Tree Diameter
(graph/tree/diameter.hpp)

• View this file on GitHub
• Last update: 2026-08-13 01:41:40+09:00
• Include: #include "graph/tree/diameter.hpp"

Overview

tree_diameter(g) returns a longest path in an undirected tree. It also works on a forest and returns the longest diameter among its connected components.

The input uses m1une::graph::Graph<T> and should be built with add_edge. Inactive edges are ignored.

For weighted trees, edge costs should be non-negative.

Result

TreeDiameter<T> contains:

Member	Description
cost	Sum of edge costs on the diameter path.
edge_count	Number of edges on the restored path.
from, to	Endpoints of the path, or -1 for an empty graph.
vertices	Vertices on the path from from to to.
edge_ids	Edge ids on the path from from to to.
empty()	Returns whether no path vertices exist.

Function

Function	Description	Complexity
tree_diameter(g)	Finds a diameter path.	$O(N)$

Example

#include "graph/graph.hpp"
#include "graph/tree/diameter.hpp"
#include <iostream>

int main() {
    m1une::graph::Graph<int> g(4);
    g.add_edge(0, 1, 2);
    g.add_edge(1, 2, 3);
    g.add_edge(1, 3, 4);

    auto diameter = m1une::tree::tree_diameter(g);
    std::cout << diameter.cost << "\n"; // 7
}

Depends on

• Graph (graph/graph.hpp)

Required by

• Graph All (graph/all.hpp)
• Tree All (graph/tree/all.hpp)
• Tree (graph/tree/tree.hpp)

Verified with

• verify/graph/cow_game.test.cpp
• verify/graph/graph_algorithms.test.cpp
• verify/graph/range_edge_graph.test.cpp
• verify/graph/tree/tree_algorithms.test.cpp
• verify/graph/tree/tree_diameter.test.cpp

Code

#ifndef M1UNE_TREE_DIAMETER_HPP
#define M1UNE_TREE_DIAMETER_HPP 1

#include <algorithm>
#include <vector>

#include "../graph.hpp"

namespace m1une {
namespace tree {

template <class T = int>
struct TreeDiameter {
    T cost;
    int edge_count;
    int from;
    int to;
    std::vector<int> vertices;
    std::vector<int> edge_ids;

    bool empty() const {
        return vertices.empty();
    }
};

namespace internal {

template <class T>
struct FarthestResult {
    int vertex;
    std::vector<char> seen;
    std::vector<T> dist;
    std::vector<int> parent;
    std::vector<int> parent_edge;
};

template <class T>
FarthestResult<T> farthest_from(const m1une::graph::Graph<T>& g, int start) {
    int n = g.size();
    FarthestResult<T> result;
    result.vertex = start;
    result.seen.assign(n, false);
    result.dist.assign(n, T(0));
    result.parent.assign(n, -1);
    result.parent_edge.assign(n, -1);

    std::vector<int> stack = {start};
    result.seen[start] = true;
    while (!stack.empty()) {
        int v = stack.back();
        stack.pop_back();
        if (result.dist[result.vertex] < result.dist[v]) result.vertex = v;
        for (const auto& e : g[v]) {
            if (!e.alive) continue;
            if (result.seen[e.to]) continue;
            result.seen[e.to] = true;
            result.dist[e.to] = result.dist[v] + e.cost;
            result.parent[e.to] = v;
            result.parent_edge[e.to] = e.id;
            stack.push_back(e.to);
        }
    }
    return result;
}

}  // namespace internal

template <class T>
TreeDiameter<T> tree_diameter(const m1une::graph::Graph<T>& g) {
    int n = g.size();
    TreeDiameter<T> best;
    best.cost = T(0);
    best.edge_count = 0;
    best.from = -1;
    best.to = -1;
    if (n == 0) return best;

    std::vector<char> done(n, false);
    for (int start = 0; start < n; start++) {
        if (done[start]) continue;
        auto first = internal::farthest_from(g, start);
        for (int v = 0; v < n; v++) {
            if (first.seen[v]) done[v] = true;
        }
        auto second = internal::farthest_from(g, first.vertex);
        int a = first.vertex;
        int b = second.vertex;
        T cost = second.dist[b];
        if (best.from != -1 && !(best.cost < cost)) continue;

