// Copyright (c) 1999  Max-Planck-Institute Saarbruecken (Germany).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL: https://github.com/CGAL/cgal/blob/v6.0.1/Convex_hull_2/include/CGAL/Convex_hull_2/ch_melkman_impl.h $
// $Id: include/CGAL/Convex_hull_2/ch_melkman_impl.h 50cfbde3b84 $
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s)     : Stefan Schirra

#ifndef CGAL_CH_MELKMAN_IMPL_H
#define CGAL_CH_MELKMAN_IMPL_H

#include <CGAL/license/Convex_hull_2.h>

#ifndef CGAL_CH_NO_POSTCONDITIONS
#include <CGAL/convexity_check_2.h>
#endif // CGAL_CH_NO_POSTCONDITIONS

#include <CGAL/assertions.h>

#include <algorithm>
#include <deque>

namespace CGAL {

template <class InputIterator, class OutputIterator, class Traits>
OutputIterator
ch_melkman( InputIterator first, InputIterator last,
            OutputIterator result, const Traits& ch_traits)
{
  typedef typename Traits::Point_2      Point;
  typedef typename Traits::Equal_2      Equal_2;

  typename Traits::Left_turn_2 left_turn  = ch_traits.left_turn_2_object();
  Equal_2  equal_points = ch_traits.equal_2_object();

  CGAL_assertion_code( \
  typename Traits::Less_xy_2 less       = ch_traits.less_xy_2_object(); )

  std::deque< Point> Q;

  CGAL_expensive_postcondition_code( std::deque< Point> IN; )
  if (first == last) return result;           // 0 elements
  Point p = *first;
  CGAL_expensive_postcondition_code( IN.push_back(p); )
  if (++first == last)
  { *result = p; ++result; return result; }   // 1 element
  Point q = *first;
  CGAL_expensive_postcondition_code( IN.push_back(q); )
  if (++first == last)                        // 2 elements
  {
    *result = p; ++result;
    if (! equal_points(p,q))
    { *result = q; ++result; }
    return result;
  }
  Q.push_back( p);

  Point r;
  while (first != last)
  {
    r = *first;
    CGAL_expensive_postcondition_code( IN.push_back(r); )
    // visited input sequence =  p,..., q, r
    if ( left_turn(p,q,r)) { Q.push_back( q);  break; }
    if ( left_turn(q,p,r)) { Q.push_front( q); break; }
    CGAL_assertion( less( p, q) ? less (p, r) : less( r, p));
    q = r;
    ++first;
  }


  Point current = q;
  if (first != last)           // non-collinear point r exists
  {

    current = r;
    // current, Q.front(), ..., Q.back()
    // ccw convex hull of visited points
    Point s;
    while ( ++first != last)
    {
      r = *first;
      CGAL_expensive_postcondition_code( IN.push_back(r); )
      if (left_turn( current, r, Q.front()) ||
          left_turn( Q.back(), r, current))
      // r outside cone Q.front(), current, Q.back() <=>
      // right_turn( current, Q.front(), r) ||
      // right_turn( Q.back(), current, r)
      {
        s = current;
        while (!Q.empty() && !left_turn( r, s, Q.front()))
        //      !left_turn( r, s, Q.front())
        { s = Q.front(); Q.pop_front(); }
        Q.push_front(s);
        s = current;
        while (!Q.empty() &&  !left_turn( s, r, Q.back()))
        //     !right_turn( r, s, Q.back())
        { s = Q.back(); Q.pop_back(); }
        Q.push_back(s);
        current = r;
      }

    }

  }


  Q.push_back( current);       // add last point to Q
  CGAL_postcondition( \
  is_ccw_strongly_convex_2( Q.begin(), Q.end(), ch_traits));
  CGAL_expensive_postcondition( \
  ch_brute_force_check_2( IN.begin(),IN.end(), Q.begin(),Q.end(), ch_traits));
  std::copy( Q.begin(), Q.end(), result);
  return result;

}

} //namespace CGAL

#endif // CGAL_CH_MELKMAN_IMPL_H

