//=======================================================================
// Copyright 2001 University of Notre Dame.
// Authors: Jeremy G. Siek and Lie-Quan Lee
//
// Distributed under the Boost Software License, Version 1.0. (See
// accompanying file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)
//=======================================================================

#ifndef BOOST_SUBGRAPH_HPP
#define BOOST_SUBGRAPH_HPP

// UNDER CONSTRUCTION

#include <boost/config.hpp>
#include <list>
#include <vector>
#include <map>
#include <cassert>
#include <boost/graph/graph_traits.hpp>
#include <boost/graph/graph_mutability_traits.hpp>
#include <boost/graph/properties.hpp>
#include <boost/iterator/indirect_iterator.hpp>

#include <boost/static_assert.hpp>
#include <boost/type_traits/is_same.hpp>

namespace boost {

struct subgraph_tag { };

/** @name Property Lookup
 * The local_property and global_property functions are used to create
 * structures that determine the lookup strategy for properties in subgraphs.
 * Note that the nested kind member is used to help interoperate with actual
 * Property types.
 */
//@{
template <typename T>
struct local_property
{
    typedef T kind;
    local_property(T x) : value(x) { }
    T value;
};

template <typename T>
inline local_property<T> local(T x)
{ return local_property<T>(x); }

template <typename T>
struct global_property
{
    typedef T kind;
    global_property(T x) : value(x) { }
    T value;
};

template <typename T>
inline global_property<T> global(T x)
{ return global_property<T>(x); }
//@}

// Invariants of an induced subgraph:
//   - If vertex u is in subgraph g, then u must be in g.parent().
//   - If edge e is in subgraph g, then e must be in g.parent().
//   - If edge e=(u,v) is in the root graph, then edge e
//     is also in any subgraph that contains both vertex u and v.

// The Graph template parameter must have a vertex_index and edge_index
// internal property. It is assumed that the vertex indices are assigned
// automatically by the graph during a call to add_vertex(). It is not
// assumed that the edge vertices are assigned automatically, they are
// explicitly assigned here.

template <typename Graph>
class subgraph {
    typedef graph_traits<Graph> Traits;
    typedef std::list<subgraph<Graph>*> ChildrenList;
public:
// Graph requirements
typedef typename Traits::vertex_descriptor         vertex_descriptor;
typedef typename Traits::edge_descriptor           edge_descriptor;
typedef typename Traits::directed_category         directed_category;
typedef typename Traits::edge_parallel_category    edge_parallel_category;
typedef typename Traits::traversal_category        traversal_category;

    // IncidenceGraph requirements
    typedef typename Traits::out_edge_iterator         out_edge_iterator;
    typedef typename Traits::degree_size_type          degree_size_type;

    // AdjacencyGraph requirements
    typedef typename Traits::adjacency_iterator        adjacency_iterator;

    // VertexListGraph requirements
    typedef typename Traits::vertex_iterator           vertex_iterator;
    typedef typename Traits::vertices_size_type        vertices_size_type;

    // EdgeListGraph requirements
    typedef typename Traits::edge_iterator             edge_iterator;
    typedef typename Traits::edges_size_type           edges_size_type;

    typedef typename Traits::in_edge_iterator          in_edge_iterator;

    typedef typename Graph::edge_property_type         edge_property_type;
    typedef typename Graph::vertex_property_type       vertex_property_type;
    typedef typename Graph::vertex_bundled             vertex_bundled;
    typedef typename Graph::edge_bundled               edge_bundled;
    typedef subgraph_tag                               graph_tag;
    typedef Graph                                      graph_type;
    typedef typename Graph::graph_property_type        graph_property_type;

    // Create the main graph, the root of the subgraph tree
    subgraph()
        : m_parent(0), m_edge_counter(0)
    { }

    subgraph(const graph_property_type& p)
        : m_graph(p), m_parent(0), m_edge_counter(0)
    { }

    subgraph(vertices_size_type n, const graph_property_type& p = graph_property_type())
        : m_graph(n, p), m_parent(0), m_edge_counter(0), m_global_vertex(n)
    {
        typename Graph::vertex_iterator v, v_end;
        vertices_size_type i = 0;
        for(boost::tie(v, v_end) = vertices(m_graph); v != v_end; ++v)
            m_global_vertex[i++] = *v;
    }

    // copy constructor
    subgraph(const subgraph& x)
        : m_graph(x.m_graph), m_parent(x.m_parent), m_edge_counter(x.m_edge_counter)
        , m_global_vertex(x.m_global_vertex), m_global_edge(x.m_global_edge)
    {
        // Do a deep copy (recursive).
        for(typename ChildrenList::const_iterator i = x.m_children.begin();
            i != x.m_children.end(); ++i)
        {
            m_children.push_back(new subgraph<Graph>( **i ));
        }
    }


    ~subgraph() {
      for(typename ChildrenList::iterator i = m_children.begin();
          i != m_children.end(); ++i)
        {
            delete *i;
        }
    }

    // Return a null vertex descriptor for the graph.
    static vertex_descriptor null_vertex()
    { return Traits::null_vertex(); }


    // Create a subgraph
    subgraph<Graph>& create_subgraph() {
        m_children.push_back(new subgraph<Graph>());
        m_children.back()->m_parent = this;
        return *m_children.back();
    }

