




from __future__ import annotations

from typing import Generic, TypeVar

lowercase__				:      Tuple     = TypeVar("T")




class       a__	( Generic[T]				):







     def __init__(     self  ,		A			)  ->   None:



          '''simple docstring'''



          a     =				data
          a     =				self
          a     =				0







class       a__	( Generic[T]				):







     def __init__(     self			)  ->   None:



          '''simple docstring'''



          a     =				{}







     def       lowerCAmelCase_    (     self  ,		A			)  ->   None:



          '''simple docstring'''



          a     =				DisjointSetTreeNode(a__			)







     def       lowerCAmelCase_    (     self  ,		A			)  ->   DisjointSetTreeNode[T]:



          '''simple docstring'''



          a     =				self.map[data]
          if elem_ref != elem_ref.parent:
               a     =				self.find_set(elem_ref.parent.data			)
          return elem_ref.parent







     def       lowerCAmelCase_    (     self  ,		A  ,		A			)  ->   None:



          '''simple docstring'''



          if nodea.rank > nodea.rank:
               a     =				nodea
          else:
               a     =				nodea
               if nodea.rank == nodea.rank:
                    nodea.rank += 1







     def       lowerCAmelCase_    (     self  ,		A  ,		A			)  ->   None:



          '''simple docstring'''



          self.link(self.find_set(a__			)  ,		self.find_set(a__			)			)







class       a__	( Generic[T]				):







     def __init__(     self			)  ->   None:



          '''simple docstring'''



          a     =				{}







     def       lowerCAmelCase_    (     self  ,		A			)  ->   None:



          '''simple docstring'''



          if node not in self.connections:
               a     =				{}







     def       lowerCAmelCase_    (     self  ,		A  ,		A  ,		A			)  ->   None:



          '''simple docstring'''



          self.add_node(a__			)
          self.add_node(a__			)
          a     =				weight
          a     =				weight







     def       lowerCAmelCase_    (     self			)  ->   GraphUndirectedWeighted[T]:



          '''simple docstring'''



          a     =				[]
          a     =				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 A			: x[2]			)

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

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







# Author: OMKAR PATHAK, Nwachukwu Chidiebere

# Use a Python dictionary to construct the graph.
from __future__ import annotations

from pprint import pformat
from typing import Generic, TypeVar

lowercase__				:      str	   = TypeVar("T")




class       a__	( Generic[T]				):







     def __init__(     self  ,		A = True			)  ->   None:



          '''simple docstring'''



          a     =				{}  # dictionary of lists
          a     =				directed







     def       lowerCAmelCase_    (     self  ,		A  ,		A			)  ->   GraphAdjacencyList[T]:



          '''simple docstring'''



          if not self.directed:  # For undirected graphs
               # if both source vertex and destination vertex are both present in the
               # adjacency list, add destination vertex to source vertex list of adjacent
               # vertices and add source vertex to destination vertex list of adjacent
               # vertices.
               if source_vertex in self.adj_list and destination_vertex in self.adj_list:
                    self.adj_list[source_vertex].append(A			)
                    self.adj_list[destination_vertex].append(A			)
               # if only source vertex is present in adjacency list, add destination vertex
               # to source vertex list of adjacent vertices, then create a new vertex with
               # destination vertex as key and assign a list containing the source vertex
               # as it's first adjacent vertex.
               elif source_vertex in self.adj_list:
                    self.adj_list[source_vertex].append(A			)
                    a     =				[source_vertex]
               # if only destination vertex is present in adjacency list, add source vertex
               # to destination vertex list of adjacent vertices, then create a new vertex
               # with source vertex as key and assign a list containing the source vertex
               # as it's first adjacent vertex.
               elif destination_vertex in self.adj_list:
                    self.adj_list[destination_vertex].append(A			)
                    a     =				[destination_vertex]
               # if both source vertex and destination vertex are not present in adjacency
               # list, create a new vertex with source vertex as key and assign a list
               # containing the destination vertex as it's first adjacent vertex also
               # create a new vertex with destination vertex as key and assign a list
               # containing the source vertex as it's first adjacent vertex.
               else:
                    a     =				[destination_vertex]
                    a     =				[source_vertex]
          else:  # For directed graphs
               # if both source vertex and destination vertex are present in adjacency
               # list, add destination vertex to source vertex list of adjacent vertices.
               if source_vertex in self.adj_list and destination_vertex in self.adj_list:
                    self.adj_list[source_vertex].append(A			)
               # if only source vertex is present in adjacency list, add destination
               # vertex to source vertex list of adjacent vertices and create a new vertex
               # with destination vertex as key, which has no adjacent vertex
               elif source_vertex in self.adj_list:
                    self.adj_list[source_vertex].append(A			)
                    a     =				[]
               # if only destination vertex is present in adjacency list, create a new
               # vertex with source vertex as key and assign a list containing destination
               # vertex as first adjacent vertex
               elif destination_vertex in self.adj_list:
                    a     =				[destination_vertex]
               # if both source vertex and destination vertex are not present in adjacency
               # list, create a new vertex with source vertex as key and a list containing
               # destination vertex as it's first adjacent vertex. Then create a new vertex
               # with destination vertex as key, which has no adjacent vertex
               else:
                    a     =				[destination_vertex]
                    a     =				[]

          return self







     def __repr__(     self			)  ->   str:



          '''simple docstring'''



          return pformat(self.adj_list			)

