Tree Diameter (木の直径)
(graph/tree_diameter.hpp)

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• Last update: 2024-01-25 10:46:02+09:00
• Include: #include "graph/tree_diameter.hpp"

• auto [d, path] = tree_diameter(G); で d に直径の長さが、path に辺の集合が入る

Depends on

• graph/graph_template.hpp

Verified with

• verify/lc_tree/lc_tree_diameter.test.cpp

Code

#pragma once

#include "graph/graph_template.hpp"

template <class T> std::pair<T, std::vector<Edge<T>>> tree_diameter(Graph<T> &G) {
    std::vector<int> to(G.size(), -1);

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

    auto s = dfs(dfs, 0, -1);
    auto t = dfs(dfs, s.second, -1);

    int cur = s.second;
    std::vector<Edge<T>> path;
    while (cur != t.second) {
        for (auto &e : G[cur]) {
            if (to[cur] == e.to) {
                path.emplace_back(e);
            }
        }
        cur = to[cur];
    }
    return {t.first, path};
}

#line 2 "graph/tree_diameter.hpp"

#line 2 "graph/graph_template.hpp"

#include <vector>
template <class T> struct Edge {
    int from, to;
    T cost;
    int id;

    Edge() = default;
    Edge(int from, int to, T cost = 1, int id = -1) : from(from), to(to), cost(cost), id(id) {}

    friend std::ostream &operator<<(std::ostream &os, const Edge<T> &e) {
        // output format: "{ id : from -> to, cost }"
        return os << "{ " << e.id << " : " << e.from << " -> " << e.to << ", " << e.cost << " }";
    }
};

template <class T> using Edges = std::vector<Edge<T>>;
template <class T> using Graph = std::vector<std::vector<Edge<T>>>;
#line 4 "graph/tree_diameter.hpp"

template <class T> std::pair<T, std::vector<Edge<T>>> tree_diameter(Graph<T> &G) {
    std::vector<int> to(G.size(), -1);

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

    auto s = dfs(dfs, 0, -1);
    auto t = dfs(dfs, s.second, -1);

    int cur = s.second;
    std::vector<Edge<T>> path;
    while (cur != t.second) {
        for (auto &e : G[cur]) {
            if (to[cur] == e.to) {
                path.emplace_back(e);
            }
        }
        cur = to[cur];
    }
    return {t.first, path};
}

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