#include <CGAL/Exact_rational.h>
#include <CGAL/Cartesian.h>
#include <CGAL/Arr_segment_traits_2.h>
#include <CGAL/Arr_curve_data_traits_2.h>
#include <CGAL/Envelope_diagram_1.h>
#include <CGAL/envelope_2.h>

#include <list>
#include <iostream>
#include <cstring>

using std::strcmp;

// leda_rational, or Gmpq, or Quotient<MP_float>
typedef CGAL::Exact_rational                            NT;
typedef CGAL::Cartesian<NT>                             Kernel;
typedef CGAL::Arr_segment_traits_2<Kernel>              Segment_traits_2;
typedef CGAL::Arr_curve_data_traits_2<Segment_traits_2, 
                                      int>              Traits_2;
typedef Traits_2::Point_2                               Point_2;
typedef Segment_traits_2::Curve_2                       Segment_2;
typedef Traits_2::Curve_2                               Curve_2;
typedef CGAL::Envelope_diagram_1<Traits_2>              Diagram_1;
typedef std::list<Curve_2>                              Curve_list;

enum Coord_input_format
{
  F_RATIONAL,            // Coordinates given as rational numbers.
  F_INTEGER,             // Coordinates given as integers.
  F_DOUBLE               // Coordinates given as doubles (with decimal points).
};

/*!
 * Read a set of line segments from an input file.
 * \param filename The name of the input file.
 * \param format The coordinate format.
 * \param segs Output: The segments.
 * \return Whether the segments were successfuly read.
 */
bool read_segments (const char* filename,
                    Coord_input_format format,
                    Curve_list& segs)
{
  segs.clear();

  // Open the input file.
  std::ifstream ifile (filename);

  if (! ifile.is_open()) {
    std::cerr << "Failed to open <" << filename << ">." << std::endl;
    return (false);
  }

  // Read the segments.
  unsigned int n_segments;
  ifile >> n_segments;

  unsigned int k;
  for (k = 0; k < n_segments; k++) {
      NT x1, y1, x2, y2;

    // Read the coordinates of the current segment.
    if (format == F_INTEGER) {
      int ix1, iy1, ix2, iy2;
      ifile >> ix1 >> iy1 >> ix2 >> iy2;
      x1 = NT (ix1);
      y1 = NT (iy1);
      x2 = NT (ix2);
      y2 = NT (iy2);
    }
    else if (format == F_DOUBLE) {
      const int denom = 100000;
      double dx1, dy1, dx2, dy2;
      ifile >> dx1 >> dy1 >> dx2 >> dy2;
      x1 = NT (static_cast<int> (denom * dx1), denom);
      y1 = NT (static_cast<int> (denom * dy1), denom);
      x2 = NT (static_cast<int> (denom * dx2), denom);
      y2 = NT (static_cast<int> (denom * dy2), denom);
    }
    else {
      ifile >> x1 >> y1 >> x2 >> y2;
    }
      
    Segment_2 seg = Segment_2 (Point_2 (x1, y1), Point_2 (x2, y2));
    segs.push_back (Curve_2(seg, static_cast<int>(segs.size())));
  }
  ifile.close();

  return (true);
}

/*!
 * Check if a $x$-monotone curve with the same associated data as the input
 * curve is in the given range.
 * \param begin The beginning of the range.
 * \param end Passed-the-end iterator.
 * \param c The curve, the data of which we are searching.
 * \return True if we found an $x$-monotone curve with the same data.
 */
template <typename I>
bool find_curve(I begin, I end, const Curve_2& c)
{
  while (begin != end)
  {
    if (begin->data() == c.data())
      return true;
    ++begin;
  }
  return false;
}

/*!
 * Check the envelope of a given set of segments.
 * \param segs The segments.
 * \param diag The diagram.
 * \param is_lower Does the diagram reprsent the lower or the upper envelope.
 * \return Whether the diagram structure is correct.
 */
bool check_envelope (const Curve_list& segs,
                     const Diagram_1& diag,
                     bool is_lower)
{
  typedef Diagram_1::Curve_const_iterator                 Curve_iterator;

  // Go over minimization diagram.
  Diagram_1::Edge_const_handle    e = diag.leftmost();
  Diagram_1::Vertex_const_handle  v;

  if (e == diag.rightmost())
    // If the diagram is empty, the segment set must also be empty.
    return (segs.empty());

  // Start from the first finite edge.
  Kernel                         ker;
  Kernel::Construct_midpoint_2   midpoint = ker.construct_midpoint_2_object();
  Kernel::Construct_min_vertex_2 min_ver = ker.construct_min_vertex_2_object();
  Kernel::Construct_max_vertex_2 max_ver = ker.construct_max_vertex_2_object();
  Kernel::Compare_y_at_x_2       comp_y_at_x = ker.compare_y_at_x_2_object();
  Point_2                        p_mid;
  CGAL::Comparison_result        res1, res2;
  CGAL::Comparison_result        y_res;
  Curve_list::const_iterator     sit;

  v = e->right();
  e = v->right();
  while (e != diag.rightmost())
  {
    // Get the midpoint of the current edge.
    p_mid = midpoint (e->left()->point(), e->right()->point());

    // Check that all associated curves are equal:
    for (Curve_iterator it = e->curves_begin();
         it != e->curves_end(); ++it)
    {
      if(comp_y_at_x(p_mid, e->curve(), *it) != CGAL::EQUAL)
      {
        std::cerr << "The edge (" << e->left()->point()
                  << ") -> (" << e->right()->point() << ") is associated with "
                  << "both of the following curve which are not equal: "
                  << " [" << e->curve() << "], [" << *it << "]"
                  << std::endl;
        return false;
      }
    }

