



snake_case__					:     str    		=   {"""a""": ["""c""", """b"""], """b""": ["""d""", """e"""], """c""": [], """d""": [], """e""": []}
snake_case__					:     List[str]    		=   ["""a""", """b""", """c""", """d""", """e"""]



def    snake_case_				(    _SCREAMING_SNAKE_CASE  ,	_SCREAMING_SNAKE_CASE  ,	_SCREAMING_SNAKE_CASE   ):
	__lowercase		       =			start
	# add current to visited
	visited.append(_SCREAMING_SNAKE_CASE   )
	__lowercase		       =			edges[current]
	for neighbor in neighbors:
		# if neighbor not in visited, visit
		if neighbor not in visited:
			__lowercase		       =			topological_sort(_SCREAMING_SNAKE_CASE  ,	_SCREAMING_SNAKE_CASE  ,	_SCREAMING_SNAKE_CASE   )
    # if all neighbors visited add current to sort
	sort.append(_SCREAMING_SNAKE_CASE   )
	# if all vertices haven't been visited select a new one to visit
	if len(_SCREAMING_SNAKE_CASE   ) != len(_SCREAMING_SNAKE_CASE   ):
		for vertice in vertices:
			if vertice not in visited:
				__lowercase		       =			topological_sort(_SCREAMING_SNAKE_CASE  ,	_SCREAMING_SNAKE_CASE  ,	_SCREAMING_SNAKE_CASE   )
    # return sort
	return sort


if __name__ == "__main__":
	snake_case__					:     Optional[int]    		=   topological_sort("""a""", [], [])
	print(sort)








def    snake_case_				(    _SCREAMING_SNAKE_CASE   ):

	# 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    snake_case_				(    _SCREAMING_SNAKE_CASE   ):

	# 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()