    // Create a subgraph with the specified vertex set.
    template <typename VertexIterator>
    subgraph<Graph>& create_subgraph(VertexIterator first, VertexIterator last) {
        m_children.push_back(new subgraph<Graph>());
        m_children.back()->m_parent = this;
        for(; first != last; ++first) {
            add_vertex(*first, *m_children.back());
        }
        return *m_children.back();
    }

    // local <-> global descriptor conversion functions
    vertex_descriptor local_to_global(vertex_descriptor u_local) const
    { return is_root() ? u_local : m_global_vertex[u_local]; }

    vertex_descriptor global_to_local(vertex_descriptor u_global) const {
        vertex_descriptor u_local; bool in_subgraph;
        if (is_root()) return u_global;
        boost::tie(u_local, in_subgraph) = this->find_vertex(u_global);
        assert(in_subgraph == true);
        return u_local;
    }

    edge_descriptor local_to_global(edge_descriptor e_local) const
    { return is_root() ? e_local : m_global_edge[get(get(edge_index, m_graph), e_local)]; }

    edge_descriptor global_to_local(edge_descriptor e_global) const
    { return is_root() ? e_global : (*m_local_edge.find(get(get(edge_index, root().m_graph), e_global))).second; }

    // Is vertex u (of the root graph) contained in this subgraph?
    // If so, return the matching local vertex.
    std::pair<vertex_descriptor, bool>
    find_vertex(vertex_descriptor u_global) const {
        if (is_root()) return std::make_pair(u_global, true);
        typename std::map<vertex_descriptor, vertex_descriptor>::const_iterator
            i = m_local_vertex.find(u_global);
        bool valid = i != m_local_vertex.end();
        return std::make_pair((valid ? (*i).second : null_vertex()), valid);
    }

    // Return the parent graph.
    subgraph& parent() { return *m_parent; }
    const subgraph& parent() const { return *m_parent; }

    // Return true if this is the root subgraph
    bool is_root() const { return m_parent == 0; }

    // Return the root graph of the subgraph tree.
    subgraph& root()
    { return is_root() ? *this : m_parent->root(); }

    const subgraph& root() const
    { return is_root() ? *this : m_parent->root(); }

    // Return the children subgraphs of this graph/subgraph.
    // Use a list of pointers because the VC++ std::list doesn't like
    // storing incomplete type.
    typedef indirect_iterator<
        typename ChildrenList::const_iterator
      , subgraph<Graph>
      , std::bidirectional_iterator_tag
    >
    children_iterator;

    typedef indirect_iterator<
        typename ChildrenList::const_iterator
      , subgraph<Graph> const
      , std::bidirectional_iterator_tag
    >
    const_children_iterator;

    std::pair<const_children_iterator, const_children_iterator> children() const {
      return std::make_pair(const_children_iterator(m_children.begin()),
                            const_children_iterator(m_children.end()));
    }

    std::pair<children_iterator, children_iterator> children() {
      return std::make_pair(children_iterator(m_children.begin()),
                            children_iterator(m_children.end()));
    }

    std::size_t num_children() const { return m_children.size(); }

#ifndef BOOST_GRAPH_NO_BUNDLED_PROPERTIES
    // Defualt property access delegates the lookup to global properties.
    template <typename Descriptor>
    typename graph::detail::bundled_result<Graph, Descriptor>::type&
    operator[](Descriptor x)
    { return is_root() ? m_graph[x] : root().m_graph[local_to_global(x)]; }

    template <typename Descriptor>
    typename graph::detail::bundled_result<Graph, Descriptor>::type const&
    operator[](Descriptor x) const
    { return is_root() ? m_graph[x] : root().m_graph[local_to_global(x)]; }

    // Local property access returns the local property of the given descripor.
    template <typename Descriptor>
    typename graph::detail::bundled_result<Graph, Descriptor>::type&
    operator[](local_property<Descriptor> x)
    { return m_graph[x.value]; }

    template <typename Descriptor>
    typename graph::detail::bundled_result<Graph, Descriptor>::type const&
    operator[](local_property<Descriptor> x) const
    { return m_graph[x.value]; }

    // Global property access returns the global property associated with the
    // given descriptor. This is an alias for the default bundled property
    // access operations.
    template <typename Descriptor>
    typename graph::detail::bundled_result<Graph, Descriptor>::type&
    operator[](global_property<Descriptor> x)
    { return (*this)[x.value]; }

    template <typename Descriptor>
    typename graph::detail::bundled_result<Graph, Descriptor>::type const&
    operator[](global_property<Descriptor> x) const
    { return (*this)[x.value]; }

#endif // BOOST_GRAPH_NO_BUNDLED_PROPERTIES

    //  private:
    typedef typename property_map<Graph, edge_index_t>::type EdgeIndexMap;
    typedef typename property_traits<EdgeIndexMap>::value_type edge_index_type;
    BOOST_STATIC_ASSERT((!is_same<edge_index_type,
                        boost::detail::error_property_not_found>::value));

private:
    typedef std::vector<vertex_descriptor> GlobalVertexList;
    typedef std::vector<edge_descriptor> GlobalEdgeList;
    typedef std::map<vertex_descriptor, vertex_descriptor> LocalVertexMap;
    typedef std::map<edge_index_type, edge_descriptor> LocalEdgeMap;
    // TODO: Should the LocalVertexMap be: map<index_type, descriptor>?
    // TODO: Can we relax the indexing requirement if both descriptors are
    // LessThanComparable?
    // TODO: Should we really be using unorderd_map for improved lookup times?

