c++ - 在 C++ 中实现图形的想法

Question

我需要帮助来设计图形的最佳数据结构。以下是我的实现。请就此设计发表您的看法。

#ifndef _GRAPH_H_
#define _GRAPH_H_

#include <map>
#include <vector>
#include <iostream>
#include <list>

template <typename T>
class Vertex {
public:
      Vertex(){};
      Vertex(T inVertex): m_vertex(inVertex), m_visited(false){}
      ~Vertex(){}
      bool operator<(const Vertex<T>& right) const { return m_vertex < right.m_vertex;}

      T getVertex  () { return m_vertex;}
      T getVisited () { return m_visited;}
      T getParent  () { return m_vertexParentVisited;}
      void setVisited(bool inVisited)  { m_visited = inVisited;}
      void setParent(T inParentVertex) { m_vertexParentVisited = inParentVertex;}

private:
      T m_vertex;
      T m_vertexParentVisited;
      bool m_visited;
};

template <typename T>
class Edge
{
public:
    enum EDGE_TYPE
    {
        TREE_EDGE,
        PARENT_EDGE,
        BACK_EDGE,
        DOWN_EDGE
    };
    Edge(Vertex<T>* inSrc, Vertex<T>* inDst)
    {
        m_SourceVertex = inSrc;
        m_DestVertex   = inDst;
    }
    void SetEdgeType( EDGE_TYPE t)
    {
        m_EdgeType = t;
    }
private:
    Vertex<T>* m_SourceVertex;
    Vertex<T>* m_DestVertex;
    EDGE_TYPE  m_EdgeType;
protected:
};

template <typename T>
class Graph
{
public:
      typedef Vertex<T>                             GraphVertex;
      // Adjancency List Datastructure and Iterator declaration.
      // Use STL List here
      typedef std::list<GraphVertex*>               AdjList;
      typedef typename AdjList::iterator            AdjListIterator;
      // Graph Data structure declaration and Iterator declaration
      // Graph is map of GraphVertex* and List of adjacency list.
      typedef std::map<GraphVertex*, AdjList>       GraphMap;
      typedef typename GraphMap::iterator           GraphIterator;
      // Graph Memory pool is map where actual memory allocation 
      // will happen.
      // Make sure you have some way to identify each vertex.
      // Map key is the identification method of the vertex.
      // Map value is the pointer to actual object.
      typedef std::map<T,GraphVertex*>              GraphMemoryPool;
      typedef typename GraphMemoryPool::iterator    GraphInMemoryIterator;
      // Edge Class Declaration.
      typedef std::vector<Edge<T> >                 GraphEdge;

private:          
      bool               m_isDirected;
      GraphMap           m_graph;
      GraphMemoryPool    m_graphMemoryPool;
      std::vector<T>     m_SearchOrderVector;
      GraphEdge          m_GraphEdge;
public:
      Graph(bool inIsDirected):m_isDirected(inIsDirected) {}
      ~Graph()
      {
            for ( GraphInMemoryIterator itr = m_graphMemoryPool.begin(); itr != m_graphMemoryPool.end(); ++itr)
            {
                  if ( itr->second) delete itr->second;
            }
            m_graphMemoryPool.clear();
            m_graph.clear();
      }
      void insert(T inSRC, T inDST) 
      {
            if ( m_isDirected) 
            {
                  __insert(inSRC,inDST);
            }
            else 
            {
                  __insert(inSRC,inDST);
                  __insert(inDST,inSRC);
            }
      }
      void printGraph()
      {
            for ( GraphIterator itr = m_graph.begin(); itr != m_graph.end(); ++itr) 
            {
                  std::cout << static_cast<GraphVertex*>(itr->first)->getVertex() << " : ";
                  AdjList tmp = static_cast<AdjList>(itr->second);
                  for ( AdjListIterator itr1 = tmp.begin(); itr1 != tmp.end(); ++itr1) 
                  {
                        std::cout << (*itr1)->getVertex() << " ";
                  }
                  std::cout << std::endl;
            }
      }
      void printSearchOrder()
      {
            std::vector<T> tmp = getSearchOrderVector();
            for ( vector<T>::iterator itr = tmp.begin(); itr != tmp.end(); ++itr)
            {
                std::cout << *itr << " ";
            }
            std::cout << std::endl;

