提升最小生成树，如何做深度优先？

Question

我想使用boost图库中提供的kruskal_minimum_spanning_tree算法构建最小生成树。

的输出

kruskal_minimum_spanning_tree(g, std::back_inserter(spanning_tree));

来自the BGL example的

是一个简单的边列表。但是，我想用深度优先算法处理树，不知道该怎么做。

有人可以给我一个提示吗？

Answer 1

<强>更新： sehe在这里提供了一个更新和更有效的解决方案： https://stackoverflow.com/a/49429372/85371

这是Kruskal问题的解决方案和编写自定义DFS访问者的好例子。它应该按原样运行。示例输出在下面的代码中显示为自包含。正如我在评论中提到的，MST算法的输出是一组边。这将向您展示如何使用该数据构建新图。

来自http://en.wikipedia.org/wiki/Kruskals_algorithm的示例。

任何改进建议都将受到赞赏。感谢。

/**

Kruskal example from http://en.wikipedia.org/wiki/Kruskal's_algorithm

MST followed by DFS

Written by Paul W. Bible

*/
#include <iostream>
#include <vector>

#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/graph_traits.hpp>
#include <boost/graph/depth_first_search.hpp>
#include <boost/graph/kruskal_min_spanning_tree.hpp>

using namespace std;
using namespace boost;

typedef adjacency_list < vecS, vecS, undirectedS,
                    property< vertex_index_t, size_t> ,
                    property< edge_index_t, size_t, property<edge_weight_t,double> > > Graph;

typedef graph_traits<Graph>::vertex_descriptor Vertex;
typedef graph_traits<Graph>::edge_descriptor Edge;

typedef boost::property_map< Graph, boost::vertex_index_t>::type VertexIndexMap;
typedef boost::property_map< Graph, boost::edge_weight_t>::type WeightMap;


//DFS visitor, got help from http://stackoverflow.com/questions/14126/how-to-create-a-c-boost-undirected-graph-and-traverse-it-in-depth-first-search
// and http://www.boost.org/doc/libs/1_55_0/libs/graph/example/dfs-example.cpp
struct MyVis:default_dfs_visitor{
    //Default dfs is templeted to work with any Edge or Graph class
    // you will need to pass external graph info to the class
    MyVis(vector<string> vNames):vertNames(vNames){}

    template < typename Edge, typename Graph >
    void tree_edge(Edge e, const Graph& g) const {
        //This works since all graph verts will have an index
        VertexIndexMap vMap = get(boost::vertex_index,g);
        //print output message, source and target get the edge vertices
        cout << "Edge " << vertNames.at(vMap[source(e,g)]) <<  " " << vertNames.at(vMap[target(e,g)]) << endl;
        //cout << vertNames.size() << endl;
    }

private:
    vector<string> vertNames;
};



int main(int argc, char* argv[]){

    Graph G;

    vector<Vertex> verts;
    vector<Edge> edges;

    /* Vertices
    0   A
    1   B
    2   C
    3   D
    4   E
    5   F
    6   G
    */

    //add 7 vertices
    for(size_t i = 0; i < 7; ++i){
        Vertex v = add_vertex(G);
        verts.push_back(v);
    }

    //vertex to index map, typdef above
    VertexIndexMap vertexIndexMap = get(boost::vertex_index, G);

    vector<string> vertexNames(num_vertices(G));
    // Create the external property map, this map wraps the storage vector vertexNames
    boost::iterator_property_map< std::vector< string >::iterator, VertexIndexMap >
        vertexNameMap(vertexNames.begin(), vertexIndexMap);

    //set names
    vertexNames.at(0) = "A";
    vertexNames.at(1) = "B";
    vertexNames.at(2) = "C";
    vertexNames.at(3) = "D";
    vertexNames.at(4) = "E";
    vertexNames.at(5) = "F";
    vertexNames.at(6) = "G";


    //get internal weight map
    WeightMap weightMap = get(edge_weight,G);

    //Edge 1 A -> B, weight 7
    pair<Edge,bool> myPair = add_edge(verts.at(0),verts.at(1),G);
    edges.push_back(myPair.first);

    weightMap[myPair.first] = 7.0;
    //Edge 2 A -> D, weight 5
    myPair = add_edge(verts.at(0),verts.at(3),G);
    edges.push_back(myPair.first);
    weightMap[myPair.first] = 5.0;


