graphs.minimum_spanning_tree_kruskal2
=====================================

.. py:module:: graphs.minimum_spanning_tree_kruskal2


Attributes
----------

.. autoapisummary::

   graphs.minimum_spanning_tree_kruskal2.T


Classes
-------

.. autoapisummary::

   graphs.minimum_spanning_tree_kruskal2.DisjointSetTree
   graphs.minimum_spanning_tree_kruskal2.DisjointSetTreeNode
   graphs.minimum_spanning_tree_kruskal2.GraphUndirectedWeighted


Module Contents
---------------

.. py:class:: DisjointSetTree

   Bases: :py:obj:`Generic`\ [\ :py:obj:`T`\ ]


   .. py:method:: find_set(data: T) -> DisjointSetTreeNode[T]


   .. py:method:: link(node1: DisjointSetTreeNode[T], node2: DisjointSetTreeNode[T]) -> None


   .. py:method:: make_set(data: T) -> None


   .. py:method:: union(data1: T, data2: T) -> None


   .. py:attribute:: map
      :type:  dict[T, DisjointSetTreeNode[T]]


.. py:class:: DisjointSetTreeNode(data: T)

   Bases: :py:obj:`Generic`\ [\ :py:obj:`T`\ ]


   .. py:attribute:: data


   .. py:attribute:: parent


   .. py:attribute:: rank
      :value: 0



.. py:class:: GraphUndirectedWeighted

   Bases: :py:obj:`Generic`\ [\ :py:obj:`T`\ ]


   .. py:method:: add_edge(node1: T, node2: T, weight: int) -> None


   .. py:method:: add_node(node: T) -> None


   .. py:method:: kruskal() -> GraphUndirectedWeighted[T]

      Details: https://en.wikipedia.org/wiki/Kruskal%27s_algorithm

      Example:
      >>> g1 = GraphUndirectedWeighted[int]()
      >>> g1.add_edge(1, 2, 1)
      >>> g1.add_edge(2, 3, 2)
      >>> g1.add_edge(3, 4, 1)
      >>> g1.add_edge(3, 5, 100) # Removed in MST
      >>> g1.add_edge(4, 5, 5)
      >>> assert 5 in g1.connections[3]
      >>> mst = g1.kruskal()
      >>> assert 5 not in mst.connections[3]

      >>> g2 = GraphUndirectedWeighted[str]()
      >>> g2.add_edge('A', 'B', 1)
      >>> g2.add_edge('B', 'C', 2)
      >>> g2.add_edge('C', 'D', 1)
      >>> g2.add_edge('C', 'E', 100) # Removed in MST
      >>> g2.add_edge('D', 'E', 5)
      >>> assert 'E' in g2.connections["C"]
      >>> mst = g2.kruskal()
      >>> assert 'E' not in mst.connections['C']



   .. py:attribute:: connections
      :type:  dict[T, dict[T, int]]


.. py:data:: T