自定义 BGL 图使用拓扑排序需要什么？

如何解决自定义 BGL 图使用拓扑排序需要什么？

我已经创建了一个自定义 BGL 图模型，就像在这个答案中一样：What is needed to use BGL algorithms on existing data structures ( edges and vertices as vector<Object *>)?。

它采用了自定义数据结构以用于某些 Boost.Graph 算法。

链接的答案足以使深度优先搜索工作 (Coliru) 但我在使用 boost::topological_sort 时遇到了问题：

std::list<V> rev_topo;
boost::topological_sort(g,back_inserter(rev_topo));

给出：Coliru

In file included from /usr/include/boost/iterator/iterator_categories.hpp:15,from /usr/include/boost/unordered/detail/implementation.hpp:18,from /usr/include/boost/unordered/detail/set.hpp:6,from /usr/include/boost/unordered/unordered_set.hpp:20,from /usr/include/boost/unordered_set.hpp:17,from /usr/include/boost/graph/adjacency_list.hpp:21,from /home/sehe/Projects/stackoverflow/test.cpp:3:
/usr/include/boost/mpl/eval_if.hpp: In instantiation of ‘struct boost::mpl::eval_if<boost::detail::has_vertex_property_type<glue::MyGraph,mpl_::bool_<false> >,boost::detail::get_vertex_property_type<glue::MyGraph>,boost::no_property>’:
/usr/include/boost/graph/graph_traits.hpp:276:12:   required from ‘struct boost::vertex_property_type<glue::MyGraph>’
/usr/include/boost/graph/properties.hpp:201:12:   required from ‘struct boost::detail::vertex_property_map<glue::MyGraph,boost::vertex_index_t>’
/usr/include/boost/graph/properties.hpp:212:10:   required from ‘struct boost::property_map<glue::MyGraph,boost::vertex_index_t,void>’
/usr/include/boost/graph/named_function_params.hpp:415:69:   required from ‘struct boost::detail::override_const_property_t<int,glue::MyGraph,false>’
/usr/include/boost/graph/named_function_params.hpp:571:31:   required from ‘struct boost::detail::map_maker_helper<false,boost::parameter::aux::arg_list<boost::parameter::aux::tagged_argument<boost::graph::keywords::tag::visitor,const boost::topo_sort_visitor<std::back_insert_iterator<std::__cxx11::list<YourLibrary::myVertex*> > > >,boost::parameter::aux::arg_list<boost::parameter::aux::tagged_argument<boost::graph::keywords::tag::buffer,const int>,boost::parameter::aux::empty_arg_list> >,boost::default_color_type,int>’
/usr/include/boost/graph/named_function_params.hpp:604:41:   [ skipping 2 instantiation contexts,use -ftemplate-backtrace-limit=0 to disable ]
/usr/include/boost/graph/depth_first_search.hpp:337:80:   required from ‘void boost::graph::detail::depth_first_search_impl<Graph>::operator()(const Graph&,const ArgPack&) const [with ArgPack = boost::parameter::aux::arg_list<boost::parameter::aux::tagged_argument<boost::graph::keywords::tag::visitor,boost::parameter::aux::empty_arg_list> >; Graph = glue::MyGraph]’
/usr/include/boost/graph/depth_first_search.hpp:342:5:   required from ‘typename boost::result_of<boost::graph::detail::depth_first_search_impl<Param0>(Param0,const ArgPack&)>::type boost::graph::depth_first_search_with_named_params(const Param0&,const ArgPack&) [with Param0 = glue::MyGraph; ArgPack = boost::parameter::aux::arg_list<boost::parameter::aux::tagged_argument<boost::graph::keywords::tag::visitor,boost::parameter::aux::empty_arg_list> >; typename boost::result_of<boost::graph::detail::depth_first_search_impl<Param0>(Param0,const ArgPack&)>::type = void]’
/usr/include/boost/graph/depth_first_search.hpp:345:3:   required from ‘typename boost::result_of<boost::graph::detail::depth_first_search_impl<Param0>(Param0,const typename boost::detail::convert_bgl_params_to_boost_parameter<boost::bgl_named_params<T,Tag,Base> >::type&)>::type boost::depth_first_search(const Param0&,const boost::bgl_named_params<T,Base>&) [with Param0 = glue::MyGraph; P = boost::topo_sort_visitor<std::back_insert_iterator<std::__cxx11::list<YourLibrary::myVertex*> > >; T = boost::graph_visitor_t; R = boost::bgl_named_params<int,boost::buffer_param_t>; typename boost::result_of<boost::graph::detail::depth_first_search_impl<Param0>(Param0,Base> >::type&)>::type = void]’
/usr/include/boost/graph/topological_sort.hpp:65:23:   required from ‘void boost::topological_sort(VertexListGraph&,OutputIterator,const boost::bgl_named_params<P,T,R>&) [with VertexListGraph = glue::MyGraph; OutputIterator = std::back_insert_iterator<std::__cxx11::list<YourLibrary::myVertex*> >; P = int; T = boost::buffer_param_t; R = boost::no_property]’