public: // Probably shouldn't be public....
    Graph m_graph;
    subgraph<Graph>* m_parent;
    edge_index_type m_edge_counter; // for generating unique edge indices
    ChildrenList m_children;
    GlobalVertexList m_global_vertex; // local -> global
    LocalVertexMap m_local_vertex;  // global -> local
    GlobalEdgeList m_global_edge;              // local -> global
    LocalEdgeMap m_local_edge; // global -> local

    edge_descriptor local_add_edge(vertex_descriptor u_local,
                                   vertex_descriptor v_local,
                                   edge_descriptor e_global)
    {
        edge_descriptor e_local;
        bool inserted;
        boost::tie(e_local, inserted) = add_edge(u_local, v_local, m_graph);
        put(edge_index, m_graph, e_local, m_edge_counter++);
        m_global_edge.push_back(e_global);
        m_local_edge[get(get(edge_index, this->root()), e_global)] = e_local;
        return e_local;
    }
};

#ifndef BOOST_GRAPH_NO_BUNDLED_PROPERTIES
// TODO: I don't think these are required since the default metafunction
// returns Graph::vertex_bundled.
template <typename Graph>
struct vertex_bundle_type<subgraph<Graph> >
    : vertex_bundle_type<Graph>
{ };

template<typename Graph>
struct edge_bundle_type<subgraph<Graph> >
    : edge_bundle_type<Graph>
{ };
#endif // BOOST_GRAPH_NO_BUNDLED_PROPERTIES

//===========================================================================
// Functions special to the Subgraph Class

template <typename G>
typename subgraph<G>::vertex_descriptor
add_vertex(typename subgraph<G>::vertex_descriptor u_global,
           subgraph<G>& g)
{
    assert(!g.is_root());
    typename subgraph<G>::vertex_descriptor u_local, v_global, uu_global;
    typename subgraph<G>::edge_descriptor e_global;

    u_local = add_vertex(g.m_graph);
    g.m_global_vertex.push_back(u_global);
    g.m_local_vertex[u_global] = u_local;

    subgraph<G>& r = g.root();

    // remember edge global and local maps
    {
        typename subgraph<G>::out_edge_iterator ei, ei_end;
        for (boost::tie(ei, ei_end) = out_edges(u_global, r);
            ei != ei_end; ++ei) {
            e_global = *ei;
            v_global = target(e_global, r);
            if (g.find_vertex(v_global).second == true)
            g.local_add_edge(u_local, g.global_to_local(v_global), e_global);
        }
    }
    if (is_directed(g)) { // not necessary for undirected graph
        typename subgraph<G>::vertex_iterator vi, vi_end;
        typename subgraph<G>::out_edge_iterator ei, ei_end;
        for(boost::tie(vi, vi_end) = vertices(r); vi != vi_end; ++vi) {
            v_global = *vi;
            if(g.find_vertex(v_global).second)
            for(boost::tie(ei, ei_end) = out_edges(*vi, r); ei != ei_end; ++ei) {
                e_global = *ei;
                uu_global = target(e_global, r);
                if(uu_global == u_global && g.find_vertex(v_global).second) {
                    g.local_add_edge(g.global_to_local(v_global), u_local, e_global);
                }
            }
        }
    }

    return u_local;
}

// NOTE: Descriptors are local unless otherwise noted.

//===========================================================================
// Functions required by the IncidenceGraph concept

template <typename G>
std::pair<typename graph_traits<G>::out_edge_iterator,
          typename graph_traits<G>::out_edge_iterator>
out_edges(typename graph_traits<G>::vertex_descriptor v, const subgraph<G>& g)
{ return out_edges(v, g.m_graph); }

template <typename G>
typename graph_traits<G>::degree_size_type
out_degree(typename graph_traits<G>::vertex_descriptor v, const subgraph<G>& g)
{ return out_degree(v, g.m_graph); }

template <typename G>
typename graph_traits<G>::vertex_descriptor
source(typename graph_traits<G>::edge_descriptor e, const subgraph<G>& g)
{ return source(e, g.m_graph); }

template <typename G>
typename graph_traits<G>::vertex_descriptor
target(typename graph_traits<G>::edge_descriptor e, const subgraph<G>& g)
{ return target(e, g.m_graph); }

//===========================================================================
// Functions required by the BidirectionalGraph concept

template <typename G>
std::pair<typename graph_traits<G>::in_edge_iterator,
          typename graph_traits<G>::in_edge_iterator>
in_edges(typename graph_traits<G>::vertex_descriptor v, const subgraph<G>& g)
{ return in_edges(v, g.m_graph); }

template <typename G>
typename graph_traits<G>::degree_size_type
in_degree(typename graph_traits<G>::vertex_descriptor v, const subgraph<G>& g)
{ return in_degree(v, g.m_graph); }

template <typename G>
typename graph_traits<G>::degree_size_type
degree(typename graph_traits<G>::vertex_descriptor v, const subgraph<G>& g)
{ return degree(v, g.m_graph); }

//===========================================================================
// Functions required by the AdjacencyGraph concept

template <typename G>
std::pair<typename subgraph<G>::adjacency_iterator,
          typename subgraph<G>::adjacency_iterator>
adjacent_vertices(typename subgraph<G>::vertex_descriptor v, const subgraph<G>& g)
{ return adjacent_vertices(v, g.m_graph); }

