Lowest common ancestor (Doubling)
(Mylib/Graph/TreeUtils/lca_doubling.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.doubling.test.cpp
• test/yukicoder/922/main.test.cpp

Code

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

namespace haar_lib {
  template <typename T>
  class lowest_common_ancestor_doubling {
    int n_, log2n_;
    std::vector<std::vector<int>> parent_;
    std::vector<int> depth_;

    void dfs(const tree<T> &tr, int cur, int par, int d) {
      parent_[cur][0] = par;
      depth_[cur]     = d;

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

  public:
    lowest_common_ancestor_doubling() {}
    lowest_common_ancestor_doubling(const tree<T> &tr, int root) : n_(tr.size()), log2n_((int) ceil(log2(n_)) + 1), parent_(n_, std::vector<int>(log2n_)), depth_(n_) {
      dfs(tr, root, -1, 0);
      for (int k = 0; k < log2n_ - 1; ++k) {
        for (int v = 0; v < n_; ++v) {
          if (parent_[v][k] == -1)
            parent_[v][k + 1] = -1;
          else
            parent_[v][k + 1] = parent_[parent_[v][k]][k];
        }
      }
    }

    int lca(int a, int b) const {
      if (depth_[a] >= depth_[b]) std::swap(a, b);
      for (int k = 0; k < log2n_; ++k) {
        if ((depth_[b] - depth_[a]) >> k & 1) b = parent_[b][k];
      }
      if (a == b) return a;
      for (int k = log2n_; --k >= 0;) {
        if (parent_[a][k] != parent_[b][k]) {
          a = parent_[a][k];
          b = parent_[b][k];
        }
      }
      return parent_[a][0];
    }

    int operator()(int a, int b) const { return lca(a, b); }

    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_doubling.cpp"
#include <cmath>
#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_doubling.cpp"

namespace haar_lib {
  template <typename T>
  class lowest_common_ancestor_doubling {
    int n_, log2n_;
    std::vector<std::vector<int>> parent_;
    std::vector<int> depth_;

    void dfs(const tree<T> &tr, int cur, int par, int d) {
      parent_[cur][0] = par;
      depth_[cur]     = d;

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

  public:
    lowest_common_ancestor_doubling() {}
    lowest_common_ancestor_doubling(const tree<T> &tr, int root) : n_(tr.size()), log2n_((int) ceil(log2(n_)) + 1), parent_(n_, std::vector<int>(log2n_)), depth_(n_) {
      dfs(tr, root, -1, 0);
      for (int k = 0; k < log2n_ - 1; ++k) {
        for (int v = 0; v < n_; ++v) {
          if (parent_[v][k] == -1)
            parent_[v][k + 1] = -1;
          else
            parent_[v][k + 1] = parent_[parent_[v][k]][k];
        }
      }
    }

    int lca(int a, int b) const {
      if (depth_[a] >= depth_[b]) std::swap(a, b);
      for (int k = 0; k < log2n_; ++k) {
        if ((depth_[b] - depth_[a]) >> k & 1) b = parent_[b][k];
      }
      if (a == b) return a;
      for (int k = log2n_; --k >= 0;) {
        if (parent_[a][k] != parent_[b][k]) {
          a = parent_[a][k];
          b = parent_[b][k];
        }
      }
      return parent_[a][0];
    }

    int operator()(int a, int b) const { return lca(a, b); }

    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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