

'''simple docstring'''

from __future__ import annotations

import math




def 				UpperCamelCase(					UpperCAmelCase_  ,	UpperCAmelCase_  ,	UpperCAmelCase_  ,	UpperCAmelCase_  ,	UpperCAmelCase_     ):






 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  ,	UpperCAmelCase_  ,	UpperCAmelCase_  ,	UpperCAmelCase_     )  ,	minimax(depth + 1  ,	node_index * 2 + 1  ,	UpperCAmelCase_  ,	UpperCAmelCase_  ,	UpperCAmelCase_     )  ,	)
     if is_max
     else min(
         minimax(depth + 1  ,	node_index * 2  ,	UpperCAmelCase_  ,	UpperCAmelCase_  ,	UpperCAmelCase_     )  ,	minimax(depth + 1  ,	node_index * 2 + 1  ,	UpperCAmelCase_  ,	UpperCAmelCase_  ,	UpperCAmelCase_     )  ,	)
 )




def 				UpperCamelCase(					):
 UpperCAmelCase	:     Dict						 =			[90, 23, 6, 33, 21, 65, 1_23, 3_44_23]
 UpperCAmelCase	:     Optional[int]						 =			math.log(len(UpperCAmelCase_     )  ,	2     )
 print(F"""Optimal value : {minimax(0  ,	0  ,	UpperCAmelCase_  ,	UpperCAmelCase_  ,	UpperCAmelCase_     )}"""     )


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 main()



'''simple docstring'''

from __future__ import annotations




def 				UpperCamelCase(					UpperCAmelCase_  ,	UpperCAmelCase_  ,	UpperCAmelCase_     ):
 if len(UpperCAmelCase_     ) == 0:
  raise ValueError('find_max() arg is an empty sequence'     )
 if (
     left >= len(UpperCAmelCase_     )
     or left < -len(UpperCAmelCase_     )
     or right >= len(UpperCAmelCase_     )
     or right < -len(UpperCAmelCase_     )
 ):
  raise IndexError('list index out of range'     )
 if left == right:
  return nums[left]
 UpperCAmelCase	:     Optional[int]						 =			(left + right) >> 1  # the middle
 UpperCAmelCase	:     Any						 =			find_max(UpperCAmelCase_  ,	UpperCAmelCase_  ,	UpperCAmelCase_     )  # find max in range[left, mid]
 UpperCAmelCase	:     Union[str, Any]						 =			find_max(UpperCAmelCase_  ,	mid + 1  ,	UpperCAmelCase_     )  # find max in range[mid + 1, right]

 return left_max if left_max >= right_max else right_max


if __name__ == "__main__":
 import doctest

 doctest.testmod(verbose=True)




