





from __future__ import annotations

import math







def       UpperCAmelCase							(     _lowerCamelCase      :  int			,   _lowerCamelCase      :  int			,   _lowerCamelCase      :  bool			,   _lowerCamelCase      :  list[int]			,   _lowerCamelCase      :  float     ):





						'''simple docstring'''


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

						if not scores:
												raise ValueError("Scores cannot be empty"     )

						if depth == height:
												return scores[node_index]

						return (
						    max(
						        minimax(depth + 1			,   node_index * 2			,   _lowerCamelCase			,   _lowerCamelCase			,   _lowerCamelCase     )			,   minimax(depth + 1			,   node_index * 2 + 1			,   _lowerCamelCase			,   _lowerCamelCase			,   _lowerCamelCase     )			,   )
						    if is_max
						    else min(
						        minimax(depth + 1			,   node_index * 2			,   _lowerCamelCase			,   _lowerCamelCase			,   _lowerCamelCase     )			,   minimax(depth + 1			,   node_index * 2 + 1			,   _lowerCamelCase			,   _lowerCamelCase			,   _lowerCamelCase     )			,   )
						)







def       UpperCAmelCase							(     ):





						'''simple docstring'''


						SCREAMING_SNAKE_CASE__     :				Optional[int]   =					[90, 23, 6, 33, 21, 65, 123, 34_423]
						SCREAMING_SNAKE_CASE__     :				List[Any]   =					math.log(len(_lowerCamelCase     )			,   2     )
						print(f"""Optimal value : {minimax(0			,   0			,   _lowerCamelCase			,   _lowerCamelCase			,   _lowerCamelCase     )}"""     )


if __name__ == "__main__":
				import doctest

				doctest.testmod()
				main()






from __future__ import annotations







def       UpperCAmelCase							(     _lowerCamelCase      :  list			,   _lowerCamelCase      :  int | None = None			,   _lowerCamelCase      :  int | None = None     ):





						'''simple docstring'''


						if start is None:
												SCREAMING_SNAKE_CASE__     :				Union[str, Any]   =					0

						if end is None:
												SCREAMING_SNAKE_CASE__     :				Any   =					len(_lowerCamelCase     ) - 1

						if start >= end:
												return

						SCREAMING_SNAKE_CASE__     :				List[str]   =					(start + end) // 2

						slowsort(_lowerCamelCase			,   _lowerCamelCase			,   _lowerCamelCase     )
						slowsort(_lowerCamelCase			,   mid + 1			,   _lowerCamelCase     )

						if sequence[end] < sequence[mid]:
												SCREAMING_SNAKE_CASE__,							SCREAMING_SNAKE_CASE__     :				Optional[int]   =					sequence[mid], sequence[end]

						slowsort(_lowerCamelCase			,   _lowerCamelCase			,   end - 1     )


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

				testmod()