//===========================================================================
// Functions required by the VertexListGraph concept

template <typename G>
std::pair<typename subgraph<G>::vertex_iterator,
          typename subgraph<G>::vertex_iterator>
vertices(const subgraph<G>& g)
{ return vertices(g.m_graph); }

template <typename G>
typename subgraph<G>::vertices_size_type
num_vertices(const subgraph<G>& g)
{ return num_vertices(g.m_graph); }

//===========================================================================
// Functions required by the EdgeListGraph concept

template <typename G>
std::pair<typename subgraph<G>::edge_iterator,
          typename subgraph<G>::edge_iterator>
edges(const subgraph<G>& g)
{ return edges(g.m_graph); }

template <typename G>
typename subgraph<G>::edges_size_type
num_edges(const subgraph<G>& g)
{ return num_edges(g.m_graph); }

//===========================================================================
// Functions required by the AdjacencyMatrix concept

template <typename G>
std::pair<typename subgraph<G>::edge_descriptor, bool>
edge(typename subgraph<G>::vertex_descriptor u,
     typename subgraph<G>::vertex_descriptor v,
     const subgraph<G>& g)
{ return edge(u, v, g.m_graph); }

//===========================================================================
// Functions required by the MutableGraph concept

namespace detail {

    template <typename Vertex, typename Edge, typename Graph>
    void add_edge_recur_down(Vertex u_global, Vertex v_global, Edge e_global,
                             subgraph<Graph>& g);

    template <typename Vertex, typename Edge, typename Children, typename G>
    void children_add_edge(Vertex u_global, Vertex v_global, Edge e_global,
                           Children& c, subgraph<G>* orig)
    {
        for(typename Children::iterator i = c.begin(); i != c.end(); ++i) {
            if ((*i)->find_vertex(u_global).second &&
                (*i)->find_vertex(v_global).second)
            {
                add_edge_recur_down(u_global, v_global, e_global, **i, orig);
            }
        }
    }

    template <typename Vertex, typename Edge, typename Graph>
    void add_edge_recur_down(Vertex u_global, Vertex v_global, Edge e_global,
                             subgraph<Graph>& g, subgraph<Graph>* orig)
    {
        if(&g != orig ) {
            // add local edge only if u_global and v_global are in subgraph g
            Vertex u_local, v_local;
            bool u_in_subgraph, v_in_subgraph;
            boost::tie(u_local, u_in_subgraph) = g.find_vertex(u_global);
            boost::tie(v_local, v_in_subgraph) = g.find_vertex(v_global);
            if(u_in_subgraph && v_in_subgraph) {
                g.local_add_edge(u_local, v_local, e_global);
            }
        }
        children_add_edge(u_global, v_global, e_global, g.m_children, orig);
    }

    template <typename Vertex, typename Graph>
    std::pair<typename subgraph<Graph>::edge_descriptor, bool>
    add_edge_recur_up(Vertex u_global, Vertex v_global,
                      const typename Graph::edge_property_type& ep,
                      subgraph<Graph>& g, subgraph<Graph>* orig)
    {
        if(g.is_root()) {
            typename subgraph<Graph>::edge_descriptor e_global;
            bool inserted;
            boost::tie(e_global, inserted) = add_edge(u_global, v_global, ep, g.m_graph);
            put(edge_index, g.m_graph, e_global, g.m_edge_counter++);
            g.m_global_edge.push_back(e_global);
            children_add_edge(u_global, v_global, e_global, g.m_children, orig);
            return std::make_pair(e_global, inserted);
        } else {
            return add_edge_recur_up(u_global, v_global, ep, *g.m_parent, orig);
        }
    }

} // namespace detail

// Add an edge to the subgraph g, specified by the local vertex descriptors u
// and v. In addition, the edge will be added to any (all) other subgraphs that
// contain vertex descriptors u and v.

template <typename G>
std::pair<typename subgraph<G>::edge_descriptor, bool>
add_edge(typename subgraph<G>::vertex_descriptor u,
         typename subgraph<G>::vertex_descriptor v,
         const typename G::edge_property_type& ep,
         subgraph<G>& g)
{
    if (g.is_root()) {
        // u and v are really global
        return detail::add_edge_recur_up(u, v, ep, g, &g);
    } else {
        typename subgraph<G>::edge_descriptor e_local, e_global;
        bool inserted;
        boost::tie(e_global, inserted) =
            detail::add_edge_recur_up(g.local_to_global(u),
                                      g.local_to_global(v),
                                      ep, g, &g);
        e_local = g.local_add_edge(u, v, e_global);
        return std::make_pair(e_local, inserted);
    }
}

template <typename G>
std::pair<typename subgraph<G>::edge_descriptor, bool>
add_edge(typename subgraph<G>::vertex_descriptor u,
         typename subgraph<G>::vertex_descriptor v,
         subgraph<G>& g)
{ return add_edge(u, v, typename G::edge_property_type(), g); }

namespace detail {
    //-------------------------------------------------------------------------
    // implementation of remove_edge(u,v,g)
    template <typename Vertex, typename Graph>
    void remove_edge_recur_down(Vertex u_global, Vertex v_global,
                                subgraph<Graph>& g);

    template <typename Vertex, typename Children>
    void children_remove_edge(Vertex u_global, Vertex v_global,
                              Children& c)
    {
        for(typename Children::iterator i = c.begin(); i != c.end(); ++i) {
            if((*i)->find_vertex(u_global).second &&
               (*i)->find_vertex(v_global).second)
            {
                remove_edge_recur_down(u_global, v_global, **i);
            }
        }
    }