/usr/include/boost/graph/topological_sort.hpp:71:21:   required from ‘void boost::topological_sort(VertexListGraph&,OutputIterator) [with VertexListGraph = glue::MyGraph; OutputIterator = std::back_insert_iterator<std::__cxx11::list<YourLibrary::myVertex*> >]’
/home/sehe/Projects/stackoverflow/test.cpp:139:55:   required from here
/usr/include/boost/mpl/eval_if.hpp:38:31: error: no type named ‘type’ in ‘boost::mpl::eval_if<boost::detail::has_vertex_property_type<glue::MyGraph,boost::no_property>::f_’ {aka ‘struct boost::no_property’}
   38 |     typedef typename f_::type type;
      |                               ^~~~
In file included from /usr/include/boost/graph/breadth_first_search.hpp:23,from /home/sehe/Projects/stackoverflow/test.cpp:4:
/usr/include/boost/graph/named_function_params.hpp: In instantiation of ‘struct boost::detail::override_const_property_t<int,false>’:
/usr/include/boost/graph/named_function_params.hpp:571:31:   required from ‘struct boost::detail::map_maker_helper<false,int>’
/usr/include/boost/graph/named_function_params.hpp:604:41:   required from ‘struct boost::detail::map_maker<glue::MyGraph,boost::graph::keywords::tag::color_map,boost::default_color_type>’
/usr/include/boost/graph/named_function_params.hpp:620:7:   required by substitution of ‘template<class Graph,class ArgPack> typename boost::detail::map_maker<Graph,ArgPack,boost::default_color_type>::map_type boost::detail::make_property_map_from_arg_pack_gen<boost::graph::keywords::tag::color_map,boost::default_color_type>::operator()<Graph,ArgPack>(const Graph&,const ArgPack&) const [with Graph = glue::MyGraph; ArgPack = boost::parameter::aux::arg_list<boost::parameter::aux::tagged_argument<boost::graph::keywords::tag::visitor,boost::parameter::aux::empty_arg_list> >]’
/usr/include/boost/graph/depth_first_search.hpp:337:80:   required from ‘void boost::graph::detail::depth_first_search_impl<Graph>::operator()(const Graph&,OutputIterator) [with VertexListGraph = glue::MyGraph; OutputIterator = std::back_insert_iterator<std::__cxx11::list<YourLibrary::myVertex*> >]’
/home/sehe/Projects/stackoverflow/test.cpp:139:55:   required from here
/usr/include/boost/graph/named_function_params.hpp:415:69: error: no type named ‘const_type’ in ‘struct boost::property_map<glue::MyGraph,void>’
  415 |       typedef typename boost::property_map<Graph,Prop>::const_type result_type;
      |                                                                     ^~~~~~~~~~~
In file included from /home/sehe/Projects/stackoverflow/test.cpp:5:
/usr/include/boost/graph/depth_first_search.hpp: In instantiation of ‘void boost::graph::detail::depth_first_search_impl<Graph>::operator()(const Graph&,boost::parameter::aux::empty_arg_list> >; Graph = glue::MyGraph]’:
/usr/include/boost/graph/depth_first_search.hpp:342:5:   required from ‘typename boost::result_of<boost::graph::detail::depth_first_search_impl<Param0>(Param0,OutputIterator) [with VertexListGraph = glue::MyGraph; OutputIterator = std::back_insert_iterator<std::__cxx11::list<YourLibrary::myVertex*> >]’
/home/sehe/Projects/stackoverflow/test.cpp:139:55:   required from here
/usr/include/boost/graph/depth_first_search.hpp:337:80: error: no match for call to ‘(const boost::detail::make_property_map_from_arg_pack_gen<boost::graph::keywords::tag::color_map,boost::default_color_type>) (const glue::MyGraph&,const boost::parameter::aux::arg_list<boost::parameter::aux::tagged_argument<boost::graph::keywords::tag::visitor,boost::parameter::aux::empty_arg_list> >&)’
  337 |                                     boost::detail::make_color_map_from_arg_pack(g,arg_pack),|                                     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~
In file included from /usr/include/boost/graph/breadth_first_search.hpp:23,from /home/sehe/Projects/stackoverflow/test.cpp:4:
/usr/include/boost/graph/named_function_params.hpp:620:7: note: candidate: ‘template<class Graph,MapTag,ValueType>::map_type boost::detail::make_property_map_from_arg_pack_gen<MapTag,ValueType>::operator()(const Graph&,const ArgPack&) const [with Graph = Graph; ArgPack = ArgPack; MapTag = boost::graph::keywords::tag::color_map; ValueType = boost::default_color_type]’
  620 |       operator()(const Graph& g,const ArgPack& ap) const {
      |       ^~~~~~~~
/usr/include/boost/graph/named_function_params.hpp:620:7: note:   substitution of deduced template arguments resulted in errors seen above

