Dijkstra图表与每个边缘上的重量表

Question

我有一个增强图,每个边都有多个权重(想象一天中每小时一组权重).这些权重值中的每一个都存储在propretyEdge类中:

class propretyEdge {
    std::map<std::string,double> weights; // Date indexed 
}

我创建了一个包含这些属性的图形,然后用正确的值填充它.现在的问题是我想在图上的特定权重集上启动Dijkstra算法:例如,一个函数可能是:

void Dijkstra (string date, parameters ... )

那将使用

weights[date]

图的每个边的值.

我一遍又一遍地阅读文档,我无法清楚地知道自己要做什么.我当然需要写这样的东西,但我不知道要开始:

boost::dijkstra_shortest_paths (
    (*graph_m), 
    vertex_origin_num_l,
    // weight_map (get (edge_weight, (*graph_m)))
    // predecessor_map(boost::make_iterator_property_map(predecessors.begin(), get(boost::vertex_index, (*graph_m)))).
    // distance_map(boost::make_iterator_property_map(distances.begin (), get(vertex_index,(*graph_m) )))
    predecessor_map(predecessorMap).
    distance_map(distanceMap)
);

谢谢您的帮助.

编辑

感谢Sehe精彩的回答,我能够在MacOS和Ubuntu上做到我想要的.

但是当我们尝试在Visual Studio 2012上编译这段代码时,似乎VS并不是很擅长理解boost的指针功能.所以我们修改了Sehe的部分:

auto dated_weight_f = [&](Graph::edge_descriptor ed) {
    return g[ed].weights.at(date);
};

auto dated_weight_map = make_function_property_map<Graph::edge_descriptor, double>(dated_weight_f);

通过:

class dated_weight_f {
public:
  dated_weight_f(Graph* graph_p,std::string date_p){
    graph_m=graph_p;
    date_m=date_p;
  }
  typedef double result_type;
    result_type operator()(Edge edge_p) const{
    return (*graph_m)[edge_p].weights.at(date_m);
  }
private:
  Graph* graph_m;
  std::string date_m;
};

const auto dated_weight_map = make_function_property_map<Edge>(dated_weight_f(graph_m,date_l));

其中有不使用指针功能的优点.

Answer 1

由于在另一个答案中回答这个问题显然不是很清楚,我会解释.

您真正需要的只是一个weight_map"有状态" 的自定义参数,可以为给定日期选择特定值.

你可以把它变得像你想要的那样复杂¹,所以你甚至可以在给定未知日期²的情况下插入/推断一个重量,但是为了这个演示的目的,让它保持简单.

让我们如上定义图表类型(大致):

struct propretyEdge {
    std::map<std::string, double> weights; // Date indexed 
};

using Graph = adjacency_list<vecS, vecS, directedS, no_property, propretyEdge>;

现在,让我们生成一个随机图,其中包含3个不同日期的随机权重:

int main() {
    Graph g;
    std::mt19937 prng { std::random_device{}() };
    generate_random_graph(g, 8, 12, prng);

    uniform_real<double> weight_dist(10,42);
    for (auto e : make_iterator_range(edges(g)))
        for (auto&& date : { "2014-01-01", "2014-02-01", "2014-03-01" })
            g[e].weights[date] = weight_dist(prng);

并且,跳到目标:

    for (std::string const& date : { "2014-01-01", "2014-02-01", "2014-03-01" }) {
        Dijkstra(date, g, 0);
    }
}

现在你如何实施Dijkstra(...)？从文档示例中收集,你会做类似的事情

void Dijkstra(std::string const& date, Graph const& g, int vertex_origin_num_l = 0) {

    // magic postponed ...

    std::vector<Graph::vertex_descriptor> p(num_vertices(g));
    std::vector<double>                   d(num_vertices(g));
    std::vector<default_color_type>       color_map(num_vertices(g));

    boost::typed_identity_property_map<Graph::vertex_descriptor> vid; // T* property maps were deprecated

    dijkstra_shortest_paths(g, vertex_origin_num_l,
            weight_map(dated_weight_map).
            predecessor_map(make_iterator_property_map(p.data(),   vid)).
            distance_map(make_iterator_property_map(d.data(),      vid)).
            color_map(make_iterator_property_map(color_map.data(), vid))
        );

现在这里唯一不清楚的一点应该是dated_weight_map.

