






A:      Optional[Any]  				=				tuple[float, float, float]
A:      Union[str, Any]  				=				tuple[float, float, float]






def 	_UpperCAmelCase    (  a		:	Pointad						,			a		:	Pointad							)			->			Vectorad:





						"""simple docstring"""
						lowercase_      :   int        =			end_pointa[0] - end_pointa[0]
						lowercase_      :   Tuple        =			end_pointa[1] - end_pointa[1]
						lowercase_      :   Any        =			end_pointa[2] - end_pointa[2]
						return (x, y, z)






def 	_UpperCAmelCase    (  a		:	Vectorad						,			a		:	Vectorad							)			->			Vectorad:





						"""simple docstring"""
						lowercase_      :   Dict        =			ab[1] * ac[2] - ab[2] * ac[1]  # *i
						lowercase_      :   Union[str, Any]        =			(ab[0] * ac[2] - ab[2] * ac[0]) * -1  # *j
						lowercase_      :   Optional[Any]        =			ab[0] * ac[1] - ab[1] * ac[0]  # *k
						return (x, y, z)






def 	_UpperCAmelCase    (  a		:	Vectorad						,			a		:	int							)			->			bool:





						"""simple docstring"""
						return tuple(round(a						,			a							) for x in vector							) == (0, 0, 0)






def 	_UpperCAmelCase    (  a		:	Pointad						,			a		:	Pointad						,			a		:	Pointad						,			a		:	int = 1_0							)			->			bool:





						"""simple docstring"""
						lowercase_      :   Union[str, Any]        =			create_vector(a						,			a							)
						lowercase_      :   Union[str, Any]        =			create_vector(a						,			a							)
						return is_zero_vector(get_ad_vectors_cross(a						,			a							)						,			a							)








'''simple docstring'''

def 	_UpperCAmelCase    (  a		:	str						,			a		:	str							)			->			float:





						"""simple docstring"""

						def get_matched_characters(a		:	str						,			a		:	str							) -> str:
												lowercase_      :   Union[str, Any]        =			[]
												lowercase_      :   Tuple        =			min(len(_stra							)						,			len(_stra							)							) // 2
												for i, l in enumerate(_stra							):
																		lowercase_      :   Optional[int]        =			int(max(0						,			i - limit							)							)
																		lowercase_      :   Union[str, Any]        =			int(min(i + limit + 1						,			len(_stra							)							)							)
																		if l in _stra[left:right]:
																								matched.append(a							)
																								lowercase_      :   Union[str, Any]        =			f"{_stra[0:_stra.index(a							)]} {_stra[_stra.index(a							) + 1:]}"

												return "".join(a							)

						# matching characters
						lowercase_      :   Union[str, Any]        =			get_matched_characters(a						,			a							)
						lowercase_      :   Optional[Any]        =			get_matched_characters(a						,			a							)
						lowercase_      :   Optional[int]        =			len(a							)

						# transposition
						lowercase_      :   Dict        =			(
						    len([(ca, ca) for ca, ca in zip(a						,			a							) if ca != ca]							) // 2
						)

						if not match_count:
												lowercase_      :   List[str]        =			0.0
						else:
												lowercase_      :   Any        =			(
												    1
												    / 3
												    * (
												        match_count / len(a							)
												        + match_count / len(a							)
												        + (match_count - transpositions) / match_count
												    )
												)

						# common prefix up to 4 characters
						lowercase_      :   Optional[Any]        =			0
						for ca, ca in zip(stra[:4]						,			stra[:4]							):
												if ca == ca:
																		prefix_len += 1
												else:
																		break

						return jaro + 0.1 * prefix_len * (1 - jaro)


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						print(jaro_winkler("hello", "world"))
