



'''simple docstring'''






class 							lowercase :


 """simple docstring"""


 def __init__(							self						,a_							)	->     None:
        _UpperCAmelCase						:		Optional[Any]      =				data
        _UpperCAmelCase						:		int
        _UpperCAmelCase						:		Node







def 					snake_case_      (  lowerCAmelCase_	)->	None:





       '''simple docstring'''


       _UpperCAmelCase						:		Tuple      =				0
       _UpperCAmelCase						:		str      =				x




def 					snake_case_      (  lowerCAmelCase_ ,     lowerCAmelCase_	)->	None:





       '''simple docstring'''


       _UpperCAmelCase						:		List[str]      =				find_set(lowerCAmelCase_	), find_set(lowerCAmelCase_	)
       if x == y:
              return

       elif x.rank > y.rank:
              _UpperCAmelCase						:		Union[str, Any]      =				x
       else:
              _UpperCAmelCase						:		List[Any]      =				y
              if x.rank == y.rank:
                     y.rank += 1




def 					snake_case_      (  lowerCAmelCase_	)->	Node:





       '''simple docstring'''


       if x != x.parent:
              _UpperCAmelCase						:		Optional[Any]      =				find_set(x.parent	)
       return x.parent




def 					snake_case_      (  lowerCAmelCase_	)->	set:





       '''simple docstring'''


       _UpperCAmelCase						:		str      =				({0, 1, 2}, {3, 4, 5})
       for s in sets:
              if node.data in s:
                     return s
       _UpperCAmelCase						:		int      =				F'''{node.data} is not in {sets}'''
       raise ValueError(lowerCAmelCase_	)




def 					snake_case_      (  )->	None:





       '''simple docstring'''


       _UpperCAmelCase						:		List[str]      =				[Node(lowerCAmelCase_	) for i in range(6	)]
       for v in vertex:
              make_set(lowerCAmelCase_	)

       union_set(vertex[0] ,     vertex[1]	)
       union_set(vertex[1] ,     vertex[2]	)
       union_set(vertex[3] ,     vertex[4]	)
       union_set(vertex[3] ,     vertex[5]	)

       for nodea in vertex:
              for nodea in vertex:
                     if find_python_set(lowerCAmelCase_	).isdisjoint(find_python_set(lowerCAmelCase_	)	):
                            assert find_set(lowerCAmelCase_	) != find_set(lowerCAmelCase_	)
                     else:
                            assert find_set(lowerCAmelCase_	) == find_set(lowerCAmelCase_	)


if __name__ == "__main__":
   test_disjoint_set()








'''simple docstring'''






def 					snake_case_      (  lowerCAmelCase_	)->	tuple[int, int]:





       '''simple docstring'''


       if len(lowerCAmelCase_	) == 1:
              return a[0], a[0]
       else:
              # split A into half.
              _UpperCAmelCase						:		Union[str, Any]      =				a[: len(lowerCAmelCase_	) // 2]
              _UpperCAmelCase						:		str      =				a[len(lowerCAmelCase_	) // 2 :]

              # 2 sub problems, 1/2 of original size.
              _UpperCAmelCase  ,_UpperCAmelCase						:		str      =				max_difference(lowerCAmelCase_	)
              _UpperCAmelCase  ,_UpperCAmelCase						:		List[str]      =				max_difference(lowerCAmelCase_	)

              # get min of first and max of second
              # linear time
              _UpperCAmelCase						:		Dict      =				min(lowerCAmelCase_	)
              _UpperCAmelCase						:		List[Any]      =				max(lowerCAmelCase_	)

              # 3 cases, either (small1, big1),
              # (min_first, max_second), (small2, big2)
              # constant comparisons
              if biga - smalla > max_second - min_first and biga - smalla > biga - smalla:
                     return smalla, biga
              elif biga - smalla > max_second - min_first:
                     return smalla, biga
              else:
                     return min_first, max_second


if __name__ == "__main__":
   import doctest

   doctest.testmod()



