



from __future__ import annotations

from collections.abc import Iterable
class lowerCAmelCase_       :







	'''simple docstring'''




	def __init__(	self   ,       lowerCamelCase   ,       lowerCamelCase       ):



				'''simple docstring'''


				a__				,       a__					=  float(lowerCamelCase       ), float(lowerCamelCase       )

	def __eq__(	self   ,       lowerCamelCase       ):



				'''simple docstring'''


				return self.x == other.x and self.y == other.y

	def __ne__(	self   ,       lowerCamelCase       ):



				'''simple docstring'''


				return not self == other

	def __gt__(	self   ,       lowerCamelCase       ):



				'''simple docstring'''


				if self.x > other.x:
							return True
				elif self.x == other.x:
							return self.y > other.y
				return False

	def __lt__(	self   ,       lowerCamelCase       ):



				'''simple docstring'''


				return not self > other

	def __ge__(	self   ,       lowerCamelCase       ):



				'''simple docstring'''


				if self.x > other.x:
							return True
				elif self.x == other.x:
							return self.y >= other.y
				return False

	def __le__(	self   ,       lowerCamelCase       ):



				'''simple docstring'''


				if self.x < other.x:
							return True
				elif self.x == other.x:
							return self.y <= other.y
				return False

	def __repr__(	self       ):



				'''simple docstring'''


				return f'({self.x}, {self.y})'







	def __hash__(	self       ):



				'''simple docstring'''


				return hash(self.x       )




def    UpperCAmelCase					(  lowercase__						:					list[Point] | list[list[float]] | Iterable[list[float]]				,					):



			'''simple docstring'''





			a__					=  []
			if list_of_tuples:
						for p in list_of_tuples:
									if isinstance(lowercase__				,					lowercase__	):
												points.append(lowercase__	)
									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    UpperCAmelCase					(  lowercase__						:					list[Point] | list[list[float]]	):



			'''simple docstring'''





			if not hasattr(lowercase__				,					"""__iter__"""	):
						a__					=  f'Expecting an iterable object but got an non-iterable type {points}'
						raise ValueError(lowercase__	)

			if not points:
						a__					=  f'Expecting a list of points but got {points}'
						raise ValueError(lowercase__	)

			return _construct_points(lowercase__	)




def    UpperCAmelCase					(  lowercase__						:					Point				,					lowercase__						:					Point				,					lowercase__						:					Point	):



			'''simple docstring'''





			a__					=  (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    UpperCAmelCase					(  lowercase__						:					list[Point]	):



			'''simple docstring'''





			a__					=  sorted(_validate_input(lowercase__	)	)
			a__					=  len(lowercase__	)
			a__					=  set()

			for i in range(n - 1	):
						for j in range(i + 1				,					lowercase__	):
									a__					=  a__					=  False
									a__					=  True
									for k in range(lowercase__	):
												if k != i and k != j:
															a__					=  _det(points[i]				,					points[j]				,					points[k]	)

															if det_k > 0:
																		a__					=  True
															elif det_k < 0:
																		a__					=  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__					=  False
																					break

												if points_left_of_ij and points_right_of_ij:
															a__					=  False
															break

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

			return sorted(lowercase__	)




def    UpperCAmelCase					(  lowercase__						:					list[Point]	):



			'''simple docstring'''





			a__					=  sorted(_validate_input(lowercase__	)	)
			a__					=  len(lowercase__	)

			# 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__					=  points[0]
			a__					=  points[n - 1]

			a__					=  {left_most_point, right_most_point}
			a__					=  []
			a__					=  []

			for i in range(1				,					n - 1	):
						a__					=  _det(lowercase__				,					lowercase__				,					points[i]	)

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

			_construct_hull(lowercase__				,					lowercase__				,					lowercase__				,					lowercase__	)
			_construct_hull(lowercase__				,					lowercase__				,					lowercase__				,					lowercase__	)

			return sorted(lowercase__	)




def    UpperCAmelCase					(  lowercase__						:					list[Point]				,					lowercase__						:					Point				,					lowercase__						:					Point				,					lowercase__						:					set[Point]	):



			'''simple docstring'''





			if points:
						a__					=  None
						a__					=  float("""-inf"""	)
						a__					=  []

						for p in points:
									a__					=  _det(lowercase__				,					lowercase__				,					lowercase__	)

									if det > 0:
												candidate_points.append(lowercase__	)

												if det > extreme_point_distance:
															a__					=  det
															a__					=  p

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




def    UpperCAmelCase					(  lowercase__						:					list[Point]	):



			'''simple docstring'''





			a__					=  sorted(_validate_input(lowercase__	)	)
			a__					=  len(lowercase__	)

			a__					=  points[:2]
			for i in range(2				,					lowercase__	):
						a__					=  _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__					=  points[i]
			i += 1

			for j in range(lowercase__				,					lowercase__	):
						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(lowercase__	) > 3 else convex_hull	)




def    UpperCAmelCase					(  ):



			'''simple docstring'''





			a__					=  [
			    (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__					=  convex_hull_bf(lowercase__	)

			a__					=  convex_hull_recursive(lowercase__	)
			assert results_bf == results_recursive

			a__					=  convex_hull_melkman(lowercase__	)
			assert results_bf == results_melkman

			print(lowercase__	)


if __name__ == "__main__":
	main()






class lowerCAmelCase_       :







	'''simple docstring'''




	def __init__(	self   ,       lowerCamelCase=None       ):



				'''simple docstring'''


				a__					=  data
				a__					=  None







	def __repr__(	self       ):



				'''simple docstring'''


				a__					=  """"""
				a__					=  self
				while temp:
							string_rep += f'<{temp.data}> ---> '
							a__					=  temp.next
				string_rep += "<END>"
				return string_rep




def    UpperCAmelCase					(  lowercase__						:					Optional[int]	):



			'''simple docstring'''





			if not elements_list:
						raise Exception("""The Elements List is empty"""	)

			# Set first element as Head
			a__					=  Node(elements_list[0]	)
			a__					=  head
			# Loop through elements from position 1
			for data in elements_list[1:]:
						a__					=  Node(lowercase__	)
						a__					=  current.next
			return head


_lowercase				:					List[Any]     					=[1, 3, 5, 32, 44, 12, 43]
print(f'''List: {list_data}''')
print("""Creating Linked List from List.""")
_lowercase				:					Dict     					=make_linked_list(list_data)
print("""Linked List:""")





print(linked_list)