输入Boost Property Maps

正如我在链接中显示的那样,可以为一个图BOOST提供多个边权重属性映射吗？,你可以拥有各种属性映射³,包括调用用户定义的函数.这是缺失的部分:

auto dated_weight_f = [&](Graph::edge_descriptor ed) {
    return g[ed].weights.at(date);
};

auto dated_weight_map = make_function_property_map<Graph::edge_descriptor, double>(dated_weight_f);

Voilà:完成了

我希望到现在为止,问题中的对应关系以及相关问题的答案是清楚的.剩下要做的就是将完整的实时样本和结果发布在漂亮的图片中:

住在Coliru

#include <boost/property_map/property_map.hpp>
#include <boost/property_map/function_property_map.hpp>
#include <boost/property_map/property_map_iterator.hpp>

#include <random>
#include <boost/graph/random.hpp>

#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/dijkstra_shortest_paths.hpp>
#include <fstream>

using namespace boost;

struct propretyEdge {
    std::map<std::string, double> weights; // Date indexed 
};

using Graph = adjacency_list<vecS, vecS, directedS, no_property, propretyEdge>;

void Dijkstra(std::string const& date, Graph const& g, int vertex_origin_num_l = 0) {

    auto dated_weight_f = [&](Graph::edge_descriptor ed) {
        return g[ed].weights.at(date);
    };

    auto dated_weight_map = make_function_property_map<Graph::edge_descriptor, double>(dated_weight_f);

    std::vector<Graph::vertex_descriptor> p(num_vertices(g));
    std::vector<double>                   d(num_vertices(g));
    std::vector<default_color_type>       color_map(num_vertices(g));

    boost::typed_identity_property_map<Graph::vertex_descriptor> vid; // T* property maps were deprecated

    dijkstra_shortest_paths(g, vertex_origin_num_l,
            weight_map(dated_weight_map).
            predecessor_map(make_iterator_property_map(p.data(),   vid)).
            distance_map(make_iterator_property_map(d.data(),      vid)).
            color_map(make_iterator_property_map(color_map.data(), vid))
        );

    std::cout << "distances and parents for '" + date + "':" << std::endl;
    for (auto vd : make_iterator_range(vertices(g)))
    {
        std::cout << "distance(" << vd << ") = " << d[vd] << ", ";
        std::cout << "parent(" << vd << ") = " << p[vd] << std::endl;
    }
    std::cout << std::endl;

    std::ofstream dot_file("dijkstra-eg-" + date + ".dot");

    dot_file << "digraph D {\n"
        "  rankdir=LR\n"
        "  size=\"6,4\"\n"
        "  ratio=\"fill\"\n"
        "  graph[label=\"shortest path on " + date + "\"];\n"
        "  edge[style=\"bold\"]\n" 
        "  node[shape=\"circle\"]\n";

    for (auto ed : make_iterator_range(edges(g))) {
        auto u = source(ed, g),
            v = target(ed, g);

        dot_file 
            << u << " -> " << v << "[label=\"" << get(dated_weight_map, ed) << "\""
            << (p[v] == u?", color=\"black\"" : ", color=\"grey\"")
            << "]";
    }
    dot_file << "}";
}

int main() {
    Graph g;
    std::mt19937 prng { std::random_device{}() };
    generate_random_graph(g, 8, 12, prng);

    uniform_real<double> weight_dist(10,42);
    for (auto e : make_iterator_range(edges(g)))
        for (auto&& date : { "2014-01-01", "2014-02-01", "2014-03-01" })
            g[e].weights[date] = weight_dist(prng);

    for (std::string const& date : { "2014-01-01", "2014-02-01", "2014-03-01" }) {
        Dijkstra(date, g, 0);
    }

}

输出,例如

¹只要保留您正在调用的算法所需的不变量即可.特别是,在给定相同边缘的情况下,必须在执行期间始终如一地返回相同的权重.此外,一些算法不支持负权重等.

²我强烈建议interval_map在这种情况下使用Boost ICL ,但我离题了

³另请参阅将set/get请求映射到C++类/结构更改中