    template <typename Vertex, typename Graph>
    void remove_edge_recur_down(Vertex u_global, Vertex v_global,
                                subgraph<Graph>& g)
    {
        Vertex u_local, v_local;
        u_local = g.m_local_vertex[u_global];
        v_local = g.m_local_vertex[v_global];
        remove_edge(u_local, v_local, g.m_graph);
        children_remove_edge(u_global, v_global, g.m_children);
    }

    template <typename Vertex, typename Graph>
    void remove_edge_recur_up(Vertex u_global, Vertex v_global,
                              subgraph<Graph>& g)
    {
        if(g.is_root()) {
            remove_edge(u_global, v_global, g.m_graph);
            children_remove_edge(u_global, v_global, g.m_children);
        } else {
            remove_edge_recur_up(u_global, v_global, *g.m_parent);
        }
    }

    //-------------------------------------------------------------------------
    // implementation of remove_edge(e,g)
    template <typename Edge, typename Graph>
    void remove_edge_recur_down(Edge e_global, subgraph<Graph>& g);

    template <typename Edge, typename Children>
    void children_remove_edge(Edge e_global, Children& c)
    {
        for(typename Children::iterator i = c.begin(); i != c.end(); ++i) {
            if((*i)->find_vertex(source(e_global, **i)).second &&
               (*i)->find_vertex(target(e_global, **i)).second)
            {
                remove_edge_recur_down(source(e_global, **i),
                                       target(e_global, **i),
                                       **i);
            }
        }
    }

    template <typename Edge, typename Graph>
    void remove_edge_recur_down(Edge e_global, subgraph<Graph>& g)
    {
        remove_edge(g.global_to_local(e_global), g.m_graph);
        children_remove_edge(e_global, g.m_children);
    }

    template <typename Edge, typename Graph>
    void remove_edge_recur_up(Edge e_global, subgraph<Graph>& g)
    {
        if (g.is_root()) {
            remove_edge(e_global, g.m_graph);
            children_remove_edge(e_global, g.m_children);
        } else {
            remove_edge_recur_up(e_global, *g.m_parent);
        }
    }

} // namespace detail

template <typename G>
void
remove_edge(typename subgraph<G>::vertex_descriptor u,
            typename subgraph<G>::vertex_descriptor v,
            subgraph<G>& g)
{
    if(g.is_root()) {
        detail::remove_edge_recur_up(u, v, g);
    } else {
        detail::remove_edge_recur_up(g.local_to_global(u),
                                     g.local_to_global(v), g);
    }
}

template <typename G>
void
remove_edge(typename subgraph<G>::edge_descriptor e, subgraph<G>& g)
{
    if(g.is_root()) {
        detail::remove_edge_recur_up(e, g);
    } else {
        detail::remove_edge_recur_up(g.local_to_global(e), g);
    }
}

// This is slow, but there may not be a good way to do it safely otherwise
template <typename Predicate, typename G>
void
remove_edge_if(Predicate p, subgraph<G>& g) {
  while (true) {
    bool any_removed = false;
    typedef typename subgraph<G>::edge_iterator ei_type;
    for (std::pair<ei_type, ei_type> ep = edges(g);
         ep.first != ep.second; ++ep.first) {
      if (p(*ep.first)) {
        any_removed = true;
        remove_edge(*ep.first, g);
        continue; /* Since iterators may be invalidated */
      }
    }
    if (!any_removed) break;
  }
}

template <typename G>
void
clear_vertex(typename subgraph<G>::vertex_descriptor v, subgraph<G>& g) {
  while (true) {
    typedef typename subgraph<G>::out_edge_iterator oei_type;
    std::pair<oei_type, oei_type> p = out_edges(v, g);
    if (p.first == p.second) break;
    remove_edge(*p.first, g);
  }
}

namespace detail {
    template <typename G>
    typename subgraph<G>::vertex_descriptor
    add_vertex_recur_up(subgraph<G>& g)
    {
        typename subgraph<G>::vertex_descriptor u_local, u_global;
        if (g.is_root()) {
            u_global = add_vertex(g.m_graph);
            g.m_global_vertex.push_back(u_global);
        } else {
            u_global = add_vertex_recur_up(*g.m_parent);
            u_local = add_vertex(g.m_graph);
            g.m_global_vertex.push_back(u_global);
            g.m_local_vertex[u_global] = u_local;
        }
        return u_global;
    }
} // namespace detail

template <typename G>
typename subgraph<G>::vertex_descriptor
add_vertex(subgraph<G>& g)
{
    typename subgraph<G>::vertex_descriptor  u_local, u_global;
    if(g.is_root()) {
        u_global = add_vertex(g.m_graph);
        g.m_global_vertex.push_back(u_global);
        u_local = u_global;
    } else {
        u_global = detail::add_vertex_recur_up(g.parent());
        u_local = add_vertex(g.m_graph);
        g.m_global_vertex.push_back(u_global);
        g.m_local_vertex[u_global] = u_local;
    }
    return u_local;
}


#if 0
// TODO: Under Construction
template <typename G>
void remove_vertex(typename subgraph<G>::vertex_descriptor u, subgraph<G>& g)
{ assert(false); }
#endif

//===========================================================================
// Functions required by the PropertyGraph concept

