
from __future__ import annotations

from collections.abc import Iterable
class    _UpperCamelCase:

						def __init__(					self		:			Optional[int]	,						_lowerCamelCase		:			Optional[Any]	,						_lowerCamelCase		:			Optional[Any]			):
													_UpperCAmelCase       ,_UpperCAmelCase  :			Tuple	       =		float(A__			), float(A__			)

						def __eq__(					self		:			Any	,						_lowerCamelCase		:			Union[str, Any]			):
													return self.x == other.x and self.y == other.y

						def __ne__(					self		:			Any	,						_lowerCamelCase		:			Union[str, Any]			):
													return not self == other

						def __gt__(					self		:			str	,						_lowerCamelCase		:			str			):
													if self.x > other.x:
																				return True
													elif self.x == other.x:
																				return self.y > other.y
													return False

						def __lt__(					self		:			Optional[int]	,						_lowerCamelCase		:			Optional[int]			):
													return not self > other

						def __ge__(					self		:			Tuple	,						_lowerCamelCase		:			int			):
													if self.x > other.x:
																				return True
													elif self.x == other.x:
																				return self.y >= other.y
													return False

						def __le__(					self		:			List[Any]	,						_lowerCamelCase		:			int			):
													if self.x < other.x:
																				return True
													elif self.x == other.x:
																				return self.y <= other.y
													return False

						def __repr__(					self		:			Any			):
													return f"""({self.x}, {self.y})"""






						def __hash__(					self		:			List[str]			):
													return hash(self.x			)







def 		lowerCAmelCase_     (     _SCREAMING_SNAKE_CASE      ,	)   ->      list[Point]:

							"""simple docstring"""






							_UpperCAmelCase  :			List[Any]	       =		[]
							if list_of_tuples:
														for p in list_of_tuples:
																					if isinstance(_UpperCamelCase      ,	_UpperCamelCase  ):
																												points.append(_UpperCamelCase  )
																					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_     (     _SCREAMING_SNAKE_CASE  )   ->      list[Point]:

							"""simple docstring"""






							if not hasattr(_UpperCamelCase      ,	"__iter__"  ):
														_UpperCAmelCase  :			Optional[int]	       =		F"""Expecting an iterable object but got an non-iterable type {points}"""
														raise ValueError(_UpperCamelCase  )

							if not points:
														_UpperCAmelCase  :			List[str]	       =		F"""Expecting a list of points but got {points}"""
														raise ValueError(_UpperCamelCase  )

							return _construct_points(_UpperCamelCase  )




def 		lowerCAmelCase_     (     _SCREAMING_SNAKE_CASE      ,	_SCREAMING_SNAKE_CASE      ,	_SCREAMING_SNAKE_CASE  )   ->      float:

							"""simple docstring"""






							_UpperCAmelCase  :			List[str]	       =		(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_     (     _SCREAMING_SNAKE_CASE  )   ->      list[Point]:

							"""simple docstring"""






							_UpperCAmelCase  :			List[str]	       =		sorted(_validate_input(_UpperCamelCase  )  )
							_UpperCAmelCase  :			List[str]	       =		len(_UpperCamelCase  )
							_UpperCAmelCase  :			List[str]	       =		set()

							for i in range(n - 1  ):
														for j in range(i + 1      ,	_UpperCamelCase  ):
																					_UpperCAmelCase  :			List[str]	       =		False
																					_UpperCAmelCase  :			str	       =		True
																					for k in range(_UpperCamelCase  ):
																												if k != i and k != j:
																																			_UpperCAmelCase  :			Any	       =		_det(points[i]      ,	points[j]      ,	points[k]  )

																																			if det_k > 0:
																																										_UpperCAmelCase  :			str	       =		True
																																			elif det_k < 0:
																																										_UpperCAmelCase  :			Union[str, Any]	       =		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]:
																																																	_UpperCAmelCase  :			int	       =		False
																																																	break

