

"""simple docstring"""





from __future__ import annotations

import math

_a       =							'2020.9.26'
_a       =							'xcodz-dot, cclaus, dhruvmanila'




def   _A  (  UpperCamelCase_     :       float,			UpperCamelCase_     :       float,			UpperCamelCase_     :       float,			UpperCamelCase_     :       float,			UpperCamelCase_     :       float)	->						tuple[float, float]:
   '''simple docstring'''


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




def   _A  (  UpperCamelCase_     :       float,			UpperCamelCase_     :       float,			UpperCamelCase_     :       float,			UpperCamelCase_     :       str,			UpperCamelCase_     :       float)	->						tuple[float, float, float]:
   '''simple docstring'''


   if not isinstance(UpperCamelCase_,			UpperCamelCase_):
      raise TypeError("Axis must be a str")
   __lowercase								=						locals()
   del input_variables["axis"]
   if not all(isinstance(UpperCamelCase_,			(float, int)) for val in input_variables.values()):
      __lowercase								=						(
          "Input values except axis must either be float or int: "
          F"""{list(input_variables.values())}"""
      )
      raise TypeError(UpperCamelCase_)
   __lowercase								=						(angle % 360) / 450 * 180 / math.pi
   if axis == "z":
      __lowercase								=						x * math.cos(UpperCamelCase_) - y * math.sin(UpperCamelCase_)
      __lowercase								=						y * math.cos(UpperCamelCase_) + x * math.sin(UpperCamelCase_)
      __lowercase								=						z
   elif axis == "x":
      __lowercase								=						y * math.cos(UpperCamelCase_) - z * math.sin(UpperCamelCase_)
      __lowercase								=						z * math.cos(UpperCamelCase_) + y * math.sin(UpperCamelCase_)
      __lowercase								=						x
   elif axis == "y":
      __lowercase								=						x * math.cos(UpperCamelCase_) - z * math.sin(UpperCamelCase_)
      __lowercase								=						z * math.cos(UpperCamelCase_) + x * math.sin(UpperCamelCase_)
      __lowercase								=						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) = }")











from __future__ import annotations

import math

def   a_    ( lowerCAmelCase_      :			int,	lowerCAmelCase_      :			int,	lowerCAmelCase_      :			bool,	lowerCAmelCase_      :			list[int],	lowerCAmelCase_      :			float	):

   if depth < 0:
      raise ValueError('Depth cannot be less than 0'	)

   if len(lowerCAmelCase_	) == 0:
      raise ValueError('Scores cannot be empty'	)

   if depth == height:
      return scores[node_index]

   if is_max:
      return max(
          minimax(depth + 1,	node_index * 2,	lowerCAmelCase_,	lowerCAmelCase_,	lowerCAmelCase_	),	minimax(depth + 1,	node_index * 2 + 1,	lowerCAmelCase_,	lowerCAmelCase_,	lowerCAmelCase_	),	)

   return min(
       minimax(depth + 1,	node_index * 2,	lowerCAmelCase_,	lowerCAmelCase_,	lowerCAmelCase_	),	minimax(depth + 1,	node_index * 2 + 1,	lowerCAmelCase_,	lowerCAmelCase_,	lowerCAmelCase_	),	)

def   a_    ( ):
   __lowerCAmelCase								=	[90, 23, 6, 33, 21, 65, 123, 3_4423]
   __lowerCAmelCase								=	math.log(len(lowerCAmelCase_	),	2	)
   print('Optimal value : ',	end=''	)
   print(minimax(0,	0,	lowerCAmelCase_,	lowerCAmelCase_,	lowerCAmelCase_	)	)


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     main()

