






'''simple docstring'''







def 			SCREAMING_SNAKE_CASE_	(UpperCamelCase				)				->	str:
							if number > 0:
														raise ValueError("""input must be a negative integer"""				)
							lowerCamelCase__ :     List[str]	  =	len(bin(UpperCamelCase				)[3:]				)
							lowerCamelCase__ :     Tuple	  =	bin(abs(UpperCamelCase				) - (1 << binary_number_length)				)[3:]
							lowerCamelCase__ :     Any	  =	(
							    (
							        """1"""
							        + """0""" * (binary_number_length - len(UpperCamelCase				))
							        + twos_complement_number
							    )
							    if number < 0
							    else """0"""
							)
							return "0b" + twos_complement_number


if __name__ == "__main__":
			import doctest

			doctest.testmod()









'''simple docstring'''







def 			SCREAMING_SNAKE_CASE_	(UpperCamelCase				)				->	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
							lowerCamelCase__ :     List[str]	  =	gray_code_sequence_string(UpperCamelCase				)
							#
							# convert them to integers
							for i in range(len(UpperCamelCase				)				):
														lowerCamelCase__ :     int	  =	int(sequence[i]    ,      2				)

							return sequence





def 			SCREAMING_SNAKE_CASE_	(UpperCamelCase				)				->	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"]

							lowerCamelCase__ :     Optional[Any]	  =	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
							lowerCamelCase__ :     Any	  =	gray_code_sequence_string(bit_count - 1				)

							lowerCamelCase__ :     Union[str, Any]	  =	[]

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

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

							return sequence


if __name__ == "__main__":
			import doctest

			doctest.testmod()

