from __future__ import annotations

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

@dataclass
class       snake_case					:
		lowercase_			=     42
		lowercase_			=     None
		lowercase_			=     None







def     _a				(      ):







					'''simple docstring'''


					SCREAMING_SNAKE_CASE__				:				Union[str, Any]			=		Node(1 )
					SCREAMING_SNAKE_CASE__				:				Union[str, Any]			=		Node(2 )
					SCREAMING_SNAKE_CASE__				:				Optional[int]			=		Node(3 )
					SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		Node(4 )
					SCREAMING_SNAKE_CASE__				:				Union[str, Any]			=		Node(5 )
					return tree







def     _a				(      lowercase__  :			Node | None ):







					'''simple docstring'''


					return [root.data, *preorder(root.left ), *preorder(root.right )] if root else []







def     _a				(      lowercase__  :			Node | None ):







					'''simple docstring'''


					return postorder(root.left ) + postorder(root.right ) + [root.data] if root else []







def     _a				(      lowercase__  :			Node | None ):







					'''simple docstring'''


					return [*inorder(root.left ), root.data, *inorder(root.right )] if root else []







def     _a				(      lowercase__  :			Node | None ):







					'''simple docstring'''


					return (max(height(root.left )     ,  height(root.right ) ) + 1) if root else 0







def     _a				(      lowercase__  :			Node | None ):







					'''simple docstring'''


					SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		[]

					if root is None:
										return output

					SCREAMING_SNAKE_CASE__				:				Optional[int]			=		deque([root] )

					while process_queue:
										SCREAMING_SNAKE_CASE__				:				List[str]			=		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     _a				(      lowercase__  :			Node | None     ,  lowercase__  :			int ):







					'''simple docstring'''


					SCREAMING_SNAKE_CASE__				:				str			=		[]

					def populate_output(lowercase__  :			Node | None     ,  lowercase__  :			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(_UpperCamelCase     ,  _UpperCamelCase )
					return output







def     _a				(      lowercase__  :			Node | None     ,  lowercase__  :			int ):







					'''simple docstring'''


					SCREAMING_SNAKE_CASE__				:				List[Any]			=		[]

					def populate_output(lowercase__  :			Node | None     ,  lowercase__  :			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(_UpperCamelCase     ,  _UpperCamelCase )
					return output







def     _a				(      lowercase__  :			Node | None ):







					'''simple docstring'''


					if root is None:
										return []

					SCREAMING_SNAKE_CASE__				:				Optional[Any]			=		[]

					SCREAMING_SNAKE_CASE__				:				int			=		0
					SCREAMING_SNAKE_CASE__				:				List[str]			=		height(_UpperCamelCase )

					for h in range(1     ,  height_tree + 1 ):
										if not flag:
															output.append(get_nodes_from_left_to_right(_UpperCamelCase     ,  _UpperCamelCase ) )
															SCREAMING_SNAKE_CASE__				:				str			=		1
										else:
															output.append(get_nodes_from_right_to_left(_UpperCamelCase     ,  _UpperCamelCase ) )
															SCREAMING_SNAKE_CASE__				:				Dict			=		0

					return output







def     _a				(      ):  # Main function for testing.







					'''simple docstring'''


					SCREAMING_SNAKE_CASE__				:				Union[str, Any]			=		make_tree()
					print(f'''In-order Traversal: {inorder(_UpperCamelCase )}''' )
					print(f'''Pre-order Traversal: {preorder(_UpperCamelCase )}''' )
					print(f'''Post-order Traversal: {postorder(_UpperCamelCase )}'''     ,  '\n' )

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

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

					print('Level-wise order Traversal: ' )

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

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


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						main()




from __future__ import annotations







def     _a				(      lowercase__  :			list[int | float]     ,  lowercase__  :			int     ,  lowercase__  :			int ):







     '''simple docstring'''


     if len(lowercase__ ) == 0:
          raise ValueError('find_max() arg is an empty sequence' )
     if (
         left >= len(lowercase__ )
         or left < -len(lowercase__ )
         or right >= len(lowercase__ )
         or right < -len(lowercase__ )
     ):
          raise IndexError('list index out of range' )
     if left == right:
          return nums[left]
     SCREAMING_SNAKE_CASE__				:				Union[str, Any]			=		(left + right) >> 1  # the middle
     SCREAMING_SNAKE_CASE__				:				int			=		find_max(lowercase__     ,  lowercase__     ,  lowercase__ )  # find max in range[left, mid]
     SCREAMING_SNAKE_CASE__				:				Tuple			=		find_max(lowercase__     ,  mid + 1     ,  lowercase__ )  # find max in range[mid + 1, right]

     return left_max if left_max >= right_max else right_max


if __name__ == "__main__":
      import doctest

      doctest.testmod(verbose=True)



