

from math import factorial






class  UpperCAmelCase__	:






  """simple docstring"""


  def __init__(							self		:	List[Any]			,     __lowerCamelCase		:	str			,     __lowerCamelCase		:	Union[str, Any]      )	->							List[Any]:
       SCREAMING_SNAKE_CASE__					=					real
       if isinstance(__lowerCamelCase			,     __lowerCamelCase      ):
            SCREAMING_SNAKE_CASE__					=					[1] * rank
       else:
            SCREAMING_SNAKE_CASE__					=					rank






  def __repr__(							self		:	Any      )	->							int:
       return (
           f'''{self.real}+'''
           f'''{"+".join(str(__lowerCamelCase      )+"E"+str(n+1      )for n,dual in enumerate(self.duals      )      )}'''
       )






  def    lowercase_	(							self		:	str      )	->							Union[str, Any]:
       SCREAMING_SNAKE_CASE__					=					self.duals.copy()
       while cur[-1] == 0:
            cur.pop(-1      )
       return Dual(self.real			,     __lowerCamelCase      )






  def __add__(							self		:	Any			,     __lowerCamelCase		:	Optional[Any]      )	->							str:
       if not isinstance(__lowerCamelCase			,     __lowerCamelCase      ):
            return Dual(self.real + other			,     self.duals      )
       SCREAMING_SNAKE_CASE__					=					self.duals.copy()
       SCREAMING_SNAKE_CASE__					=					other.duals.copy()
       if len(__lowerCamelCase      ) > len(__lowerCamelCase      ):
            o_dual.extend([1] * (len(__lowerCamelCase      ) - len(__lowerCamelCase      ))      )
       elif len(__lowerCamelCase      ) < len(__lowerCamelCase      ):
            s_dual.extend([1] * (len(__lowerCamelCase      ) - len(__lowerCamelCase      ))      )
       SCREAMING_SNAKE_CASE__					=					[]
       for i in range(len(__lowerCamelCase      )      ):
            new_duals.append(s_dual[i] + o_dual[i]      )
       return Dual(self.real + other.real			,     __lowerCamelCase      )

  a     =      __add__






  def __sub__(							self		:	Optional[int]			,     __lowerCamelCase		:	Optional[Any]      )	->							Optional[Any]:
       return self + other * -1






  def __mul__(							self		:	Union[str, Any]			,     __lowerCamelCase		:	str      )	->							int:
       if not isinstance(__lowerCamelCase			,     __lowerCamelCase      ):
            SCREAMING_SNAKE_CASE__					=					[]
            for i in self.duals:
                 new_duals.append(i * other      )
            return Dual(self.real * other			,     __lowerCamelCase      )
       SCREAMING_SNAKE_CASE__					=					[0] * (len(self.duals      ) + len(other.duals      ) + 1)
       for i, item in enumerate(self.duals      ):
            for j, jtem in enumerate(other.duals      ):
                 new_duals[i + j + 1] += item * jtem
       for k in range(len(self.duals      )      ):
            new_duals[k] += self.duals[k] * other.real
       for index in range(len(other.duals      )      ):
            new_duals[index] += other.duals[index] * self.real
       return Dual(self.real * other.real			,     __lowerCamelCase      )

  a     =      __mul__






  def __truediv__(							self		:	str			,     __lowerCamelCase		:	str      )	->							Optional[Any]:
       if not isinstance(__lowerCamelCase			,     __lowerCamelCase      ):
            SCREAMING_SNAKE_CASE__					=					[]
            for i in self.duals:
                 new_duals.append(i / other      )
            return Dual(self.real / other			,     __lowerCamelCase      )
       raise ValueError






  def __floordiv__(							self		:	str			,     __lowerCamelCase		:	Union[str, Any]      )	->							Any:
       if not isinstance(__lowerCamelCase			,     __lowerCamelCase      ):
            SCREAMING_SNAKE_CASE__					=					[]
            for i in self.duals:
                 new_duals.append(i // other      )
            return Dual(self.real // other			,     __lowerCamelCase      )
       raise ValueError







