



'''simple docstring'''






from random import randint, random
def 				lowerCamelCase__	(						_A			,      _A			,      _A			,      _A = False			,      _A = False			,      _A = 5			,      ):
  a						: Union[str, Any]					       =					[[-1] * number_of_cells]  # Create a highway without any car
  a						: Optional[int]					       =					0
  a						: int					       =					max(_A			,      0    )
  while i < number_of_cells:
    a						: Optional[Any]					       =					(
        randint(0			,      _A    ) if random_speed else initial_speed
    )  # Place the cars
    i += (
        randint(1			,      max_speed * 2    ) if random_frequency else frequency
    )  # Arbitrary number, may need tuning
  return highway
def 				lowerCamelCase__	(						_A			,      _A    ):
  a						: Dict					       =					0
  a						: Optional[int]					       =					highway_now[car_index + 1 :]
  for cell in range(len(_A    )    ):  # May need a better name for this
    if cells[cell] != -1:  # If the cell is not empty then
      return distance  # we have the distance we wanted
    distance += 1
  # Here if the car is near the end of the highway
  return distance + get_distance(_A			,      -1    )
def 				lowerCamelCase__	(						_A			,      _A			,      _A    ):
  a						: Any					       =					len(_A    )
  # Beforce calculations, the highway is empty
  a						: Dict					       =					[-1] * number_of_cells

  for car_index in range(_A    ):
    if highway_now[car_index] != -1:
      # Add 1 to the current speed of the car and cap the speed
      a						: Tuple					       =					min(highway_now[car_index] + 1			,      _A    )
      # Number of empty cell before the next car
      a						: Optional[Any]					       =					get_distance(_A			,      _A    ) - 1
      # We can't have the car causing an accident
      a						: List[Any]					       =					min(next_highway[car_index]			,      _A    )
      if random() < probability:
        # Randomly, a driver will slow down
        a						: List[str]					       =					max(next_highway[car_index] - 1			,      0    )
  return next_highway
def 				lowerCamelCase__	(						_A			,      _A			,      _A			,      _A    ):
  a						: Optional[Any]					       =					len(highway[0]    )

  for i in range(_A    ):
    a						: Optional[int]					       =					update(highway[i]			,      _A			,      _A    )
    a						: List[str]					       =					[-1] * number_of_cells

    for car_index in range(_A    ):
      a						: Dict					       =					next_speeds_calculated[car_index]
      if speed != -1:
        # Change the position based on the speed (with % to create the loop)
        a						: List[Any]					       =					(car_index + speed) % number_of_cells
        # Commit the change of position
        a						: Optional[Any]					       =					speed
    highway.append(_A    )

  return highway


if __name__ == "__main__":
     import doctest

     doctest.testmod()




'''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))