// Copyright (c) 2013  GeometryFactory (France). All rights reserved.
//
// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public License as
// published by the Free Software Foundation; either version 3 of the License,
// or (at your option) any later version.
//
// Licensees holding a valid commercial license may use this file in
// accordance with the commercial license agreement provided with the software.
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// $URL$
// $Id$
//
// Author(s)     : Laurent Rineau, Xiang Gao
//

#ifndef CGAL_SPLIT_GRAPH_INTO_POLYLINES
#define CGAL_SPLIT_GRAPH_INTO_POLYLINES

#include <map> 
#include <set> 
#include <boost/foreach.hpp>
#include <boost/graph/adjacency_list.hpp>
#include <iostream>


namespace CGAL {

namespace internal{
struct IsTerminalDefault
{
  template <typename VertexDescriptor, typename Graph>
  bool operator ()(VertexDescriptor& , const Graph& )
  {
    return false;
  }
};

template <class Graph>
struct Dummy_visitor_for_split_graph_into_polylines
{
  void start_new_polyline(){}
  void add_node(typename boost::graph_traits<Graph>::vertex_descriptor){}
  void end_polyline(){}
};
} //end of namespace internal


namespace internal {

template <typename G_copy, typename Less_on_orig_vertex_descriptors>
class Less_on_G_copy_vertex_descriptors {
  const G_copy& g_copy;
  const Less_on_orig_vertex_descriptors& less;
public:
  Less_on_G_copy_vertex_descriptors ( const G_copy& g_copy,
    const Less_on_orig_vertex_descriptors& less)
    : g_copy(g_copy), less(less) {}

  typedef typename boost::graph_traits<G_copy>::vertex_descriptor
    g_copy_vertex_descriptor;
  typedef typename boost::graph_traits<G_copy>::out_edge_iterator
    g_copy_out_edge_iterator;
  typedef typename boost::graph_traits<G_copy>::degree_size_type
    g_copy_degree_size_type;

  bool operator()(g_copy_vertex_descriptor v1,
                  g_copy_vertex_descriptor v2) const {
    if(less(g_copy[v1], g_copy[v2]))
      return true;
    else if(less(g_copy[v2], g_copy[v1]))
      return false;
    // If g_copy[v1] and g_copy[v2] are equivalent, then compare the
    // descriptors:
    if(v1 == v2) return false;
    //   - compare degrees:
    const g_copy_degree_size_type dv1 = degree(v1, g_copy);
    const g_copy_degree_size_type dv2 = degree(v2, g_copy);
    if(dv1 != dv2)
      return dv1 < dv2;
    if(dv1 == 0) return v1 < v2;
    ///  - then compare an adjacent vertex:
    g_copy_vertex_descriptor other_v1 = target(*out_edges(v1, g_copy).first,
                                               g_copy);
    g_copy_vertex_descriptor other_v2 = target(*out_edges(v2, g_copy).first,
                                               g_copy);
    return less(g_copy[other_v1], g_copy[other_v2]);
  }
}; // end class Less_on_G_copy_vertex_descriptors

/// Splits a graph at vertices with degree higher than two and at vertices where `is_terminal` returns `true`
/// The vertices are duplicated, and new incident edges created.
/// `OrigGraph` must be undirected
template <typename Graph,
          typename OrigGraph,
          typename IsTerminal>
void duplicate_terminal_vertices(Graph& graph,
                                const OrigGraph& orig,
                                IsTerminal is_terminal)
{
  typedef typename boost::graph_traits<Graph>::vertex_descriptor vertex_descriptor;
  typedef typename boost::graph_traits<Graph>::edge_descriptor edge_descriptor;
  typedef typename boost::graph_traits<Graph>::vertex_iterator vertex_iterator;
  typedef typename boost::graph_traits<Graph>::out_edge_iterator out_edge_iterator;

