
class     __UpperCamelCase :






     """simple docstring"""







     def __init__(				self							:							List[str] ):







       """simple docstring"""




       __SCREAMING_SNAKE_CASE      :	Optional[Any]					=		0
       __SCREAMING_SNAKE_CASE      :	Optional[Any]					=		0
       __SCREAMING_SNAKE_CASE      :	Optional[Any]					=		{}



     def  UpperCAmelCase__							(				self							:							Tuple     ,						_A							:							List[Any] ):







       """simple docstring"""




       if vertex not in self.adjacency:
         __SCREAMING_SNAKE_CASE      :	List[str]					=		{}
         self.num_vertices += 1



     def  UpperCAmelCase__							(				self							:							Dict     ,						_A							:							Optional[Any]     ,						_A							:							Optional[Any]     ,						_A							:							List[str] ):







       """simple docstring"""




       self.add_vertex(_A )
       self.add_vertex(_A )

       if head == tail:
         return

       __SCREAMING_SNAKE_CASE      :	Optional[int]					=		weight
       __SCREAMING_SNAKE_CASE      :	Optional[int]					=		weight



     def  UpperCAmelCase__							(				self							:							Optional[Any] ):







       """simple docstring"""




       __SCREAMING_SNAKE_CASE      :	Tuple					=		self.get_edges()
       for edge in edges:
         __SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE      :	Tuple					=		edge
         edges.remove((tail, head, weight) )
       for i in range(len(_A ) ):
         __SCREAMING_SNAKE_CASE      :	List[Any]					=		list(edges[i] )

       edges.sort(key=lambda _A : e[2] )
       for i in range(len(_A ) - 1 ):
         if edges[i][2] >= edges[i + 1][2]:
           __SCREAMING_SNAKE_CASE      :	Dict					=		edges[i][2] + 1
       for edge in edges:
         __SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE      :	List[Any]					=		edge
         __SCREAMING_SNAKE_CASE      :	Any					=		weight
         __SCREAMING_SNAKE_CASE      :	Tuple					=		weight



     def __str__(				self							:							Union[str, Any] ):







       """simple docstring"""




       __SCREAMING_SNAKE_CASE      :	Optional[int]					=		''''''
       for tail in self.adjacency:
         for head in self.adjacency[tail]:
           __SCREAMING_SNAKE_CASE      :	str					=		self.adjacency[head][tail]
           string += F'''{head} -> {tail} == {weight}\n'''
       return string.rstrip('''\n''' )



     def  UpperCAmelCase__							(				self							:							Tuple ):







       """simple docstring"""




       __SCREAMING_SNAKE_CASE      :	Dict					=		[]
       for tail in self.adjacency:
         for head in self.adjacency[tail]:
           output.append((tail, head, self.adjacency[head][tail]) )
       return output



     def  UpperCAmelCase__							(				self							:							Any ):







       """simple docstring"""




       return self.adjacency.keys()



     @staticmethod
     def  UpperCAmelCase__							(				_A							:							List[Any]=None     ,						_A							:							List[str]=None ):







       """simple docstring"""




       __SCREAMING_SNAKE_CASE      :	Union[str, Any]					=		Graph()
       if vertices is None:
         __SCREAMING_SNAKE_CASE      :	Optional[int]					=		[]
       if edges is None:
         __SCREAMING_SNAKE_CASE      :	Optional[Any]					=		[]
       for vertex in vertices:
         g.add_vertex(_A )
       for edge in edges:
         g.add_edge(*_A )
       return g





     class     __UpperCamelCase :






          """simple docstring"""







          def __init__(				self							:							List[Any] ):







            """simple docstring"""




            __SCREAMING_SNAKE_CASE      :	Optional[Any]					=		{}
            __SCREAMING_SNAKE_CASE      :	List[Any]					=		{}



          def __len__(				self							:							Any ):







            """simple docstring"""




            return len(self.parent )



          def  UpperCAmelCase__							(				self							:							Dict     ,						_A							:							Optional[int] ):







            """simple docstring"""




            if item in self.parent:
              return self.find(_A )

