



from collections.abc import Callable

def 	_lowerCAmelCase (    A__    ,	A__    ,	A__						):
      lowercase__  =	a
      lowercase__  =	b
      if function(_lowerCamelCase						) == 0:  # one of the a or b is a root for the function
            return a
      elif function(_lowerCamelCase						) == 0:
            return b
      elif (
          function(_lowerCamelCase						) * function(_lowerCamelCase						) > 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:
            lowercase__  =	start + (end - start) / 2.0
            while abs(start - mid						) > 10**-7:  # until precisely equals to 10^-7
                  if function(_lowerCamelCase						) == 0:
                        return mid
                  elif function(_lowerCamelCase						) * function(_lowerCamelCase						) < 0:
                        lowercase__  =	mid
                  else:
                        lowercase__  =	mid
                  lowercase__  =	start + (end - start) / 2.0
            return mid

def 	_lowerCAmelCase (    A__						):
      return x**3 - 2 * x - 5


if __name__ == "__main__":
       print(bisection(f, 1, 10_00))

       import doctest

       doctest.testmod()







'''simple docstring'''

from __future__ import annotations





def 		UpperCamelCase							(				_lowerCamelCase   :   list[int]			):  # This function is recursive
    A__							=     len(_lowerCamelCase			)
    # If the array contains only one element, we return it (it's the stop condition of
    # recursion)
    if array_length <= 1:
        return array
        # Else
    A__							=     array[0]
    A__							=     False
    A__							=     1
    A__							=     []
    while not is_found and i < array_length:
        if array[i] < pivot:
            A__							=     True
            A__							=     [element for element in array[i:] if element >= array[i]]
            A__							=     longest_subsequence(_lowerCamelCase			)
            if len(_lowerCamelCase			) > len(_lowerCamelCase			):
                A__							=     temp_array
        else:
            i += 1

    A__							=     [element for element in array[1:] if element >= pivot]
    A__							=     [pivot, *longest_subsequence(_lowerCamelCase			)]
    if len(_lowerCamelCase			) > len(_lowerCamelCase			):
        return temp_array
    else:
        return longest_subseq


if __name__ == "__main__":
  import doctest

  doctest.testmod()



