VhNdZddgZddlmZddlZej dddZej d d Zedd Z edd Z dd Z dZ dZ dZdZy)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_trees) lru_cacheNT)graphs returns_graphc#K|dkrttt|dzdzttd|dzdzz}|)t|}|t |t |}|(yyw)zGenerates lists of nonisomorphic trees Parameters ---------- order : int order of the desired tree(s) Yields ------ list of `networkx.Graph` instances A list of nonisomorphic trees N) ValueErrorlistrange _next_tree_layout_to_graph_next_rooted_tree)orderlayouts W/home/dcms/DCMS/lib/python3.12/site-packages/networkx/generators/nonisomorphic_trees.pyrrsy qy % Q' (4a%!)9I0J+K KF  F#  "6* *&v.F  s A+A0.A0)rc.|dkrtt|S)a]Returns the number of nonisomorphic trees Based on an algorithm by Alois P. Heinz in `OEIS entry A000055 `_. Complexity is ``O(n ** 3)`` Parameters ---------- order : int order of the desired tree(s) Returns ------- int Number of nonisomorphic graphs for the given order r )r _unlabeled_trees)rs rrr,s" qy E ""cd}t|dzD]}|t|t||z zz }!|dzdk(r|t|dzz}t||dzz S)z4Implements OEIS A000055 (number of unlabeled trees).rr r r _rooted_trees)nvalueks rrrBso E 1q5\9 q!M!a%$88891uz qAv&&  eqj ((rc|dkr|Sd}td|D]<}td|D]+}||zdk(s ||t|zt||z zz }->||dz zS)z;Implements OEIS A000081 (number of unlabeled rooted trees).r rr r)rrjds rrrNs 1u E 1a[Eq! EA1uz]1-- a!e0DDD EE QU rc|$t|dz }||dk(r|dz}||dk(r|dk(ry|dz }||||dz k7r|dz}||||dz k7rt|}t|t|D]}|||z |z||<|S)z0One iteration of the Beyer-Hedetniemi algorithm.Nr r)lenr r ) predecessorpqresultis rrr\s y  q !n! FA!n!Av AA a.KNQ. . Q a.KNQ. . + F 1c&k "&1q519%q & Mrct|\}}t|}t|}||k\}|r=||k(r8t|t|kDrd}nt|t|k(r||kDrd}|r|St|}t||}||dkDr7t|\}} t|} t d| dz} | |t|  d|S)zGOne iteration of the Wright, Richmond, Odlyzko and McKay algorithm.Fr r N) _split_treemaxr!rr ) candidateleftrest left_height rest_heightvalidr# new_candidatenew_leftnew_restnew_left_heightsuffixs rrrosY'JD$d)Kd)K ; &E  + t9s4y EY#d) #t E  I))Q7 Q ! y K#(A; /aF1IM /D / 3U1c&k%:;&); ;D $< 0;s B 4 BcPtt|Dcgc]}dgt|z}}g}tt|D]Y}||}|r?|d}||}||k\r |j|d}||}||k\r dx|||<|||<|j|[|Scc}w)z\Create the adjacency matrix for the tree specified by the given layout (level sequence).rr )r r!popappend)rr&r%stacki_levelrj_levels r_layout_to_matrixr?s*/s6{); s rrrs  A E 3v;  ) b AQiGW$ "I )W$ JJq!  Q  Hr)N)__doc____all__ functoolsrnetworkxrA _dispatchablerrrrrrr(r?rrrrKs !"A BT2/3/4##* 4)) 4  &$N.( r