
def 	UpperCamelCase__  (     SCREAMING_SNAKE_CASE_	:	int       )  ->     list:

						# bit count represents no. of bits in the gray code
						if bit_count < 0:
												raise ValueError("""The given input must be positive"""       )

						# get the generated string sequence
						_lowercase					       =					gray_code_sequence_string(SCREAMING_SNAKE_CASE_       )
						#
						# convert them to integers
						for i in range(len(SCREAMING_SNAKE_CASE_       )       ):
												_lowercase					       =					int(sequence[i]		,   2       )

						return sequence




def 	UpperCamelCase__  (     SCREAMING_SNAKE_CASE_	:	int       )  ->     list:

						# The approach is a recursive one
						# Base case achieved when either n = 0 or n=1
						if bit_count == 0:
												return ["0"]

						if bit_count == 1:
												return ["0", "1"]

						_lowercase					       =					1 << bit_count  # defines the length of the sequence
						# 1<< n is equivalent to 2^n

						# recursive answer will generate answer for n-1 bits
						_lowercase					       =					gray_code_sequence_string(bit_count - 1       )

						_lowercase					       =					[]

						# append 0 to first half of the smaller sequence generated
						for i in range(seq_len // 2       ):
												_lowercase					       =					"""0""" + smaller_sequence[i]
												sequence.append(SCREAMING_SNAKE_CASE_       )

						# append 1 to second half ... start from the end of the list
						for i in reversed(range(seq_len // 2       )       ):
												_lowercase					       =					"""1""" + smaller_sequence[i]
												sequence.append(SCREAMING_SNAKE_CASE_       )

						return sequence


if __name__ == "__main__":
		import doctest

		doctest.testmod()

def 	UpperCamelCase__  (     SCREAMING_SNAKE_CASE_	:	list[int]		,   SCREAMING_SNAKE_CASE_	:	int       )  ->     bool:
						_lowercase					       =					len(SCREAMING_SNAKE_CASE_       )
						_lowercase					       =					[[False] * (required_sum + 1) for _ in range(arr_len + 1       )]

						# for each arr value, a sum of zero(0) can be formed by not taking any element
						# hence True/1
						for i in range(arr_len + 1       ):
												_lowercase					       =					True

						# sum is not zero and set is empty then false
						for i in range(1		,   required_sum + 1       ):
												_lowercase					       =					False

						for i in range(1		,   arr_len + 1       ):
												for j in range(1		,   required_sum + 1       ):
																		if arr[i - 1] > j:
																								_lowercase					       =					subset[i - 1][j]
																		if arr[i - 1] <= j:
																								_lowercase					       =					subset[i - 1][j] or subset[i - 1][j - arr[i - 1]]

						return subset[arr_len][required_sum]


if __name__ == "__main__":
		import doctest

		doctest.testmod()