Centroid decomposition
(Mylib/Graph/TreeUtils/centroid_decomposition.cpp)

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• Last update: 2021-04-23 23:44:44+09:00

Operations

Requirements

Notes

Problems

• Codeforces Round #199 (Div. 2) E. Xenia and Tree

References

• https://www.hamayanhamayan.com/entry/2017/12/19/152143
• http://techtipshoge.blogspot.com/2016/09/centroid-decomposition.html
• https://ferin-tech.hatenablog.com/entry/2020/03/06/162311

Depends on

• Basic graph (Mylib/Graph/Template/graph.cpp)

Code

#pragma once
#include <vector>
#include "Mylib/Graph/Template/graph.cpp"

namespace haar_lib {
  template <typename T>
  class centroid_decomposition {
    int N_;
    std::vector<int> parent_, subsize_;
    std::vector<std::vector<int>> children_;
    std::vector<bool> check_;

  public:
    centroid_decomposition() {}
    centroid_decomposition(const tree<T> &tr) : N_(tr.size()), parent_(N_), subsize_(N_), children_(N_), check_(N_) {
      decompose(tr, 0, -1);
    }

  private:
    void decompose(const tree<T> &tr, int cur, int par) {
      dfs_subsize(tr, cur, -1);
      auto c = get_centroid(tr, cur, -1, subsize_[cur]);

      check_[c]  = true;
      parent_[c] = par;
      if (par != -1) children_[par].push_back(c);

      for (auto &e : tr[c]) {
        if (check_[e.to]) continue;
        decompose(tr, e.to, c);
      }
    }

    int get_centroid(const tree<T> &tr, int cur, int par, int total_size) {
      for (auto &e : tr[cur]) {
        if (e.to == par or check_[e.to]) continue;

        if (2 * subsize_[e.to] > total_size) {
          return get_centroid(tr, e.to, cur, total_size);
        }
      }

      return cur;
    }

    void dfs_subsize(const tree<T> &tr, int cur, int par) {
      subsize_[cur] = 1;
      for (auto &e : tr[cur]) {
        if (e.to == par or check_[e.to]) continue;
        dfs_subsize(tr, e.to, cur);
        subsize_[cur] += subsize_[e.to];
      }
    }

  public:
    auto bottom_up(int i) const {
      std::vector<int> ret;
      while (i >= 0) {
        ret.push_back(i);
        i = parent_[i];
      }
      return ret;
    }
  };
}  // namespace haar_lib

#line 2 "Mylib/Graph/TreeUtils/centroid_decomposition.cpp"
#include <vector>
#line 2 "Mylib/Graph/Template/graph.cpp"
#include <iostream>
#line 4 "Mylib/Graph/Template/graph.cpp"

namespace haar_lib {
  template <typename T>
  struct edge {
    int from, to;
    T cost;
    int index = -1;
    edge() {}
    edge(int from, int to, T cost) : from(from), to(to), cost(cost) {}
    edge(int from, int to, T cost, int index) : from(from), to(to), cost(cost), index(index) {}
  };

  template <typename T>
  struct graph {
    using weight_type = T;
    using edge_type   = edge<T>;

    std::vector<std::vector<edge<T>>> data;

    auto& operator[](size_t i) { return data[i]; }
    const auto& operator[](size_t i) const { return data[i]; }

    auto begin() const { return data.begin(); }
    auto end() const { return data.end(); }

    graph() {}
    graph(int N) : data(N) {}

    bool empty() const { return data.empty(); }
    int size() const { return data.size(); }

    void add_edge(int i, int j, T w, int index = -1) {
      data[i].emplace_back(i, j, w, index);
    }

    void add_undirected(int i, int j, T w, int index = -1) {
      add_edge(i, j, w, index);
      add_edge(j, i, w, index);
    }

    template <size_t I, bool DIRECTED = true, bool WEIGHTED = true>
    void read(int M) {
      for (int i = 0; i < M; ++i) {
        int u, v;
        std::cin >> u >> v;
        u -= I;
        v -= I;
        T w = 1;
        if (WEIGHTED) std::cin >> w;
        if (DIRECTED)
          add_edge(u, v, w, i);
        else
          add_undirected(u, v, w, i);
      }
    }
  };

  template <typename T>
  using tree = graph<T>;
}  // namespace haar_lib
#line 4 "Mylib/Graph/TreeUtils/centroid_decomposition.cpp"

namespace haar_lib {
  template <typename T>
  class centroid_decomposition {
    int N_;
    std::vector<int> parent_, subsize_;
    std::vector<std::vector<int>> children_;
    std::vector<bool> check_;

  public:
    centroid_decomposition() {}
    centroid_decomposition(const tree<T> &tr) : N_(tr.size()), parent_(N_), subsize_(N_), children_(N_), check_(N_) {
      decompose(tr, 0, -1);
    }

  private:
    void decompose(const tree<T> &tr, int cur, int par) {
      dfs_subsize(tr, cur, -1);
      auto c = get_centroid(tr, cur, -1, subsize_[cur]);

      check_[c]  = true;
      parent_[c] = par;
      if (par != -1) children_[par].push_back(c);

      for (auto &e : tr[c]) {
        if (check_[e.to]) continue;
        decompose(tr, e.to, c);
      }
    }

    int get_centroid(const tree<T> &tr, int cur, int par, int total_size) {
      for (auto &e : tr[cur]) {
        if (e.to == par or check_[e.to]) continue;

        if (2 * subsize_[e.to] > total_size) {
          return get_centroid(tr, e.to, cur, total_size);
        }
      }

      return cur;
    }

    void dfs_subsize(const tree<T> &tr, int cur, int par) {
      subsize_[cur] = 1;
      for (auto &e : tr[cur]) {
        if (e.to == par or check_[e.to]) continue;
        dfs_subsize(tr, e.to, cur);
        subsize_[cur] += subsize_[e.to];
      }
    }

  public:
    auto bottom_up(int i) const {
      std::vector<int> ret;
      while (i >= 0) {
        ret.push_back(i);
        i = parent_[i];
      }
      return ret;
    }
  };
}  // namespace haar_lib

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