


"""simple docstring"""
def 						_a				(      _SCREAMING_SNAKE_CASE				, _SCREAMING_SNAKE_CASE				)    ->				Dict:
							snake_case_           =		[1]
							for i in range(2				, _SCREAMING_SNAKE_CASE				):
														factorials.append(factorials[-1] * i				)
							assert 0 <= k < factorials[-1] * n, "k out of bounds"

							snake_case_           =		[]
							snake_case_           =		list(range(_SCREAMING_SNAKE_CASE				)				)

							# Find permutation
							while factorials:
														snake_case_           =		factorials.pop()
														snake_case_           =		divmod(_SCREAMING_SNAKE_CASE				, _SCREAMING_SNAKE_CASE				)
														permutation.append(elements[number]				)
														elements.remove(elements[number]				)
							permutation.append(elements[0]				)

							return permutation


if __name__ == "__main__":
				import doctest

				doctest.testmod()







"""simple docstring"""
def 						_a				(      _SCREAMING_SNAKE_CASE				)    ->				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
							snake_case_           =		gray_code_sequence_string(_SCREAMING_SNAKE_CASE				)
							#
							# convert them to integers
							for i in range(len(_SCREAMING_SNAKE_CASE				)				):
														snake_case_           =		int(sequence[i]				, 2				)

							return sequence







def 						_a				(      _SCREAMING_SNAKE_CASE				)    ->				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"]

							snake_case_           =		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
							snake_case_           =		gray_code_sequence_string(bit_count - 1				)

							snake_case_           =		[]

							# append 0 to first half of the smaller sequence generated
							for i in range(seq_len // 2				):
														snake_case_           =		"""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				)				):
														snake_case_           =		"""1""" + smaller_sequence[i]
														sequence.append(_SCREAMING_SNAKE_CASE				)

							return sequence


if __name__ == "__main__":
				import doctest

				doctest.testmod()



