





"""simple docstring"""




from __future__ import annotations

import math





def 	a_    (							_lowercase	,						_lowercase	,						_lowercase	,						_lowercase	,						_lowercase       ):

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

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

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





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


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						main()










"""simple docstring"""




from __future__ import annotations

from random import choice





def 	a_    (							_lowercase       ):
						return choice(_lowercase       )





def 	a_    (							_lowercase	,						_lowercase       ):
						_UpperCamelCase      : Optional[int]         =   random_pivot(_lowercase       )

						# partition based on pivot
						# linear time
						_UpperCamelCase      : Union[str, Any]         =   [e for e in lst if e < pivot]
						_UpperCamelCase      : int         =   [e for e in lst if e > pivot]

						# if we get lucky, pivot might be the element we want.
						# we can easily see this:
						# small (elements smaller than k)
						# + pivot (kth element)
						# + big (elements larger than k)
						if len(_lowercase       ) == k - 1:
												return pivot
						# pivot is in elements bigger than k
						elif len(_lowercase       ) < k - 1:
												return kth_number(_lowercase	,						k - len(_lowercase       ) - 1       )
						# pivot is in elements smaller than k
						else:
												return kth_number(_lowercase	,						_lowercase       )


if __name__ == "__main__":
						import doctest

						doctest.testmod()



