


from __future__ import annotations

from typing import Any


def     lowercase	(    a ):



		'''simple docstring'''




		create_state_space_tree(a     , []     , 0 )


def     lowercase	(    a     , a     , a ):



		'''simple docstring'''




		if index == len(a ):
				print(a )
				return

		create_state_space_tree(a     , a     , index + 1 )
		current_subsequence.append(sequence[index] )
		create_state_space_tree(a     , a     , index + 1 )
		current_subsequence.pop()


if __name__ == "__main__":
		SCREAMING_SNAKE_CASE__     					=			[3, 1, 2, 4]
		generate_all_subsequences(seq)

		seq.clear()
		seq.extend(["A", "B", "C"])
		generate_all_subsequences(seq)










from __future__ import annotations

import math


def     lowercase	(    a     , a ):



		'''simple docstring'''




		SCREAMING_SNAKE_CASE_				:List[Any]				     =						u
		for i in range(1     , a ):
				SCREAMING_SNAKE_CASE_				:Union[str, Any]				     =						temp * (u - i)
		return temp


def     lowercase	(    ):



		'''simple docstring'''




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

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

		print("enter the values of corresponding parameters: " )
		for i in range(a ):
				SCREAMING_SNAKE_CASE_				:List[Any]				     =						float(input() )

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

		# for calculating forward difference table

		for i in range(1     , a ):
				for j in range(n - i ):
						SCREAMING_SNAKE_CASE_				:List[str]				     =						y[j + 1][i - 1] - y[j][i - 1]

		SCREAMING_SNAKE_CASE_				:Tuple				     =						y[0][0]
		for i in range(1     , a ):
				summ += (ucal(a     , a ) * y[0][i]) / math.factorial(a )

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


if __name__ == "__main__":
		main()






