Tree Diameter - 木の直径
(Library/Tree/TreeDiameter.hpp)

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Last update: 2026-02-13 15:23:31+09:00
Include: #include "Library/Tree/TreeDiameter.hpp"

Tree Diameter - 木の直径

頂点数 $V$ の木 $T$ の直径に関するライブラリです。

Function

Constructor

TreeDiameter(Graph<WeightType> &tree)

木 $T$ を頂点数 $V$ の tree で初期化し、その直径を求めます。

制約

tree は木

計算量

$\textrm{O}(V)$

Diameter

WeightType Diameter() const

木 $T$ の直径を返します。

計算量

$\textrm{O}(1)$

Height

WeightType Height(Vertex v) const

木 $T$ について、頂点 $v$ を根としたときの木の高さを返します。
- 木の高さとは、根から最も遠い葉までの距離を指します。

制約

$0 \le v \lt V$

計算量

$\textrm{O}(1)$

EndPoints

pair<Vertex, Vertex> EndPoints() const

木 $T$ の直径の端点の頂点を返します。

計算量

$\textrm{O}(1)$

Path

vector<Vertex> &Path()

木 $T$ の直径を成すパスの頂点列を返します。

計算量

$\textrm{O}(1)$

Depends on

Verified with

Code

#include "Tree.hpp"

template<typename WeightType>
class TreeDiameter{
    public:
    TreeDiameter(Graph<WeightType> &tree) : T(tree){
        int V = T.VertexSize(), s = 0;
        dist_s_ = CalculateTreeDistance(T, s);
        s = distance(dist_s_.begin(), max_element(dist_s_.begin(), dist_s_.end()));
        dist_s_ = CalculateTreeDistance(T, s);
        vector<int> par = CalculateTreeParent(T, s);
        int t = distance(dist_s_.begin(), max_element(dist_s_.begin(), dist_s_.end()));
        diameter_ = dist_s_[t];
        dist_t_ = CalculateTreeDistance(T, t);
        int u = t;
        while(u != s){
            path_.emplace_back(u);
            u = par[u];
        }
        path_.emplace_back(s);
    }
    
    WeightType Diameter() const {
        return diameter_;
    }
    
    WeightType Height(Vertex v) const {
        return max(dist_s_[v], dist_t_[v]);
    }

    pair<Vertex, Vertex> EndPoints() const {
        return pair<Vertex, Vertex>(path_.front(), path_.back());
    }

    vector<Vertex> &Path(){
        return path_;
    }

    private:
    Graph<WeightType> &T;
    vector<WeightType> dist_s_, dist_t_;
    vector<Vertex> path_;
    WeightType diameter_;
};

#line 2 "Library/Tree/Tree.hpp"

#line 2 "Library/Graph/Graph.hpp"

#line 2 "Library/Common.hpp"

/**
 * @file Common.hpp
 */

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cstdint>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <utility>
#include <vector>
using namespace std;

using ll = int64_t;
using ull = uint64_t;

constexpr const ll INF = (1LL << 62) - (3LL << 30) - 1;
#line 4 "Library/Graph/Graph.hpp"

using Vertex = int;

template<typename WeightType = int32_t>
struct Edge{
    public:
    Edge() = default;

    Edge(Vertex from_, Vertex to_, WeightType weight_ = 1, int idx_ = -1) :
        from(from_), to(to_), cost(weight_), idx(idx_){}
    
    bool operator<(const Edge<WeightType> &e) const {return cost < e.cost;}

    operator int() const {return to;}

    Vertex from, to;
    WeightType cost;
    int idx;
};

template<typename WeightType = int32_t>
class Graph{
    public:
    Graph() = default;

    Graph(int V) : edge_size_(0), adjacent_list_(V){}
    
    inline void AddUndirectedEdge(Vertex u, Vertex v, WeightType w = 1){
        int idx = edge_size_++;
        adjacent_list_[u].push_back(Edge<WeightType>(u, v, w, idx));
        adjacent_list_[v].push_back(Edge<WeightType>(v, u, w, idx));
    }
    
    inline void AddDirectedEdge(Vertex u, Vertex v, WeightType w = 1){
        int idx = edge_size_++;
        adjacent_list_[u].push_back(Edge<WeightType>(u, v, w, idx));
    }

    inline size_t VertexSize() const {
        return adjacent_list_.size();
    }

    inline size_t EdgeSize() const {
        return edge_size_;
    }

    inline vector<Edge<WeightType>> &operator[](const Vertex v){
        return adjacent_list_[v];
    }

    inline const vector<Edge<WeightType>> &operator[](const Vertex v) const {
        return adjacent_list_[v];
    }
    
    private:
    size_t edge_size_;
    vector<vector<Edge<WeightType>>> adjacent_list_;
};

template<typename WeightType = int32_t>
Graph<WeightType> InputGraph(int N, int M, int padding = -1, bool weighted = false, bool directed = false){
    Graph<WeightType> G(N);
    for(int i = 0; i < M; ++i){
        Vertex u, v; WeightType w = 1;
        cin >> u >> v, u += padding, v += padding;
        if(weighted) cin >> w;
        if(directed) G.AddDirectedEdge(u, v, w);
        else G.AddUndirectedEdge(u, v, w);
    }
    return G;
}
#line 4 "Library/Tree/Tree.hpp"

template<typename WeightType = int32_t>
Graph<WeightType> InputTree(int V, int padding = -1, bool weighted = false){
    Graph<WeightType> G(V);
    for(int i = 0; i < V - 1; ++i){
        Vertex u, v; WeightType w = 1;
        cin >> u >> v, u += padding, v += padding;
        if(weighted) cin >> w;
        G.AddUndirectedEdge(u, v, w);
    }
    return G;
}

