Euler Tour (オイラーツアー)
(graph/euler_tour.hpp)

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

使用例

• ABC294 G

Depends on

• graph/graph_template.hpp

Code

#pragma once

#include "graph/graph_template.hpp"

// Euler Tour
// complexity: O(N + M)
// N = 5
// edges = [{0, 1}, {0, 2}, {2, 3}, {2, 4}]
//   0
//  / \
// 1   2
//    / \
//   3   4
// vertices = [0, 1, 0, 2, 3, 2, 4, 2, 0]
// vertex_id = [{0, 8}, {1, 1}, {3, 7}, {4, 4}, {6, 6}]
// edges = [0, 0+N, 1, 2, 2+N, 3, 3+N, 1+N]
// edge_id = [{0, 1}, {2, 7}, {3, 4}, {5, 6}]
// edges[vertex_id[i].first, vertex_id[i].second) = edges in subtree with root i
template <class T>
std::tuple<std::vector<int>, std::vector<std::pair<int, int>>, std::vector<int>, std::vector<std::pair<int, int>>>  //
euler_tour(Graph<T> &G, int root = 0) {
    // compiler bugs
    // const int n = (int)G.size();
    // fix
    int n = (int)G.size();
    std::vector<int> vertices, edges;
    std::vector<std::pair<int, int>> vertex_id(n), edge_id(n - 1);
    vertices.reserve(2 * n - 1);
    edges.reserve(2 * (n - 1));

    auto dfs = [&](auto f, int cur, int par) -> void {
        vertex_id[cur].first = (int)vertices.size();
        vertices.push_back(cur);
        for (auto &&e : G[cur]) {
            if (e.to == par) continue;
            edge_id[e.id].first = (int)edges.size();
            edges.push_back(e.id);

            f(f, e.to, cur);
            vertices.push_back(cur);

            edge_id[e.id].second = (int)edges.size();
            edges.push_back(e.id + n);
        }
        vertex_id[cur].second = (int)vertices.size() - 1;
    };
    dfs(dfs, root, -1);

    assert((int)vertices.size() == 2 * n - 1);
    assert((int)edges.size() == 2 * (n - 1));
    return {vertices, vertex_id, edges, edge_id};
}

#line 2 "graph/euler_tour.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/euler_tour.hpp"

// Euler Tour
// complexity: O(N + M)
// N = 5
// edges = [{0, 1}, {0, 2}, {2, 3}, {2, 4}]
//   0
//  / \
// 1   2
//    / \
//   3   4
// vertices = [0, 1, 0, 2, 3, 2, 4, 2, 0]
// vertex_id = [{0, 8}, {1, 1}, {3, 7}, {4, 4}, {6, 6}]
// edges = [0, 0+N, 1, 2, 2+N, 3, 3+N, 1+N]
// edge_id = [{0, 1}, {2, 7}, {3, 4}, {5, 6}]
// edges[vertex_id[i].first, vertex_id[i].second) = edges in subtree with root i
template <class T>
std::tuple<std::vector<int>, std::vector<std::pair<int, int>>, std::vector<int>, std::vector<std::pair<int, int>>>  //
euler_tour(Graph<T> &G, int root = 0) {
    // compiler bugs
    // const int n = (int)G.size();
    // fix
    int n = (int)G.size();
    std::vector<int> vertices, edges;
    std::vector<std::pair<int, int>> vertex_id(n), edge_id(n - 1);
    vertices.reserve(2 * n - 1);
    edges.reserve(2 * (n - 1));

    auto dfs = [&](auto f, int cur, int par) -> void {
        vertex_id[cur].first = (int)vertices.size();
        vertices.push_back(cur);
        for (auto &&e : G[cur]) {
            if (e.to == par) continue;
            edge_id[e.id].first = (int)edges.size();
            edges.push_back(e.id);

            f(f, e.to, cur);
            vertices.push_back(cur);

            edge_id[e.id].second = (int)edges.size();
            edges.push_back(e.id + n);
        }
        vertex_id[cur].second = (int)vertices.size() - 1;
    };
    dfs(dfs, root, -1);

    assert((int)vertices.size() == 2 * n - 1);
    assert((int)edges.size() == 2 * (n - 1));
    return {vertices, vertex_id, edges, edge_id};
}

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