        best.cost = cost;
        best.from = a;
        best.to = b;
        best.vertices.clear();
        best.edge_ids.clear();
        for (int v = b; v != -1; v = second.parent[v]) {
            best.vertices.push_back(v);
            if (v != a) best.edge_ids.push_back(second.parent_edge[v]);
        }
        std::reverse(best.vertices.begin(), best.vertices.end());
        std::reverse(best.edge_ids.begin(), best.edge_ids.end());
        best.edge_count = int(best.edge_ids.size());
    }

    return best;
}

}  // namespace tree
}  // namespace m1une

#endif  // M1UNE_TREE_DIAMETER_HPP

#line 1 "graph/tree/diameter.hpp"



#include <algorithm>
#include <vector>

#line 1 "graph/graph.hpp"



#include <array>
#include <cassert>
#include <utility>
#line 8 "graph/graph.hpp"

namespace m1une {
namespace graph {

template <class T = int>
struct Edge {
    using cost_type = T;

    int from;
    int to;
    T cost;
    int id;
    bool alive;

    Edge() : from(-1), to(-1), cost(T()), id(-1), alive(true) {}
    Edge(int from_, int to_, T cost_ = T(1), int id_ = -1, bool alive_ = true)
        : from(from_), to(to_), cost(cost_), id(id_), alive(alive_) {}

    int other(int v) const {
        assert(v == from || v == to);
        return from ^ to ^ v;
    }
};

template <class T = int>
struct Graph {
    using edge_type = Edge<T>;
    using cost_type = T;

   private:
    struct EdgePositions {
        std::array<std::pair<int, int>, 2> value{};
        int size = 0;

        void push_back(std::pair<int, int> position) {
            assert(size < 2);
            value[size++] = position;
        }
    };

    int _n;
    int _edge_count;
    std::vector<std::vector<edge_type>> _g;
    std::vector<EdgePositions> _edge_positions;

   public:
    Graph() : _n(0), _edge_count(0) {}
    explicit Graph(int n) : _n(n), _edge_count(0), _g(n) {
        assert(0 <= n);
    }

    int size() const {
        return _n;
    }

    bool empty() const {
        return _n == 0;
    }

    int edge_count() const {
        return _edge_count;
    }

    int add_vertex() {
        _g.emplace_back();
        return _n++;
    }

    int add_directed_edge(int from, int to, T cost = T(1)) {
        assert(0 <= from && from < _n);
        assert(0 <= to && to < _n);
        int id = _edge_count++;
        int idx = int(_g[from].size());
        _g[from].push_back(edge_type(from, to, cost, id));
        _edge_positions.emplace_back();
        _edge_positions.back().push_back({from, idx});
        return id;
    }

    int add_edge(int u, int v, T cost = T(1)) {
        assert(0 <= u && u < _n);
        assert(0 <= v && v < _n);
        int id = _edge_count++;
        int u_idx = int(_g[u].size());
        _g[u].push_back(edge_type(u, v, cost, id));
        int v_idx = int(_g[v].size());
        _g[v].push_back(edge_type(v, u, cost, id));
        _edge_positions.emplace_back();
        _edge_positions.back().push_back({u, u_idx});
        _edge_positions.back().push_back({v, v_idx});
        return id;
    }

    void set_edge_alive(int id, bool alive) {
        assert(0 <= id && id < _edge_count);
        for (int i = 0; i < _edge_positions[id].size; ++i) {
            auto [v, idx] = _edge_positions[id].value[i];
            _g[v][idx].alive = alive;
        }
    }

    void erase_edge(int id) {
        set_edge_alive(id, false);
    }

    void revive_edge(int id) {
        set_edge_alive(id, true);
    }

    bool is_edge_alive(int id) const {
        assert(0 <= id && id < _edge_count);
        assert(_edge_positions[id].size != 0);
        auto [v, idx] = _edge_positions[id].value[0];
        return _g[v][idx].alive;
    }

    const std::vector<edge_type>& operator[](int v) const {
        assert(0 <= v && v < _n);
        return _g[v];
    }

    std::vector<edge_type>& operator[](int v) {
        assert(0 <= v && v < _n);
        return _g[v];
    }