为了使用boost::topological_sort，“胶水”层必须满足哪些额外要求？在内部，拓扑排序使用 depth_first_search，但看起来它可能需要顶点索引图。

解决方法

正如您正确推测的那样，错误小说告诉您没有索引图。那是required for the default color map：

UTIL/OUT：color_map(ColorMap color) 这被算法用于 通过图表跟踪其进度。类型 ColorMap 必须 是读/写属性映射的模型，其键类型必须是 图的顶点描述符类型和颜色图的值类型 必须建模 ColorValue。

默认：iterator_property_map 创建于 大小为 std::vector 的 default_color_type 的 num_vertices(g) 和 使用 索引映射的 i_map。

事实上，如果您自己满足彩色地图要求，甚至不需要索引地图：Live On Coliru

std::map<V,boost::default_color_type> vertex_colors;
boost::topological_sort(
        g,back_inserter(rev_topo),boost::color_map(boost::make_assoc_property_map(vertex_colors))
    );

更多思考：教授 BGL 顶点索引

现在，许多算法都需要索引图，而且很多算法会变得更加方便，就像上面一样，当您的图模型确实有顶点索引图时。

顶点索引应该将顶点描述符映射到整数 [0,n)（其中 n 是顶点的总数）。在示例图模型的情况下，平凡索引将是顶点向量中的元素索引。

因此，您也可以将索引映射表示为：

auto idmap = boost::make_function_property_map<V>([&](V v) {
    auto match = std::find(begin(vv),end(vv),v);
    assert(match != end(vv));
    return std::distance(begin(vv),match);
});

现在您可以根据默认颜色映射调用算法：Coliru

boost::topological_sort(
        g,boost::vertex_index_map(idmap)
    );

这不是一个大胜利，因为现在我们仍然需要可选的命名参数，甚至需要 idmap 装置，它看起来比之前的 vertex_colors 映射更复杂？

简化/集成到模型中

我们可以通过教 BGL 如何从 Glue::MyGraph 模型获取我们的属性映射来改进它。

BGL 将使用

找到属性图

• 类型特征 boost::property_map<Graph,Tag> 告诉 BGL 属性映射的类型。

  在这里，Tag 将是例如boost::vertex_index_t 用于顶点索引图。

• 访问器函数

  • get(tag,graph)

    返回该类型的属性映射的副本

  • get(tag_type,graph,descriptor)