    // Check that all associated curves are equal:
    for (Curve_iterator it = v->curves_begin();
         it != v->curves_end(); ++it)
    {
      if(comp_y_at_x(v->point(), *it) != CGAL::EQUAL)
      {
        std::cerr << "The vertex (" << v->point() << ") is associated with "
                  << "is associated with"
                  << " [" << *it << "] but they are not equal at the vertex."
                  << std::endl;
        return false;
      }
    }

    

    // Go over all segments.
    for (sit = segs.begin(); sit != segs.end(); ++sit)
    {
      // Check if p_mid lies in the x-range of the current segment.
      res1 = compare_x (p_mid, min_ver(*sit));
      res2 = compare_x (p_mid, max_ver(*sit));

      if (res1 != CGAL::SMALLER && res2 != CGAL::LARGER)
      {
        // Check the diagram edge.
        if (e->is_empty())
        {
          // If p_mid is in the x-range of the given segment, the current edge
          // cannot by empty.
          std::cerr << "The edge (" << e->left()->point()
                    << ") -> (" << e->right()->point() << ") is empty, "
                    << "but the segment [" << *sit << "] is defined over it."
                    << std::endl;
          return (false);
        }
        else
        {
          // Compare the segment with the segment associated with the edge.
          y_res = comp_y_at_x (p_mid, *sit, e->curve());
          
          // Check for violations of the diagram properties.
          if ((is_lower && y_res == CGAL::SMALLER) ||
              (! is_lower && y_res == CGAL::LARGER))
          {
            std::cerr << "The edge (" << e->left()->point()
                      << ") -> (" << e->right()->point() 
                      << ") is associated with the segment ["
                      << e->curve() << "], but the segment [" 
                      << *sit << "] violates the envelope properties."
                      << std::endl;
            return (false);
          }
          
          // If it is equal, the segment should be in the diagram.
          if (y_res == CGAL::EQUAL && 
              find_curve(e->curves_begin(), e->curves_end(), *sit) == false)
          {
            std::cerr << "The edge (" << e->left()->point()
                      << ") -> (" << e->right()->point() 
                      << ") is associated with the segment ["
                      << e->curve() << "], but the segment [" 
                      << *sit << "] is not in the list of its curves."
                      << std::endl;
            return (false);
          }
        }
      }


      // Check if v lies in the x-range of the current segment.
      res1 = compare_x (v->point(), min_ver(*sit));
      res2 = compare_x (v->point(), max_ver(*sit));

      if (res1 != CGAL::SMALLER && res2 != CGAL::LARGER)
      {
        // Check the diagram vertex.
        if (v->number_of_curves() == 0)
        {
          // If v is in the x-range of the given segment, the current vertex
          // cannot by empty.
          std::cerr << "The vertex (" << v->point()
                    << ") is empty, "
                    << "but the segment [" << *sit << "] is defined over it."
                    << std::endl;
          return (false);
        }
        else
        {
          // Compare the segment with the segment associated with the edge.
          y_res = comp_y_at_x (v->point(), *sit);
          
          // Check for violations of the diagram properties.
          if ((is_lower && y_res == CGAL::LARGER) ||
              (! is_lower && y_res == CGAL::SMALLER))
          {
            std::cerr << "The vertex (" << v->point()
                      << ") and the segment [" 
                      << *sit << "] violate the envelope properties."
                      << std::endl;
            return (false);
          }
          
          // If it is equal, the segment should be in the diagram.
          if (y_res == CGAL::EQUAL && 
              find_curve(v->curves_begin(), v->curves_end(), *sit) == false)
          {
            std::cerr << "The vertex (" << v->point()
                      << ") does not contain the segment [" 
                      << *sit << "] in the list of its curves, but they have" 
                      << " equal values."
                      << std::endl;
            return (false);
          }
        }
      }

    }
    v = e->right();
    e = v->right();
  }

    
  // If we reached here, the diagram is valid.
  return (true);
}

/*!
 * The main program.
 */
int main (int argc, char *argv[])
{
  if (argc % 2 == 0 || argc == 1)
  {
    std::cerr << "Usage: " << argv[0] 
              << "<input file> [ -q | -i | -d ]" << std::endl;
    return (1);
  }

  int number_of_tests = (argc - 1) / 2;
  for (int i = 0; i < number_of_tests; ++i)
  {
    std::cout << "Checking input file: " << argv[2*i + 1] << std::endl;
    
    // Determine the input format.
    Coord_input_format   format = F_RATIONAL;
    
    if (strcmp (argv[2*i + 2], "-i") == 0 || strcmp (argv[2*i + 2], "-I") == 0)
      format = F_INTEGER;
    else if (strcmp (argv[2*i + 2], "-d") == 0 || strcmp (argv[2*i + 2], "-D") == 0)
      format = F_DOUBLE;
    
    // Read the input segments.
    Curve_list   segments;
    
    if (! read_segments (argv[2*i + 1], format, segments))
      return (1);
    
    // Compute their lower envelope.
    Diagram_1              min_diag;
    
    lower_envelope_2 (segments.begin(), segments.end(),
                      min_diag);
    
    // Check the lower envelope.
    if (! check_envelope (segments, min_diag, true))
    {
      std::cerr << "Problems in the lower-envelope computation." << std::endl;
      return (1);
    }
    else
    {
      std::cout << "The lower envelope is valid." << std::endl;
    }
    
    // Compute the upper envelope.
    Diagram_1              max_diag;
    
    upper_envelope_2 (segments.begin(), segments.end(),
                      max_diag);
    
    // Check the upper envelope.
    if (! check_envelope (segments, max_diag, false))
    {
      std::cerr << "Problems in the upper-envelope computation." << std::endl;
      return (1);
    }
    else
    {
      std::cout << "The upper envelope is valid." << std::endl;
    }
  }
  return (0);
}