




'''simple docstring'''



def 			_UpperCamelCase (_lowerCamelCase							:     Dict	)->   str:




     '''simple docstring'''





     if len(__lowerCamelCase	) == 0 or not all(len(__lowerCamelCase	) == 2 for pair in coordinates	):
          raise ValueError('''The program cannot work out a fitting polynomial.'''	)

     if len({tuple(__lowerCamelCase	) for pair in coordinates}	) != len(__lowerCamelCase	):
          raise ValueError('''The program cannot work out a fitting polynomial.'''	)

     __snake_case    					=  {x for x, _ in coordinates}
     if len(__lowerCamelCase	) == 1:
          return f'''x={coordinates[0][0]}'''

     if len(__lowerCamelCase	) != len(__lowerCamelCase	):
          raise ValueError('''The program cannot work out a fitting polynomial.'''	)

     __snake_case    					=  len(__lowerCamelCase	)

     __snake_case    					=  0
     __snake_case    					=  []
     # put the x and x to the power values in a matrix
     while count_of_line < x:
          __snake_case    					=  0
          __snake_case    					=  coordinates[count_of_line][0]
          __snake_case    					=  []
          while count_in_line < x:
               count_line.append(a ** (x - (count_in_line + 1))	)
               count_in_line += 1
          matrix.append(__lowerCamelCase	)
          count_of_line += 1

     __snake_case    					=  0
     # put the y values into a vector
     __snake_case    					=  []
     while count_of_line < x:
          vector.append(coordinates[count_of_line][1]	)
          count_of_line += 1

     __snake_case    					=  0

     while count < x:
          __snake_case    					=  0
          while zahlen < x:
               if count == zahlen:
                    zahlen += 1
               if zahlen == x:
                    break
               __snake_case    					=  matrix[zahlen][count] / matrix[count][count]
               for counting_columns, item in enumerate(matrix[count]	):
                    # manipulating all the values in the matrix
                    matrix[zahlen][counting_columns] -= item * bruch
               # manipulating the values in the vector
               vector[zahlen] -= vector[count] * bruch
               zahlen += 1
          count += 1

     __snake_case    					=  0
     # make solutions
     __snake_case    					=  []
     while count < x:
          solution.append(str(vector[count] / matrix[count][count]	)	)
          count += 1

     __snake_case    					=  0
     __snake_case    					=  """f(x)="""

     while count < x:
          __snake_case    					=  solution[count].split('''E'''	)
          if len(__lowerCamelCase	) > 1:
               __snake_case    					=  f'''{remove_e[0]}*10^{remove_e[1]}'''
          solved += f'''x^{x - (count + 1)}*{solution[count]}'''
          if count + 1 != x:
               solved += "+"
          count += 1

     return solved


if __name__ == "__main__":
       print(points_to_polynomial([]))
       print(points_to_polynomial([[]]))
       print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
       print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
       print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
       print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
       print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
       print(points_to_polynomial([[1, 3], [2, 6], [3, 1_1]]))
       print(points_to_polynomial([[1, -3], [2, -6], [3, -1_1]]))
       print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))












'''simple docstring'''



from ..utils import deprecate
from .attention_processor import (  # noqa: F401
    Attention,
    AttentionProcessor,
    AttnAddedKVProcessor,
    AttnProcessor2_0,
    LoRAAttnProcessor,
    LoRALinearLayer,
    LoRAXFormersAttnProcessor,
    SlicedAttnAddedKVProcessor,
    SlicedAttnProcessor,
    XFormersAttnProcessor,
)
from .attention_processor import AttnProcessor as AttnProcessorRename  # noqa: F401


deprecate(
    '''cross_attention''',
    '''0.20.0''',
    '''Importing from cross_attention is deprecated. Please import from diffusers.models.attention_processor instead.''',
    standard_warn=False,
)


UpperCAmelCase_       :  Optional[int]      =		AttentionProcessor





class     lowerCAmelCase   ( __lowerCAmelCase):


       def __init__(   self    ,  *__SCREAMING_SNAKE_CASE    ,  **__SCREAMING_SNAKE_CASE  )      ->  Optional[int]:



            '''simple docstring'''




            __snake_case    					=  F'''{self.__class__.__name__} is deprecated and will be removed in `0.20.0`. Please use `from diffusers.models.attention_processor import {"".join(self.__class__.__name__.split("Cross"  )  )} instead.'''
            deprecate('''cross_attention'''    ,  '''0.20.0'''    ,  __SCREAMING_SNAKE_CASE    ,  standard_warn=__SCREAMING_SNAKE_CASE  )
            super().__init__(*__SCREAMING_SNAKE_CASE    ,  **__SCREAMING_SNAKE_CASE  )





class     lowerCAmelCase   ( __lowerCAmelCase):


       def __init__(   self    ,  *__SCREAMING_SNAKE_CASE    ,  **__SCREAMING_SNAKE_CASE  )      ->  Any:



            '''simple docstring'''




