


'''simple docstring'''





from math import atan, cos, radians, sin, tan

from .haversine_distance import haversine_distance

__lowerCamelCase												=						6_37_81_37.0
__lowerCamelCase												=						6_35_67_52.31_42_45
__lowerCamelCase												=						637_8137


def        a__     (					UpperCamelCase_						:      float,   UpperCamelCase_						:      float,   UpperCamelCase_						:      float,   UpperCamelCase_						:      float						):
   UpperCAmelCase__	:str      =      (AXIS_A - AXIS_B) / AXIS_A
   # Parametric latitudes
   # https://en.wikipedia.org/wiki/Latitude#Parametric_(or_reduced)_latitude
   UpperCAmelCase__	:Dict      =      atan((1 - flattening) * tan(radians(UpperCamelCase_						)						)						)
   UpperCAmelCase__	:Dict      =      atan((1 - flattening) * tan(radians(UpperCamelCase_						)						)						)

   # Compute central angle between two points
   # using haversine theta. sigma =  haversine_distance / equatorial radius
   UpperCAmelCase__	:List[Any]      =      haversine_distance(UpperCamelCase_,   UpperCamelCase_,   UpperCamelCase_,   UpperCamelCase_						) / EQUATORIAL_RADIUS

   # Intermediate P and Q values
   UpperCAmelCase__	:Optional[int]      =      (b_lata + b_lata) / 2
   UpperCAmelCase__	:Optional[int]      =      (b_lata - b_lata) / 2

   # Intermediate X value
   # X = (sigma - sin(sigma)) * sin^2Pcos^2Q / cos^2(sigma/2)
   UpperCAmelCase__	:Tuple      =      (sin(UpperCamelCase_						) ** 2) * (cos(UpperCamelCase_						) ** 2)
   UpperCAmelCase__	:Optional[int]      =      cos(sigma / 2						) ** 2
   UpperCAmelCase__	:Any      =      (sigma - sin(UpperCamelCase_						)) * (x_numerator / x_demonimator)

   # Intermediate Y value
   # Y = (sigma + sin(sigma)) * cos^2Psin^2Q / sin^2(sigma/2)
   UpperCAmelCase__	:int      =      (cos(UpperCamelCase_						) ** 2) * (sin(UpperCamelCase_						) ** 2)
   UpperCAmelCase__	:str      =      sin(sigma / 2						) ** 2
   UpperCAmelCase__	:Tuple      =      (sigma + sin(UpperCamelCase_						)) * (y_numerator / y_denominator)

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


if __name__ == "__main__":
    import doctest

    doctest.testmod()







'''simple docstring'''





class 				UpperCAmelCase			:


 def __init__(      self							:	Union[str, Any] ):
    UpperCAmelCase__	:dict[str, TrieNode]      =      {}  # Mapping from char to TrieNode
    UpperCAmelCase__	:Union[str, Any]      =      False


 def        __SCREAMING_SNAKE_CASE					(      self							:	Optional[int]			,       __lowerCamelCase							:	list[str] ):
    for word in words:
       self.insert(__lowerCamelCase )


 def        __SCREAMING_SNAKE_CASE					(      self							:	Dict			,       __lowerCamelCase							:	str ):
    UpperCAmelCase__	:Tuple      =      self
    for char in word:
       if char not in curr.nodes:
          UpperCAmelCase__	:Optional[int]      =      TrieNode()
       UpperCAmelCase__	:Dict      =      curr.nodes[char]
    UpperCAmelCase__	:Optional[int]      =      True


 def        __SCREAMING_SNAKE_CASE					(      self							:	Any			,       __lowerCamelCase							:	str ):
    UpperCAmelCase__	:str      =      self
    for char in word:
       if char not in curr.nodes:
          return False
       UpperCAmelCase__	:Dict      =      curr.nodes[char]
    return curr.is_leaf





 def        __SCREAMING_SNAKE_CASE					(      self							:	Optional[Any]			,       __lowerCamelCase							:	str ):

    def _delete(__lowerCamelCase							:	TrieNode			,       __lowerCamelCase							:	str			,       __lowerCamelCase							:	int ) -> bool:
       if index == len(__lowerCamelCase ):
          # If word does not exist
          if not curr.is_leaf:
             return False
          UpperCAmelCase__	:int      =      False
          return len(curr.nodes ) == 0
       UpperCAmelCase__	:str      =      word[index]
       UpperCAmelCase__	:Optional[Any]      =      curr.nodes.get(__lowerCamelCase )
       # If char not in current trie node
       if not char_node:
          return False
       # Flag to check if node can be deleted
       UpperCAmelCase__	:Any      =      _delete(__lowerCamelCase			,       __lowerCamelCase			,       index + 1 )
       if delete_curr:
          del curr.nodes[char]
          return len(curr.nodes ) == 0
       return delete_curr

    _delete(self			,       __lowerCamelCase			,       0 )


def        a__     (					UpperCamelCase_						:      TrieNode,   UpperCamelCase_						:      str						):
   if node.is_leaf:
      print(UpperCamelCase_,   end=''' '''						)

   for key, value in node.nodes.items():
      print_words(UpperCamelCase_,   word + key						)


def        a__     (					):
   UpperCAmelCase__	:Union[str, Any]      =      '''banana bananas bandana band apple all beast'''.split()
   UpperCAmelCase__	:Union[str, Any]      =      TrieNode()
   root.insert_many(UpperCamelCase_						)
   # print_words(root, "")
   assert all(root.find(UpperCamelCase_						) for word in words						)
   assert root.find('''banana'''						)
   assert not root.find('''bandanas'''						)
   assert not root.find('''apps'''						)
   assert root.find('''apple'''						)
   assert root.find('''all'''						)
   root.delete('''all'''						)
   assert not root.find('''all'''						)
   root.delete('''banana'''						)
   assert not root.find('''banana'''						)
   assert root.find('''bananas'''						)
   return True


def        a__     (					UpperCamelCase_						:      str,   UpperCamelCase_						:      bool						):
   print(str(UpperCamelCase_						),   '''works!''' if passes else '''doesn\'t work :('''						)


def        a__     (					):
   assert test_trie()


def        a__     (					):
   print_results('''Testing trie functionality''',   test_trie()						)


if __name__ == "__main__":
    main()



