单源最短路径算法dijkstra_dijistra using boost adjacency list

boost库中最短单源路径算法，主要是 dijkstra_shortest_paths函数。

输入数据:
 

{
  "start": "A",
  "end": "D",
  "edge_list": [ 
   ["A", "C"],
   ["B", "B"],
   ["B", "D"],
   ["B", "E"],
   ["C", "B"],
   ["C", "D"],
   ["D", "E"],
   ["E", "A"],
   ["E", "B"]
   ],
  "weight_list": [
   1, 2, 1, 2, 7, 3, 1, 1, 1
   ]  
}

其中 start是 起点A，end是终点D,  然后 到各个点的权重是 weight_list.

输出为: 其中 path是 A->D的最短路径和权重， parent是 对应的父路径和权重。

{
  "parent": [
    [ "A", "A", 0.0 ],
    [ "B", "E", 6.0 ],
    [ "C", "A", 1.0 ],
    [ "D", "C", 4.0 ],
    [ "E", "D", 5.0 ]
  ],
  "path": [
    [ "A", 0.0 ],
    [ "C", 1.0 ],
    [ "D", 3.0 ]
  ]
}

可视化算法为:

 boost库代码的demo如下:

#include <boost/config.hpp>
#include <iostream>
#include <fstream>
 
#include <boost/graph/graph_traits.hpp>
#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/dijkstra_shortest_paths.hpp>
 
using namespace boost;
 
int main(int, char*[])
{
    typedef adjacency_list_traits< listS, listS, directedS >::vertex_descriptor
        vertex_descriptor;
    typedef adjacency_list< listS, listS, directedS,
        property< vertex_index_t, int,
            property< vertex_name_t, char,
                property< vertex_distance_t, int,
                    property< vertex_predecessor_t, vertex_descriptor > > > >,
        property< edge_weight_t, int > >
        graph_t;
    typedef std::pair< int, int > Edge;
 
    const int num_nodes = 5;
    enum nodes
    {
        A,
        B,
        C,
        D,
        E
    };
    Edge edge_array[] = { Edge(A, C), Edge(B, B), Edge(B, D), Edge(B, E),
        Edge(C, B), Edge(C, D), Edge(D, E), Edge(E, A), Edge(E, B) };
    int weights[] = { 1, 2, 1, 2, 7, 3, 1, 1, 1 };
    int num_arcs = sizeof(edge_array) / sizeof(Edge);
    graph_traits< graph_t >::vertex_iterator i, iend;
 
    graph_t g(edge_array, edge_array + num_arcs, weights, num_nodes);
    property_map< graph_t, edge_weight_t >::type weightmap
        = get(edge_weight, g);
 
    // Manually intialize the vertex index and name maps
    property_map< graph_t, vertex_index_t >::type indexmap
        = get(vertex_index, g);
    property_map< graph_t, vertex_name_t >::type name = get(vertex_name, g);
    int c = 0;
    for (boost::tie(i, iend) = vertices(g); i != iend; ++i, ++c)
    {
        indexmap[*i] = c;
        name[*i] = 'A' + c;
    }
 
    vertex_descriptor s = vertex(A, g);
 
    property_map< graph_t, vertex_distance_t >::type d
        = get(vertex_distance, g);
    property_map< graph_t, vertex_predecessor_t >::type p
        = get(vertex_predecessor, g);
    dijkstra_shortest_paths(g, s, predecessor_map(p).distance_map(d));
 
    std::cout << "distances and parents:" << std::endl;
    graph_traits< graph_t >::vertex_iterator vi, vend;
    for (boost::tie(vi, vend) = vertices(g); vi != vend; ++vi)
    {
        std::cout << "distance(" << name[*vi] << ") = " << d[*vi] << ", ";
        std::cout << "parent(" << name[*vi] << ") = " << name[p[*vi]]
                  << std::endl;
    }
    std::cout << std::endl;
 
    return EXIT_SUCCESS;
}