



'''simple docstring'''






from collections.abc import Callable

A_							:				Any						=			Callable[[float], float]  # type alias for a real -> real function




def 					snake_case_      (  lowerCAmelCase_ ,     lowerCAmelCase_ ,     lowerCAmelCase_ ,     )->	float:





       '''simple docstring'''


       _UpperCAmelCase						:		List[str]      =				float(lowerCAmelCase_	)
       while True:
              try:
                     _UpperCAmelCase						:		List[str]      =				prev_guess - function(lowerCAmelCase_	) / derivative(lowerCAmelCase_	)
              except ZeroDivisionError:
                     raise ZeroDivisionError("""Could not find root"""	) from None
              if abs(prev_guess - next_guess	) < 10**-5:
                     return next_guess
              _UpperCAmelCase						:		Tuple      =				next_guess




def 					snake_case_      (  lowerCAmelCase_	)->	float:





       '''simple docstring'''


       return (x**3) - (2 * x) - 5




def 					snake_case_      (  lowerCAmelCase_	)->	float:





       '''simple docstring'''


       return 3 * (x**2) - 2


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








'''simple docstring'''






def 					snake_case_      (  lowerCAmelCase_	)->	tuple[int, int]:





       '''simple docstring'''


       if len(lowerCAmelCase_	) == 1:
              return a[0], a[0]
       else:
              # split A into half.
              _UpperCAmelCase						:		Union[str, Any]      =				a[: len(lowerCAmelCase_	) // 2]
              _UpperCAmelCase						:		str      =				a[len(lowerCAmelCase_	) // 2 :]

              # 2 sub problems, 1/2 of original size.
              _UpperCAmelCase  ,_UpperCAmelCase						:		str      =				max_difference(lowerCAmelCase_	)
              _UpperCAmelCase  ,_UpperCAmelCase						:		List[str]      =				max_difference(lowerCAmelCase_	)

              # get min of first and max of second
              # linear time
              _UpperCAmelCase						:		Dict      =				min(lowerCAmelCase_	)
              _UpperCAmelCase						:		List[Any]      =				max(lowerCAmelCase_	)

              # 3 cases, either (small1, big1),
              # (min_first, max_second), (small2, big2)
              # constant comparisons
              if biga - smalla > max_second - min_first and biga - smalla > biga - smalla:
                     return smalla, biga
              elif biga - smalla > max_second - min_first:
                     return smalla, biga
              else:
                     return min_first, max_second


if __name__ == "__main__":
   import doctest

   doctest.testmod()



