

from collections.abc import Iterable
from typing import Any






class 						__magic_name__					:






     def __init__(				self		,						_lowercase = None	)->     Tuple:
         UpperCamelCase_			  =						value
         UpperCamelCase_			  =						None  # Added in order to delete a node easier
         UpperCamelCase_			  =						None
         UpperCamelCase_			  =						None






     def __repr__(				self	)->     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 						__magic_name__					:






     def __init__(				self		,						_lowercase = None	)->     int:
         UpperCamelCase_			  =						root






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






     def 	UpperCAmelCase_				(				self		,						_lowercase		,						_lowercase	)->     None:
         if new_children is not None:  # reset its kids
             UpperCamelCase_			  =						node.parent
         if node.parent is not None:  # reset its parent
             if self.is_right(_lowercase	):  # If it is the right children
                 UpperCamelCase_			  =						new_children
             else:
                 UpperCamelCase_			  =						new_children
         else:
             UpperCamelCase_			  =						new_children






     def 	UpperCAmelCase_				(				self		,						_lowercase	)->     bool:
         if node.parent and node.parent.right:
             return node == node.parent.right
         return False






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






     def 	UpperCAmelCase_				(				self		,						_lowercase	)->     None:
         UpperCamelCase_			  =						Node(_lowercase	)  # create a new Node
         if self.empty():  # if Tree is empty
             UpperCamelCase_			  =						new_node  # set its root
         else:  # Tree is not empty
             UpperCamelCase_			  =						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_			  =						new_node  # We insert the new node in a leaf
                         break
                     else:
                         UpperCamelCase_			  =						parent_node.left
                 else:
                     if parent_node.right is None:
                         UpperCamelCase_			  =						new_node
                         break
                     else:
                         UpperCamelCase_			  =						parent_node.right
             UpperCamelCase_			  =						parent_node






     def 	UpperCAmelCase_				(				self		,						*_lowercase	)->     None:
         for value in values:
             self.__insert(_lowercase	)






     def 	UpperCAmelCase_				(				self		,						_lowercase	)->     Node | None:
         if self.empty():
             raise IndexError("Warning: Tree is empty! please use another."	)
         else:
             UpperCamelCase_			  =						self.root
             # use lazy evaluation here to avoid NoneType Attribute error
             while node is not None and node.value is not value:
                 UpperCamelCase_			  =						node.left if value < node.value else node.right
             return node






     def 	UpperCAmelCase_				(				self		,						_lowercase = None	)->     Node | None:
         if node is None:
             if self.root is None:
                 return None
             UpperCamelCase_			  =						self.root

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






     def 	UpperCAmelCase_				(				self		,						_lowercase = None	)->     Node | None:
         if node is None:
             UpperCamelCase_			  =						self.root
         if self.root is None:
             return None
         if not self.empty():
             UpperCamelCase_			  =						self.root
             while node.left is not None:
                 UpperCamelCase_			  =						node.left
         return node






     def 	UpperCAmelCase_				(				self		,						_lowercase	)->     None:
         UpperCamelCase_			  =						self.search(_lowercase	)  # 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(_lowercase		,						_lowercase	)
             elif node.left is None:  # Has only right children
                 self.__reassign_nodes(_lowercase		,						node.right	)
             elif node.right is None:  # Has only left children
                 self.__reassign_nodes(_lowercase		,						node.left	)
             else:
                 UpperCamelCase_			  =						self.get_max(
                     node.left	)  # Gets the max value of the left branch
                 self.remove(tmp_node.value	)  # type: ignore
                 UpperCamelCase_			  =						(
                     tmp_node.value  # type: ignore
                 )  # Assigns the value to the node to delete and keep tree structure






     def 	UpperCAmelCase_				(				self		,						_lowercase	)->     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		,						_lowercase=None	)->     Any:
         if traversal_function is None:
             return self.preorder_traverse(self.root	)
         else:
             return traversal_function(self.root	)






     def 	UpperCAmelCase_				(				self		,						_lowercase		,						_lowercase	)->     None:
         if node:
             self.inorder(_lowercase		,						node.left	)
             arr.append(node.value	)
             self.inorder(_lowercase		,						node.right	)






     def 	UpperCAmelCase_				(				self		,						_lowercase		,						_lowercase	)->     int:
         UpperCamelCase_			  =						[]
         self.inorder(_lowercase		,						_lowercase	)  # append all values to list using inorder traversal
         return arr[k - 1]




def 			lowerCAmelCase(      SCREAMING_SNAKE_CASE_			)->						list[Node]:



    """simple docstring"""






    UpperCamelCase_			  =						[]
    if curr_node is not None:
        UpperCamelCase_			  =						postorder(curr_node.left			) + postorder(curr_node.right			) + [curr_node]
    return node_list




def 			lowerCAmelCase(      )->						None:



    """simple docstring"""






    UpperCamelCase_			  =						(8, 3, 6, 1, 1_0, 1_4, 1_3, 4, 7)
    UpperCamelCase_			  =						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)



from __future__ import annotations

import math




def 			lowerCAmelCase(      SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			)->						int:



    """simple docstring"""






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

    if len(SCREAMING_SNAKE_CASE_			) == 0:
        raise ValueError("Scores cannot be empty"			)

    if depth == height:
        return scores[node_index]

    if is_max:
        return max(
            minimax(depth + 1			,						node_index * 2			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			)			,						minimax(depth + 1			,						node_index * 2 + 1			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			)			,						)

    return min(
        minimax(depth + 1			,						node_index * 2			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			)			,						minimax(depth + 1			,						node_index * 2 + 1			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			)			,						)




def 			lowerCAmelCase(      )->						None:



    """simple docstring"""






    UpperCamelCase_			  =						[9_0, 2_3, 6, 3_3, 2_1, 6_5, 1_2_3, 3_4_4_2_3]
    UpperCamelCase_			  =						math.log(len(SCREAMING_SNAKE_CASE_			)			,						2			)
    print("Optimal value : "			,						end=""			)
    print(minimax(0			,						0			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			)			)


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 main()
