"""simple docstring"""


from __future__ import annotations

import math

UpperCAmelCase__  		=						"""2020.9.26"""
UpperCAmelCase__  		=						"""xcodz-dot, cclaus, dhruvmanila"""






def     __UpperCAmelCase					(			lowercase   ,lowercase   ,lowercase   ,lowercase   ,lowercase		):







  """simple docstring"""
  if not all(isinstance(lowercase   ,(float, int)		) for val in locals().values()		):
    _UpperCAmelCase						 =      f'''Input values must either be float or int: {list(locals().values()		)}'''
    raise TypeError(lowercase		)
  _UpperCAmelCase						 =      ((x * distance) / (z + distance)) * scale
  _UpperCAmelCase						 =      ((y * distance) / (z + distance)) * scale
  return projected_x, projected_y






def     __UpperCAmelCase					(			lowercase   ,lowercase   ,lowercase   ,lowercase   ,lowercase		):







  """simple docstring"""
  if not isinstance(lowercase   ,lowercase		):
    raise TypeError("""Axis must be a str"""		)
  _UpperCAmelCase						 =      locals()
  del input_variables["axis"]
  if not all(isinstance(lowercase   ,(float, int)		) for val in input_variables.values()		):
    _UpperCAmelCase						 =      (
        """Input values except axis must either be float or int: """
        f'''{list(input_variables.values()		)}'''
    )
    raise TypeError(lowercase		)
  _UpperCAmelCase						 =      (angle % 3_60) / 4_50 * 1_80 / math.pi
  if axis == "z":
    _UpperCAmelCase						 =      x * math.cos(lowercase		) - y * math.sin(lowercase		)
    _UpperCAmelCase						 =      y * math.cos(lowercase		) + x * math.sin(lowercase		)
    _UpperCAmelCase						 =      z
  elif axis == "x":
    _UpperCAmelCase						 =      y * math.cos(lowercase		) - z * math.sin(lowercase		)
    _UpperCAmelCase						 =      z * math.cos(lowercase		) + y * math.sin(lowercase		)
    _UpperCAmelCase						 =      x
  elif axis == "y":
    _UpperCAmelCase						 =      x * math.cos(lowercase		) - z * math.sin(lowercase		)
    _UpperCAmelCase						 =      z * math.cos(lowercase		) + x * math.sin(lowercase		)
    _UpperCAmelCase						 =      y
  else:
    raise ValueError("""not a valid axis, choose one of 'x', 'y', 'z'"""		)

  return new_x, new_y, new_z


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    print(F'''{convert_to_ad(1.0, 2.0, 3.0, 10.0, 10.0) = }''')
    print(F'''{rotate(1.0, 2.0, 3.0, "y", 90.0) = }''')

"""simple docstring"""


from __future__ import annotations

from random import choice






def     __UpperCAmelCase					(			lowercase		):







  """simple docstring"""
  return choice(lowercase		)






def     __UpperCAmelCase					(			lowercase   ,lowercase		):







  """simple docstring"""
  _UpperCAmelCase						 =      random_pivot(lowercase		)

  # partition based on pivot
  # linear time
  _UpperCAmelCase						 =      [e for e in lst if e < pivot]
  _UpperCAmelCase						 =      [e for e in lst if e > pivot]

  # if we get lucky, pivot might be the element we want.
  # we can easily see this:
  # small (elements smaller than k)
  # + pivot (kth element)
  # + big (elements larger than k)
  if len(lowercase		) == k - 1:
    return pivot
  # pivot is in elements bigger than k
  elif len(lowercase		) < k - 1:
    return kth_number(lowercase   ,k - len(lowercase		) - 1		)
  # pivot is in elements smaller than k
  else:
    return kth_number(lowercase   ,lowercase		)


if __name__ == "__main__":
    import doctest

    doctest.testmod()