      }
      void printParentLinkMap()
      {
          std::vector<T> tmp = getSearchOrderVector();
          for ( vector<T>::iterator itr = tmp.begin(); itr != tmp.end(); ++itr)
          {
                GraphVertex *tmp = __VertexInstance(*itr);
                std::cout << "[" << tmp->getParent() << "]  Parent Of [" << tmp->getVertex() << "]" << std::endl;
          }
      }
      void DFS()
      {
            for ( GraphInMemoryIterator itr = m_graphMemoryPool.begin(); itr != m_graphMemoryPool.end(); ++itr)
            {
                  (*itr).second->setVisited(false);
            }
            m_SearchOrderVector.clear();
            // This loop handles the case when the grpah is not
            // Connected.
            for ( GraphIterator itr = m_graph.begin(); itr != m_graph.end(); ++itr) 
            {
                GraphVertex *currentVertex = static_cast<GraphVertex*>(itr->first);
                if ( currentVertex->getVisited() == false) 
                {
                    T curVertex = currentVertex->getVertex();
                    // Insert new element in Search Order Vector.
                    m_SearchOrderVector.push_back(curVertex);
                    // Set the parent of this root node in the DFS search tree
                    currentVertex->setParent(curVertex);
                    // Create Edge with itself here.
                    __setTypeAndInsertNewEdge( curVertex, 
                                               curVertex,
                                               Edge<T>::TREE_EDGE);
                    // Mark the vertex as visited.
                    currentVertex->setVisited(true);
                    __rundfs(itr);
                }
            }
      }
    std::vector<T> getSearchOrderVector() { return m_SearchOrderVector;}
    int getNumberOfVertex(){ return (int)m_graph.size();}
private:
    void __setTypeAndInsertNewEdge( T inSRC, T inDST, typename Edge<T>::EDGE_TYPE t )
    {
        Edge<T> tmp(__VertexInstance(inSRC), 
                    __VertexInstance(inDST));
        tmp.SetEdgeType(t);
        m_GraphEdge.push_back(tmp);
    }
    // Recursive DFS function.
    // Apart from visiting vertices 
    // this implementatioin will be doing following.
    // 1. Maintain the order in which vertices are visited.   
    // 2. Update Parent link map
    // 3. Create Edge and update the type of the edge.
    void __rundfs( typename GraphMap::iterator &itr) 
    {
        for (AdjListIterator itr1 = itr->second.begin(); itr1 != itr->second.end(); ++itr1) 
        {
            GraphVertex *childVertex = (*itr1);
            GraphVertex *parentVertex = itr->first;
            if ( childVertex->getVisited() == false) 
            {
                m_SearchOrderVector.push_back(childVertex->getVertex()); // Update the search order Vector.
                childVertex->setParent(parentVertex->getVertex());         // Update the parent-link map.
                childVertex->setVisited(true);                           // Mark the vertex as visited.
                __setTypeAndInsertNewEdge(parentVertex->getVertex(),
                                          childVertex->getVertex(),
                                          Edge<T>::TREE_EDGE); // setup the edge type 
                __rundfs(m_graph.find(
                        __VertexInstance(childVertex->getVertex())));
            }     
            else
            {
                if ( childVertex->getVertex() == parentVertex->getVertex())
                {
                }
            }
        }
    }
    void __insert(T inSRC, T inDST) 
    {
        GraphIterator itr = m_graph.find(__VertexInstance(inSRC));
        if ( itr != m_graph.end()) 
        {
            // Update the Adjancency list 
            itr->second.push_back(__VertexInstance(inDST));
        }
        else 
        {
            // Create new Adjancy list
            m_graph.insert(std::make_pair(__VertexInstance(inSRC),AdjList() ));
            GraphIterator itr = m_graph.find(__VertexInstance(inSRC));
            // Update the Adjacency List
            itr->second.push_back(__VertexInstance(inDST));
        }
    }
    // Searches if the Vertex is already allocated in the pool map
    // If ye return the pointer from the map.
    // Else Create new Vertex instance
    // Insert into the memory pool map
    // Return the pointer.
    GraphVertex *__VertexInstance(T inVertex) 
    {
        GraphVertex *newVertex    = (GraphVertex *)0;
        GraphInMemoryIterator itr = m_graphMemoryPool.find(inVertex);
        if ( itr == m_graphMemoryPool.end()) 
        {
            newVertex = new GraphVertex(inVertex);
            m_graphMemoryPool.insert(std::make_pair(inVertex,newVertex));
        }
        else 
        {
            newVertex = ( GraphVertex *)itr->second;
        }           
        return newVertex;
    }
};
#endif

Answer 1

看来你知道这一点，但我正在审查以使所有人受益:

有两种典型的图实现方式:边矩阵和稀疏矩阵(表示为每个顶点的边 vector )。

矩阵是一个 NxN 结构，其中 N 是顶点数。每个数据是两个顶点之间的边长，因此 G[1][2] 是从 1 到 2 的距离。这也允许有向图。

另一种更适合稀疏图的方法是为每个顶点设置一个边 vector 。所以你会得到 vector> g，其中 g[1] 是顶点 1 的边 vector 。该 vector 中的每个项目都是 edge，其中包含它到达的顶点和距离。

有关更多详细信息，请访问此处:http://en.wikipedia.org/wiki/Graph_(data_structure)#Representations

鉴于所有这些，其中一种实现可能对您非常有用。

编辑1

为了在图中存储权重，on 可能会使用诸如 vector> 之类的结构(如上所述)。在这种情况下，边缘类可能是这样的:

class edge {
  int weight;
  int destination_vertex;
};

这样，从1到2的边就是g[1][2]。