o ]Zh5@sndZddgZddlZejddddddZejdd d dZdd d Zd dZddZ ddZ ddZ dS)a Implementation of the Wright, Richmond, Odlyzko and McKay (WROM) algorithm for the enumeration of all non-isomorphic free trees of a given order. Rooted trees are represented by level sequences, i.e., lists in which the i-th element specifies the distance of vertex i to the root. nonisomorphic_treesnumber_of_nonisomorphic_treesNT)graphsZ returns_graphgraphccs|dkrttt|ddttd|dd}|durQt|}|durK|dkr2t|Vn|dkrGddl}|jdtddt|Vt |}|dus dSdS) a Generates lists of nonisomorphic trees Parameters ---------- order : int order of the desired tree(s) create : one of {"graph", "matrix"} (default="graph") If ``"graph"`` is selected a list of ``Graph`` instances will be returned, if matrix is selected a list of adjacency matrices will be returned. .. deprecated:: 3.3 The `create` argument is deprecated and will be removed in NetworkX version 3.5. In the future, `nonisomorphic_trees` will yield graph instances by default. To generate adjacency matrices, call ``nx.to_numpy_array`` on the output, e.g.:: [nx.to_numpy_array(G) for G in nx.nonisomorphic_trees(N)] Yields ------ list A list of nonisomorphic trees, in one of two formats depending on the value of the `create` parameter: - ``create="graph"``: yields a list of `networkx.Graph` instances - ``create="matrix"``: yields a list of list-of-lists representing adjacency matrices Nrmatrixrz The 'create=matrix' argument of nonisomorphic_trees is deprecated and will be removed in version 3.5. Use ``nx.to_numpy_array`` to convert graphs to adjacency matrices, e.g.:: [nx.to_numpy_array(G) for G in nx.nonisomorphic_trees(N)])category stacklevel) ValueErrorlistrange _next_tree_layout_to_graphwarningswarnDeprecationWarning_layout_to_matrix_next_rooted_tree)ordercreatelayoutrrV/var/www/auris/lib/python3.10/site-packages/networkx/generators/nonisomorphic_trees.pyrs&*  )rcCstddt|DS)zReturns the number of nonisomorphic trees Parameters ---------- order : int order of the desired tree(s) Returns ------- length : Number of nonisomorphic graphs for the given order References ---------- css|]}dVqdS)rNr).0_rrr \sz0number_of_nonisomorphic_trees..)sumr)rrrrrKscCs|durt|d}||dkr|d8}||dks|dkr dS|d}||||dkr<|d8}||||dks.t|}t|t|D] }||||||<qG|S)z0One iteration of the Beyer-Hedetniemi algorithm.Nrr)lenr r )Z predecessorpqresultirrrr_s   rc Cst|\}}t|}t|}||k}|r1||kr1t|t|kr#d}nt|t|kr1||kr1d}|r5|St|}t||}||dkr^t|\}} t|} td| d} | |t|  d<|S)zGOne iteration of the Wright, Richmond, Odlyzko and McKay algorithm.FrrN) _split_treemaxrrr ) candidateleftrestZ left_heightZ rest_heightZvalidrZ new_candidateZnew_leftZnew_restZnew_left_heightsuffixrrrrrs&     rcsd}d}ttD]}|dkr|r|}nd}q |dur#t}fddtd|D}dgfddt|tD}||fS) zReturns a tuple of two layouts, one containing the left subtree of the root vertex, and one containing the original tree with the left subtree removed.FNrTcsg|]}|dqS)rrrr"rrr sz_split_tree..rcsg|]}|qSrrr)r*rrr+s)r r)rZ one_foundmr"r&r'rr*rr#s "r#csfddttD}g}ttD]5}|}|rE|d}|}||kr9||d}|}||ks)d|||<|||<||q|S)z\Create the adjacency matrix for the tree specified by the given layout (level sequence).csg|] }dgtqS)r)rr)r*rrr+sz%_layout_to_matrix..r)r rpopappend)rr!stackr"i_leveljj_levelrr*rrs rcCs|t}g}tt|D]/}||}|r6|d}||}||kr0||d}||}||ks |||||q |S)zVCreate a NetworkX Graph for the tree specified by the given layout(level sequence)r-)nxZGraphr rr.Zadd_edger/)rGr0r"r1r2r3rrrrs  r)r)N) __doc____all__Znetworkxr4Z _dispatchablerrrrr#rrrrrrs    ;  '