btj( dZddlZddlmZmZdgZededejddZdS) z= Algorithm to find a maximal (not maximum) independent set. N)not_implemented_forpy_random_statemaximal_independent_setdirectedc|s$|th}nt|}|st j|dtjfd|D}t||rt j|dt|}t ||}|rj|t|}| || tj ||gz|j|S)a'Returns a random maximal independent set guaranteed to contain a given set of nodes. An independent set is a set of nodes such that the subgraph of G induced by these nodes contains no edges. A maximal independent set is an independent set such that it is not possible to add a new node and still get an independent set. Parameters ---------- G : NetworkX graph nodes : list or iterable Nodes that must be part of the independent set. This set of nodes must be independent. seed : integer, random_state, or None (default) Indicator of random number generation state. See :ref:`Randomness`. Returns ------- indep_nodes : list List of nodes that are part of a maximal independent set. Raises ------ NetworkXUnfeasible If the nodes in the provided list are not part of the graph or do not form an independent set, an exception is raised. NetworkXNotImplemented If `G` is directed. Examples -------- >>> G = nx.path_graph(5) >>> nx.maximal_independent_set(G) # doctest: +SKIP [4, 0, 2] >>> nx.maximal_independent_set(G, [1]) # doctest: +SKIP [1, 3] Notes ----- This algorithm does not solve the maximum independent set problem. z" is not a subset of the nodes of GcDg|]}tj|S)setadj).0vGs U/var/www/html/CA-Chatbot/venv/lib/python3.11/site-packages/networkx/algorithms/mis.py z+maximal_independent_set..Es%999aCaMM999z is not an independent set of G) choicelistr issubsetnxNetworkXUnfeasibleunion intersectionnodes differenceappenddifference_updater )rrseed neighbors indep_nodesavailable_nodesnodes` rrr sbf T!WW%%&E  >>!  R#u$P$P$PQQQ 99995999:I  5))O#u$M$M$MNNNu++K!''))nn// 0F0FGGO F{{400114   ))$quT{*;*;tf*DEEE F r)NN) __doc__networkxrnetworkx.utilsrr__all__ _dispatchablerr rrr(s ???????? $ %Z  ???! ???r