

'''simple docstring'''




import math




def 						UpperCamelCase	(			a		,						a			)				->     float:






     '''simple docstring'''
     if (
         not isinstance(a		,						(int, float)			)
         or power_factor < -1
         or power_factor > 1
     ):
          raise ValueError('''power_factor must be a valid float value between -1 and 1.'''			)
     return apparent_power * power_factor




def 						UpperCamelCase	(			a		,						a			)				->     float:






     '''simple docstring'''
     if (
         not isinstance(a		,						(int, float)			)
         or power_factor < -1
         or power_factor > 1
     ):
          raise ValueError('''power_factor must be a valid float value between -1 and 1.'''			)
     return apparent_power * math.sqrt(1 - power_factor**2			)


if __name__ == "__main__":
  import doctest

  doctest.testmod()









'''simple docstring'''




import functools




def 						UpperCamelCase	(			a		,						a			)				->     int:






     '''simple docstring'''
     __magic_name__						       =    len(a			)
     __magic_name__						       =    len(a			)

     @functools.cache
     def min_distance(a		,						a			) -> int:
          # if first word index is overflow - delete all from the second word
          if indexa >= len_worda:
               return len_worda - indexa
          # if second word index is overflow - delete all from the first word
          if indexa >= len_worda:
               return len_worda - indexa
          __magic_name__						       =    int(worda[indexa] != worda[indexa]			)  # current letters not identical
          return min(
              1 + min_distance(indexa + 1		,						a			)		,						1 + min_distance(a		,						indexa + 1			)		,						diff + min_distance(indexa + 1		,						indexa + 1			)		,						)

     return min_distance(0		,						0			)


if __name__ == "__main__":
      import doctest

      doctest.testmod()






