





'''simple docstring'''







from __future__ import annotations

from scipy.special import comb  # type: ignore


class 					__a      :

							def __init__(							self							:     Tuple       ,     __magic_name__							:     list[tuple[float, float]]   )					->       Optional[Any]:







													"""simple docstring"""
													UpperCAmelCase_			:      Dict     						=  list_of_points
													# Degree determines the flexibility of the curve.
													# Degree = 1 will produce a straight line.
													UpperCAmelCase_			:      List[str]     						=  len(__magic_name__   ) - 1

							def     UpperCAmelCase__	(							self							:     Tuple       ,     __magic_name__							:     float   )					->       list[float]:







													"""simple docstring"""
													assert 0 <= t <= 1, "Time t must be between 0 and 1."
													UpperCAmelCase_			:      list[float]     						=  []
													for i in range(len(self.list_of_points   )   ):
																			# basis function for each i
																			output_values.append(
																			    comb(self.degree       ,     __magic_name__   ) * ((1 - t) ** (self.degree - i)) * (t**i)   )
													# the basis must sum up to 1 for it to produce a valid Bezier curve.
													assert round(sum(__magic_name__   )       ,     5   ) == 1
													return output_values

							def     UpperCAmelCase__	(							self							:     Optional[Any]       ,     __magic_name__							:     float   )					->       tuple[float, float]:







													"""simple docstring"""
													assert 0 <= t <= 1, "Time t must be between 0 and 1."

													UpperCAmelCase_			:      Any     						=  self.basis_function(__magic_name__   )
													UpperCAmelCase_			:      Union[str, Any]     						=  0.0
													UpperCAmelCase_			:      Tuple     						=  0.0
													for i in range(len(self.list_of_points   )   ):
																			# For all points, sum up the product of i-th basis function and i-th point.
																			x += basis_function[i] * self.list_of_points[i][0]
																			y += basis_function[i] * self.list_of_points[i][1]
													return (x, y)



							def     UpperCAmelCase__	(							self							:     Optional[Any]       ,     __magic_name__							:     float = 0.0_1   )					->       List[str]:







													"""simple docstring"""
													from matplotlib import pyplot as plt  # type: ignore

													UpperCAmelCase_			:      list[float]     						=  []  # x coordinates of points to plot
													UpperCAmelCase_			:      list[float]     						=  []  # y coordinates of points to plot

													UpperCAmelCase_			:      int     						=  0.0
													while t <= 1:
																			UpperCAmelCase_			:      str     						=  self.bezier_curve_function(__magic_name__   )
																			to_plot_x.append(value[0]   )
																			to_plot_y.append(value[1]   )
																			t += step_size

													UpperCAmelCase_			:      Any     						=  [i[0] for i in self.list_of_points]
													UpperCAmelCase_			:      Union[str, Any]     						=  [i[1] for i in self.list_of_points]

													plt.plot(
													    __magic_name__       ,     __magic_name__       ,     color='''blue'''       ,     label='''Curve of Degree ''' + str(self.degree   )       ,     )
													plt.scatter(__magic_name__       ,     __magic_name__       ,     color='''red'''       ,     label='''Control Points'''   )
													plt.legend()
													plt.show()


if __name__ == "__main__":
					import doctest

					doctest.testmod()

					BezierCurve([(1, 2), (3, 5)]).plot_curve()  # degree 1
					BezierCurve([(0, 0), (5, 5), (5, 0)]).plot_curve()  # degree 2
					BezierCurve([(0, 0), (5, 5), (5, 0), (2.5, -2.5)]).plot_curve()  # degree 3












'''simple docstring'''







from collections.abc import Iterable
from typing import Any


class 					__a      :

							def __init__(							self							:     Optional[Any]       ,     __magic_name__							:     int | None = None   )					->       Tuple:







													"""simple docstring"""
													UpperCAmelCase_			:      List[str]     						=  value
													UpperCAmelCase_			:      Node | None     						=  None  # Added in order to delete a node easier
													UpperCAmelCase_			:      Node | None     						=  None
													UpperCAmelCase_			:      Node | None     						=  None



							def __repr__(							self							:     List[str]   )					->       str:







													"""simple docstring"""
													from pprint import pformat

													if self.left is None and self.right is None:
																			return str(self.value   )
													return pformat({F"""{self.value}""": (self.left, self.right)}       ,     indent=1   )





class 					__a      :

							def __init__(							self							:     int       ,     __magic_name__							:     Node | None = None   )					->       Optional[int]:







													"""simple docstring"""
													UpperCAmelCase_			:      str     						=  root

							def __str__(							self							:     Any   )					->       str:







													"""simple docstring"""
													return str(self.root   )

							def     UpperCAmelCase__	(							self							:     Any       ,     __magic_name__							:     Node       ,     __magic_name__							:     Node | None   )					->       None:







													"""simple docstring"""
													if new_children is not None:  # reset its kids
																			UpperCAmelCase_			:      Dict     						=  node.parent
													if node.parent is not None:  # reset its parent
																			if self.is_right(__magic_name__   ):  # If it is the right children
																									UpperCAmelCase_			:      Optional[Any]     						=  new_children
																			else:
																									UpperCAmelCase_			:      Optional[int]     						=  new_children
													else:
																			UpperCAmelCase_			:      List[str]     						=  new_children

							def     UpperCAmelCase__	(							self							:     List[str]       ,     __magic_name__							:     Node   )					->       bool:







													"""simple docstring"""
													if node.parent and node.parent.right:
																			return node == node.parent.right
													return False

							def     UpperCAmelCase__	(							self							:     Union[str, Any]   )					->       bool:







													"""simple docstring"""
													return self.root is None

							def     UpperCAmelCase__	(							self							:     Any       ,     __magic_name__							:     str   )					->       None:







													"""simple docstring"""
													UpperCAmelCase_			:      Tuple     						=  Node(__magic_name__   )  # create a new Node
													if self.empty():  # if Tree is empty
																			UpperCAmelCase_			:      List[Any]     						=  new_node  # set its root
													else:  # Tree is not empty
																			UpperCAmelCase_			:      str     						=  self.root  # from root
																			if parent_node is None:
																									return
																			while True:  # While we don't get to a leaf
																									if value < parent_node.value:  # We go left
																															if parent_node.left is None:
																																					UpperCAmelCase_			:      Union[str, Any]     						=  new_node  # We insert the new node in a leaf
																																					break
																															else:
																																					UpperCAmelCase_			:      List[Any]     						=  parent_node.left
																									else:
																															if parent_node.right is None:
																																					UpperCAmelCase_			:      List[Any]     						=  new_node
																																					break
																															else:
																																					UpperCAmelCase_			:      Union[str, Any]     						=  parent_node.right
																			UpperCAmelCase_			:      Union[str, Any]     						=  parent_node

							def     UpperCAmelCase__	(							self							:     Optional[Any]       ,     *__magic_name__							:     List[str]   )					->       None:







													"""simple docstring"""
													for value in values:
																			self.__insert(__magic_name__   )

							def     UpperCAmelCase__	(							self							:     Dict       ,     __magic_name__							:     int   )					->       Node | None:







													"""simple docstring"""
													if self.empty():
																			raise IndexError('''Warning: Tree is empty! please use another.'''   )
													else:
																			UpperCAmelCase_			:      str     						=  self.root
																			# use lazy evaluation here to avoid NoneType Attribute error
																			while node is not None and node.value is not value:
																									UpperCAmelCase_			:      List[str]     						=  node.left if value < node.value else node.right
																			return node

							def     UpperCAmelCase__	(							self							:     Optional[int]       ,     __magic_name__							:     Node | None = None   )					->       Node | None:







													"""simple docstring"""
													if node is None:
																			if self.root is None:
																									return None
																			UpperCAmelCase_			:      Dict     						=  self.root

													if not self.empty():
																			while node.right is not None:
																									UpperCAmelCase_			:      Any     						=  node.right
													return node

							def     UpperCAmelCase__	(							self							:     Dict       ,     __magic_name__							:     Node | None = None   )					->       Node | None:







