U ?h<@sTdZddgZddlZdddZddZddd Zd d Zd d ZddZ 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_treesNgraphccs|dkr ttt|ddttd|dd}|dk r~t|}|dk r6|dkrbt|Vn|dkrtt|Vt|}q6dS)aReturns a list of nonisomporphic trees Parameters ---------- order : int order of the desired tree(s) create : graph or matrix (default="Graph) If graph is selected a list of trees will be returned, if matrix is selected a list of adjancency matrix will be returned Returns ------- G : List of NetworkX Graphs M : List of Adjacency matrices References ---------- Nrmatrix) ValueErrorlistrange _next_tree_layout_to_graph_layout_to_matrix_next_rooted_tree)ordercreatelayoutrY/var/www/html/venv/lib/python3.8/site-packages/networkx/generators/nonisomorphic_trees.pyrs*  cCstddt|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 Fsz0number_of_nonisomorphic_trees..)sumr)rrrrr6scCs|dkr*t|d}||dkr*|d8}q|dkr6dS|d}||||dkr\|d8}q>t|}t|t|D]}||||||<qr|S)z0One iteration of the Beyer-Hedetniemi algorithm.Nrr)lenr r )Z predecessorpqresultirrrrIs    rc Cst|\}}t|}t|}||k}|rb||krbt|t|krFd}nt|t|krb||krbd}|rj|St|}t||}||dkrt|\}} t|} td| d} | |t|  d<|SdS)zGOne iteration of the Wright, Richmond, Odlyzko and McKay algorithm.FrrN) _split_treemaxrrr ) candidateleftrestZ left_heightZ rest_heightZvalidrZ new_candidateZnew_leftZnew_restZnew_left_heightsuffixrrrr \s&     r csd}d}ttD]"}|dkr|r2|}q8qd}q|dkrHt}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)rrrrrrr sz_split_tree..rcsg|] }|qSrrr#r$rrr%s)r r)rZ one_foundmrr r!rr$rrs "rcsfddttD}g}ttD]d}|}|r|d}|}||krl||d}|}qJd|||<|||<||q*|S)z\Create the adjacency matrix for the tree specified by the given layout (level sequence).csg|]}dgtqS)r)rr#r$rrr%sz%_layout_to_matrix..r)r rpopappend)rrstackri_leveljj_levelrr$rr s  r cCsvt}g}tt|D]X}||}|rf|d}||}||krZ||d}||}q8|||||q|S)zVCreate a NetworkX Graph for the tree specified by the given layout(level sequence)r')nxZGraphr rr(Zadd_edger))rGr*rr+r,r-rrrr s   r )r)N) __doc____all__Znetworkxr.rrrr rr r rrrrs  ' '