/**
 * The global property map returns the global properties associated with local
 * descriptors.
 */
template <typename GraphPtr, typename PropertyMap, typename Tag>
class subgraph_global_property_map
    : public put_get_helper<
        typename property_traits<PropertyMap>::reference,
        subgraph_global_property_map<GraphPtr, PropertyMap, Tag>
    >
{
    typedef property_traits<PropertyMap> Traits;
public:
    typedef typename Traits::category category;
    typedef typename Traits::value_type value_type;
    typedef typename Traits::key_type key_type;
    typedef typename Traits::reference reference;

    subgraph_global_property_map()
    { }

    subgraph_global_property_map(GraphPtr g)
        : m_g(g)
    { }

    reference operator[](key_type e) const {
        PropertyMap pmap = get(Tag(), m_g->root().m_graph);
        return m_g->is_root()
            ? pmap[e]
            : pmap[m_g->local_to_global(e)];
    }

    GraphPtr m_g;
};

/**
 * The local property map returns the local property associated with the local
 * descriptors.
 */
template <typename GraphPtr, typename PropertyMap, typename Tag>
class subgraph_local_property_map
    : public put_get_helper<
        typename property_traits<PropertyMap>::reference,
        subgraph_local_property_map<GraphPtr, PropertyMap, Tag>
    >
{
    typedef property_traits<PropertyMap> Traits;
public:
    typedef typename Traits::category category;
    typedef typename Traits::value_type value_type;
    typedef typename Traits::key_type key_type;
    typedef typename Traits::reference reference;

    typedef Tag tag;
    typedef PropertyMap pmap;

    subgraph_local_property_map()
    { }

    subgraph_local_property_map(GraphPtr g)
        : m_g(g)
    { }

    reference operator[](key_type e) const {
        // Get property map on the underlying graph.
        PropertyMap pmap = get(Tag(), m_g->m_graph);
        return pmap[e];
    }

    GraphPtr m_g;
};

namespace detail {
    // Extract the actual tags from local or global property maps so we don't
    // try to find non-properties.
    template <typename P> struct extract_lg_tag { typedef P type; };
    template <typename P> struct extract_lg_tag< local_property<P> > {
        typedef P type;
    };
    template <typename P> struct extract_lg_tag< global_property<P> > {
        typedef P type;
    };

    // NOTE: Mysterious Property template parameter unused in both metafunction
    // classes.
    struct subgraph_global_pmap {
        template <class Tag, class SubGraph, class Property>
        struct bind_ {
            typedef typename SubGraph::graph_type Graph;
            typedef SubGraph* SubGraphPtr;
            typedef const SubGraph* const_SubGraphPtr;
            typedef typename extract_lg_tag<Tag>::type TagType;
            typedef typename property_map<Graph, TagType>::type PMap;
            typedef typename property_map<Graph, TagType>::const_type const_PMap;
        public:
            typedef subgraph_global_property_map<SubGraphPtr, PMap, TagType> type;
            typedef subgraph_global_property_map<const_SubGraphPtr, const_PMap, TagType>
            const_type;
        };
    };

    struct subgraph_local_pmap {
        template <class Tag, class SubGraph, class Property>
        struct bind_ {
            typedef typename SubGraph::graph_type Graph;
            typedef SubGraph* SubGraphPtr;
            typedef const SubGraph* const_SubGraphPtr;
            typedef typename extract_lg_tag<Tag>::type TagType;
            typedef typename property_map<Graph, TagType>::type PMap;
            typedef typename property_map<Graph, TagType>::const_type const_PMap;
        public:
            typedef subgraph_local_property_map<SubGraphPtr, PMap, TagType> type;
            typedef subgraph_local_property_map<const_SubGraphPtr, const_PMap, TagType>
            const_type;
        };
    };

    // These metafunctions select the corresponding metafunctions above, and
    // are used by the choose_pmap metafunction below to specialize the choice
    // of local/global property map. By default, we defer to the global
    // property.
    template <class Tag>
    struct subgraph_choose_pmap_helper {
        typedef subgraph_global_pmap type;
    };
    template <class Tag>
    struct subgraph_choose_pmap_helper< local_property<Tag> > {
        typedef subgraph_local_pmap type;
    };
    template <class Tag>
    struct subgraph_choose_pmap_helper< global_property<Tag> > {
        typedef subgraph_global_pmap type;
    };

    // As above, unless we're requesting vertex_index_t. Then it's always a
    // local property map. This enables the correct translation of descriptors
    // between local and global layers.
    template <>
    struct subgraph_choose_pmap_helper<vertex_index_t> {
        typedef subgraph_local_pmap type;
    };
    template <>
    struct subgraph_choose_pmap_helper< local_property<vertex_index_t> > {
        typedef subgraph_local_pmap type;
    };
    template <>
    struct subgraph_choose_pmap_helper< global_property<vertex_index_t> > {
        typedef subgraph_local_pmap type;
    };

    // Determine the kind of property. If SameType<Tag, vertex_index_t>, then
    // the property lookup is always local. Otherwise, the lookup is global.
    // NOTE: Property parameter is basically unused.
    template <class Tag, class Graph, class Property>
    struct subgraph_choose_pmap {
        typedef typename subgraph_choose_pmap_helper<Tag>::type Helper;
        typedef typename Helper::template bind_<Tag, Graph, Property> Bind;
        typedef typename Bind::type type;
        typedef typename Bind::const_type const_type;
    };

