

from collections.abc import Iterable
from typing import Any






class      lowerCamelCase_      :




	def __init__(     self						:     Optional[int]					,      __A						:     int | None = None							):
		__A :			str		    =			value
		__A :			Node | None		    =			None  # Added in order to delete a node easier
		__A :			Node | None		    =			None
		__A :			Node | None		    =			None




	def __repr__(     self						:     Any							):
		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      lowerCamelCase_      :




	def __init__(     self						:     int					,      __A						:     Node | None = None							):
		__A :			Tuple		    =			root




	def __str__(     self						:     List[str]							):
		return str(self.root							)




	def        lowerCAmelCase_       (     self						:     Any					,      __A						:     Node					,      __A						:     Node | None							):

		if new_children is not None:  # reset its kids
			__A :			Dict		    =			node.parent
		if node.parent is not None:  # reset its parent
			if self.is_right(__A							):  # If it is the right children
				__A :			Any		    =			new_children
			else:
				__A :			Optional[Any]		    =			new_children
		else:
			__A :			Dict		    =			new_children




	def        lowerCAmelCase_       (     self						:     Optional[Any]					,      __A						:     Node							):

		if node.parent and node.parent.right:
			return node == node.parent.right
		return False




	def        lowerCAmelCase_       (     self						:     Optional[int]							):
		return self.root is None




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




	def        lowerCAmelCase_       (     self						:     Dict					,      *__A						:     Union[str, Any]							):

		for value in values:
			self.__insert(__A							)




	def        lowerCAmelCase_       (     self						:     int					,      __A						:     Tuple							):

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




	def        lowerCAmelCase_       (     self						:     Union[str, Any]					,      __A						:     Node | None = None							):

		if node is None:
			if self.root is None:
				return None
			__A :			List[str]		    =			self.root

		if not self.empty():
			while node.right is not None:
				__A :			Optional[Any]		    =			node.right
		return node




	def        lowerCAmelCase_       (     self						:     Optional[int]					,      __A						:     Node | None = None							):

		if node is None:
			__A :			List[str]		    =			self.root
		if self.root is None:
			return None
		if not self.empty():
			__A :			Dict		    =			self.root
			while node.left is not None:
				__A :			Optional[Any]		    =			node.left
		return node




	def        lowerCAmelCase_       (     self						:     str					,      __A						:     int							):
		__A :			Dict		    =			self.search(__A							)  # 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(__A					,      __A							)
			elif node.left is None:  # Has only right children
				self.__reassign_nodes(__A					,      node.right							)
			elif node.right is None:  # Has only left children
				self.__reassign_nodes(__A					,      node.left							)
			else:
				__A :			Tuple		    =			self.get_max(
				    node.left							)  # Gets the max value of the left branch
				self.remove(tmp_node.value							)  # type: ignore
				__A :			Any		    =			(
				    tmp_node.value  # type: ignore
				)  # Assigns the value to the node to delete and keep tree structure




	def        lowerCAmelCase_       (     self						:     List[Any]					,      __A						:     Node | None							):

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




	def        lowerCAmelCase_       (     self						:     int					,      __A						:     Optional[int]=None							):

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




	def        lowerCAmelCase_       (     self						:     str					,      __A						:     list					,      __A						:     Node | None							):

		if node:
			self.inorder(__A					,      node.left							)
			arr.append(node.value							)
			self.inorder(__A					,      node.right							)




	def        lowerCAmelCase_       (     self						:     int					,      __A						:     int					,      __A						:     Node							):
		__A :			list[int]		    =			[]
		self.inorder(__A					,      __A							)  # append all values to list using inorder traversal
		return arr[k - 1]






def 							__SCREAMING_SNAKE_CASE     (   a__    :   List[Any]       )					->				list[Node]:
	__A :			int		    =			[]
	if curr_node is not None:
		__A :			List[Any]		    =			postorder(curr_node.left       ) + postorder(curr_node.right       ) + [curr_node]
	return node_list
def 							__SCREAMING_SNAKE_CASE     (   )					->				None:
	__A :			Optional[Any]		    =			(8, 3, 6, 1, 10, 14, 13, 4, 7)
	__A :			str		    =			BinarySearchTree()
	for i in testlist:
		t.insert(_lowerCamelCase       )

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

	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(_lowerCamelCase       )
		print(_lowerCamelCase       )


if __name__ == "__main__":
			import doctest

			doctest.testmod(verbose=True)












'''simple docstring'''






from __future__ import annotations

import math







def 					_a						(       _lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase ) ->				int:



			"""simple docstring"""


			if depth < 0:
						raise ValueError("""Depth cannot be less than 0""" )

			if not scores:
						raise ValueError("""Scores cannot be empty""" )

			if depth == height:
						return scores[node_index]

			return (
			    max(
			        minimax(depth + 1    ,	node_index * 2    ,	_lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase )    ,	minimax(depth + 1    ,	node_index * 2 + 1    ,	_lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase )    ,	)
			    if is_max
			    else min(
			        minimax(depth + 1    ,	node_index * 2    ,	_lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase )    ,	minimax(depth + 1    ,	node_index * 2 + 1    ,	_lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase )    ,	)
			)







def 					_a						(       ) ->				None:



			"""simple docstring"""


			__snake_case					:      Union[str, Any]							      =     [90, 23, 6, 33, 21, 65, 123, 3_4423]
			__snake_case					:      Optional[int]							      =     math.log(len(_lowerCamelCase )    ,	2 )
			print(F'''Optimal value : {minimax(0    ,	0    ,	_lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase )}''' )


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	main()


