


'''simple docstring'''







from __future__ import annotations

from collections.abc import Iterable


class 				__lowerCamelCase				:
    """simple docstring"""


    def __init__(						self    :							int   ,							SCREAMING_SNAKE_CASE    :							str   ,							SCREAMING_SNAKE_CASE    :							int):
           _A						,				_A  :			Optional[int]											=      float(SCREAMING_SNAKE_CASE), float(SCREAMING_SNAKE_CASE)


    def __eq__(						self    :							int   ,							SCREAMING_SNAKE_CASE    :							str):
           return self.x == other.x and self.y == other.y


    def __ne__(						self    :							Optional[int]   ,							SCREAMING_SNAKE_CASE    :							int):
           return not self == other


    def __gt__(						self    :							Tuple   ,							SCREAMING_SNAKE_CASE    :							Dict):
           if self.x > other.x:
                  return True
           elif self.x == other.x:
                  return self.y > other.y
           return False


    def __lt__(						self    :							Dict   ,							SCREAMING_SNAKE_CASE    :							Optional[Any]):
           return not self > other


    def __ge__(						self    :							Dict   ,							SCREAMING_SNAKE_CASE    :							str):
           if self.x > other.x:
                  return True
           elif self.x == other.x:
                  return self.y >= other.y
           return False


    def __le__(						self    :							int   ,							SCREAMING_SNAKE_CASE    :							Tuple):
           if self.x < other.x:
                  return True
           elif self.x == other.x:
                  return self.y <= other.y
           return False


    def __repr__(						self    :							int):
           return F'({self.x}, {self.y})'


    def __hash__(						self    :							Any):
           return hash(self.x)






def    lowerCAmelCase__ (       lowerCamelCase  :    list[Point] | list[list[float]] | Iterable[list[float]]						,):
       _A  :			list[Point]											=      []
       if list_of_tuples:
              for p in list_of_tuples:
                     if isinstance(lowerCamelCase						,lowerCamelCase     ):
                            points.append(lowerCamelCase     )
                     else:
                            try:
                                   points.append(Point(p[0]						,p[1]     )     )
                            except (IndexError, TypeError):
                                   print(
                                       F'Ignoring deformed point {p}. All points'
                                       ' must have at least 2 coordinates.'     )
       return points






def    lowerCAmelCase__ (       lowerCamelCase  :    list[Point] | list[list[float]]     ):

       if not hasattr(lowerCamelCase						,'__iter__'     ):
              _A  :			int											=      F'Expecting an iterable object but got an non-iterable type {points}'
              raise ValueError(lowerCamelCase     )

       if not points:
              _A  :			Optional[Any]											=      F'Expecting a list of points but got {points}'
              raise ValueError(lowerCamelCase     )

       return _construct_points(lowerCamelCase     )






def    lowerCAmelCase__ (       lowerCamelCase  :    Point						,lowerCamelCase  :    Point						,lowerCamelCase  :    Point     ):
       _A  :			List[Any]											=      (a.x * b.y + b.x * c.y + c.x * a.y) - (a.y * b.x + b.y * c.x + c.y * a.x)
       return det






def    lowerCAmelCase__ (       lowerCamelCase  :    list[Point]     ):
       _A  :			Union[str, Any]											=      sorted(_validate_input(lowerCamelCase     )     )
       _A  :			Dict											=      len(lowerCamelCase     )
       _A  :			Optional[int]											=      set()

       for i in range(n - 1     ):
              for j in range(i + 1						,lowerCamelCase     ):
                     _A  :			List[Any]											=      False
                     _A  :			Optional[int]											=      True
                     for k in range(lowerCamelCase     ):
                            if k != i and k != j:
                                   _A  :			Dict											=      _det(points[i]						,points[j]						,points[k]     )

                                   if det_k > 0:
                                          _A  :			Union[str, Any]											=      True
                                   elif det_k < 0:
                                          _A  :			int											=      True
                                   else:
                                          # point[i], point[j], point[k] all lie on a straight line
                                          # if point[k] is to the left of point[i] or it's to the
                                          # right of point[j], then point[i], point[j] cannot be
                                          # part of the convex hull of A
                                          if points[k] < points[i] or points[k] > points[j]:
                                                 _A  :			Tuple											=      False
                                                 break

                            if points_left_of_ij and points_right_of_ij:
                                   _A  :			List[Any]											=      False
                                   break

                     if ij_part_of_convex_hull:
                            convex_set.update([points[i], points[j]]     )

       return sorted(lowerCamelCase     )






def    lowerCAmelCase__ (       lowerCamelCase  :    list[Point]     ):
       _A  :			Tuple											=      sorted(_validate_input(lowerCamelCase     )     )
       _A  :			Optional[int]											=      len(lowerCamelCase     )

       # divide all the points into an upper hull and a lower hull
       # the left most point and the right most point are definitely
       # members of the convex hull by definition.
       # use these two anchors to divide all the points into two hulls,
       # an upper hull and a lower hull.

