


def 					lowerCamelCase_   (	_a	):




  """simple docstring"""






  assert (
      isinstance(a__     ,       a__	) and number_of_steps > 0
  ), f'number_of_steps needs to be positive integer, your input {number_of_steps}'
  if number_of_steps == 1:
    return 1
  lowerCAmelCase__					,     lowerCAmelCase__       :      List[str]   					= 1, 1
  for _ in range(number_of_steps - 1	):
    lowerCAmelCase__					,     lowerCAmelCase__       :      Tuple   					= current + previous, current
  return current


if __name__ == "__main__":
  import doctest

  doctest.testmod()








from collections.abc import Iterable
from typing import Any





class  _a							:




	def __init__( self						:		Union[str, Any]		, _SCREAMING_SNAKE_CASE						:		int | None = None		)->	Tuple:
			lowerCAmelCase__       :      Union[str, Any]   					= value
			lowerCAmelCase__       :      Node | None   					= None  # Added in order to delete a node easier
			lowerCAmelCase__       :      Node | None   					= None
			lowerCAmelCase__       :      Node | None   					= None




	def __repr__( self						:		List[Any]		)->	str:
			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						:		Tuple		, _SCREAMING_SNAKE_CASE						:		Node | None = None		)->	int:
			lowerCAmelCase__       :      Dict   					= root




	def __str__( self						:		Tuple		)->	str:
			return str(self.root		)




	def 							UpperCAmelCase__( self						:		List[str]		, _SCREAMING_SNAKE_CASE						:		Node		, _SCREAMING_SNAKE_CASE						:		Node | None		)->	None:
			if new_children is not None:  # reset its kids
					lowerCAmelCase__       :      Union[str, Any]   					= node.parent
			if node.parent is not None:  # reset its parent
					if self.is_right(_SCREAMING_SNAKE_CASE		):  # If it is the right children
							lowerCAmelCase__       :      List[str]   					= new_children
					else:
							lowerCAmelCase__       :      Any   					= new_children
			else:
					lowerCAmelCase__       :      Optional[Any]   					= new_children




	def 							UpperCAmelCase__( self						:		List[Any]		, _SCREAMING_SNAKE_CASE						:		Node		)->	bool:
			if node.parent and node.parent.right:
					return node == node.parent.right
			return False




	def 							UpperCAmelCase__( self						:		int		)->	bool:
			return self.root is None




	def 							UpperCAmelCase__( self						:		Optional[int]		, _SCREAMING_SNAKE_CASE						:		Optional[int]		)->	None:
			lowerCAmelCase__       :      Any   					= Node(_SCREAMING_SNAKE_CASE		)  # create a new Node
			if self.empty():  # if Tree is empty
					lowerCAmelCase__       :      Optional[Any]   					= new_node  # set its root
			else:  # Tree is not empty
					lowerCAmelCase__       :      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:
											lowerCAmelCase__       :      Dict   					= new_node  # We insert the new node in a leaf
											break
									else:
											lowerCAmelCase__       :      List[Any]   					= parent_node.left
							else:
									if parent_node.right is None:
											lowerCAmelCase__       :      Tuple   					= new_node
											break
									else:
											lowerCAmelCase__       :      Union[str, Any]   					= parent_node.right
					lowerCAmelCase__       :      Dict   					= parent_node




	def 							UpperCAmelCase__( self						:		str		, *_SCREAMING_SNAKE_CASE						:		List[Any]		)->	None:
			for value in values:
					self.__insert(_SCREAMING_SNAKE_CASE		)




	def 							UpperCAmelCase__( self						:		Union[str, Any]		, _SCREAMING_SNAKE_CASE						:		Optional[int]		)->	Node | None:
			if self.empty():
					raise IndexError('''Warning: Tree is empty! please use another.'''		)
			else:
					lowerCAmelCase__       :      Union[str, Any]   					= self.root
					# use lazy evaluation here to avoid NoneType Attribute error
					while node is not None and node.value is not value:
							lowerCAmelCase__       :      List[str]   					= node.left if value < node.value else node.right
					return node




