






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							:						int
       a							:						Node | None										=None
       a							:						Node | None										=None







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

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

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

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

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

def     snake_case   (UpperCAmelCase__    )			->							Sequence[Node | None]:
  UpperCamelCase_:   list[Any]        =							[]

  if root is None:
    return output

  UpperCamelCase_:   List[str]        =							deque([root]    )

  while process_queue:
    UpperCamelCase_:   Dict        =							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   (UpperCAmelCase__      ,       UpperCAmelCase__    )			->							Sequence[Node | None]:
  UpperCamelCase_:   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(UpperCAmelCase__      ,       UpperCAmelCase__    )
  return output

def     snake_case   (UpperCAmelCase__      ,       UpperCAmelCase__    )			->							Sequence[Node | None]:
  UpperCamelCase_:   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(UpperCAmelCase__      ,       UpperCAmelCase__    )
  return output

def     snake_case   (UpperCAmelCase__    )			->							Sequence[Node | None] | list[Any]:
  if root is None:
    return []

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

  UpperCamelCase_:   Optional[int]        =							0
  UpperCamelCase_:   Optional[Any]        =							height(UpperCAmelCase__    )

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

  return output

def     snake_case   ()			->							None:  # Main function for testing.
  UpperCamelCase_:   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 math import atan, cos, radians, sin, tan

from .haversine_distance import haversine_distance

_lowerCamelCase      :						Dict							=  6_378_137.0
_lowerCamelCase      :						Union[str, Any]							=  6_356_752.314_245
_lowerCamelCase      :						List[Any]							=  6378137







def SCREAMING_SNAKE_CASE							(			lowercase_					,							lowercase_					,							lowercase_					,							lowercase_		)  ->			float:



       """simple docstring"""

       A__ 					=       (AXIS_A - AXIS_B) / AXIS_A
       # Parametric latitudes
       # https://en.wikipedia.org/wiki/Latitude#Parametric_(or_reduced)_latitude
       A__ 					=       atan((1 - flattening) * tan(radians(lowercase_		)		)		)
       A__ 					=       atan((1 - flattening) * tan(radians(lowercase_		)		)		)

       # Compute central angle between two points
       # using haversine theta. sigma =  haversine_distance / equatorial radius
       A__ 					=       haversine_distance(lowercase_					,							lowercase_					,							lowercase_					,							lowercase_		) / EQUATORIAL_RADIUS

       # Intermediate P and Q values
       A__ 					=       (b_lata + b_lata) / 2
       A__ 					=       (b_lata - b_lata) / 2

       # Intermediate X value
       # X = (sigma - sin(sigma)) * sin^2Pcos^2Q / cos^2(sigma/2)
       A__ 					=       (sin(lowercase_		) ** 2) * (cos(lowercase_		) ** 2)
       A__ 					=       cos(sigma / 2		) ** 2
       A__ 					=       (sigma - sin(lowercase_		)) * (x_numerator / x_demonimator)

       # Intermediate Y value
       # Y = (sigma + sin(sigma)) * cos^2Psin^2Q / sin^2(sigma/2)
       A__ 					=       (cos(lowercase_		) ** 2) * (sin(lowercase_		) ** 2)
       A__ 					=       sin(sigma / 2		) ** 2
       A__ 					=       (sigma + sin(lowercase_		)) * (y_numerator / y_denominator)

       return EQUATORIAL_RADIUS * (sigma - ((flattening / 2) * (x_value + y_value)))


if __name__ == "__main__":
  import doctest

  doctest.testmod()


