Lowest common ancestor (HLD)
(Mylib/Graph/TreeUtils/lca_hld.cpp)

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

Requirements

Notes

Problems

References

Depends on

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

Verified with

• test/aoj/GRL_5_C/main.hld.test.cpp

Code

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

namespace haar_lib {
  template <typename T>
  class lowest_common_ancestor_hld {
    int n_;
    std::vector<int> sub_, par_, head_, id_;

    int dfs_sub(int cur, int p, tree<T> &tr) {
      par_[cur] = p;
      int t     = 0;
      for (auto &e : tr[cur]) {
        if (e.to == p) continue;
        sub_[cur] += dfs_sub(e.to, cur, tr);
        if (sub_[e.to] > t) {
          t = sub_[e.to];
          std::swap(e, tr[cur][0]);
        }
      }
      return sub_[cur];
    }

    void dfs_build(int cur, int &i, tree<T> &tr) {
      id_[cur] = i;
      ++i;

      for (auto &e : tr[cur]) {
        if (e.to == par_[cur]) continue;
        head_[e.to] = (e.to == tr[cur][0].to ? head_[cur] : e.to);
        dfs_build(e.to, i, tr);
      }
    }

  public:
    lowest_common_ancestor_hld() {}
    lowest_common_ancestor_hld(tree<T> tr, int root) : n_(tr.size()), sub_(n_, 1), par_(n_, -1), head_(n_), id_(n_) {
      dfs_sub(root, -1, tr);
      int i = 0;
      dfs_build(root, i, tr);
    }

    int lca(int u, int v) const {
      while (1) {
        if (id_[u] > id_[v]) std::swap(u, v);
        if (head_[u] == head_[v]) return u;
        v = par_[head_[v]];
      }
    }

    int operator()(int u, int v) const { return lca(u, v); }

    T distance(int u, int v, const std::vector<T> &dist) const {
      return dist[u] + dist[v] - 2 * dist[lca(u, v)];
    }
  };
}  // namespace haar_lib

#line 2 "Mylib/Graph/TreeUtils/lca_hld.cpp"
#include <utility>
#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/lca_hld.cpp"

namespace haar_lib {
  template <typename T>
  class lowest_common_ancestor_hld {
    int n_;
    std::vector<int> sub_, par_, head_, id_;

    int dfs_sub(int cur, int p, tree<T> &tr) {
      par_[cur] = p;
      int t     = 0;
      for (auto &e : tr[cur]) {
        if (e.to == p) continue;
        sub_[cur] += dfs_sub(e.to, cur, tr);
        if (sub_[e.to] > t) {
          t = sub_[e.to];
          std::swap(e, tr[cur][0]);
        }
      }
      return sub_[cur];
    }

    void dfs_build(int cur, int &i, tree<T> &tr) {
      id_[cur] = i;
      ++i;

      for (auto &e : tr[cur]) {
        if (e.to == par_[cur]) continue;
        head_[e.to] = (e.to == tr[cur][0].to ? head_[cur] : e.to);
        dfs_build(e.to, i, tr);
      }
    }

  public:
    lowest_common_ancestor_hld() {}
    lowest_common_ancestor_hld(tree<T> tr, int root) : n_(tr.size()), sub_(n_, 1), par_(n_, -1), head_(n_), id_(n_) {
      dfs_sub(root, -1, tr);
      int i = 0;
      dfs_build(root, i, tr);
    }

    int lca(int u, int v) const {
      while (1) {
        if (id_[u] > id_[v]) std::swap(u, v);
        if (head_[u] == head_[v]) return u;
        v = par_[head_[v]];
      }
    }

    int operator()(int u, int v) const { return lca(u, v); }

    T distance(int u, int v, const std::vector<T> &dist) const {
      return dist[u] + dist[v] - 2 * dist[lca(u, v)];
    }
  };
}  // namespace haar_lib

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