	def 							UpperCAmelCase__( self						:		Dict		, _SCREAMING_SNAKE_CASE						:		Node | None = None		)->	Node | None:
			if node is None:
					if self.root is None:
							return None
					lowerCAmelCase__       :      List[Any]   					= self.root

			if not self.empty():
					while node.right is not None:
							lowerCAmelCase__       :      str   					= node.right
			return node




	def 							UpperCAmelCase__( self						:		List[str]		, _SCREAMING_SNAKE_CASE						:		Node | None = None		)->	Node | None:
			if node is None:
					lowerCAmelCase__       :      Any   					= self.root
			if self.root is None:
					return None
			if not self.empty():
					lowerCAmelCase__       :      Dict   					= self.root
					while node.left is not None:
							lowerCAmelCase__       :      Tuple   					= node.left
			return node




	def 							UpperCAmelCase__( self						:		Any		, _SCREAMING_SNAKE_CASE						:		int		)->	None:
			lowerCAmelCase__       :      Optional[Any]   					= self.search(_SCREAMING_SNAKE_CASE		)  # 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(_SCREAMING_SNAKE_CASE		, _SCREAMING_SNAKE_CASE		)
					elif node.left is None:  # Has only right children
							self.__reassign_nodes(_SCREAMING_SNAKE_CASE		, node.right		)
					elif node.right is None:  # Has only left children
							self.__reassign_nodes(_SCREAMING_SNAKE_CASE		, node.left		)
					else:
							lowerCAmelCase__       :      Tuple   					= self.get_max(
							    node.left		)  # Gets the max value of the left branch
							self.remove(tmp_node.value		)  # type: ignore
							lowerCAmelCase__       :      Optional[Any]   					= (
							    tmp_node.value  # type: ignore
							)  # Assigns the value to the node to delete and keep tree structure




	def 							UpperCAmelCase__( self						:		Union[str, Any]		, _SCREAMING_SNAKE_CASE						:		Node | None		)->	Iterable:
			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						:		Union[str, Any]		, _SCREAMING_SNAKE_CASE						:		Tuple=None		)->	Any:
			if traversal_function is None:
					return self.preorder_traverse(self.root		)
			else:
					return traversal_function(self.root		)




	def 							UpperCAmelCase__( self						:		Union[str, Any]		, _SCREAMING_SNAKE_CASE						:		list		, _SCREAMING_SNAKE_CASE						:		Node | None		)->	None:
			if node:
					self.inorder(_SCREAMING_SNAKE_CASE		, node.left		)
					arr.append(node.value		)
					self.inorder(_SCREAMING_SNAKE_CASE		, node.right		)




	def 							UpperCAmelCase__( self						:		Optional[Any]		, _SCREAMING_SNAKE_CASE						:		int		, _SCREAMING_SNAKE_CASE						:		Node		)->	int:
			lowerCAmelCase__       :      list[int]   					= []
			self.inorder(_SCREAMING_SNAKE_CASE		, _SCREAMING_SNAKE_CASE		)  # append all values to list using inorder traversal
			return arr[k - 1]






def 					lowerCamelCase_   (	_a	):




		"""simple docstring"""






		lowerCAmelCase__       :      List[str]   					= []
		if curr_node is not None:
				lowerCAmelCase__       :      Optional[int]   					= postorder(curr_node.left	) + postorder(curr_node.right	) + [curr_node]
		return node_list






def 					lowerCamelCase_   (	):




		"""simple docstring"""






		lowerCAmelCase__       :      List[Any]   					= (8, 3, 6, 1, 10, 14, 13, 4, 7)
		lowerCAmelCase__       :      str   					= BinarySearchTree()
		for i in testlist:
				t.insert(_a	)

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

		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(_a	)
				print(_a	)


if __name__ == "__main__":
		import doctest

		doctest.testmod(verbose=True)