																												if points_left_of_ij and points_right_of_ij:
																																			_UpperCAmelCase  :			Any	       =		False
																																			break

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

							return sorted(_UpperCamelCase  )




def 		lowerCAmelCase_     (     _SCREAMING_SNAKE_CASE  )   ->      list[Point]:

							"""simple docstring"""






							_UpperCAmelCase  :			List[str]	       =		sorted(_validate_input(_UpperCamelCase  )  )
							_UpperCAmelCase  :			Union[str, Any]	       =		len(_UpperCamelCase  )

							# 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

							_UpperCAmelCase  :			Tuple	       =		points[0]
							_UpperCAmelCase  :			Tuple	       =		points[n - 1]

							_UpperCAmelCase  :			Optional[Any]	       =		{left_most_point, right_most_point}
							_UpperCAmelCase  :			Union[str, Any]	       =		[]
							_UpperCAmelCase  :			str	       =		[]

							for i in range(1      ,	n - 1  ):
														_UpperCAmelCase  :			List[str]	       =		_det(_UpperCamelCase      ,	_UpperCamelCase      ,	points[i]  )

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

							_construct_hull(_UpperCamelCase      ,	_UpperCamelCase      ,	_UpperCamelCase      ,	_UpperCamelCase  )
							_construct_hull(_UpperCamelCase      ,	_UpperCamelCase      ,	_UpperCamelCase      ,	_UpperCamelCase  )

							return sorted(_UpperCamelCase  )




def 		lowerCAmelCase_     (     _SCREAMING_SNAKE_CASE      ,	_SCREAMING_SNAKE_CASE      ,	_SCREAMING_SNAKE_CASE      ,	_SCREAMING_SNAKE_CASE  )   ->      None:

							"""simple docstring"""






							if points:
														_UpperCAmelCase  :			List[str]	       =		None
														_UpperCAmelCase  :			Dict	       =		float("-inf"  )
														_UpperCAmelCase  :			List[Any]	       =		[]

														for p in points:
																					_UpperCAmelCase  :			Dict	       =		_det(_UpperCamelCase      ,	_UpperCamelCase      ,	_UpperCamelCase  )

																					if det > 0:
																												candidate_points.append(_UpperCamelCase  )

																												if det > extreme_point_distance:
																																			_UpperCAmelCase  :			int	       =		det
																																			_UpperCAmelCase  :			List[Any]	       =		p

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




def 		lowerCAmelCase_     (     _SCREAMING_SNAKE_CASE  )   ->      list[Point]:

							"""simple docstring"""






							_UpperCAmelCase  :			Union[str, Any]	       =		sorted(_validate_input(_UpperCamelCase  )  )
							_UpperCAmelCase  :			List[Any]	       =		len(_UpperCamelCase  )

							_UpperCAmelCase  :			Optional[Any]	       =		points[:2]
							for i in range(2      ,	_UpperCamelCase  ):
														_UpperCAmelCase  :			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:
																					_UpperCAmelCase  :			Optional[int]	       =		points[i]
							i += 1

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




def 		lowerCAmelCase_     (     )   ->      List[Any]:

							"""simple docstring"""






							_UpperCAmelCase  :			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)]
							_UpperCAmelCase  :			Optional[int]	       =		convex_hull_bf(_UpperCamelCase  )

							_UpperCAmelCase  :			Dict	       =		convex_hull_recursive(_UpperCamelCase  )
							assert results_bf == results_recursive

