





'''simple docstring'''


from __future__ import annotations

from collections import deque
from collections.abc import Sequence
from dataclasses import dataclass
from typing import Any






@dataclass
class     lowerCAmelCase__ :

       '''simple docstring'''
       _lowerCamelCase								=42
       _lowerCamelCase								=None
       _lowerCamelCase								=None


def       __snake_case		( )							->     Node | None:

       """simple docstring"""


       UpperCAmelCase  =						Node(1 )
       UpperCAmelCase  =						Node(2 )
       UpperCAmelCase  =						Node(3 )
       UpperCAmelCase  =						Node(4 )
       UpperCAmelCase  =						Node(5 )
       return tree
def       __snake_case		( SCREAMING_SNAKE_CASE_ :			Node | None )							->     list[int]:

       """simple docstring"""


       return [root.data, *preorder(root.left ), *preorder(root.right )] if root else []
def       __snake_case		( SCREAMING_SNAKE_CASE_ :			Node | None )							->     list[int]:

       """simple docstring"""


       return postorder(root.left ) + postorder(root.right ) + [root.data] if root else []
def       __snake_case		( SCREAMING_SNAKE_CASE_ :			Node | None )							->     list[int]:

       """simple docstring"""


       return [*inorder(root.left ), root.data, *inorder(root.right )] if root else []
def       __snake_case		( SCREAMING_SNAKE_CASE_ :			Node | None )							->     int:

       """simple docstring"""


       return (max(height(root.left )			,	height(root.right ) ) + 1) if root else 0
def       __snake_case		( SCREAMING_SNAKE_CASE_ :			Node | None )							->     Sequence[Node | None]:

       """simple docstring"""


       UpperCAmelCase  =						[]

       if root is None:
              return output

       UpperCAmelCase  =						deque([root] )

       while process_queue:
              UpperCAmelCase  =						process_queue.popleft()
              output.append(node.data )

              if node.left:
                     process_queue.append(node.left )
              if node.right:
                     process_queue.append(node.right )
       return output
def       __snake_case		( SCREAMING_SNAKE_CASE_ :			Node | None			,	SCREAMING_SNAKE_CASE_ :			int )							->     Sequence[Node | None]:

       """simple docstring"""


       UpperCAmelCase  =						[]

       def populate_output(SCREAMING_SNAKE_CASE_ :			Node | None			,	SCREAMING_SNAKE_CASE_ :			int ) -> None:
              if not root:
                     return
              if level == 1:
                     output.append(root.data )
              elif level > 1:
                     populate_output(root.left			,	level - 1 )
                     populate_output(root.right			,	level - 1 )

       populate_output(SCREAMING_SNAKE_CASE_			,	SCREAMING_SNAKE_CASE_ )
       return output
def       __snake_case		( SCREAMING_SNAKE_CASE_ :			Node | None			,	SCREAMING_SNAKE_CASE_ :			int )							->     Sequence[Node | None]:

       """simple docstring"""


       UpperCAmelCase  =						[]

       def populate_output(SCREAMING_SNAKE_CASE_ :			Node | None			,	SCREAMING_SNAKE_CASE_ :			int ) -> None:
              if root is None:
                     return
              if level == 1:
                     output.append(root.data )
              elif level > 1:
                     populate_output(root.right			,	level - 1 )
                     populate_output(root.left			,	level - 1 )

       populate_output(SCREAMING_SNAKE_CASE_			,	SCREAMING_SNAKE_CASE_ )
       return output
def       __snake_case		( SCREAMING_SNAKE_CASE_ :			Node | None )							->     Sequence[Node | None] | list[Any]:

       """simple docstring"""


       if root is None:
              return []

       UpperCAmelCase  =						[]

       UpperCAmelCase  =						0
       UpperCAmelCase  =						height(SCREAMING_SNAKE_CASE_ )

       for h in range(1			,	height_tree + 1 ):
              if not flag:
                     output.append(get_nodes_from_left_to_right(SCREAMING_SNAKE_CASE_			,	SCREAMING_SNAKE_CASE_ ) )
                     UpperCAmelCase  =						1
              else:
                     output.append(get_nodes_from_right_to_left(SCREAMING_SNAKE_CASE_			,	SCREAMING_SNAKE_CASE_ ) )
                     UpperCAmelCase  =						0

       return output
def       __snake_case		( )							->     None:  # Main function for testing.

       """simple docstring"""


       UpperCAmelCase  =						make_tree()
       print(f"In-order Traversal: {inorder(SCREAMING_SNAKE_CASE_ )}" )
       print(f"Pre-order Traversal: {preorder(SCREAMING_SNAKE_CASE_ )}" )
       print(f"Post-order Traversal: {postorder(SCREAMING_SNAKE_CASE_ )}"			,	'''\n''' )

       print(f"Height of Tree: {height(SCREAMING_SNAKE_CASE_ )}"			,	'''\n''' )

       print('''Complete Level Order Traversal: ''' )
       print(level_order(SCREAMING_SNAKE_CASE_ )			,	'''\n''' )

       print('''Level-wise order Traversal: ''' )

       for level in range(1			,	height(SCREAMING_SNAKE_CASE_ ) + 1 ):
              print(f"Level {level}:"			,	get_nodes_from_left_to_right(SCREAMING_SNAKE_CASE_			,	level=SCREAMING_SNAKE_CASE_ ) )

       print('''\nZigZag order Traversal: ''' )
       print(zigzag(SCREAMING_SNAKE_CASE_ ) )


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    main()









def      UpperCAmelCase_    (    _UpperCAmelCase							:Any  ,						_UpperCAmelCase							:Dict				)	->				Union[str, Any]:
     '''simple docstring'''


     A_          =       [1]
     for i in range(2  ,						_UpperCAmelCase				):
          factorials.append(factorials[-1] * i				)
     assert 0 <= k < factorials[-1] * n, "k out of bounds"

     A_          =       []
     A_          =       list(range(_UpperCAmelCase				)				)

     # Find permutation
     while factorials:
          A_          =       factorials.pop()
          A_   ,    A_          =       divmod(_UpperCAmelCase  ,						_UpperCAmelCase				)
          permutation.append(elements[number]				)
          elements.remove(elements[number]				)
     permutation.append(elements[0]				)

     return permutation


if __name__ == "__main__":
      import doctest

      doctest.testmod()