    // Used by the vertex/edge property selectors to determine the kind(s) of
    // property maps used by the property_map type generator.
    struct subgraph_property_generator {
        template <class SubGraph, class Property, class Tag>
        struct bind_ {
            typedef subgraph_choose_pmap<Tag, SubGraph, Property> Choice;
            typedef typename Choice::type type;
            typedef typename Choice::const_type const_type;
        };
    };

  } // namespace detail

template <>
struct vertex_property_selector<subgraph_tag> {
    typedef detail::subgraph_property_generator type;
};

template <>
struct edge_property_selector<subgraph_tag> {
    typedef detail::subgraph_property_generator type;
};

#ifndef BOOST_GRAPH_NO_BUNDLED_PROPERTIES
/** @internal
 * This property map implements local or global bundled property access on
 * an underlying graph. The LocalGlobal template template parameter must be
 * one of the local_property or global_property templates.
 */
template <
    typename Graph, typename Descriptor, typename Bundle, typename T,
    template <typename> class LocalGlobal>
struct subgraph_lg_bundle_property_map
    : put_get_helper<
        T&,
        subgraph_lg_bundle_property_map<Graph, Descriptor, Bundle, T, LocalGlobal>
    >
{
private:
    typedef LocalGlobal<Descriptor> Wrap;
public:
    typedef Descriptor key_type;
    typedef typename remove_const<T>::type value_type;
    typedef T& reference;
    typedef lvalue_property_map_tag category;

    subgraph_lg_bundle_property_map()
    { }

    subgraph_lg_bundle_property_map(Graph* g, T Bundle::* p)
        : m_g(g), m_prop(p)
    { }

    reference operator[](key_type k) const
    { return (*m_g)[Wrap(k)].*m_prop; }

private:
    Graph* m_g;
    T Bundle::* m_prop;
};

// Specialize the property map template to generate bundled property maps.
// NOTE: I'm cheating (actually double-dipping) with the local/global subgraph
// property templates. I'm not using them store descriptors, just specialize
// the property map template for specific lookups.
namespace graph_detail {
    // Help decoding some of the types required for property map definitions.
    template <typename Graph, typename T, typename Bundle>
    struct bundled_subgraph_pmap_helper {
        typedef subgraph<Graph> Subgraph;
        typedef graph_traits<Subgraph> Traits;
        typedef typename Subgraph::vertex_bundled VertBundled;
        typedef typename Subgraph::edge_bundled EdgeBundled;

        // Deduce the descriptor from the template params
        typedef typename mpl::if_<
            detail::is_vertex_bundle<VertBundled, EdgeBundled, Bundle>,
            typename Traits::vertex_descriptor, typename Traits::edge_descriptor
        >::type Desc;

        // Deduce the bundled property type
        typedef typename mpl::if_<
            detail::is_vertex_bundle<VertBundled, EdgeBundled, Bundle>,
            VertBundled, EdgeBundled
        >::type Prop;
    };
} // namespace graph_detail

template <typename Graph, typename T, typename Bundle>
struct property_map<subgraph<Graph>, local_property<T Bundle::*> >
    : graph_detail::bundled_subgraph_pmap_helper<Graph, T, Bundle>
{
private:
    typedef graph_detail::bundled_subgraph_pmap_helper<Graph, T, Bundle> Base;
    typedef typename Base::Subgraph Subgraph;
    typedef typename Base::Desc Desc;
    typedef typename Base::Prop Prop;
public:
    typedef subgraph_lg_bundle_property_map<
        Subgraph, Desc, Prop, T, local_property
    > type;
    typedef subgraph_lg_bundle_property_map<
        Subgraph const, Desc, Prop, T const, local_property
    > const_type;
};

template <typename Graph, typename T, typename Bundle>
struct property_map<subgraph<Graph>, global_property<T Bundle::*> >
    : graph_detail::bundled_subgraph_pmap_helper<Graph, T, Bundle>
{
private:
    typedef graph_detail::bundled_subgraph_pmap_helper<Graph, T, Bundle> Base;
    typedef typename Base::Subgraph Subgraph;
    typedef typename Base::Desc Desc;
    typedef typename Base::Prop Prop;
public:
    typedef subgraph_lg_bundle_property_map<
        Subgraph, Desc, Prop, T, global_property
    > type;
    typedef subgraph_lg_bundle_property_map<
        Subgraph const, Desc, Prop, T const, global_property
    > const_type;
};
#endif

// ==================================================
// get(p, g), get(p, g, k), and put(p, g, k, v)
// ==================================================
template <typename G, typename Property>
typename property_map<subgraph<G>, Property>::type
get(Property, subgraph<G>& g) {
    typedef typename property_map< subgraph<G>, Property>::type PMap;
    return PMap(&g);
}

template <typename G, typename Property>
typename property_map<subgraph<G>, Property>::const_type
get(Property, const subgraph<G>& g) {
    typedef typename property_map< subgraph<G>, Property>::const_type PMap;
    return PMap(&g);
}

template <typename G, typename Property, typename Key>
typename property_traits<
    typename property_map<subgraph<G>, Property>::const_type
>::value_type
get(Property, const subgraph<G>& g, const Key& k) {
    typedef typename property_map< subgraph<G>, Property>::const_type PMap;
    PMap pmap(&g);
    return pmap[k];
}

template <typename G, typename Property, typename Key, typename Value>
void put(Property, subgraph<G>& g, const Key& k, const Value& val) {
    typedef typename property_map< subgraph<G>, Property>::type PMap;
    PMap pmap(&g);
    pmap[k] = val;
}

