

'''simple docstring'''
from collections.abc import Callable

_snake_case     						=						Callable[[float], float]  # type alias for a real -> real function







def       _A	(			snake_case	,							snake_case	,							snake_case	,							)    ->			float:
   _lowercase    :   Any      =     float(snake_case  )
   while True:
      try:
         _lowercase    :   List[Any]      =     prev_guess - function(snake_case  ) / derivative(snake_case  )
      except ZeroDivisionError:
         raise ZeroDivisionError("Could not find root"  ) from None
      if abs(prev_guess - next_guess  ) < 10**-5:
         return next_guess
      _lowercase    :   List[str]      =     next_guess







def       _A	(			snake_case  )    ->			float:
   return (x**3) - (2 * x) - 5







def       _A	(			snake_case  )    ->			float:
   return 3 * (x**2) - 2


if __name__ == "__main__":
    print(newton(f, fa, 3))









'''simple docstring'''
def       _A	(			snake_case  )    ->			int:

   # validate:
   if not isinstance(snake_case	,							snake_case  ) or not all(
       isinstance(snake_case	,							snake_case  ) and item >= 0 for item in citations  ):
      raise ValueError("The citations should be a list of non negative integers."  )

   citations.sort()
   _lowercase    :   Tuple      =     len(snake_case  )

   for i in range(snake_case  ):
      if citations[len_citations - 1 - i] <= i:
         return i

   return len_citations


if __name__ == "__main__":
    import doctest

    doctest.testmod()






