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:heavy_check_mark: Centroid-Decomosition(重心分解) (graph/tree/centroid-decomposition.hpp)

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#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;
  }
};
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