Store μ,φ,ρ in nodes

Also, add simple property checkers whether nodes are
inner/outer/out-of-forest.

graph.cpp

@@ -178,4 +178,22 @@ std::ostream & operator<<(std::ostream & output, Graph const & graph)
    return output;
 }
 
+bool Graph::is_outer(NodeId const id) const {
+   return matched_neighbor(id) == id or \
+   ear_or_root_neighbor(matched_neighbor(id)) != matched_neighbor(id);
+}
+
+bool Graph::is_inner(NodeId const id) const
+{
+   return ear_or_root_neighbor(id) != id and \
+   ear_or_root_neighbor(matched_neighbor(id)) == matched_neighbor(id);
+}
+
+bool Graph::is_out_of_forest(const ED::NodeId id) const
+{
+   return matched_neighbor(id) != id and \
+   ear_or_root_neighbor(id) == id and \
+   ear_or_root_neighbor(matched_neighbor(id)) == matched_neighbor(id);
+}
+
 } // namespace ED

graph.hpp

@@ -69,6 +69,7 @@ using size_type = uint32_t;
  * Note the same Id may be used by different graphs though!
  */
 using NodeId = size_type;
+constexpr NodeId invalid_node_id = std::numeric_limits<NodeId>::max();
 
 /**
    @class Node
@@ -103,6 +104,9 @@ private:
    void add_neighbor(NodeId const id);
 
    std::vector<NodeId> _neighbors;
+   NodeId _matched_neighbor {invalid_node_id};
+   NodeId _ear_or_root_neighbor {invalid_node_id};
+   NodeId _root_of_ear_component {invalid_node_id};
 }; // class Node
 
 /**
@@ -159,6 +163,18 @@ public:
      @brief Prints the graph to the given ostream in DIMACS format.
    **/
    friend std::ostream & operator<<(std::ostream & str, Graph const & graph);
+
+   NodeId matched_neighbor(NodeId const id) const;
+
+   NodeId ear_or_root_neighbor(NodeId const id) const;
+
+   NodeId root_of_ear_component(NodeId const id) const;
+
+   bool is_outer(NodeId const id) const;
+
+   bool is_inner(NodeId const id) const;
+
+   bool is_out_of_forest(NodeId const id) const;
 private:
    std::vector<Node> _nodes;
    size_type _num_edges;
@@ -206,6 +222,25 @@ Node const & Graph::node(NodeId const id) const
 }
 //END: Inline section
 
+
+inline
+NodeId Graph::matched_neighbor(NodeId const id) const
+{
+   return _nodes[id]._matched_neighbor;
+}
+
+inline
+NodeId Graph::ear_or_root_neighbor(const ED::NodeId id) const
+{
+   return _nodes[id]._ear_or_root_neighbor;
+}
+
+inline
+NodeId Graph::root_of_ear_component(const ED::NodeId id) const
+{
+   return _nodes[id]._root_of_ear_component;
+}
+
 } // namespace ED
 
 #endif /* GRAPH_HPP */