我正在尝试完成以下任务:
有一个computeTspTour(size, start, distance)函数，它使我可以从size开始，通过start遍历许多顶点，这是最短的近似过程。在这里，distance是一个函数对象，它接受两个索引并返回它们之间的距离。
我想利用boost::graph的metric_tsp_approx。为此，我需要一个完整的基数size图，因此我想为此使用一个隐式定义的图，以避免创建无用的琐碎巨大图结构。
看起来一切正常，但是我的问题是metric_tsp_approx在某些时候使用了dijkstra_shortest_paths，它定义了ColorMap。这导致以下两个问题:
但是，我看不到如何从自己的位置修复ColorMap的特征，仅靠自己创建颜色属性图没有任何好处。
下面是我用来创建隐式图并在其上运行tsp_metric_approx的代码。很抱歉，我希望它简单明了。它的作用是设置一个CompleteGraph类，该类具有一个模板参数F，该参数指定distance函数的返回类型。此类具有必要的迭代器，分别是VertexListGraph和IncidenceGraph，以便tsp_metric_approx可以在其上运行。
#include <algorithm>
#include <functional>
#include <iostream>
#include <iterator>
#include <vector>
#include <boost/iterator/iterator_facade.hpp>
#include <boost/graph/metric_tsp_approx.hpp>
using namespace boost;
typedef std::size_t VertexDescriptor;
typedef std::pair<VertexDescriptor, VertexDescriptor> EdgeDescriptor;
class VertexIterator : public boost::iterator_facade<VertexIterator, VertexDescriptor const, boost::bidirectional_traversal_tag>
{
public:
//! Default constructor
VertexIterator() : pos_(0) {}
//! Constructor setting the position
explicit VertexIterator(VertexDescriptor pos) : pos_(pos) {}
//! Dereference the iterator
VertexDescriptor const& dereference() const { return pos_; }
//! Check for equality
bool equal(VertexIterator const& other) const { return pos_ == other.pos_; }
//! Increment
void increment() { ++pos_; }
//! Decrement
void decrement() { --pos_; }
private:
//! Grant access to boost::iterator_facade
friend class boost::iterator_core_access;
//! The current position
VertexDescriptor pos_ = 0;
};
class OutEdgeIterator : public boost::iterator_facade<OutEdgeIterator, EdgeDescriptor const, boost::bidirectional_traversal_tag>
{
public:
//! Constructor setting the source vertex
explicit OutEdgeIterator(VertexDescriptor source) { const std::size_t target = source == 0 ? 1 : 0; pos_ = EdgeDescriptor(source, target); }
//! Constructor setting the source vertex and the target
explicit OutEdgeIterator(VertexDescriptor source, VertexDescriptor target) : pos_(source, target) {}
//! Dereference the iterator
EdgeDescriptor const& dereference() const { return pos_; }
//! Check for equality
bool equal(OutEdgeIterator const& other) const { return pos_ == other.pos_; }
//! Increment
void increment() { ++pos_.second; if(pos_.first == pos_.second) { ++pos_.second; } }
//! Decrement
void decrement() { --pos_.second; if(pos_.first == pos_.second) { --pos_.second; } }
private:
//! Grant access to boost::iterator_facade
friend class boost::iterator_core_access;
//! The current edge
EdgeDescriptor pos_ = EdgeDescriptor(0, 1);
};
//! Class representing a complete graph
/*!
* This class works as a complete graph.
* It defines a distance property map between any two points by calling the passed distance function.
* \tparam F The return type of the distance function
*/
template<typename F>
class CompleteGraph
{
public:
typedef VertexDescriptor vertex_descriptor;
typedef EdgeDescriptor edge_descriptor;
typedef void adjacency_iterator;
typedef OutEdgeIterator out_edge_iterator;
typedef void in_edge_iterator;
typedef void edge_iterator;
typedef VertexIterator vertex_iterator;
typedef std::size_t degree_size_type;
typedef std::size_t vertices_size_type;
typedef std::size_t edges_size_type;
typedef undirected_tag directed_category;
typedef disallow_parallel_edge_tag edge_parallel_category;
typedef vertex_list_graph_tag traversal_category;
//! Delete default constructor
CompleteGraph() = delete;
//! Constructor from a given size
/*!
* If no distance is specified, we default to a constant function returning F(1)
*/
explicit CompleteGraph(std::size_t size) : size_(size), distance_(returnOne) {}
//! Constructor from a given size and a distance function of type F
/*!
* The constructed graph will have size many vertices.
* Its distance map will be of the following form: The distance between points i and j is distance(i, j).