    const std::vector<std::vector<edge_type>>& adjacency() const {
        return _g;
    }

    std::vector<std::vector<edge_type>>& adjacency() {
        return _g;
    }

    std::vector<edge_type> edges(bool include_inactive = false) const {
        std::vector<edge_type> result;
        result.reserve(_edge_count);
        std::vector<char> used(_edge_count, false);
        for (int v = 0; v < _n; v++) {
            for (const auto& e : _g[v]) {
                if (!include_inactive && !e.alive) continue;
                if (0 <= e.id && e.id < _edge_count) {
                    if (used[e.id]) continue;
                    used[e.id] = true;
                }
                result.push_back(e);
            }
        }
        return result;
    }

    Graph reversed() const {
        Graph result(_n);
        result._edge_count = _edge_count;
        result._edge_positions.assign(_edge_count, {});
        for (int v = 0; v < _n; v++) {
            for (const auto& e : _g[v]) {
                int idx = int(result._g[e.to].size());
                result._g[e.to].push_back(edge_type(e.to, e.from, e.cost, e.id, e.alive));
                if (0 <= e.id && e.id < _edge_count) result._edge_positions[e.id].push_back({e.to, idx});
            }
        }
        return result;
    }
};

}  // namespace graph
}  // namespace m1une


#line 8 "graph/tree/diameter.hpp"

namespace m1une {
namespace tree {

template <class T = int>
struct TreeDiameter {
    T cost;
    int edge_count;
    int from;
    int to;
    std::vector<int> vertices;
    std::vector<int> edge_ids;

    bool empty() const {
        return vertices.empty();
    }
};

namespace internal {

template <class T>
struct FarthestResult {
    int vertex;
    std::vector<char> seen;
    std::vector<T> dist;
    std::vector<int> parent;
    std::vector<int> parent_edge;
};

template <class T>
FarthestResult<T> farthest_from(const m1une::graph::Graph<T>& g, int start) {
    int n = g.size();
    FarthestResult<T> result;
    result.vertex = start;
    result.seen.assign(n, false);
    result.dist.assign(n, T(0));
    result.parent.assign(n, -1);
    result.parent_edge.assign(n, -1);

    std::vector<int> stack = {start};
    result.seen[start] = true;
    while (!stack.empty()) {
        int v = stack.back();
        stack.pop_back();
        if (result.dist[result.vertex] < result.dist[v]) result.vertex = v;
        for (const auto& e : g[v]) {
            if (!e.alive) continue;
            if (result.seen[e.to]) continue;
            result.seen[e.to] = true;
            result.dist[e.to] = result.dist[v] + e.cost;
            result.parent[e.to] = v;
            result.parent_edge[e.to] = e.id;
            stack.push_back(e.to);
        }
    }
    return result;
}

}  // namespace internal

template <class T>
TreeDiameter<T> tree_diameter(const m1une::graph::Graph<T>& g) {
    int n = g.size();
    TreeDiameter<T> best;
    best.cost = T(0);
    best.edge_count = 0;
    best.from = -1;
    best.to = -1;
    if (n == 0) return best;

    std::vector<char> done(n, false);
    for (int start = 0; start < n; start++) {
        if (done[start]) continue;
        auto first = internal::farthest_from(g, start);
        for (int v = 0; v < n; v++) {
            if (first.seen[v]) done[v] = true;
        }
        auto second = internal::farthest_from(g, first.vertex);
        int a = first.vertex;
        int b = second.vertex;
        T cost = second.dist[b];
        if (best.from != -1 && !(best.cost < cost)) continue;

        best.cost = cost;
        best.from = a;
        best.to = b;
        best.vertices.clear();
        best.edge_ids.clear();
        for (int v = b; v != -1; v = second.parent[v]) {
            best.vertices.push_back(v);
            if (v != a) best.edge_ids.push_back(second.parent_edge[v]);
        }
        std::reverse(best.vertices.begin(), best.vertices.end());
        std::reverse(best.edge_ids.begin(), best.edge_ids.end());
        best.edge_count = int(best.edge_ids.size());
    }

    return best;
}

}  // namespace tree
}  // namespace m1une

Back to top page