Euler tour (BFS)
(Mylib/Graph/TreeUtils/euler_tour_bfs.cpp)

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

• EulerTourBFS(tree, int root)
• query_children(int i, int d, f)
  • iのd個下の子孫にfを適用する。
• query_at(int i, f)
  • query_children(i, 0, f)と同等。
• get_parent
  • iの親を返す。
• get_ancestor(int i, int k)
  • iのk個遡った祖先を返す。
  • get_ancestor(i, 0) = i
  • get_ancestor(i, 1) = get_parent(i)
  • Time complexity $O(k)$

Requirements

Notes

Problems

• yukicoder No.899 γatheree

References

• https://niuez.hatenablog.com/entry/2019/10/05/002503
• https://niuez.github.io/posts/entry/2019/10/05/002503/

Depends on

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

Verified with

• test/yukicoder/899/main.test.cpp

Code

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

namespace haar_lib {
  template <typename T>
  class euler_tour_bfs {
    int N_;
    std::vector<int> parent_, depth_, left_, right_;
    std::vector<std::vector<int>> bfs_order_, dfs_order_;

  public:
    euler_tour_bfs() {}
    euler_tour_bfs(const tree<T> &tr, int root) : N_(tr.size()), parent_(N_), depth_(N_), left_(N_), right_(N_) {
      {
        int ord = 0;
        dfs(tr, root, -1, 0, ord);
      }

      {
        std::queue<std::pair<int, int>> q;
        q.emplace(root, 0);
        int ord = 0;

        while (not q.empty()) {
          auto [i, d] = q.front();
          q.pop();

          if ((int) bfs_order_.size() <= d) bfs_order_.emplace_back();
          bfs_order_[d].push_back(ord);
          ++ord;

          for (auto &e : tr[i]) {
            if (e.to == parent_[i]) continue;
            q.emplace(e.to, d + 1);
          }
        }
      }
    }

  private:
    void dfs(const tree<T> &tr, int cur, int par, int d, int &ord) {
      parent_[cur] = par;
      depth_[cur]  = d;

      if ((int) dfs_order_.size() <= d) dfs_order_.emplace_back();
      dfs_order_[d].push_back(ord);
      left_[cur] = ord;
      ++ord;

      for (auto &e : tr[cur]) {
        if (e.to == par) continue;
        dfs(tr, e.to, cur, d + 1, ord);
      }

      right_[cur] = ord;
    }

  public:
    template <typename Func>
    void query_children(int i, int d, const Func &f) const {
      if (i != -1) {
        d += depth_[i];
        if ((int) bfs_order_.size() > d) {
          int l = std::lower_bound(dfs_order_[d].begin(), dfs_order_[d].end(), left_[i]) - dfs_order_[d].begin();
          int r = std::lower_bound(dfs_order_[d].begin(), dfs_order_[d].end(), right_[i]) - dfs_order_[d].begin();

          if (l >= (int) bfs_order_[d].size()) return;
          if (r == l) return;

          f(bfs_order_[d][l], bfs_order_[d][r - 1] + 1);
        }
      }
    }

    template <typename Func>
    void query_at(int i, const Func &f) const {
      query_children(i, 0, f);
    }

    int get_parent(int i) const {
      if (i == -1) return -1;
      return parent_[i];
    }

    int get_ancestor(int i, int k) const {
      int ret = i;
      for (int i = 0; i < k; ++i) {
        ret = get_parent(ret);
        if (ret == -1) break;
      }
      return ret;
    }
  };
}  // namespace haar_lib

#line 2 "Mylib/Graph/TreeUtils/euler_tour_bfs.cpp"
#include <queue>
#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 5 "Mylib/Graph/TreeUtils/euler_tour_bfs.cpp"

namespace haar_lib {
  template <typename T>
  class euler_tour_bfs {
    int N_;
    std::vector<int> parent_, depth_, left_, right_;
    std::vector<std::vector<int>> bfs_order_, dfs_order_;

  public:
    euler_tour_bfs() {}
    euler_tour_bfs(const tree<T> &tr, int root) : N_(tr.size()), parent_(N_), depth_(N_), left_(N_), right_(N_) {
      {
        int ord = 0;
        dfs(tr, root, -1, 0, ord);
      }

      {
        std::queue<std::pair<int, int>> q;
        q.emplace(root, 0);
        int ord = 0;

        while (not q.empty()) {
          auto [i, d] = q.front();
          q.pop();

          if ((int) bfs_order_.size() <= d) bfs_order_.emplace_back();
          bfs_order_[d].push_back(ord);
          ++ord;

          for (auto &e : tr[i]) {
            if (e.to == parent_[i]) continue;
            q.emplace(e.to, d + 1);
          }
        }
      }
    }

  private:
    void dfs(const tree<T> &tr, int cur, int par, int d, int &ord) {
      parent_[cur] = par;
      depth_[cur]  = d;

      if ((int) dfs_order_.size() <= d) dfs_order_.emplace_back();
      dfs_order_[d].push_back(ord);
      left_[cur] = ord;
      ++ord;

      for (auto &e : tr[cur]) {
        if (e.to == par) continue;
        dfs(tr, e.to, cur, d + 1, ord);
      }

      right_[cur] = ord;
    }

  public:
    template <typename Func>
    void query_children(int i, int d, const Func &f) const {
      if (i != -1) {
        d += depth_[i];
        if ((int) bfs_order_.size() > d) {
          int l = std::lower_bound(dfs_order_[d].begin(), dfs_order_[d].end(), left_[i]) - dfs_order_[d].begin();
          int r = std::lower_bound(dfs_order_[d].begin(), dfs_order_[d].end(), right_[i]) - dfs_order_[d].begin();

          if (l >= (int) bfs_order_[d].size()) return;
          if (r == l) return;

          f(bfs_order_[d][l], bfs_order_[d][r - 1] + 1);
        }
      }
    }

    template <typename Func>
    void query_at(int i, const Func &f) const {
      query_children(i, 0, f);
    }

    int get_parent(int i) const {
      if (i == -1) return -1;
      return parent_[i];
    }

    int get_ancestor(int i, int k) const {
      int ret = i;
      for (int i = 0; i < k; ++i) {
        ret = get_parent(ret);
        if (ret == -1) break;
      }
      return ret;
    }
  };
}  // namespace haar_lib

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