


from __future__ import annotations

import math




def     UpperCamelCase    (      _a       ,		_a       ,		_a       ,		_a       ,		_a		)					->							Union[str, Any]:
     '''simple docstring'''





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

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

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




def     UpperCamelCase    (      )					->							List[str]:
     '''simple docstring'''





     lowercase_       :Union[str, Any]     =       [9_0, 2_3, 6, 3_3, 2_1, 6_5, 1_2_3, 3_4_4_2_3]
     lowercase_       :List[str]     =       math.log(len(SCREAMING_SNAKE_CASE_		)       ,		2		)
     print('''Optimal value : '''       ,		end=''''''		)
     print(minimax(0       ,		0       ,		SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_       ,		SCREAMING_SNAKE_CASE_		)		)


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   main()





from __future__ import annotations




def     UpperCamelCase    (      _a       ,		_a = None       ,		_a = None		)					->							None:
     '''simple docstring'''





     if start is None:
          lowercase_       :str     =       0

     if end is None:
          lowercase_       :str     =       len(_a		) - 1

     if start >= end:
          return

     lowercase_       :Dict     =       (start + end) // 2

     slowsort(_a       ,		_a       ,		_a		)
     slowsort(_a       ,		mid + 1       ,		_a		)

     if sequence[end] < sequence[mid]:
          lowercase_    ,      lowercase_       :List[Any]     =       sequence[mid], sequence[end]

     slowsort(_a       ,		_a       ,		end - 1		)


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

   testmod()

