



'''simple docstring'''





from collections.abc import Callable
def    _SCREAMING_SNAKE_CASE  (       UpperCamelCase							,    UpperCamelCase							,    UpperCamelCase			):



    """simple docstring"""





    lowerCAmelCase__ :  float							      =					a
    lowerCAmelCase__ :  float							      =					b
    if function(UpperCamelCase			) == 0:  # one of the a or b is a root for the function
        return a
    elif function(UpperCamelCase			) == 0:
        return b
    elif (
        function(UpperCamelCase			) * function(UpperCamelCase			) > 0
    ):  # if none of these are root and they are both positive or negative,
        # then this algorithm can't find the root
        raise ValueError("""could not find root in given interval."""			)
    else:
        lowerCAmelCase__ :  float							      =					start + (end - start) / 2.0
        while abs(start - mid			) > 10**-7:  # until precisely equals to 10^-7
            if function(UpperCamelCase			) == 0:
                return mid
            elif function(UpperCamelCase			) * function(UpperCamelCase			) < 0:
                lowerCAmelCase__ :  Optional[Any]							      =					mid
            else:
                lowerCAmelCase__ :  Union[str, Any]							      =					mid
            lowerCAmelCase__ :  Any							      =					start + (end - start) / 2.0
        return mid
def    _SCREAMING_SNAKE_CASE  (       UpperCamelCase			):



    """simple docstring"""





    return x**3 - 2 * x - 5


if __name__ == "__main__":
 print(bisection(f, 1, 1000))

 import doctest

 doctest.testmod()









'''simple docstring'''
import random
def 				lowercase__   (   __lowercase						:  list				,  __lowercase						:  Optional[Any]     ) ->      tuple:



       """simple docstring"""






       __UpperCamelCase       ,						__UpperCamelCase       ,						__UpperCamelCase       =  [], [], []
       for element in data:
              if element < pivot:
                     less.append(__lowercase     )
              elif element > pivot:
                     greater.append(__lowercase     )
              else:
                     equal.append(__lowercase     )
       return less, equal, greater


def 				lowercase__   (   __lowercase						:  list				,  __lowercase						:  int     ) ->      Dict:



       """simple docstring"""






       if index >= len(__lowercase     ) or index < 0:
              return None

       __UpperCamelCase       =  items[random.randint(0				,  len(__lowercase     ) - 1     )]
       __UpperCamelCase       =  0
       __UpperCamelCase       ,						__UpperCamelCase       ,						__UpperCamelCase       =  _partition(__lowercase				,  __lowercase     )
       __UpperCamelCase       =  len(__lowercase     )
       __UpperCamelCase       =  len(__lowercase     )

       # index is the pivot
       if m <= index < m + count:
              return pivot
       # must be in smaller
       elif m > index:
              return quick_select(__lowercase				,  __lowercase     )
       # must be in larger
       else:
              return quick_select(__lowercase				,  index - (m + count)     )