            __snake_case    					=  F'''{self.__class__.__name__} is deprecated and will be removed in `0.20.0`. Please use `from diffusers.models.attention_processor import {"".join(self.__class__.__name__.split("Cross"  )  )} instead.'''
            deprecate('''cross_attention'''    ,  '''0.20.0'''    ,  __SCREAMING_SNAKE_CASE    ,  standard_warn=__SCREAMING_SNAKE_CASE  )
            super().__init__(*__SCREAMING_SNAKE_CASE    ,  **__SCREAMING_SNAKE_CASE  )





class     lowerCAmelCase   ( __lowerCAmelCase):


       def __init__(   self    ,  *__SCREAMING_SNAKE_CASE    ,  **__SCREAMING_SNAKE_CASE  )      ->  Tuple:



            '''simple docstring'''




            __snake_case    					=  F'''{self.__class__.__name__} is deprecated and will be removed in `0.20.0`. Please use `from diffusers.models.attention_processor import {"".join(self.__class__.__name__.split("Cross"  )  )} instead.'''
            deprecate('''cross_attention'''    ,  '''0.20.0'''    ,  __SCREAMING_SNAKE_CASE    ,  standard_warn=__SCREAMING_SNAKE_CASE  )
            super().__init__(*__SCREAMING_SNAKE_CASE    ,  **__SCREAMING_SNAKE_CASE  )





class     lowerCAmelCase   ( __lowerCAmelCase):


       def __init__(   self    ,  *__SCREAMING_SNAKE_CASE    ,  **__SCREAMING_SNAKE_CASE  )      ->  Optional[Any]:



            '''simple docstring'''




            __snake_case    					=  F'''{self.__class__.__name__} is deprecated and will be removed in `0.20.0`. Please use `from diffusers.models.attention_processor import {"".join(self.__class__.__name__.split("Cross"  )  )} instead.'''
            deprecate('''cross_attention'''    ,  '''0.20.0'''    ,  __SCREAMING_SNAKE_CASE    ,  standard_warn=__SCREAMING_SNAKE_CASE  )
            super().__init__(*__SCREAMING_SNAKE_CASE    ,  **__SCREAMING_SNAKE_CASE  )





class     lowerCAmelCase   ( __lowerCAmelCase):


       def __init__(   self    ,  *__SCREAMING_SNAKE_CASE    ,  **__SCREAMING_SNAKE_CASE  )      ->  Optional[int]:



            '''simple docstring'''




            __snake_case    					=  F'''{self.__class__.__name__} is deprecated and will be removed in `0.20.0`. Please use `from diffusers.models.attention_processor import {"".join(self.__class__.__name__.split("Cross"  )  )} instead.'''
            deprecate('''cross_attention'''    ,  '''0.20.0'''    ,  __SCREAMING_SNAKE_CASE    ,  standard_warn=__SCREAMING_SNAKE_CASE  )
            super().__init__(*__SCREAMING_SNAKE_CASE    ,  **__SCREAMING_SNAKE_CASE  )





class     lowerCAmelCase   ( __lowerCAmelCase):


       def __init__(   self    ,  *__SCREAMING_SNAKE_CASE    ,  **__SCREAMING_SNAKE_CASE  )      ->  Tuple:



            '''simple docstring'''




            __snake_case    					=  F'''{self.__class__.__name__} is deprecated and will be removed in `0.20.0`. Please use `from diffusers.models.attention_processor import {"".join(self.__class__.__name__.split("Cross"  )  )} instead.'''
            deprecate('''cross_attention'''    ,  '''0.20.0'''    ,  __SCREAMING_SNAKE_CASE    ,  standard_warn=__SCREAMING_SNAKE_CASE  )
            super().__init__(*__SCREAMING_SNAKE_CASE    ,  **__SCREAMING_SNAKE_CASE  )





class     lowerCAmelCase   ( __lowerCAmelCase):


       def __init__(   self    ,  *__SCREAMING_SNAKE_CASE    ,  **__SCREAMING_SNAKE_CASE  )      ->  int:



            '''simple docstring'''




            __snake_case    					=  F'''{self.__class__.__name__} is deprecated and will be removed in `0.20.0`. Please use `from diffusers.models.attention_processor import {"".join(self.__class__.__name__.split("Cross"  )  )} instead.'''
            deprecate('''cross_attention'''    ,  '''0.20.0'''    ,  __SCREAMING_SNAKE_CASE    ,  standard_warn=__SCREAMING_SNAKE_CASE  )
            super().__init__(*__SCREAMING_SNAKE_CASE    ,  **__SCREAMING_SNAKE_CASE  )





class     lowerCAmelCase   ( __lowerCAmelCase):


       def __init__(   self    ,  *__SCREAMING_SNAKE_CASE    ,  **__SCREAMING_SNAKE_CASE  )      ->  List[str]:



            '''simple docstring'''




            __snake_case    					=  F'''{self.__class__.__name__} is deprecated and will be removed in `0.20.0`. Please use `from diffusers.models.attention_processor import {"".join(self.__class__.__name__.split("Cross"  )  )} instead.'''
            deprecate('''cross_attention'''    ,  '''0.20.0'''    ,  __SCREAMING_SNAKE_CASE    ,  standard_warn=__SCREAMING_SNAKE_CASE  )
            super().__init__(*__SCREAMING_SNAKE_CASE    ,  **__SCREAMING_SNAKE_CASE  )