  vertex_iterator b,e;
  boost::tie(b,e) = vertices(graph);
  std::vector<vertex_descriptor> V(b,e);
  BOOST_FOREACH(vertex_descriptor v, V)
  {
    typename boost::graph_traits<OrigGraph>::vertex_descriptor orig_v = graph[v];
    typename boost::graph_traits<Graph>::degree_size_type deg = degree(v, graph);
    if ((deg != 0 && is_terminal(orig_v, orig)) || deg > 2)
      {
        out_edge_iterator b, e;
        boost::tie(b, e) = out_edges(v, graph);
        std::vector<edge_descriptor> out_edges_of_v(b, e);
        for (unsigned int i = 1; i < out_edges_of_v.size(); ++i)
          {
            edge_descriptor e = out_edges_of_v[i];
            vertex_descriptor w = target(e, graph);
            remove_edge(e, graph);
            vertex_descriptor vc = add_vertex(graph);
            graph[vc] = orig_v;
            add_edge(vc, w, graph);
          }
        CGAL_assertion(degree(v, graph) == 1);
      }
  }

  // check all vertices are of degree 1 or 2 and that the source
  // and target of each edge are different vertices with different ids
  CGAL_assertion_code(
                      BOOST_FOREACH(vertex_descriptor v, vertices(graph)){
                        typename boost::graph_traits<Graph>::degree_size_type
                          n = degree(v, graph);
                        CGAL_assertion( n == 0 || n == 1 || n == 2);
                      }
                      BOOST_FOREACH(edge_descriptor e, edges(graph)){
                        vertex_descriptor v = target(e, graph);
                        vertex_descriptor w = source(e, graph);
                        CGAL_assertion(v != w);
                      }
                      ) // end of CGAL_assertion_code
} // end of duplicate_terminal_vertices
    
} // namespace internal

  
/*!
\ingroup PkgBGL
splits into polylines the graph `g` at vertices of degree greater than 2
and at vertices for which `is_terminal(v,graph)==true`.
The polylines are reported using a visitor.
\tparam Graph a model of the `boost` concepts `VertexListGraph` and `EdgeListGraph`.
\tparam Visitor a class that provides:
        - <code>void start_new_polyline()</code>
          called when starting the description of a polyline.
        - <code>void add_node(typename boost::graph_traits<Graph>::%vertex_descriptor v)</code>
          called for each vertex `v` of the polyline currently described.
        - <code>void end_polyline()</code>
          called when the description of a polyline is finished.
\tparam IsTerminal A functor providing `bool operator()(boost::graph_traits<Graph>::%vertex_descriptor v, const Graph& g) const`
                   returning true if the vertex `v` of degree 2 is a polyline endpoint and false otherwise.

An overload without `is_terminal` is provided if no vertices but those of degree
different from 2 are polyline endpoints.

@todo Document the version with four parameters
*/
template <typename Graph,
          typename Visitor,
          typename IsTerminal>
void
split_graph_into_polylines(const Graph& graph,
                           Visitor& polyline_visitor,
                           IsTerminal is_terminal)
{
  typedef typename boost::graph_traits<Graph>::vertex_descriptor Graph_vertex_descriptor;
  std::less<Graph_vertex_descriptor> less;
  split_graph_into_polylines(graph, polyline_visitor, is_terminal, less);
}

template <typename Graph,
          typename Visitor,
          typename IsTerminal,
          typename LessForVertexDescriptors>
void
split_graph_into_polylines(const Graph& graph,
                           Visitor& polyline_visitor,
                           IsTerminal is_terminal,
                           LessForVertexDescriptors less)
{
  typedef typename boost::graph_traits<Graph>::vertex_descriptor Graph_vertex_descriptor;
  typedef typename boost::graph_traits<Graph>::edge_descriptor Graph_edge_descriptor;
  
  typedef boost::adjacency_list <boost::setS, // this avoids parallel edges
                                 boost::vecS, 
                                 boost::undirectedS,
                                 Graph_vertex_descriptor > G_copy;

  typedef typename boost::graph_traits<G_copy>::vertex_descriptor vertex_descriptor;
  typedef typename boost::graph_traits<G_copy>::edge_descriptor edge_descriptor;
  typedef typename boost::graph_traits<G_copy>::out_edge_iterator out_edge_iterator;
  
  // we make a copy of the input graph
  G_copy g_copy;
  {
    typedef std::map<typename boost::graph_traits<Graph>::vertex_descriptor,
                     typename boost::graph_traits<G_copy>::vertex_descriptor> V2vmap;
    V2vmap v2vmap;
    