* \param[in] size The size the graph should have
* \param[in] distance Binary function taking std::size_t arguments and returning the distance between two points
*/
explicit CompleteGraph(std::size_t size, std::function<F(std::size_t, std::size_t)> const& distance) : size_(size), distance_(distance) {}
//! Access to size_
std::size_t size() const { return size_; }
//! Access to distance_
std::function<F(std::size_t, std::size_t)> const& distance() const { return distance_; }
private:
//! The size of the graph
std::size_t size_;
//! The distance function used to find the distance between point i and point j
std::function<F(std::size_t, std::size_t)> const& distance_;
//! Distance function that just returns F(1)
std::function<F(std::size_t, std::size_t)> returnOne = [] (std::size_t, std::size_t) { return F(1); };
};
//! Weigth map for all edges
template<typename F>
class EdgeWeightMap
{
public:
typedef F value_type;
typedef F reference_type;
typedef reference_type reference;
typedef EdgeDescriptor key_type;
typedef readable_property_map_tag category;
//! Constructor from a distance function
explicit EdgeWeightMap(std::function<F(std::size_t, std::size_t)> const& distance) : distance_(distance) {}
//! Operator to dereference the property map
value_type operator[](key_type key) const { return distance_(key.first, key.second); }
//! Get function
friend inline value_type get(EdgeWeightMap<F> const& edgeWeightMap, EdgeWeightMap<F>::key_type const& key) { return edgeWeightMap[key]; }
private:
//! The distance function
std::function<F(std::size_t, std::size_t)> const& distance_;
};
//! Return the number of vertices of a CompleteGraph
template<typename F>
std::size_t num_vertices(CompleteGraph<F> const& g) { return g.size(); }
//! Return a pair allowing iteration over all vertices
template<typename F>
std::pair<VertexIterator, VertexIterator> vertices(CompleteGraph<F> const& g) { return std::make_pair(VertexIterator(0), VertexIterator(g.size())); }
//! Return a pair allowing iteration over all outgoing edges of a vertex
template<typename F>
std::pair<OutEdgeIterator, OutEdgeIterator> out_edges(VertexDescriptor s, CompleteGraph<F> const& g) { return std::make_pair(OutEdgeIterator(s), OutEdgeIterator(s, g.size())); }
//! Return the out-degree which is constant size - 1 for all vertices
template<typename F>
std::size_t out_degree(VertexDescriptor, CompleteGraph<F> const& g) { return g.size() - 1; }
//! Return the source of an edge
template<typename F>
VertexDescriptor source(EdgeDescriptor e, CompleteGraph<F> const&) { return e.first; }
//! Return the target of an edge
template<typename F>
VertexDescriptor target(EdgeDescriptor e, CompleteGraph<F> const&) { return e.second; }
//! Return the index map
template<typename F>
identity_property_map get(vertex_index_t, CompleteGraph<F> const&) { return identity_property_map(); }
//! Return the distance map
template<typename F>
EdgeWeightMap<F> get(edge_weight_t, CompleteGraph<F> const& g) { return EdgeWeightMap<F>(g.distance()); }
//! Wrapper function for automatic template parameter
template<typename F>
CompleteGraph<F> makeCompleteGraph(std::size_t size, std::function<F(std::size_t, std::size_t)> const& distance) { return CompleteGraph<F>(size, distance); }
//! Compute a metric TSP solution through the points supplied
/*!
* This function finds a solution through n many points whose pairwise distance is given by a function argument.
* The supplied distance function needs to satisfy the triangle inequality and must be symmetric.
* \tparam F The type of the return value of distance
* \param[in] size The number of points through which the TSP tour should be found
* \param[in] start The index of the point at which to start
* \param[in] distance A function taking two std::size_t's and returning the distance between point i and point j
* \return A vector representing the TSP tour
*/
template<typename F>
std::vector<std::size_t> computeTspTour(std::size_t size, std::size_t start, std::function<F(std::size_t, std::size_t)> const& distance)
{
std::vector<std::size_t> tour;
const auto completeGraph = makeCompleteGraph(size, distance);
metric_tsp_approx_tour_from_vertex(completeGraph, start, std::back_inserter(tour));
return tour;
}
int main()
{
typedef std::complex<double> Point;
const std::vector<Point> points{{.0, .0}, {1.0, 2.0}, {1.0, 5.0}, {2.5, 9.2}, {-100.2, 24.1}, {.1, 10.0}};
const std::function<double(std::size_t, std::size_t)> distance = [&points] (std::size_t i, std::size_t j) { return std::abs(points[i] - points[j]); };
const auto tour = computeTspTour(points.size(), 0, distance);
std::cout << "Found TSP tour:\n";
std::copy(tour.cbegin(), tour.cend(), std::ostream_iterator<char>(std::cout, " "));
return EXIT_SUCCESS;
}
最佳答案
DFS和TSP算法要求图既是“顶点列表”又是“事件图”(即可以访问顶点邻居的图)。
您的图表必须具有类似
struct traversal_category
: public virtual boost::vertex_list_graph_tag
, public virtual boost::adjacency_graph_tag
, public virtual boost::incidence_graph_tag
{
};
typedef typename boost::adjacency_iterator_generator<CompleteGraph<F>, vertex_descriptor, out_edge_iterator>::type adjacency_iterator;
代替
typedef vertex_list_graph_tag traversal_category;
typedef void adjacency_iterator;
通过这些更改以及一些修饰性的更改，您的代码即可通过编译。
顶点索引图是可选的，Boost将使用VertexMap和ColorMap包装您的代码，可能基于unordered_map。它的效率不如“身份”或类似的自定义 map ，但可以使用。
祝好运!