


"""simple docstring"""





def    _snake_case  (  _snake_case :	List[Any]       ,      _snake_case :	Union[str, Any]	):
      return (pointa[0] - pointa[0]) ** 2 + (pointa[1] - pointa[1]) ** 2


def    _snake_case  (  _snake_case :	Optional[Any]       ,      _snake_case :	Optional[int]=0	):
      return sorted(_snake_case       ,      key=lambda _snake_case	: x[column]	)


def    _snake_case  (  _snake_case :	Optional[int]       ,      _snake_case :	Any       ,      _snake_case :	Optional[int]=float('''inf'''	)	):

      for i in range(points_counts - 1	):
            for j in range(i + 1       ,      _snake_case	):
                  lowerCAmelCase    :		Any				=      euclidean_distance_sqr(points[i]       ,      points[j]	)
                  if current_dis < min_dis:
                        lowerCAmelCase    :		str				=      current_dis
      return min_dis


def    _snake_case  (  _snake_case :	List[str]       ,      _snake_case :	List[str]       ,      _snake_case :	str=float('''inf'''	)	):

      for i in range(min(6       ,      points_counts - 1	)       ,      _snake_case	):
            for j in range(max(0       ,      i - 6	)       ,      _snake_case	):
                  lowerCAmelCase    :		List[str]				=      euclidean_distance_sqr(points[i]       ,      points[j]	)
                  if current_dis < min_dis:
                        lowerCAmelCase    :		Tuple				=      current_dis
      return min_dis


def    _snake_case  (  _snake_case :	Tuple       ,      _snake_case :	Optional[Any]       ,      _snake_case :	Any	):

      # base case
      if points_counts <= 3:
            return dis_between_closest_pair(_snake_case       ,      _snake_case	)

      # recursion
      lowerCAmelCase    :		List[str]				=      points_counts // 2
      lowerCAmelCase    :		List[str]				=      closest_pair_of_points_sqr(
          _snake_case       ,      points_sorted_on_y[:mid]       ,      _snake_case	)
      lowerCAmelCase    :		List[Any]				=      closest_pair_of_points_sqr(
          _snake_case       ,      points_sorted_on_y[mid:]       ,      points_counts - mid	)
      lowerCAmelCase    :		List[Any]				=      min(_snake_case       ,      _snake_case	)
      lowerCAmelCase    :		Optional[Any]				=      []
      for point in points_sorted_on_x:
            if abs(point[0] - points_sorted_on_x[mid][0]	) < closest_pair_dis:
                  cross_strip.append(_snake_case	)

      lowerCAmelCase    :		List[str]				=      dis_between_closest_in_strip(
          _snake_case       ,      len(_snake_case	)       ,      _snake_case	)
      return min(_snake_case       ,      _snake_case	)


def    _snake_case  (  _snake_case :	int       ,      _snake_case :	Union[str, Any]	):
      lowerCAmelCase    :		Union[str, Any]				=      column_based_sort(_snake_case       ,      column=0	)
      lowerCAmelCase    :		Dict				=      column_based_sort(_snake_case       ,      column=1	)
      return (
          closest_pair_of_points_sqr(
              _snake_case       ,      _snake_case       ,      _snake_case	)
      ) ** 0.5


if __name__ == "__main__":
 snake_case__						:   str			 = [(2, 3), (12, 30), (40, 50), (5, 1), (12, 10), (3, 4)]
 print('''Distance:''', closest_pair_of_points(points, len(points)))







"""simple docstring"""






from ..utils import DummyObject, requires_backends



class 			A__   (  metaclass=__SCREAMING_SNAKE_CASE							):




	'''simple docstring'''





	SCREAMING_SNAKE_CASE          =	['torch', 'torchsde']

	def __init__(     self:		int       ,			*_SCREAMING_SNAKE_CASE:		Optional[Any]       ,			**_SCREAMING_SNAKE_CASE:		str)				->       Dict:

				"""simple docstring"""

				requires_backends(self       ,			["torch", "torchsde"])

	@classmethod
	def 							_SCREAMING_SNAKE_CASE   (     cls:		Optional[Any]       ,			*_SCREAMING_SNAKE_CASE:		Optional[int]       ,			**_SCREAMING_SNAKE_CASE:		Optional[int])				->       Optional[Any]:

				"""simple docstring"""

				requires_backends(cls       ,			["torch", "torchsde"])







	@classmethod
	def 							_SCREAMING_SNAKE_CASE   (     cls:		Dict       ,			*_SCREAMING_SNAKE_CASE:		List[Any]       ,			**_SCREAMING_SNAKE_CASE:		Any)				->       Optional[int]:

				"""simple docstring"""

				requires_backends(cls       ,			["torch", "torchsde"])