  对于可写属性映射，还有相应的 put 访问器，但为了简洁起见，我将保留它。有关该库功能的更多信息，请参阅 Boost PropertyMap Library 的文档。

让我们这样做。我们首先将 idmap 生成器移至我们的 MyGraph 模型，因此我们不再需要了解实现细节：

    auto idmap() const {
        using V = YourLibrary::myVertex const*;
        return boost::make_function_property_map<V>([this](V v) {
            auto match = std::find(begin(_vertices),end(_vertices),v);
            assert(match != end(_vertices));
            return std::distance(begin(_vertices),match);
        });
    }

这意味着您只需调用 g.idmap() 即可获得相同的属性映射。但是，我们希望图书馆“神奇地”知道。所以，首先我们特化这个特质：

namespace boost {
    template <> struct property_map<Glue::MyGraph,boost::vertex_index_t> {
        using const_type = decltype(std::declval<Glue::MyGraph>().idmap());
    };
}

c++14 的一大乐趣是我们可以推导出所有这些类型。剩下的唯一步骤：访问器函数，它们也是支持 ADL 的自定义点，因此我们将它们放入我们的 Glue 命名空间：

    auto get(boost::vertex_index_t,MyGraph const& g) {
        return g.idmap();
    }
    auto get(boost::vertex_index_t,MyGraph const& g,YourLibrary::myVertex const* v) {
        return g.idmap()[v];
    }
}  // namespace Glue

布丁的证明

现在，由于库“只理解”我们模型的顶点索引，我们可以享受需要的算法，而无需任何额外的帮助：

std::list<V> order;
boost::topological_sort(g,back_inserter(order));

而且我们可以为了好玩而练习另一个访问器：

std::cout << "Topo order:\n";
order.reverse(); // output is reversed
for (auto v : order)
    std::cout << "Vertex index:" << get(boost::vertex_index,g,v)
              << " name:" << v->name << "\n";

在您自己的（非通用库）代码中，您可能会编写

auto idmap = g.idmap(); // or
auto idmap = get(boost::vertex_index,v);

并使用 idmap[v] 来获取值。

现场演示

Live On Coliru

#include <algorithm>
#include <boost/container/flat_map.hpp>
#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/breadth_first_search.hpp>
#include <boost/graph/depth_first_search.hpp>
#include <boost/graph/topological_sort.hpp>
#include <boost/property_map/function_property_map.hpp>
#include <iostream>
#include <utility>

namespace YourLibrary {
    struct myVertex {
        myVertex(std::string n) : name(std::move(n)) {}
        std::string name;
    };

    struct myEdge {
        myVertex* _s = nullptr;
        myVertex* _t = nullptr;

        [[nodiscard]] myVertex* source() const { return _s; }
        [[nodiscard]] myVertex* target() const { return _t; }
    };

    using Vertices = std::vector<myVertex *>;
    using Edges = std::vector<myEdge *>;
}  // namespace YourLibrary

namespace Glue {

    struct MyGraph {
        struct EdgeOrder {
            template <typename A,typename B>
                bool operator()(A const* a,B const* b) const { return source(a) < source(b); }
            private:
            static auto source(YourLibrary::myVertex const* v) { return v; }
            static auto source(YourLibrary::myEdge const* e) { return e->source(); }
        };

        using Vertices = YourLibrary::Vertices;
        using Edges = YourLibrary::Edges;

        Vertices& _vertices;
        Edges& _edges;

        auto idmap() const {
            using V = YourLibrary::myVertex const*;
            return boost::make_function_property_map<V>([this](V v) {
                auto match = std::find(begin(_vertices),v);
                assert(match != end(_vertices));
                return std::distance(begin(_vertices),match);
            });
        }

        MyGraph(Vertices& vv,Edges& ee) : _vertices(vv),_edges(ee)  { 
            assert(std::is_sorted(_edges.begin(),_edges.end(),EdgeOrder{}));
        }
    };
}  // namespace Glue

namespace boost {

    template <> struct graph_traits<Glue::MyGraph> {
        // Due to Graph concept
        using vertex_descriptor      = YourLibrary::myVertex*;
        using edge_descriptor        = YourLibrary::myEdge*;
        using directed_category      = directed_tag;
        using edge_parallel_category = allow_parallel_edge_tag;
        static vertex_descriptor null_vertex() { return nullptr; }