       # all points to the left (above) the line joining the extreme points belong to the
       # upper hull
       # all points to the right (below) the line joining the extreme points below to the
       # lower hull
       # ignore all points on the line joining the extreme points since they cannot be
       # part of the convex hull

       _A  :			str											=      points[0]
       _A  :			Union[str, Any]											=      points[n - 1]

       _A  :			List[Any]											=      {left_most_point, right_most_point}
       _A  :			List[str]											=      []
       _A  :			List[str]											=      []

       for i in range(1						,n - 1     ):
              _A  :			Any											=      _det(lowerCamelCase						,lowerCamelCase						,points[i]     )

              if det > 0:
                     upper_hull.append(points[i]     )
              elif det < 0:
                     lower_hull.append(points[i]     )

       _construct_hull(lowerCamelCase						,lowerCamelCase						,lowerCamelCase						,lowerCamelCase     )
       _construct_hull(lowerCamelCase						,lowerCamelCase						,lowerCamelCase						,lowerCamelCase     )

       return sorted(lowerCamelCase     )






def    lowerCAmelCase__ (       lowerCamelCase  :    list[Point]						,lowerCamelCase  :    Point						,lowerCamelCase  :    Point						,lowerCamelCase  :    set[Point]     ):
       if points:
              _A  :			Optional[Any]											=      None
              _A  :			Optional[int]											=      float('-inf'     )
              _A  :			List[str]											=      []

              for p in points:
                     _A  :			List[str]											=      _det(lowerCamelCase						,lowerCamelCase						,lowerCamelCase     )

                     if det > 0:
                            candidate_points.append(lowerCamelCase     )

                            if det > extreme_point_distance:
                                   _A  :			List[str]											=      det
                                   _A  :			Union[str, Any]											=      p

              if extreme_point:
                     _construct_hull(lowerCamelCase						,lowerCamelCase						,lowerCamelCase						,lowerCamelCase     )
                     convex_set.add(lowerCamelCase     )
                     _construct_hull(lowerCamelCase						,lowerCamelCase						,lowerCamelCase						,lowerCamelCase     )






def    lowerCAmelCase__ (       lowerCamelCase  :    list[Point]     ):
       _A  :			Tuple											=      sorted(_validate_input(lowerCamelCase     )     )
       _A  :			Optional[Any]											=      len(lowerCamelCase     )

       _A  :			List[str]											=      points[:2]
       for i in range(2						,lowerCamelCase     ):
              _A  :			List[Any]											=      _det(convex_hull[1]						,convex_hull[0]						,points[i]     )
              if det > 0:
                     convex_hull.insert(0						,points[i]     )
                     break
              elif det < 0:
                     convex_hull.append(points[i]     )
                     break
              else:
                     _A  :			str											=      points[i]
       i += 1

       for j in range(lowerCamelCase						,lowerCamelCase     ):
              if (
                  _det(convex_hull[0]						,convex_hull[-1]						,points[j]     ) > 0
                  and _det(convex_hull[-1]						,convex_hull[0]						,points[1]     ) < 0
              ):
                     # The point lies within the convex hull
                     continue

              convex_hull.insert(0						,points[j]     )
              convex_hull.append(points[j]     )
              while _det(convex_hull[0]						,convex_hull[1]						,convex_hull[2]     ) >= 0:
                     del convex_hull[1]
              while _det(convex_hull[-1]						,convex_hull[-2]						,convex_hull[-3]     ) <= 0:
                     del convex_hull[-2]

    # `convex_hull` is contains the convex hull in circular order
       return sorted(convex_hull[1:] if len(lowerCamelCase     ) > 3 else convex_hull     )






def    lowerCAmelCase__ (       ):
       _A  :			Optional[int]											=      [
           (0, 3),
           (2, 2),
           (1, 1),
           (2, 1),
           (3, 0),
           (0, 0),
           (3, 3),
           (2, -1),
           (2, -4),
           (1, -3),
       ]
       # the convex set of points is
       # [(0, 0), (0, 3), (1, -3), (2, -4), (3, 0), (3, 3)]
       _A  :			Dict											=      convex_hull_bf(lowerCamelCase     )

       _A  :			Optional[Any]											=      convex_hull_recursive(lowerCamelCase     )
       assert results_bf == results_recursive

       _A  :			int											=      convex_hull_melkman(lowerCamelCase     )
       assert results_bf == results_melkman

       print(lowerCamelCase     )


if __name__ == "__main__":
   main()










'''simple docstring'''







from unittest.mock import patch

import datasets
from datasets import Dataset






def    lowerCAmelCase__ (       ):
       _A  :			Optional[int]											=      Dataset.from_dict({'col_1': [3, 2, 0, 1]}     )

       with patch('tqdm.auto.tqdm'     ) as mock_tqdm:
              datasets.disable_progress_bar()
              dset.map(lambda lowerCamelCase     : {"col_2": x["col_1"] + 1}     )
              mock_tqdm.assert_not_called()

              mock_tqdm.reset_mock()

              datasets.enable_progress_bar()
              dset.map(lambda lowerCamelCase     : {"col_2": x["col_1"] + 1}     )
              mock_tqdm.assert_called()






