


"""simple docstring"""
def 						_a				(      _SCREAMING_SNAKE_CASE				)    ->				list:
							if any(not isinstance(_SCREAMING_SNAKE_CASE				, _SCREAMING_SNAKE_CASE				) or x < 0 for x in sequence				):
														raise TypeError("""Sequence must be list of non-negative integers"""				)
							for _ in range(len(_SCREAMING_SNAKE_CASE				)				):
														for i, (rod_upper, rod_lower) in enumerate(zip(_SCREAMING_SNAKE_CASE				, sequence[1:]				)				):
																					if rod_upper > rod_lower:
																												sequence[i] -= rod_upper - rod_lower
																												sequence[i + 1] += rod_upper - rod_lower
							return sequence


if __name__ == "__main__":
				assert bead_sort([5, 4, 3, 2, 1]) == [1, 2, 3, 4, 5]
				assert bead_sort([7, 9, 4, 3, 5]) == [3, 4, 5, 7, 9]







"""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()