            __SCREAMING_SNAKE_CASE      :	List[Any]					=		item
            __SCREAMING_SNAKE_CASE      :	str					=		0
            return item



          def  UpperCAmelCase__							(				self							:							str     ,						_A							:							Tuple ):







            """simple docstring"""




            if item not in self.parent:
              return self.make_set(_A )
            if item != self.parent[item]:
              __SCREAMING_SNAKE_CASE      :	Tuple					=		self.find(self.parent[item] )
            return self.parent[item]




          def  UpperCAmelCase__							(				self							:							Any     ,						_A							:							Tuple     ,						_A							:							Any ):







            """simple docstring"""




            __SCREAMING_SNAKE_CASE      :	List[str]					=		self.find(_A )
            __SCREAMING_SNAKE_CASE      :	Optional[Any]					=		self.find(_A )

            if roota == roota:
              return roota

            if self.rank[roota] > self.rank[roota]:
              __SCREAMING_SNAKE_CASE      :	Tuple					=		roota
              return roota

            if self.rank[roota] < self.rank[roota]:
              __SCREAMING_SNAKE_CASE      :	str					=		roota
              return roota

            if self.rank[roota] == self.rank[roota]:
              self.rank[roota] += 1
              __SCREAMING_SNAKE_CASE      :	Any					=		roota
              return roota
            return None






     @staticmethod
     def  UpperCAmelCase__							(				_A							:							List[str] ):







       """simple docstring"""




       __SCREAMING_SNAKE_CASE      :	str					=		graph.num_vertices

       __SCREAMING_SNAKE_CASE      :	List[Any]					=		Graph.UnionFind()
       __SCREAMING_SNAKE_CASE      :	Union[str, Any]					=		[]
       while num_components > 1:
         __SCREAMING_SNAKE_CASE      :	str					=		{}
         for vertex in graph.get_vertices():
           __SCREAMING_SNAKE_CASE      :	str					=		-1

         __SCREAMING_SNAKE_CASE      :	List[Any]					=		graph.get_edges()
         for edge in edges:
           __SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE      :	Tuple					=		edge
           edges.remove((tail, head, weight) )
         for edge in edges:
           __SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE      :	Optional[int]					=		edge
           __SCREAMING_SNAKE_CASE      :	List[Any]					=		union_find.find(_A )
           __SCREAMING_SNAKE_CASE      :	Tuple					=		union_find.find(_A )
           if seta != seta:
             if cheap_edge[seta] == -1 or cheap_edge[seta][2] > weight:
               __SCREAMING_SNAKE_CASE      :	Dict					=		[head, tail, weight]

             if cheap_edge[seta] == -1 or cheap_edge[seta][2] > weight:
               __SCREAMING_SNAKE_CASE      :	int					=		[head, tail, weight]
         for vertex in cheap_edge:
           if cheap_edge[vertex] != -1:
             __SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE,		__SCREAMING_SNAKE_CASE      :	Optional[Any]					=		cheap_edge[vertex]
             if union_find.find(_A ) != union_find.find(_A ):
               union_find.union(_A     ,						_A )
               mst_edges.append(cheap_edge[vertex] )
               __SCREAMING_SNAKE_CASE      :	Optional[Any]					=		num_components - 1
       __SCREAMING_SNAKE_CASE      :	str					=		Graph.build(edges=_A )
       return mst


"""simple docstring"""




from __future__ import annotations

from math import pow, sqrt


def     __magic_name__      ( __snake_case							:			float	,					__snake_case							:			float	,					__snake_case							:			float    )					->							dict[str, float]:
       if (resistance, reactance, impedance).count(0    ) != 1:
              raise ValueError("One and only one argument must be 0"    )
       if resistance == 0:
              return {"resistance": sqrt(pow(__snake_case	,					2    ) - pow(__snake_case	,					2    )    )}
       elif reactance == 0:
              return {"reactance": sqrt(pow(__snake_case	,					2    ) - pow(__snake_case	,					2    )    )}
       elif impedance == 0:
              return {"impedance": sqrt(pow(__snake_case	,					2    ) + pow(__snake_case	,					2    )    )}
       else:
              raise ValueError("Exactly one argument must be 0"    )


if __name__ == "__main__":
   import doctest

   doctest.testmod()