// ==================================================
// get(global(p), g)
// NOTE: get(global(p), g, k) and put(global(p), g, k, v) not supported
// ==================================================
template <typename G, typename Property>
typename property_map<subgraph<G>, global_property<Property> >::type
get(global_property<Property>, subgraph<G>& g) {
    typedef typename property_map<
        subgraph<G>, global_property<Property>
    >::type Map;
    return Map(&g);
}

template <typename G, typename Property>
typename property_map<subgraph<G>, global_property<Property> >::const_type
get(global_property<Property>, const subgraph<G>& g) {
    typedef typename property_map<
        subgraph<G>, global_property<Property>
    >::const_type Map;
    return Map(&g);
}

// ==================================================
// get(local(p), g)
// NOTE: get(local(p), g, k) and put(local(p), g, k, v) not supported
// ==================================================
template <typename G, typename Property>
typename property_map<subgraph<G>, local_property<Property> >::type
get(local_property<Property>, subgraph<G>& g) {
    typedef typename property_map<
        subgraph<G>, local_property<Property>
    >::type Map;
    return Map(&g);
}

template <typename G, typename Property>
typename property_map<subgraph<G>, local_property<Property> >::const_type
get(local_property<Property>, const subgraph<G>& g) {
    typedef typename property_map<
        subgraph<G>, local_property<Property>
    >::const_type Map;
    return Map(&g);
}

#ifndef BOOST_GRAPH_NO_BUNDLED_PROPERTIES
// ==================================================
// get(bundle(p), g)
// ==================================================

template<typename G, typename T, typename Bundle>
inline typename property_map<subgraph<G>, T Bundle::*>::type
get(T Bundle::* p, subgraph<G>& g) {
    typedef typename property_map<subgraph<G>, T Bundle::*>::type Map;
    return Map(&g, p);
}

template<typename G, typename T, typename Bundle>
inline typename property_map<subgraph<G>, T Bundle::*>::const_type
get(T Bundle::* p, subgraph<G> const& g) {
    typedef typename property_map<subgraph<G>, T Bundle::*>::const_type Map;
    return Map(&g, p);
}

template <typename Graph, typename Type, typename Bundle, typename Key>
inline Type get(Type Bundle::* p, subgraph<Graph> const& g, Key const& k)
{ return get(get(p, g), k); }

template <typename Graph, typename Type, typename Bundle, typename Key,
          typename Value>
inline void put(Type Bundle::* p, Graph& g, Key const& k, Value const& v)
{ put(get(p, g), k, v); }

// =========================================================
// Local bundled, get

template<typename G, typename T, typename Bundle>
inline typename property_map<
    subgraph<G>, local_property<T Bundle::*>
>::type
get(local_property<T Bundle::*> p, subgraph<G>& g) {
    typedef typename property_map<
        subgraph<G>, local_property<T Bundle::*>
    >::type Map;
    return Map(&g, p.value);
}

template<typename G, typename T, typename Bundle>
inline typename property_map<
    subgraph<G>, local_property<T Bundle::*>
>::const_type
get(local_property<T Bundle::*> p, subgraph<G> const& g) {
    typedef typename property_map<
        subgraph<G>, local_property<T Bundle::*>
    >::const_type Map;
    return Map(&g, p.value);
}

template <typename Graph, typename Type, typename Bundle, typename Key>
inline Type get(local_property<Type Bundle::*> p, subgraph<Graph> const& g,
                Key const& k)
{ return get(get(p, g), k); }

// =========================================================
// Global bundled, get

template<typename G, typename T, typename Bundle>
inline typename property_map<
    subgraph<G>, global_property<T Bundle::*>
>::type
get(global_property<T Bundle::*> p, subgraph<G>& g) {
    typedef typename property_map<
        subgraph<G>, global_property<T Bundle::*>
    >::type Map;
    return Map(&g, p.value);
}

template<typename G, typename T, typename Bundle>
inline typename property_map<
    subgraph<G>, global_property<T Bundle::*>
>::const_type
get(global_property<T Bundle::*> p, subgraph<G> const& g) {
    typedef typename property_map<
        subgraph<G>, global_property<T Bundle::*>
    >::const_type Map;
    return Map(&g, p.value);
}

template <typename Graph, typename Type, typename Bundle, typename Key>
inline Type get(global_property<Type Bundle::*> p, subgraph<Graph> const& g,
                Key const& k)
{ return get(get(p, g), k); }

#endif

template <typename G, typename Tag>
inline typename graph_property<G, Tag>::type&
get_property(subgraph<G>& g, Tag tag) {
    return get_property(g.m_graph, tag);
}

template <typename G, typename Tag>
inline const typename graph_property<G, Tag>::type&
get_property(const subgraph<G>& g, Tag tag) {
    return get_property(g.m_graph, tag);
}

//===========================================================================
// Miscellaneous Functions

template <typename G>
typename subgraph<G>::vertex_descriptor
vertex(typename subgraph<G>::vertices_size_type n, const subgraph<G>& g)
{ return vertex(n, g.m_graph); }

//===========================================================================
// Mutability Traits
// Just pull the mutability traits form the underlying graph. Note that this
// will probably fail (badly) for labeled graphs.
template <typename G>
struct graph_mutability_traits< subgraph<G> > {
    typedef typename graph_mutability_traits<G>::category category;
};

} // namespace boost

#endif // BOOST_SUBGRAPH_HPP