サイクル検出
(library/graph/cycle.hpp)

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

サイクル検出

辺素なサイクルを 1 つ検出する。

見つかった場合、 (頂点 index リスト, 辺 index リスト) を返す。なければ nullopt を返す。

リストの長さを $L$ とすると、 $v_0 \to v_1 \to \cdots \to v_{L-1} \to v_0$ がサイクルになる。 $e_i$ は $v_{i} \to v_{i+1}$ を表す。頂点 index リストと辺 index リストの長さは等しい。

$O(n + m)$

digraph.cycle() -> optional<pair<vector<size_t>, vector<size_t>>>
graph.cycle() -> optional<pair<vector<size_t>, vector<size_t>>>

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#pragma once

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

#include "../_internal/graph/cycle.hpp"
#include "../data-structure/digraph.hpp"
#include "../data-structure/graph.hpp"

namespace asalib {
  namespace graph {
    optional<pair<vector<size_t>, vector<size_t>>> digraph::cycle() const { return _internal::graph::cycleDetection<true>(n_vertex, n_edge, adj_list, edge_list); }
    optional<pair<vector<size_t>, vector<size_t>>> graph::cycle() const { return _internal::graph::cycleDetection<false>(n_vertex, n_edge, adj_list, edge_list); }
  }  // namespace graph
}  // namespace asalib

#line 2 "library/graph/cycle.hpp"

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

#line 2 "library/_internal/graph/cycle.hpp"

#include <cassert>
#line 6 "library/_internal/graph/cycle.hpp"
#include <stack>
#include <utility>
#line 9 "library/_internal/graph/cycle.hpp"
using namespace std;

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

#line 6 "library/data-structure/graph.hpp"
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
#line 12 "library/_internal/graph/cycle.hpp"

namespace asalib {
  namespace _internal {
    namespace graph {
      template<bool is_directed>
      optional<pair<vector<size_t>, vector<size_t>>> cycleDetection(const size_t& n_vertex, const size_t& n_edge, const adjlist_t& adj_list, const edgelist_t& edge_list) {
        vector<bool> visited(n_vertex, false);
        vector<bool> finished(n_vertex, false);
        vector<bool> used(n_edge, false);
        stack<size_t> st;
        size_t base_point = -1;

        function<bool(size_t)> dfs = [&](size_t v) -> bool {
          visited[v] = true;
          for (auto [to, edge_id] : adj_list[v]) {
            if (used[edge_id]) continue;
            used[edge_id] = true;
            st.push(edge_id);
            if (!finished[to] && visited[to]) {
              base_point = to;
              return true;
            }
            if (!visited[to] && dfs(to)) return true;
            st.pop();
            used[edge_id] = false;
          }
          finished[v] = true;
          return false;
        };

        for (size_t i = 0; i < n_vertex; ++i) {
          if (!visited[i]) {
            if (dfs(i)) {
              size_t v = base_point;
              vector<size_t> edges, verts;
              while (!st.empty()) {
                size_t edge_id = st.top();
                st.pop();
                edges.push_back(edge_id);
                if constexpr (is_directed) {
                  assert(edge_list[edge_id].second == v);
                  v = edge_list[edge_id].first;
                }
                else {
                  assert(edge_list[edge_id].first == v || edge_list[edge_id].second == v);
                  v = (edge_list[edge_id].first == v ? edge_list[edge_id].second : edge_list[edge_id].first);
                }
                verts.push_back(v);
                if (v == base_point) break;
              }
              reverse(verts.begin(), verts.end());
              reverse(edges.begin(), edges.end());
              assert(verts.size() == edges.size());
              assert(verts[0] == base_point);
              return make_pair(verts, edges);
            }
          }
        }
        return nullopt;
      }
    }  // namespace graph
  }  // namespace _internal
}  // namespace asalib
#line 2 "library/data-structure/digraph.hpp"

#line 6 "library/data-structure/digraph.hpp"
using namespace std;

#line 10 "library/data-structure/digraph.hpp"

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

      void add_edge(size_t from, size_t to) {
        assert(0 <= from && from < n_vertex);
        assert(0 <= to && to < n_vertex);
        adj_list[from].push_back({ to, n_edge });
        adj_list_rev[to].push_back({ from, n_edge });
        edge_list.push_back({ from, to });
        underlying_graph.add_edge(from, to);
        ++n_edge;
      }

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

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

      // (from, edgeId)
      vector<pair<size_t, size_t>> get_adjrev(size_t vertex) const {
        assert(0 <= vertex && vertex < n_vertex);
        return adj_list_rev[vertex];
      }

      // ---------- prototype ---------- //
      vector<vector<size_t>> scc() const;
      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, adj_list_rev;
      asalib::_internal::edgelist_t edge_list;
      graph underlying_graph;
    };
  }  // namespace graph
}  // namespace asalib
#line 11 "library/graph/cycle.hpp"

namespace asalib {
  namespace graph {
    optional<pair<vector<size_t>, vector<size_t>>> digraph::cycle() const { return _internal::graph::cycleDetection<true>(n_vertex, n_edge, adj_list, edge_list); }
    optional<pair<vector<size_t>, vector<size_t>>> graph::cycle() const { return _internal::graph::cycleDetection<false>(n_vertex, n_edge, adj_list, edge_list); }
  }  // namespace graph
}  // namespace asalib

サイクル検出 (library/graph/cycle.hpp)

サイクル検出

Depends on

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サイクル検出
(library/graph/cycle.hpp)