
"""simple docstring"""






from math import isclose, sqrt






def 						_snake_case       (	lowercase__		:  float      ,     lowercase__		:  float      ,     lowercase__		:  float		)  ->				tuple[float, float, float]:


			'''simple docstring'''





			lowerCAmelCase_    :Optional[int]			     =  point_y / 4 / point_x
			lowerCAmelCase_    :Dict			     =  2 * normal_gradient / (1 + normal_gradient * normal_gradient)
			lowerCAmelCase_    :Union[str, Any]			     =  (1 - normal_gradient * normal_gradient) / (
			    1 + normal_gradient * normal_gradient
			)
			lowerCAmelCase_    :str			     =  (sa - ca * incoming_gradient) / (ca + sa * incoming_gradient)

			# to find the next point, solve the simultaeneous equations:
			# y^2 + 4x^2 = 100
			# y - b = m * (x - a)
			# ==> A x^2 + B x + C = 0
			lowerCAmelCase_    :Tuple			     =  outgoing_gradient**2 + 4
			lowerCAmelCase_    :Tuple			     =  2 * outgoing_gradient * (point_y - outgoing_gradient * point_x)
			lowerCAmelCase_    :str			     =  (point_y - outgoing_gradient * point_x) ** 2 - 1_0_0

			lowerCAmelCase_    :Optional[Any]			     =  (
			    -linear_term - sqrt(linear_term**2 - 4 * quadratic_term * constant_term		)
			) / (2 * quadratic_term)
			lowerCAmelCase_    :Optional[int]			     =  (
			    -linear_term + sqrt(linear_term**2 - 4 * quadratic_term * constant_term		)
			) / (2 * quadratic_term)

			# two solutions, one of which is our input point
			lowerCAmelCase_    :List[Any]			     =  x_minus if isclose(lowercase__      ,     lowercase__		) else x_plus
			lowerCAmelCase_    :List[str]			     =  point_y + outgoing_gradient * (next_x - point_x)

			return next_x, next_y, outgoing_gradient






def 						_snake_case       (	lowercase__		:  float = 1.4      ,     lowercase__		:  float = -9.6		)  ->				int:


			'''simple docstring'''





			lowerCAmelCase_    :int			     =  0
			lowerCAmelCase_    :float			     =  first_x_coord
			lowerCAmelCase_    :float			     =  first_y_coord
			lowerCAmelCase_    :float			     =  (10.1 - point_y) / (0.0 - point_x)

			while not (-0.01 <= point_x <= 0.01 and point_y > 0):
						lowerCAmelCase_     ,       lowerCAmelCase_     ,       lowerCAmelCase_    :List[str]			     =  next_point(lowercase__      ,     lowercase__      ,     lowercase__		)
						num_reflections += 1

			return num_reflections


if __name__ == "__main__":
				print(F"""{solution() = }""")







from ...processing_utils import ProcessorMixin


class      lowerCamelCase    (SCREAMING_SNAKE_CASE__    ):
  """simple docstring"""







  lowerCamelCase__   =  ['''image_processor''', '''feature_extractor''']
  lowerCamelCase__   =  '''TvltImageProcessor'''
  lowerCamelCase__   =  '''TvltFeatureExtractor'''







  def __init__(							self       :				List[str]     ,   __magic_name__       :				Any     ,   __magic_name__       :				Any      )     ->		int:
        super().__init__(image_processor=__magic_name__     ,   feature_extractor=__magic_name__      )

        SCREAMING_SNAKE_CASE_      =     image_processor
        SCREAMING_SNAKE_CASE_      =     feature_extractor







  def __call__(							self       :				List[str]     ,   __magic_name__       :				Optional[Any]=None     ,   __magic_name__       :				Union[str, Any]=None     ,   __magic_name__       :				int=None     ,   __magic_name__       :				str=None     ,   __magic_name__       :				Any=False     ,   __magic_name__       :				int=False     ,   *__magic_name__       :				int     ,   **__magic_name__       :				Any     ,   )     ->		List[Any]:

        if images is None and audio is None:
              raise ValueError("You need to specify either an `images` or `audio` input to process."      )

        SCREAMING_SNAKE_CASE_      =     None
        if images is not None:
              SCREAMING_SNAKE_CASE_      =     self.image_processor(__magic_name__     ,   mask_pixel=__magic_name__     ,   *__magic_name__     ,   **__magic_name__      )
        if images_mixed is not None:
              SCREAMING_SNAKE_CASE_      =     self.image_processor(__magic_name__     ,   is_mixed=__magic_name__     ,   *__magic_name__     ,   **__magic_name__      )
        if audio is not None:
              SCREAMING_SNAKE_CASE_      =     self.feature_extractor(
                  __magic_name__     ,   *__magic_name__     ,   sampling_rate=__magic_name__     ,   mask_audio=__magic_name__     ,   **__magic_name__      )

        SCREAMING_SNAKE_CASE_      =     {}
        if audio is not None:
              output_dict.update(__magic_name__      )
        if images is not None:
              output_dict.update(__magic_name__      )
        if images_mixed_dict is not None:
              output_dict.update(__magic_name__      )
        return output_dict







  @property
  def       __A   (							self       :				Optional[Any]      )     ->		int:
        SCREAMING_SNAKE_CASE_      =     self.image_processor.model_input_names
        SCREAMING_SNAKE_CASE_      =     self.feature_extractor.model_input_names
        return list(dict.fromkeys(image_processor_input_names + feature_extractor_input_names      )      )