        // Due to Vertex List concept
        struct traversal_category : vertex_list_graph_tag,incidence_graph_tag { };
        using vertex_iterator        = Glue::MyGraph::Vertices::const_iterator;
        using vertices_size_type     = std::size_t;

        // Due to Incidence Graph concept
        using out_edge_iterator = Glue::MyGraph::Edges::const_iterator;
        using degree_size_type = std::size_t;
    };

}  // namespace boost

namespace Glue {
    // Due to Vertex List concept
    auto vertices(MyGraph const& g) {
        return std::make_pair(g._vertices.begin(),g._vertices.end());
    }

    std::size_t num_vertices(MyGraph const& g) {
        return g._vertices.size();
    }

    // Due to Incidence Graph concept
    auto source(YourLibrary::myEdge const* e,MyGraph const& /*g*/) {
        return e->source();
    }
    auto target(YourLibrary::myEdge const* e,MyGraph const& /*g*/) {
        return e->target();
    }

    auto out_edges(YourLibrary::myVertex const* v,MyGraph const& g) {
        return std::equal_range(g._edges.begin(),g._edges.end(),v,MyGraph::EdgeOrder{});;
    }
    std::size_t out_degree(YourLibrary::myVertex const* v,MyGraph const& g) {
        auto oee = std::equal_range(g._edges.begin(),MyGraph::EdgeOrder{});
        return std::distance(oee.first,oee.second);
    }

    auto get(boost::vertex_index_t,YourLibrary::myVertex const* v) {
        return g.idmap()[v];
    }
}  // namespace Glue

namespace boost {
    template <> struct property_map<Glue::MyGraph,boost::vertex_index_t> {
        using const_type = decltype(std::declval<Glue::MyGraph>().idmap());
    };
}

int main() {
    // I hate manual memory management,so let's own some objects
    auto a = std::make_unique<YourLibrary::myVertex>("a");
    auto b = std::make_unique<YourLibrary::myVertex>("b");
    auto c = std::make_unique<YourLibrary::myVertex>("c");
    auto ab = std::make_unique<YourLibrary::myEdge>(YourLibrary::myEdge{a.get(),b.get()});
    auto cb = std::make_unique<YourLibrary::myEdge>(YourLibrary::myEdge{c.get(),b.get()});

    // These were given in your question:
    YourLibrary::Vertices vv { a.get(),b.get(),c.get() };
    YourLibrary::Edges ee { ab.get(),cb.get() };

    // this is the glue required to fulfill the BGL concepts:
    using boost::make_iterator_range;

    Glue::MyGraph g(vv,ee);
    for (auto v : make_iterator_range(vertices(g)))
        for (auto e : make_iterator_range(out_edges(v,g)))
            std::cout << "out edge ("
                      << source(e,g)->name << " -> "
                      << target(e,g)->name << ")\n";

    // this is showing that you can now BFS on it
    using V = boost::graph_traits<Glue::MyGraph>::vertex_descriptor;
    V start_vertex = a.get();
    std::map<V,boost::default_color_type> color_data;

    boost::breadth_first_search(g,start_vertex,boost::visitor(boost::default_bfs_visitor {})
            .color_map(boost::make_assoc_property_map(color_data)));

    boost::depth_first_search(g,boost::default_dfs_visitor {},boost::make_assoc_property_map(color_data),start_vertex);

    // named params
    boost::depth_first_search(g,boost::visitor(boost::default_dfs_visitor {})
            .color_map(boost::make_assoc_property_map(color_data))
            .root_vertex(start_vertex));

    std::list<V> order;
    boost::topological_sort(g,back_inserter(order));

    std::cout << "Topo order:\n";
    order.reverse(); // output is reversed

    auto idmap = g.idmap();
    for (auto v : order)
        std::cout << "Vertex index:" << idmap[v] << " name:" << v->name << "\n";
}

打印

out edge (a -> b)
out edge (c -> b)
Topo order:
Vertex index:2 name:c
Vertex index:0 name:a
Vertex index:1 name:b