o ˷e<@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|dkrttt|ddttd|dd}|durEt|}|dur?|dkr2t|Vn |dkr;t|Vt|}|dus dSdS)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)ordercreatelayoutr^/var/www/ideatree/venv/lib/python3.10/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|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 ) predecessorpqresultirrrrIs   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 ) candidateleftrest left_height rest_heightvalidr new_candidatenew_leftnew_restnew_left_heightsuffixrrrr \s&     r csd}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)rrrrrrr sz_split_tree..rcsg|]}|qSrrr+r,rrr-s)r r)r one_foundmrr!r"rr,rrs "rcsfddttD}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)rrstackri_leveljj_levelrr,rr s r cCs|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)r0)nxGraphr rr1add_edger2)rGr3rr4r5r6rrrr s  r )r)N) __doc____all__networkxr7rrrr rr r rrrrs  ' '