"""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			:
				_snake_case     =  42
				_snake_case     =  None
				_snake_case     =  None



def      __lowerCAmelCase(		):






							"""simple docstring"""





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


def      __lowerCAmelCase(		__UpperCAmelCase			):






							"""simple docstring"""





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


def      __lowerCAmelCase(		__UpperCAmelCase			):






							"""simple docstring"""





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


def      __lowerCAmelCase(		__UpperCAmelCase			):






							"""simple docstring"""





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


def      __lowerCAmelCase(		__UpperCAmelCase			):






							"""simple docstring"""





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


def      __lowerCAmelCase(		__UpperCAmelCase			):






							"""simple docstring"""





							_lowercase :    list[Any]							=							[]

							if root is None:
														return output

							_lowercase :    Tuple							=							deque([root]			)

							while process_queue:
														_lowercase :    Optional[Any]							=							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      __lowerCAmelCase(		__UpperCAmelCase     ,__UpperCAmelCase			):






							"""simple docstring"""





							_lowercase :    list[Any]							=							[]

							def populate_output(__UpperCAmelCase     ,__UpperCAmelCase			) -> 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(_lowerCamelCase     ,_lowerCamelCase			)
							return output


def      __lowerCAmelCase(		__UpperCAmelCase     ,__UpperCAmelCase			):






							"""simple docstring"""





							_lowercase :    list[Any]							=							[]

							def populate_output(__UpperCAmelCase     ,__UpperCAmelCase			) -> 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(_lowerCamelCase     ,_lowerCamelCase			)
							return output


def      __lowerCAmelCase(		__UpperCAmelCase			):






							"""simple docstring"""





							if root is None:
														return []

							_lowercase :    list[Sequence[Node | None]]							=							[]

							_lowercase :    List[str]							=							0
							_lowercase :    Optional[Any]							=							height(_lowerCamelCase			)

							for h in range(1     ,height_tree + 1			):
														if not flag:
																					output.append(get_nodes_from_left_to_right(_lowerCamelCase     ,_lowerCamelCase			)			)
																					_lowercase :    Any							=							1
														else:
																					output.append(get_nodes_from_right_to_left(_lowerCamelCase     ,_lowerCamelCase			)			)
																					_lowercase :    Optional[Any]							=							0

							return output


def      __lowerCAmelCase(		):  # Main function for testing.






							"""simple docstring"""





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

							print(F'''Height of Tree: {height(_lowerCamelCase			)}'''     ,'\n'			)

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

							print('Level-wise order Traversal: '			)

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

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


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						main()




"""simple docstring"""







def      __lowerCAmelCase(		__UpperCAmelCase     ,__UpperCAmelCase     ,__UpperCAmelCase			):






	"""simple docstring"""





	return not any(
	    neighbour == 1 and colored_vertices[i] == color
	    for i, neighbour in enumerate(__UpperCAmelCase			)			)


def      __lowerCAmelCase(		__UpperCAmelCase     ,__UpperCAmelCase     ,__UpperCAmelCase     ,__UpperCAmelCase			):






	"""simple docstring"""





	if index == len(__UpperCAmelCase			):
		return True

	# Recursive Step
	for i in range(__UpperCAmelCase			):
		if valid_coloring(graph[index]     ,__UpperCAmelCase     ,__UpperCAmelCase			):
			# Color current vertex
			_lowercase :    str							=							i
			# Validate coloring
			if util_color(__UpperCAmelCase     ,__UpperCAmelCase     ,__UpperCAmelCase     ,index + 1			):
				return True
			# Backtrack
			_lowercase :    List[str]							=							-1
	return False







def      __lowerCAmelCase(		__UpperCAmelCase     ,__UpperCAmelCase			):






	"""simple docstring"""





	_lowercase :    Any							=							[-1] * len(__UpperCAmelCase			)

	if util_color(__UpperCAmelCase     ,__UpperCAmelCase     ,__UpperCAmelCase     ,0			):
		return colored_vertices

	return []



