build_dfs(0); } explicit CentroidDecomposition(const Graph< T > &g) : Graph< T >(g) {} private: vector< int > sub; vector< int > v; inline int build_dfs(int idx, int par) { sub[idx] = 1; for(auto &to : g[idx]) { if(to == par || v[to]) continue; sub[idx] += build_dfs(to, idx); } return sub[idx]; } inline int search_centroid(int idx, int par, const int mid) { for(auto &to : g[idx]) { if(to == par || v[to]) continue; if(sub[to] > mid) return search_centroid(to, idx, mid); } return idx; } inline int build_dfs(int idx) { int centroid = search_centroid(idx, -1, build_dfs(idx, -1) / 2); v[centroid] = true; for(auto &to : g[centroid]) { if(!v[to]) tree.add_directed_edge(centroid, build_dfs(to)); } v[centroid] = false; return centroid; } };