



'''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"""




  a_				   =42
  a_				   =None
  a_				   =None




def 			a_	(				) -> Node | None:
  __lowerCamelCase			:			Optional[Any]       			=					Node(1			)
  __lowerCamelCase			:			List[str]       			=					Node(2			)
  __lowerCamelCase			:			Optional[int]       			=					Node(3			)
  __lowerCamelCase			:			int       			=					Node(4			)
  __lowerCamelCase			:			Optional[int]       			=					Node(5			)
  return tree

def 			a_	(				_lowerCAmelCase			) -> list[int]:
  return [root.data, *preorder(root.left			), *preorder(root.right			)] if root else []

def 			a_	(				_lowerCAmelCase			) -> list[int]:
  return postorder(root.left			) + postorder(root.right			) + [root.data] if root else []

def 			a_	(				_lowerCAmelCase			) -> list[int]:
  return [*inorder(root.left			), root.data, *inorder(root.right			)] if root else []

def 			a_	(				_lowerCAmelCase			) -> int:
  return (max(height(root.left			)			,height(root.right			)			) + 1) if root else 0

def 			a_	(				_lowerCAmelCase			) -> Sequence[Node | None]:
  __lowerCamelCase			:			list[Any]       			=					[]

  if root is None:
    return output

  __lowerCamelCase			:			Dict       			=					deque([root]			)

  while process_queue:
    __lowerCamelCase			:			Tuple       			=					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_	(				_lowerCAmelCase			,_lowerCAmelCase			) -> Sequence[Node | None]:
  __lowerCamelCase			:			list[Any]       			=					[]

  def populate_output(_lowerCAmelCase			,_lowerCAmelCase			) -> 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 			a_	(				_lowerCAmelCase			,_lowerCAmelCase			) -> Sequence[Node | None]:
  __lowerCamelCase			:			list[Any]       			=					[]

  def populate_output(_lowerCAmelCase			,_lowerCAmelCase			) -> 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 			a_	(				_lowerCAmelCase			) -> Sequence[Node | None] | list[Any]:
  if root is None:
    return []

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

  __lowerCamelCase			:			List[Any]       			=					0
  __lowerCamelCase			:			Dict       			=					height(_lowerCAmelCase			)

  for h in range(1			,height_tree + 1			):
    if not flag:
      output.append(get_nodes_from_left_to_right(_lowerCAmelCase			,_lowerCAmelCase			)			)
      __lowerCamelCase			:			Any       			=					1
    else:
      output.append(get_nodes_from_right_to_left(_lowerCAmelCase			,_lowerCAmelCase			)			)
      __lowerCamelCase			:			Union[str, Any]       			=					0

  return output

def 			a_	(				) -> None:  # Main function for testing.
  __lowerCamelCase			:			str       			=					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'''





# Algorithm for the pigeonhole sorting



def 			a_	(				_lowerCAmelCase			) -> List[str]:
  __lowerCamelCase			:			int       			=					min(_lowerCAmelCase			)  # min() finds the minimum value
  __lowerCamelCase			:			List[Any]       			=					max(_lowerCAmelCase			)  # max() finds the maximum value

  __lowerCamelCase			:			List[Any]       			=					max_val - min_val + 1  # size is difference of max and min values plus one

  # list of pigeonholes of size equal to the variable size
  __lowerCamelCase			:			List[Any]       			=					[0] * size

  # Populate the pigeonholes.
  for x in a:
    assert isinstance(_lowerCAmelCase			,_lowerCAmelCase			), "integers only please"
    holes[x - min_val] += 1

  # Putting the elements back into the array in an order.
  __lowerCamelCase			:			Tuple       			=					0
  for count in range(_lowerCAmelCase			):
    while holes[count] > 0:
      holes[count] -= 1
      __lowerCamelCase			:			List[Any]       			=					count + min_val
      i += 1

def 			a_	(				) -> str:
  __lowerCamelCase			:			Optional[Any]       			=					[8, 3, 2, 7, 4, 6, 8]
  pigeonhole_sort(_lowerCAmelCase			)
  print('Sorted order is:'			,' '.join(_lowerCAmelCase			)			)


if __name__ == "__main__":
   main()






