無向グラフ
(library/data-structure/graph.hpp)

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• Last update: 2025-03-03 00:33:48+09:00
• Include: #include "library/data-structure/graph.hpp"

無向グラフ

無向グラフを扱う。

使い方

• コンストラクタ graph(n): $n$ 頂点の無向グラフを構築する。 $O(n)$
• add_edge(v1, v2) : 頂点 v1 ・頂点 v2 間の辺を追加する。 $O(1)$
• get_edge(i) : 辺 i の情報を取得する。 $O(1)$
• get_adj(i) : 頂点 i の隣接リスト (頂点番号, 辺番号) を取得する。 $O(1)$?

実装は別ファイル

• cycle(): サイクル検出
• is_connected(): 連結判定
• eulerian_walk(): オイラー路

Depends on

• library/_internal/graph-base.hpp

Required by

• library/_internal/graph/connection.hpp
• library/_internal/graph/cycle.hpp
• library/_internal/graph/eulerian-walk.hpp
• 有向グラフ (library/data-structure/digraph.hpp)
• 連結判定 (library/graph/connection.hpp)
• サイクル検出 (library/graph/cycle.hpp)
• オイラー路 (library/graph/eulerian-walk.hpp)
• SCC (Strongly Connected Components) (library/graph/scc.hpp)

Verified with

• tests/graph/cycle/libchecker-directed.test.cpp
• tests/graph/cycle/libchecker-undirected.test.cpp
• tests/graph/eulerian-walk/libchecker-directed.test.cpp
• tests/graph/eulerian-walk/libchecker-undirected.test.cpp
• tests/graph/scc/abc256-e.test.cpp
• tests/graph/scc/abc296-e.test.cpp
• tests/graph/scc/libchecker.test.cpp

Code

#pragma once

#include <cassert>
#include <optional>
#include <vector>
using namespace std;

#include "../_internal/graph-base.hpp"

namespace asalib {
  namespace graph {
    class graph: public _internal::notweighted_graph_base {
      public:
      graph(): n_vertex(0), n_edge(0) {}
      explicit graph(size_t n_vertex): n_vertex(n_vertex), n_edge(0) {
        adj_list.reserve(n_vertex);
        adj_list.resize(n_vertex);
      }

      void add_edge(size_t v1, size_t v2) {
        assert(0 <= v1 && v1 < n_vertex);
        assert(0 <= v2 && v2 < n_vertex);
        adj_list[v1].push_back({ v2, n_edge });
        adj_list[v2].push_back({ v1, n_edge });
        edge_list.push_back({ v1, v2 });
        ++n_edge;
      }

      // (v1, v2)
      pair<size_t, size_t> get_edge(size_t edgeId) const {
        assert(0 <= edgeId && edgeId < n_edge);
        return edge_list[edgeId];
      }

      // (v2, edgeId)
      vector<pair<size_t, size_t>> get_adj(size_t vertex) const {
        assert(0 <= vertex && vertex < n_vertex);
        return adj_list[vertex];
      }

      // ---------- prototype ---------- //
      optional<pair<vector<size_t>, vector<size_t>>> cycle() const;
      bool is_connected() const;
      optional<pair<vector<size_t>, vector<size_t>>> eulerian_walk() const;

      private:
      size_t n_vertex, n_edge;
      asalib::_internal::adjlist_t adj_list;
      asalib::_internal::edgelist_t edge_list;
    };
  }  // namespace graph
}  // namespace asalib

#line 2 "library/data-structure/graph.hpp"

#include <cassert>
#include <optional>
#include <vector>
using namespace std;

#line 2 "library/_internal/graph-base.hpp"

#include <concepts>
#include <type_traits>
using namespace std;

namespace asalib {
  namespace _internal {
    class graph_base {};
    class notweighted_graph_base: public graph_base {};
    class weighted_graph_base: public graph_base {};

    template<typename T>
    concept is_graph = is_base_of_v<graph_base, T>;

    template<typename T>
    concept notweighted_graph = is_base_of_v<notweighted_graph_base, T>;

    template<typename T>
    concept weighted_graph = is_base_of_v<weighted_graph_base, T>;

    using adjlist_t = vector<vector<pair<size_t, size_t>>>;
    using edgelist_t = vector<pair<size_t, size_t>>;
  }  // namespace _internal
}  // namespace asalib
#line 9 "library/data-structure/graph.hpp"

namespace asalib {
  namespace graph {
    class graph: public _internal::notweighted_graph_base {
      public:
      graph(): n_vertex(0), n_edge(0) {}
      explicit graph(size_t n_vertex): n_vertex(n_vertex), n_edge(0) {
        adj_list.reserve(n_vertex);
        adj_list.resize(n_vertex);
      }

      void add_edge(size_t v1, size_t v2) {
        assert(0 <= v1 && v1 < n_vertex);
        assert(0 <= v2 && v2 < n_vertex);
        adj_list[v1].push_back({ v2, n_edge });
        adj_list[v2].push_back({ v1, n_edge });
        edge_list.push_back({ v1, v2 });
        ++n_edge;
      }

      // (v1, v2)
      pair<size_t, size_t> get_edge(size_t edgeId) const {
        assert(0 <= edgeId && edgeId < n_edge);
        return edge_list[edgeId];
      }

      // (v2, edgeId)
      vector<pair<size_t, size_t>> get_adj(size_t vertex) const {
        assert(0 <= vertex && vertex < n_vertex);
        return adj_list[vertex];
      }

      // ---------- prototype ---------- //
      optional<pair<vector<size_t>, vector<size_t>>> cycle() const;
      bool is_connected() const;
      optional<pair<vector<size_t>, vector<size_t>>> eulerian_walk() const;

      private:
      size_t n_vertex, n_edge;
      asalib::_internal::adjlist_t adj_list;
      asalib::_internal::edgelist_t edge_list;
    };
  }  // namespace graph
}  // namespace asalib

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