'''simple docstring'''

from __future__ import annotations

from typing import Generic, TypeVar

A_     :						List[Any]    							=TypeVar('''T''')


class     __UpperCAmelCase       ( Generic[T]		):





  def __init__(	self    ,     _lowerCamelCase ):
     lowerCAmelCase_			=      data
     lowerCAmelCase_			=      self
     lowerCAmelCase_			=      0






class     __UpperCAmelCase       ( Generic[T]		):





  def __init__(	self ):
     # map from node name to the node object
     lowerCAmelCase_			=      {}





  def 						UpperCAmelCase_	(	self    ,     _lowerCamelCase ):
     # create a new set with x as its member
     lowerCAmelCase_			=      DisjointSetTreeNode(lowercase_ )





  def 						UpperCAmelCase_	(	self    ,     _lowerCamelCase ):
     # find the set x belongs to (with path-compression)
     lowerCAmelCase_			=      self.map[data]
     if elem_ref != elem_ref.parent:
        lowerCAmelCase_			=      self.find_set(elem_ref.parent.data )
     return elem_ref.parent





  def 						UpperCAmelCase_	(	self    ,     _lowerCamelCase    ,     _lowerCamelCase ):
     # helper function for union operation
     if nodea.rank > nodea.rank:
        lowerCAmelCase_			=      nodea
     else:
        lowerCAmelCase_			=      nodea
        if nodea.rank == nodea.rank:
           nodea.rank += 1







  def 						UpperCAmelCase_	(	self    ,     _lowerCamelCase    ,     _lowerCamelCase ):
     # merge 2 disjoint sets
     self.link(self.find_set(lowercase_ )    ,     self.find_set(lowercase_ ) )






class     __UpperCAmelCase       ( Generic[T]		):





  def __init__(	self ):
     # connections: map from the node to the neighbouring nodes (with weights)
     lowerCAmelCase_			=      {}





  def 						UpperCAmelCase_	(	self    ,     _lowerCamelCase ):
     # add a node ONLY if its not present in the graph
     if node not in self.connections:
        lowerCAmelCase_			=      {}





  def 						UpperCAmelCase_	(	self    ,     _lowerCamelCase    ,     _lowerCamelCase    ,     _lowerCamelCase ):
     # add an edge with the given weight
     self.add_node(lowercase_ )
     self.add_node(lowercase_ )
     lowerCAmelCase_			=      weight
     lowerCAmelCase_			=      weight







  def 						UpperCAmelCase_	(	self ):
     lowerCAmelCase_			=      []
     lowerCAmelCase_			=      set()
     for start in self.connections:
        for end in self.connections[start]:
           if (start, end) not in seen:
              seen.add((end, start) )
              edges.append((start, end, self.connections[start][end]) )
     edges.sort(key=lambda _lowerCamelCase : x[2] )

     # creating the disjoint set
     lowerCAmelCase_			=      DisjointSetTree[T]()
     for node in self.connections:
        disjoint_set.make_set(lowercase_ )

     # MST generation
     lowerCAmelCase_			=      0
     lowerCAmelCase_			=      0
     lowerCAmelCase_			=      GraphUndirectedWeighted[T]()
     while num_edges < len(self.connections ) - 1:
        lowerCAmelCase_	,lowerCAmelCase_	,lowerCAmelCase_			=      edges[index]
        index += 1
        lowerCAmelCase_			=      disjoint_set.find_set(lowercase_ )
        lowerCAmelCase_			=      disjoint_set.find_set(lowercase_ )
        if parent_u != parent_v:
           num_edges += 1
           graph.add_edge(lowercase_    ,     lowercase_    ,     lowercase_ )
           disjoint_set.union(lowercase_    ,     lowercase_ )
     return graph







"""simple docstring"""

from __future__ import annotations

from collections.abc import Iterator
class   _UpperCAmelCase				:




      def __init__(				self ,							lowercase_				)    ->       None:
          UpperCAmelCase          =       value
          UpperCAmelCase          =       None
          UpperCAmelCase          =       None

class   _UpperCAmelCase				:




      def __init__(				self ,							lowercase_				)    ->       None:
          UpperCAmelCase          =       tree




      def      a_   (				self ,							lowercase_				)    ->       int:
          if node is None:
              return 0
          return node.value + (
              self.depth_first_search(node.left				) + self.depth_first_search(node.right				)
          )




      def __iter__(				self				)    ->       Iterator[int]:
          yield self.depth_first_search(self.tree				)


if __name__ == "__main__":
   import doctest

   doctest.testmod()