							_UpperCAmelCase  :			Optional[int]	       =		convex_hull_melkman(_UpperCamelCase  )
							assert results_bf == results_melkman

							print(_UpperCamelCase  )


if __name__ == "__main__":
				main()







import numpy as np



class     lowercase_       :



      def __init__(     self :							Any     ,   A__ :							Optional[int]=5     ,   A__ :							Any=5						)       ->	Any:
        _snake_case		=				depth
        _snake_case		=				0
        _snake_case		=				None
        _snake_case		=				None
        _snake_case		=				min_leaf_size
        _snake_case		=				None



      def 		UpperCamelCase_						(     self :							List[Any]     ,   A__ :							Tuple     ,   A__ :							Union[str, Any]						)       ->	int:
        if labels.ndim != 1:
          print('''Error: Input labels must be one dimensional'''						)

        return np.mean((labels - prediction) ** 2						)



      def 		UpperCamelCase_						(     self :							str     ,   A__ :							str     ,   A__ :							int						)       ->	Optional[Any]:
        if x.ndim != 1:
          print('''Error: Input data set must be one dimensional'''						)
          return
        if len(A__						) != len(A__						):
          print('''Error: X and y have different lengths'''						)
          return
        if y.ndim != 1:
          print('''Error: Data set labels must be one dimensional'''						)
          return

        if len(A__						) < 2 * self.min_leaf_size:
          _snake_case		=				np.mean(A__						)
          return

        if self.depth == 1:
          _snake_case		=				np.mean(A__						)
          return

        _snake_case		=				0
        _snake_case		=				self.mean_squared_error(A__     ,   np.mean(A__						)						) * 2
        for i in range(len(A__						)						):
          if len(x[:i]						) < self.min_leaf_size:
            continue
          elif len(x[i:]						) < self.min_leaf_size:
            continue
          else:
            _snake_case		=				self.mean_squared_error(x[:i]     ,   np.mean(y[:i]						)						)
            _snake_case		=				self.mean_squared_error(x[i:]     ,   np.mean(y[i:]						)						)
            _snake_case		=				error_left + error_right
            if error < min_error:
              _snake_case		=				i
              _snake_case		=				error

        if best_split != 0:
          _snake_case		=				x[:best_split]
          _snake_case		=				y[:best_split]
          _snake_case		=				x[best_split:]
          _snake_case		=				y[best_split:]

          _snake_case		=				x[best_split]
          _snake_case		=				DecisionTree(
              depth=self.depth - 1     ,   min_leaf_size=self.min_leaf_size						)
          _snake_case		=				DecisionTree(
              depth=self.depth - 1     ,   min_leaf_size=self.min_leaf_size						)
          self.left.train(A__     ,   A__						)
          self.right.train(A__     ,   A__						)
        else:
          _snake_case		=				np.mean(A__						)

        return







      def 		UpperCamelCase_						(     self :							Optional[int]     ,   A__ :							Tuple						)       ->	Any:
        if self.prediction is not None:
          return self.prediction
        elif self.left or self.right is not None:
          if x >= self.decision_boundary:
            return self.right.predict(A__						)
          else:
            return self.left.predict(A__						)
        else:
          print('''Error: Decision tree not yet trained'''						)
          return None



class     lowercase_       :



      @staticmethod
      def 		UpperCamelCase_						(     A__ :							Union[str, Any]     ,   A__ :							Union[str, Any]						)       ->	int:
        _snake_case		=				float(0						)
        for label in labels:
          squared_error_sum += (label - prediction) ** 2

        return float(squared_error_sum / labels.size						)



def  snake_case_()				->      Any:



  """simple docstring"""






  _snake_case		=				np.arange(-1.0					,			1.0					,			0.005	)
  _snake_case		=				np.sin(_UpperCamelCase	)

  _snake_case		=				DecisionTree(depth=10					,			min_leaf_size=10	)
  tree.train(_UpperCamelCase					,			_UpperCamelCase	)

  _snake_case		=				(np.random.rand(10	) * 2) - 1
  _snake_case		=				np.array([tree.predict(_UpperCamelCase	) for x in test_cases]	)
  _snake_case		=				np.mean((predictions - test_cases) ** 2	)

  print('''Test values: ''' + str(_UpperCamelCase	)	)
  print('''Predictions: ''' + str(_UpperCamelCase	)	)
  print('''Average error: ''' + str(_UpperCamelCase	)	)


if __name__ == "__main__":
 main()
 import doctest

 doctest.testmod(name='''mean_squarred_error''', verbose=True)