template<typename WeightType = int32_t>
Graph<WeightType> InputRootedTreeChild(int V, int padding = -1){
    Graph<WeightType> G(V);
    for(Vertex u = 0; u < V; ++u){
        int k; cin >> k;
        for(int i = 0; i < k; ++i){
            Vertex v; cin >> v, v += padding;
            G.AddUndirectedEdge(u, v);
        }
    }
    return G;
}

template<typename WeightType = int32_t>
Graph<WeightType> InputRootedTreeParent(int V, int padding = -1){
    Graph<WeightType> G(V);
    for(Vertex u = 1; u < V; ++u){
        Vertex v; cin >> v, v += padding;
        G.AddUndirectedEdge(u, v);
    }
    return G;
}

template<typename WeightType = int32_t>
vector<vector<Vertex>> RootedTreeAdjacentList(const Graph<WeightType> &T, const Vertex r = 0){
    int V = T.VertexSize();
    vector<vector<Vertex>> ret(V);
    auto rec = [&](auto &self, Vertex u, Vertex p) -> void {
        for(Vertex v : T[u]){
            if(v == p) continue;
            ret[u].push_back(v);
            self(self, v, u);
        }
    };
    rec(rec, r, -1);
    return ret;
}

template<typename WeightType>
vector<Vertex> CalculateTreeParent(Graph<WeightType> &T, Vertex r = 0){
    int V = T.VertexSize();
    vector<Vertex> ret(V, -1);
    auto rec = [&](auto &self, Vertex u) -> void {
        for(Vertex v : T[u]){
            if(v == ret[u]) continue;
            ret[v] = u;
            self(self, v);
        }
    };
    rec(rec, r);
    return ret;
}

template<typename WeightType>
vector<WeightType> CalculateTreeCost(Graph<WeightType> &T, Vertex r = 0){
    int V = T.VertexSize();
    vector<WeightType> ret(V);
    auto rec = [&](auto &self, Vertex u, Vertex p) -> void {
        for(const Edge<WeightType> &e : T[u]){
            Vertex v = e.to;
            if(v == p) continue;
            ret[v] = e.cost;
            self(self, v, u);
        }
    };
    rec(rec, r, -1);
    return ret;
}

template<typename WeightType>
vector<int> CalculateTreeDepth(Graph<WeightType> &T, Vertex r = 0){
    int V = T.VertexSize();
    vector<int> ret(V, 0);
    auto rec = [&](auto &self, Vertex u, Vertex p, int d) -> void {
        ret[u] = d;
        for(Vertex v : T[u]){
            if(v == p) continue;
            self(self, v, u, d + 1);
        }
    };
    rec(rec, r, -1, 0);
    return ret;
}

template<typename WeightType>
vector<WeightType> CalculateTreeDistance(Graph<WeightType> &T, Vertex r = 0){
    int V = T.VertexSize();
    vector<WeightType> ret(V, WeightType(INF));
    auto rec = [&](auto &self, Vertex u) -> void {
        for(const Edge<WeightType> &e : T[u]){
            if(ret[e.to] > ret[u] + e.cost){
                ret[e.to] = ret[u] + e.cost;
                self(self, e.to);
            }
        }
    };
    ret[r] = 0;
    rec(rec, r);
    return ret;
}

template<typename WeightType>
vector<int> CalculateSubtreeSize(Graph<WeightType> &tree, Vertex r = 0){
    int V = tree.VertexSize();
    vector<int> ret(V, 1);
    auto rec = [&](auto self, Vertex u, Vertex p) -> int {
        for(const int v : tree[u]){
            if(v == p) continue;
            ret[u] += self(self, v, u);
        }
        return ret[u];
    };
    rec(rec, r, -1);
    return ret;
}
#line 2 "Library/Tree/TreeDiameter.hpp"

template<typename WeightType>
class TreeDiameter{
    public:
    TreeDiameter(Graph<WeightType> &tree) : T(tree){
        int V = T.VertexSize(), s = 0;
        dist_s_ = CalculateTreeDistance(T, s);
        s = distance(dist_s_.begin(), max_element(dist_s_.begin(), dist_s_.end()));
        dist_s_ = CalculateTreeDistance(T, s);
        vector<int> par = CalculateTreeParent(T, s);
        int t = distance(dist_s_.begin(), max_element(dist_s_.begin(), dist_s_.end()));
        diameter_ = dist_s_[t];
        dist_t_ = CalculateTreeDistance(T, t);
        int u = t;
        while(u != s){
            path_.emplace_back(u);
            u = par[u];
        }
        path_.emplace_back(s);
    }
    
    WeightType Diameter() const {
        return diameter_;
    }
    
    WeightType Height(Vertex v) const {
        return max(dist_s_[v], dist_t_[v]);
    }

    pair<Vertex, Vertex> EndPoints() const {
        return pair<Vertex, Vertex>(path_.front(), path_.back());
    }

    vector<Vertex> &Path(){
        return path_;
    }

    private:
    Graph<WeightType> &T;
    vector<WeightType> dist_s_, dist_t_;
    vector<Vertex> path_;
    WeightType diameter_;
};

Tree Diameter - 木の直径 (Library/Tree/TreeDiameter.hpp)

Tree Diameter - 木の直径

Function

Constructor

Diameter

Height

EndPoints

Path

Depends on

Verified with

Code

Tree Diameter - 木の直径
(Library/Tree/TreeDiameter.hpp)