





'''simple docstring'''






from __future__ import annotations

import math







def 					_a						(       _lowerCamelCase    ,	_lowerCamelCase ) ->				float:



			"""simple docstring"""


			__snake_case					:      Any							      =     u
			for i in range(1    ,	_lowerCamelCase ):
						__snake_case					:      Optional[Any]							      =     temp * (u - i)
			return temp







def 					_a						(       ) ->				None:



			"""simple docstring"""


			__snake_case					:      str							      =     int(input("""enter the numbers of values: """ ) )
			__snake_case					:      list[list[float]]							      =     []
			for _ in range(_lowerCamelCase ):
						y.append([] )
			for i in range(_lowerCamelCase ):
						for j in range(_lowerCamelCase ):
									y[i].append(_lowerCamelCase )
									__snake_case					:      Any							      =     0

			print("""enter the values of parameters in a list: """ )
			__snake_case					:      Dict							      =     list(map(_lowerCamelCase    ,	input().split() ) )

			print("""enter the values of corresponding parameters: """ )
			for i in range(_lowerCamelCase ):
						__snake_case					:      Optional[int]							      =     float(input() )

			__snake_case					:      List[str]							      =     int(input("""enter the value to interpolate: """ ) )
			__snake_case					:      int							      =     (value - x[0]) / (x[1] - x[0])

			# for calculating forward difference table

			for i in range(1    ,	_lowerCamelCase ):
						for j in range(n - i ):
									__snake_case					:      List[Any]							      =     y[j + 1][i - 1] - y[j][i - 1]

			__snake_case					:      Union[str, Any]							      =     y[0][0]
			for i in range(1    ,	_lowerCamelCase ):
						summ += (ucal(_lowerCamelCase    ,	_lowerCamelCase ) * y[0][i]) / math.factorial(_lowerCamelCase )

			print(F'''the value at {value} is {summ}''' )


if __name__ == "__main__":
	main()









'''simple docstring'''






from __future__ import annotations

import math







def 					_a						(       _lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase ) ->				int:



			"""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 					_a						(       ) ->				None:



			"""simple docstring"""


			__snake_case					:      Union[str, Any]							      =     [90, 23, 6, 33, 21, 65, 123, 3_4423]
			__snake_case					:      Optional[int]							      =     math.log(len(_lowerCamelCase )    ,	2 )
			print(F'''Optimal value : {minimax(0    ,	0    ,	_lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase )}''' )


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	main()