    //Edge 3 B -> C, weight 8
    myPair = add_edge(verts.at(1),verts.at(2),G);
    edges.push_back(myPair.first);
    weightMap[myPair.first] = 8.0;
    //Edge 4 B -> D, weight 9
    myPair = add_edge(verts.at(1),verts.at(3),G);
    edges.push_back(myPair.first);
    weightMap[myPair.first] = 9.0;
    //Edge 5 B -> E, weight 7
    myPair = add_edge(verts.at(1),verts.at(4),G);
    edges.push_back(myPair.first);
    weightMap[myPair.first] = 7.0;

    //Edge 6 C -> E, weight 5
    myPair = add_edge(verts.at(2),verts.at(4),G);
    edges.push_back(myPair.first);
    weightMap[myPair.first] = 5.0;

    //Edge 7 D -> E, weight 15
    myPair = add_edge(verts.at(3),verts.at(4),G);
    edges.push_back(myPair.first);
    weightMap[myPair.first] = 15.0;
    //Edge 8 D -> F, weight 6
    myPair = add_edge(verts.at(3),verts.at(5),G);
    edges.push_back(myPair.first);
    weightMap[myPair.first] = 6.0;

    //Edge 9 E -> F, weight 8
    myPair = add_edge(verts.at(4),verts.at(5),G);
    edges.push_back(myPair.first);
    weightMap[myPair.first] = 8.0;
    //Edge 10 E -> G, weight 9
    myPair = add_edge(verts.at(4),verts.at(6),G);
    edges.push_back(myPair.first);
    weightMap[myPair.first] = 9.0;

    //Edge 11 F -> G, weight 11
    myPair = add_edge(verts.at(5),verts.at(6),G);
    edges.push_back(myPair.first);
    weightMap[myPair.first] = 11.0;


    //output
    cout << "vertices " << num_vertices(G) << endl;
    cout << "edges    " << num_edges(G) << endl;

    //create a stoage vector for MST edges
    vector<Edge> spanning_tree_edges;
    kruskal_minimum_spanning_tree(G, std::back_inserter(spanning_tree_edges));

    cout << "num MST edges " << spanning_tree_edges.size() << endl;


    //create a graph for the MST
    Graph MST;

    //get a weight map for the MST, may be used later
    WeightMap mstWeightMap = get(edge_weight,MST);

    //create a list of original names for the MST graph.
    vector<string> mstNames(num_vertices(G)); //the MST must span all verts in G
    //Index map for verts in MST, all graphs use an indepenent index system.
    VertexIndexMap mstIndexMap = get(boost::vertex_index, MST);

    cout << "MST Edges" << endl;
    for(size_t i = 0; i < spanning_tree_edges.size(); ++i){
        //get the edge
        Edge e = spanning_tree_edges.at(i);
        //get the vertices
        Vertex v1 = source(e,G);
        Vertex v2 = target(e,G);

        // output edge information
        cout << "edge weight " << weightMap[e] << " v1 " << vertexNameMap[v1] << " v2 " << vertexNameMap[v2] << endl;

        //insert the edge to the MST graph
        // Both graphs will share the vertices in verts list.
        myPair = add_edge(v1,v2,MST);

        //set the correct weights
        // may be needed at some point
        Edge mstE = myPair.first;
        mstWeightMap[mstE] = weightMap[e];


        //get the vertex index in the MST and set the name to that of original graph
        // mstNames will be used by the visitor
        mstNames.at(mstIndexMap[v1]) = vertexNameMap[v1];
        mstNames.at(mstIndexMap[v2]) = vertexNameMap[v2];


    }

    //Create your custom visitor and pass names to the visitor
    MyVis vis(mstNames);

    cout << "DFS on MST: start node E" << endl;
    //call dfs, see visitor implimentation above.
    boost::depth_first_search(MST, visitor(vis).root_vertex(verts.at(4)));

    cout << "DFS on MST: start node B" << endl;
    //call dfs, see visitor implimentation above.
    boost::depth_first_search(MST, visitor(vis).root_vertex(verts.at(1)));

    /* output
    vertices 7
    edges    11
    num MST edges 6
    MST Edges
    edge weight 5 v1 A v2 D
    edge weight 5 v1 C v2 E
    edge weight 6 v1 D v2 F
    edge weight 7 v1 B v2 E
    edge weight 7 v1 A v2 B
    edge weight 9 v1 E v2 G
    DFS on MST: start node E
    Edge E C
    Edge E B
    Edge B A
    Edge A D
    Edge D F
    Edge E G
    DFS on MST: start node B
    Edge B E
    Edge E C
    Edge E G
    Edge B A
    Edge A D
    Edge D F

    */

    //hold for output
    cin.get();
}