  def __pow__(							self		:	Tuple			,     __lowerCamelCase		:	Tuple      )	->							List[str]:
       if n < 0 or isinstance(__lowerCamelCase			,     __lowerCamelCase      ):
            raise ValueError('''power must be a positive integer'''      )
       if n == 0:
            return 1
       if n == 1:
            return self
       SCREAMING_SNAKE_CASE__					=					self
       for _ in range(n - 1      ):
            x *= self
       return x



def        UpperCAmelCase_     (		_A   ,	_A   ,	_A       ):





     '''simple docstring'''




     if not callable(_A       ):
          raise ValueError('''differentiate() requires a function as input for func'''       )
     if not isinstance(_A   ,	(float, int)       ):
          raise ValueError('''differentiate() requires a float as input for position'''       )
     if not isinstance(_A   ,	_A       ):
          raise ValueError('''differentiate() requires an int as input for order'''       )
     SCREAMING_SNAKE_CASE__					=					Dual(_A   ,	1       )
     SCREAMING_SNAKE_CASE__					=					func(_A       )
     if order == 0:
          return result.real
     return result.duals[order - 1] * factorial(_A       )


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   def        UpperCAmelCase_     (		_A       ):





        '''simple docstring'''




        return y**2 * y**4







   print(differentiate(f, 9, 2))





import math






class  UpperCAmelCase__	:






  """simple docstring"""


  def    lowercase_	(							self		:	int			,     __lowerCamelCase		:	list[list[float]]			,     __lowerCamelCase		:	list[int]      )	->							int:
       SCREAMING_SNAKE_CASE__					=					0.0
       SCREAMING_SNAKE_CASE__					=					0.0
       for i in range(len(__lowerCamelCase      )      ):
            da += math.pow((sample[i] - weights[0][i])			,     2      )
            da += math.pow((sample[i] - weights[1][i])			,     2      )
            return 0 if da > da else 1
       return 0







  def    lowercase_	(							self		:	Optional[int]			,     __lowerCamelCase		:	list[list[int | float]]			,     __lowerCamelCase		:	list[int]			,     __lowerCamelCase		:	int			,     __lowerCamelCase		:	float      )	->							list[list[int | float]]:
       for i in range(len(__lowerCamelCase      )      ):
            weights[j][i] += alpha * (sample[i] - weights[j][i])
       return weights



def        UpperCAmelCase_     (		):





     '''simple docstring'''




     SCREAMING_SNAKE_CASE__					=					[[1, 1, 0, 0], [0, 0, 0, 1], [1, 0, 0, 0], [0, 0, 1, 1]]

     # weight initialization ( n, C )
     SCREAMING_SNAKE_CASE__					=					[[0.2, 0.6, 0.5, 0.9], [0.8, 0.4, 0.7, 0.3]]

     # training
     SCREAMING_SNAKE_CASE__					=					SelfOrganizingMap()
     SCREAMING_SNAKE_CASE__					=					3
     SCREAMING_SNAKE_CASE__					=					0.5

     for _ in range(_A       ):
          for j in range(len(_A       )       ):
               # training sample
               SCREAMING_SNAKE_CASE__					=					training_samples[j]

               # Compute the winning vector
               SCREAMING_SNAKE_CASE__					=					self_organizing_map.get_winner(_A   ,	_A       )

               # Update the winning vector
               SCREAMING_SNAKE_CASE__					=					self_organizing_map.update(_A   ,	_A   ,	_A   ,	_A       )

    # classify test sample
     SCREAMING_SNAKE_CASE__					=					[0, 0, 0, 1]
     SCREAMING_SNAKE_CASE__					=					self_organizing_map.get_winner(_A   ,	_A       )

     # results
     print(F'''Clusters that the test sample belongs to : {winner}'''       )
     print(F'''Weights that have been trained : {weights}'''       )


# running the main() function
if __name__ == "__main__":
       main()


