




from __future__ import annotations



def       UpperCAmelCase__  (     lowerCamelCase,			lowerCamelCase   ):
  lowercase    :Dict      	=						0
  lowercase    :Optional[Any]      	=						len(lowerCamelCase   ) - 1

  while i < j:
    if nums[i] + nums[j] == target:
      return [i, j]
    elif nums[i] + nums[j] < target:
      lowercase    :List[Any]      	=						i + 1
    else:
      lowercase    :str      	=						j - 1

  return []


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     print(f'''{two_pointer([2, 7, 11, 15], 9) = }''')









def       UpperCAmelCase__  (     lowerCamelCase   ):
  return 10 - x * x



def       UpperCAmelCase__  (     lowerCamelCase,			lowerCamelCase   ):
  # Bolzano theory in order to find if there is a root between a and b
  if equation(lowerCamelCase   ) * equation(lowerCamelCase   ) >= 0:
    raise ValueError("Wrong space!"   )

  lowercase    :Optional[int]      	=						a
  while (b - a) >= 0.01:
    # Find middle point
    lowercase    :Optional[Any]      	=						(a + b) / 2
    # Check if middle point is root
    if equation(lowerCamelCase   ) == 0.0:
      break
    # Decide the side to repeat the steps
    if equation(lowerCamelCase   ) * equation(lowerCamelCase   ) < 0:
      lowercase    :Any      	=						c
    else:
      lowercase    :List[Any]      	=						c
  return c


if __name__ == "__main__":
     import doctest

     doctest.testmod()

     print(bisection(-2, 5))
     print(bisection(0, 6))



