Tree-Diameter(木の直径) (graph/tree/tree-diameter.hpp)

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• Last update: 2024-04-27 01:27:28+09:00
• Include: #include "graph/tree/tree-diameter.hpp"

概要

木の直径を求める.

適当な頂点から DFS して最も遠い点 $u$ を求める, $u$ から DFS して最も遠い点 $v$ を見つけると, そのペア $(u, v)$ が直径の端点.

使い方

• build(): 木の直径を返す. path には直径を構成する辺が格納される.

計算量

$O(V)$

Depends on

• Graph Template(グラフテンプレート) (graph/graph-template.hpp)

Verified with

• test/verify/aoj-grl-5-a.test.cpp
• test/verify/yosupo-tree-diameter.test.cpp

Code

#pragma once

#include "../graph-template.hpp"

/**
 * @brief Tree-Diameter(木の直径)
 *
 */
template <typename T = int>
struct TreeDiameter : Graph<T> {
 public:
  using Graph<T>::Graph;
  using Graph<T>::g;
  vector<Edge<T> > path;

  T build() {
    to.assign(g.size(), -1);
    auto p = dfs(0, -1);
    auto q = dfs(p.second, -1);

    int now = p.second;
    while (now != q.second) {
      for (auto &e : g[now]) {
        if (to[now] == e.to) {
          path.emplace_back(e);
        }
      }
      now = to[now];
    }
    return q.first;
  }

  explicit TreeDiameter(const Graph<T> &g) : Graph<T>(g) {}

 private:
  vector<int> to;

  pair<T, int> dfs(int idx, int par) {
    pair<T, int> ret(0, idx);
    for (auto &e : g[idx]) {
      if (e.to == par) continue;
      auto cost = dfs(e.to, idx);
      cost.first += e.cost;
      if (ret < cost) {
        ret = cost;
        to[idx] = e.to;
      }
    }
    return ret;
  }
};

#line 2 "graph/tree/tree-diameter.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/tree-diameter.hpp"

/**
 * @brief Tree-Diameter(木の直径)
 *
 */
template <typename T = int>
struct TreeDiameter : Graph<T> {
 public:
  using Graph<T>::Graph;
  using Graph<T>::g;
  vector<Edge<T> > path;

  T build() {
    to.assign(g.size(), -1);
    auto p = dfs(0, -1);
    auto q = dfs(p.second, -1);

    int now = p.second;
    while (now != q.second) {
      for (auto &e : g[now]) {
        if (to[now] == e.to) {
          path.emplace_back(e);
        }
      }
      now = to[now];
    }
    return q.first;
  }

  explicit TreeDiameter(const Graph<T> &g) : Graph<T>(g) {}

 private:
  vector<int> to;

  pair<T, int> dfs(int idx, int par) {
    pair<T, int> ret(0, idx);
    for (auto &e : g[idx]) {
      if (e.to == par) continue;
      auto cost = dfs(e.to, idx);
      cost.first += e.cost;
      if (ret < cost) {
        ret = cost;
        to[idx] = e.to;
      }
    }
    return ret;
  }
};

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