


'''simple docstring'''

from __future__ import annotations





def lowerCamelCase      (      lowerCAmelCase    :     list[int]		):  # This function is recursive





	"""simple docstring"""







	__magic_name__	:   Dict					     =					len(lowerCAmelCase		)
	# If the array contains only one element, we return it (it's the stop condition of
	# recursion)
	if array_length <= 1:
		return array
		# Else
	__magic_name__	:   List[str]					     =					array[0]
	__magic_name__	:   Optional[int]					     =					False
	__magic_name__	:   int					     =					1
	__magic_name__	:   list[int]					     =					[]
	while not is_found and i < array_length:
		if array[i] < pivot:
			__magic_name__	:   Dict					     =					True
			__magic_name__	:   Dict					     =					[element for element in array[i:] if element >= array[i]]
			__magic_name__	:   Tuple					     =					longest_subsequence(lowerCAmelCase		)
			if len(lowerCAmelCase		) > len(lowerCAmelCase		):
				__magic_name__	:   Optional[int]					     =					temp_array
		else:
			i += 1

	__magic_name__	:   Optional[int]					     =					[element for element in array[1:] if element >= pivot]
	__magic_name__	:   Optional[int]					     =					[pivot, *longest_subsequence(lowerCAmelCase		)]
	if len(lowerCAmelCase		) > len(lowerCAmelCase		):
		return temp_array
	else:
		return longest_subseq


if __name__ == "__main__":
							import doctest

							doctest.testmod()



'''simple docstring'''

def lowerCamelCase      (      lowerCAmelCase    :     str		,		lowerCAmelCase    :     Any		,		lowerCAmelCase    :     Any=False		):





	"""simple docstring"""







	if isinstance(lowerCAmelCase		,		lowerCAmelCase		) and isinstance(lowerCAmelCase		,		lowerCAmelCase		):
		__magic_name__	:   str					     =					len(set_a.intersection(lowerCAmelCase		)		)

		if alternative_union:
			__magic_name__	:   List[str]					     =					len(lowerCAmelCase		) + len(lowerCAmelCase		)
		else:
			__magic_name__	:   Any					     =					len(set_a.union(lowerCAmelCase		)		)

		return intersection / union

	if isinstance(lowerCAmelCase		,		(list, tuple)		) and isinstance(lowerCAmelCase		,		(list, tuple)		):
		__magic_name__	:   str					     =					[element for element in set_a if element in set_b]

		if alternative_union:
			__magic_name__	:   Dict					     =					len(lowerCAmelCase		) + len(lowerCAmelCase		)
			return len(lowerCAmelCase		) / union
		else:
			__magic_name__	:   Any					     =					set_a + [element for element in set_b if element not in set_a]
			return len(lowerCAmelCase		) / len(lowerCAmelCase		)

		return len(lowerCAmelCase		) / len(lowerCAmelCase		)
	return None


if __name__ == "__main__":
							lowerCAmelCase				:Dict        =      {'''a''', '''b''', '''c''', '''d''', '''e'''}
							lowerCAmelCase				:Tuple        =      {'''c''', '''d''', '''e''', '''f''', '''h''', '''i'''}
							print(jaccard_similarity(set_a, set_b))