



'''simple docstring'''






def 				lowerCamelCase__	(						_A			,      _A    ):
  a						: Any					       =					0
  a						: Tuple					       =					len(_A    ) - 1

  while left <= right:
    # avoid divided by 0 during interpolation
    if sorted_collection[left] == sorted_collection[right]:
      if sorted_collection[left] == item:
        return left
      else:
        return None

    a						: Tuple					       =					left + ((item - sorted_collection[left]) * (right - left)) // (
        sorted_collection[right] - sorted_collection[left]
    )

    # out of range check
    if point < 0 or point >= len(_A    ):
      return None

    a						: List[str]					       =					sorted_collection[point]
    if current_item == item:
      return point
    else:
      if point < left:
        a						: Union[str, Any]					       =					left
        a						: Any					       =					point
      elif point > right:
        a						: Optional[Any]					       =					right
        a						: List[Any]					       =					point
      else:
        if item < current_item:
          a						: Any					       =					point - 1
        else:
          a						: Tuple					       =					point + 1
  return None
def 				lowerCamelCase__	(						_A			,      _A			,      _A			,      _A    ):

  # avoid divided by 0 during interpolation
  if sorted_collection[left] == sorted_collection[right]:
    if sorted_collection[left] == item:
      return left
    else:
      return None

  a						: Tuple					       =					left + ((item - sorted_collection[left]) * (right - left)) // (
      sorted_collection[right] - sorted_collection[left]
  )

  # out of range check
  if point < 0 or point >= len(_A    ):
    return None

  if sorted_collection[point] == item:
    return point
  elif point < left:
    return interpolation_search_by_recursion(_A			,      _A			,      _A			,      _A    )
  elif point > right:
    return interpolation_search_by_recursion(_A			,      _A			,      _A			,      _A    )
  else:
    if sorted_collection[point] > item:
      return interpolation_search_by_recursion(
          _A			,      _A			,      _A			,      point - 1    )
    else:
      return interpolation_search_by_recursion(
          _A			,      _A			,      point + 1			,      _A    )
def 				lowerCamelCase__	(						_A    ):
  if collection != sorted(_A    ):
    raise ValueError('Collection must be ascending sorted'    )
  return True


if __name__ == "__main__":
     import sys
     lowerCAmelCase: Any							=						0
     if debug == 1:
          lowerCAmelCase: Dict							=						[1_0, 3_0, 4_0, 4_5, 5_0, 6_6, 7_7, 9_3]
          try:
               __assert_sorted(collection)
          except ValueError:
               sys.exit('Sequence must be ascending sorted to apply interpolation search')
          lowerCAmelCase: List[Any]							=						6_7

     lowerCAmelCase: List[Any]							=						interpolation_search(collection, target)
     if result is not None:
          print(F"{target} found at positions: {result}")
     else:
          print('Not found')




'''simple docstring'''






from math import factorial, pi
def 				lowerCamelCase__	(						_A			,      _A = 30    ):

  if not isinstance(_A			,      (int, float)    ):
    raise ValueError('maclaurin_sin() requires either an int or float for theta'    )

  if not isinstance(_A			,      _A    ) or accuracy <= 0:
    raise ValueError('maclaurin_sin() requires a positive int for accuracy'    )

  a						: Dict					       =					float(_A    )
  a						: List[Any]					       =					theta // (2 * pi)
  theta -= 2 * div * pi
  return sum(
      (-1) ** r * theta ** (2 * r + 1) / factorial(2 * r + 1    ) for r in range(_A    )    )
def 				lowerCamelCase__	(						_A			,      _A = 30    ):

  if not isinstance(_A			,      (int, float)    ):
    raise ValueError('maclaurin_cos() requires either an int or float for theta'    )

  if not isinstance(_A			,      _A    ) or accuracy <= 0:
    raise ValueError('maclaurin_cos() requires a positive int for accuracy'    )

  a						: int					       =					float(_A    )
  a						: str					       =					theta // (2 * pi)
  theta -= 2 * div * pi
  return sum((-1) ** r * theta ** (2 * r) / factorial(2 * r    ) for r in range(_A    )    )


if __name__ == "__main__":
     import doctest

     doctest.testmod()

     print(maclaurin_sin(1_0))
     print(maclaurin_sin(-1_0))
     print(maclaurin_sin(1_0, 1_5))
     print(maclaurin_sin(-1_0, 1_5))

     print(maclaurin_cos(5))
     print(maclaurin_cos(-5))
     print(maclaurin_cos(1_0, 1_5))
     print(maclaurin_cos(-1_0, 1_5))