


from __future__ import annotations

import math






def 							_lowercase    (		SCREAMING_SNAKE_CASE_   :		int       ,  SCREAMING_SNAKE_CASE_   :		int       ,  SCREAMING_SNAKE_CASE_   :		bool       ,  SCREAMING_SNAKE_CASE_   :		list[int]       ,  SCREAMING_SNAKE_CASE_   :		float	):





   """simple docstring"""




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

   if len(_UpperCamelCase	) == 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       ,  _UpperCamelCase       ,  _UpperCamelCase       ,  _UpperCamelCase	)       ,  minimax(depth + 1       ,  node_index * 2 + 1       ,  _UpperCamelCase       ,  _UpperCamelCase       ,  _UpperCamelCase	)       ,  )

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






def 							_lowercase    (		):





   """simple docstring"""




   UpperCamelCase         =					[90, 23, 6, 33, 21, 65, 123, 34_423]
   UpperCamelCase         =					math.log(len(_UpperCamelCase	)       ,  2	)
   print("""Optimal value : """       ,  end=""""""	)
   print(minimax(0       ,  0       ,  _UpperCamelCase       ,  _UpperCamelCase       ,  _UpperCamelCase	)	)


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   main()








def 							_lowercase    (		SCREAMING_SNAKE_CASE_   :		int	):





			"""simple docstring"""




			UpperCamelCase         =					int(SCREAMING_SNAKE_CASE_	)
			if decimal in (0, 1):  # Exit cases for the recursion
						return str(SCREAMING_SNAKE_CASE_	)
			UpperCamelCase  ,  UpperCamelCase         =					divmod(SCREAMING_SNAKE_CASE_       ,  2	)
			return binary_recursive(SCREAMING_SNAKE_CASE_	) + str(SCREAMING_SNAKE_CASE_	)






def 							_lowercase    (		SCREAMING_SNAKE_CASE_   :		str	):





			"""simple docstring"""




			UpperCamelCase         =					str(SCREAMING_SNAKE_CASE_	).strip()
			if not number:
						raise ValueError("""No input value was provided"""	)
			UpperCamelCase         =					"""-""" if number.startswith("""-"""	) else """"""
			UpperCamelCase         =					number.lstrip("""-"""	)
			if not number.isnumeric():
						raise ValueError("""Input value is not an integer"""	)
			return f'{negative}0b{binary_recursive(int(SCREAMING_SNAKE_CASE_	)	)}'


if __name__ == "__main__":
			from doctest import testmod

			testmod()