													"""simple docstring"""
													if node is None:
																			UpperCAmelCase_			:      Optional[int]     						=  self.root
													if self.root is None:
																			return None
													if not self.empty():
																			UpperCAmelCase_			:      Union[str, Any]     						=  self.root
																			while node.left is not None:
																									UpperCAmelCase_			:      Dict     						=  node.left
													return node

							def     UpperCAmelCase__	(							self							:     Tuple       ,     __magic_name__							:     int   )					->       None:







													"""simple docstring"""
													UpperCAmelCase_			:      List[str]     						=  self.search(__magic_name__   )  # Look for the node with that label
													if node is not None:
																			if node.left is None and node.right is None:  # If it has no children
																									self.__reassign_nodes(__magic_name__       ,     __magic_name__   )
																			elif node.left is None:  # Has only right children
																									self.__reassign_nodes(__magic_name__       ,     node.right   )
																			elif node.right is None:  # Has only left children
																									self.__reassign_nodes(__magic_name__       ,     node.left   )
																			else:
																									UpperCAmelCase_			:      List[str]     						=  self.get_max(
																									    node.left   )  # Gets the max value of the left branch
																									self.remove(tmp_node.value   )  # type: ignore
																									UpperCAmelCase_			:      Optional[int]     						=  (
																									    tmp_node.value  # type: ignore
																									)  # Assigns the value to the node to delete and keep tree structure

							def     UpperCAmelCase__	(							self							:     List[Any]       ,     __magic_name__							:     Node | None   )					->       Iterable:







													"""simple docstring"""
													if node is not None:
																			yield node  # Preorder Traversal
																			yield from self.preorder_traverse(node.left   )
																			yield from self.preorder_traverse(node.right   )

							def     UpperCAmelCase__	(							self							:     List[Any]       ,     __magic_name__							:     List[Any]=None   )					->       Any:







													"""simple docstring"""
													if traversal_function is None:
																			return self.preorder_traverse(self.root   )
													else:
																			return traversal_function(self.root   )

							def     UpperCAmelCase__	(							self							:     Optional[int]       ,     __magic_name__							:     list       ,     __magic_name__							:     Node | None   )					->       None:







													"""simple docstring"""
													if node:
																			self.inorder(__magic_name__       ,     node.left   )
																			arr.append(node.value   )
																			self.inorder(__magic_name__       ,     node.right   )



							def     UpperCAmelCase__	(							self							:     Tuple       ,     __magic_name__							:     int       ,     __magic_name__							:     Node   )					->       int:







													"""simple docstring"""
													UpperCAmelCase_			:      list[int]     						=  []
													self.inorder(__magic_name__       ,     __magic_name__   )  # append all values to list using inorder traversal
													return arr[k - 1]





def        lowerCamelCase_      (  SCREAMING_SNAKE_CASE__      :			Node | None   ) ->	list[Node]:
						UpperCAmelCase_			:      Any     						=  []
						if curr_node is not None:
												UpperCAmelCase_			:      Any     						=  postorder(curr_node.left   ) + postorder(curr_node.right   ) + [curr_node]
						return node_list





def        lowerCamelCase_      (  ) ->	None:
						UpperCAmelCase_			:      str     						=  (8, 3, 6, 1, 10, 14, 13, 4, 7)
						UpperCAmelCase_			:      Tuple     						=  BinarySearchTree()
						for i in testlist:
												t.insert(SCREAMING_SNAKE_CASE__   )

						# Prints all the elements of the list in order traversal
						print(SCREAMING_SNAKE_CASE__   )

						if t.search(6   ) is not None:
												print('''The value 6 exists'''   )
						else:
												print('''The value 6 doesn\'t exist'''   )

						if t.search(-1   ) is not None:
												print('''The value -1 exists'''   )
						else:
												print('''The value -1 doesn\'t exist'''   )

						if not t.empty():
												print('''Max Value: ''',			t.get_max().value   )  # type: ignore
												print('''Min Value: ''',			t.get_min().value   )  # type: ignore

						for i in testlist:
												t.remove(SCREAMING_SNAKE_CASE__   )
												print(SCREAMING_SNAKE_CASE__   )


if __name__ == "__main__":
					import doctest

					doctest.testmod(verbose=True)