    BOOST_FOREACH(Graph_vertex_descriptor v, vertices(graph)){
      vertex_descriptor vc = add_vertex(g_copy);
      g_copy[vc] = v;
      v2vmap[v] = vc; 
    }
    

    BOOST_FOREACH(Graph_edge_descriptor e, edges(graph)){
      Graph_vertex_descriptor vs = source(e,graph);
      Graph_vertex_descriptor vt = target(e,graph);
      vertex_descriptor vsc, vtc;
      if(vs == vt){
        std::cerr << "ignore self loop\n";
      }else{
        typename V2vmap::iterator it;

        if((it = v2vmap.find(vs)) == v2vmap.end()){
          vsc = add_vertex(g_copy);
          g_copy[vsc] = vs;
          v2vmap[vs] = vsc;
        }else{
          vsc = it->second;
        }
        if((it = v2vmap.find(vt)) == v2vmap.end()){
          vtc = add_vertex(g_copy);
          g_copy[vtc] = vt;
          v2vmap[vt] = vtc;
        }else{
          vtc = it->second;
        }
        add_edge(vsc,vtc,g_copy);
      }
    }
  }  
  // duplicate terminal vertices and vertices of degree more than 2
  internal::duplicate_terminal_vertices(g_copy, graph, is_terminal);

  // put polylines endpoint in a set
  typedef internal::Less_on_G_copy_vertex_descriptors<
    G_copy,
    LessForVertexDescriptors> G_copy_less;
  G_copy_less g_copy_less(g_copy, less);
  std::set<vertex_descriptor, G_copy_less> terminal(g_copy_less);

  BOOST_FOREACH(vertex_descriptor v, vertices(g_copy)){
    typename boost::graph_traits<Graph>::degree_size_type n = degree(v, g_copy);
    if ( n == 1 ) terminal.insert(v);
    if ( n ==0 ){
      //isolated vertex
      polyline_visitor.start_new_polyline();
      polyline_visitor.add_node(g_copy[v]);
      polyline_visitor.end_polyline();
    }
  }

  // go over all polylines and provide the description to the visitor
  while (!terminal.empty())
  {
    typename std::set<vertex_descriptor>::iterator it = terminal.begin();
    vertex_descriptor u = *it;
    terminal.erase(it);
    polyline_visitor.start_new_polyline();
    polyline_visitor.add_node(g_copy[u]);
    while (degree(u,g_copy) != 0)
    {
      CGAL_assertion(degree(u,g_copy) == 1);
      out_edge_iterator b = out_edges(u, g_copy).first;
      vertex_descriptor v = target(*b, g_copy);
      CGAL_assertion(u!=v);
      polyline_visitor.add_node(g_copy[v]);
      if (degree(v, g_copy)==1)
        terminal.erase(v);
      remove_edge(b, g_copy);
      u = v;
    }
    polyline_visitor.end_polyline();
  }

  // do the same but for cycles
  while (num_edges(g_copy) != 0)
  {
    edge_descriptor first_edge = *edges(g_copy).first;
    vertex_descriptor u = source(first_edge, g_copy);

    polyline_visitor.start_new_polyline();
    polyline_visitor.add_node(g_copy[u]);

    u = target(first_edge, g_copy);
    remove_edge(first_edge, g_copy);
    polyline_visitor.add_node(g_copy[u]);

    while (degree(u,g_copy) != 0)
    {
      CGAL_assertion(degree(u,g_copy) == 1);
      out_edge_iterator b = out_edges(u, g_copy).first;
      vertex_descriptor v = target(*b, g_copy);
      CGAL_assertion(u!=v);
      polyline_visitor.add_node(g_copy[v]);
      remove_edge(b, g_copy);
      u = v;
    }
    polyline_visitor.end_polyline();
  }
}

/// \cond SKIP_IN_MANUAL
/// Split graph into polylines delimited by vertices of degree different from 2.
/// Then the graph is visited and Visitor is called to describe the polylines
/// Graph must be undirected
template <typename Graph,
          typename Visitor>
void
split_graph_into_polylines(const Graph& graph,
                           Visitor& polyline_visitor)
{
  split_graph_into_polylines(graph, polyline_visitor, internal::IsTerminalDefault());
}
/// \endcond

} //end of namespace CGAL

#endif //CGAL_SPLIT_GRAPH_INTO_POLYLINES
