ܛ7iQdZddgZddlmZddlZej 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#4K|dkr td|dk(ry|dk(rtjdytt |dzdztt d|dzdzz}|)t |}|t |t|}|(yyw)aGenerate nonisomorphic trees of specified `order`. Parameters ---------- order : int order of the desired tree(s) Yields ------ `networkx.Graph` instances A tree with `order` number of nodes that is not isomorphic to any other yielded tree. Raises ------ ValueError If `order` is negative. Examples -------- There are 11 unique (non-isomorphic) trees with 7 nodes. >>> n = 7 >>> nit_list = list(nx.nonisomorphic_trees(n)) >>> len(nit_list) == nx.number_of_nonisomorphic_trees(n) == 11 True All trees yielded by the generator have the specified order. >>> all(len(G) == n for G in nx.nonisomorphic_trees(n)) True Each tree is nonisomorphic to every other tree yielded by the generator. >>> seen = [] >>> for G in nx.nonisomorphic_trees(n): ... assert not any(nx.is_isomorphic(G, H) for H in seen) ... seen.append(G) See Also -------- number_of_nonisomorphic_trees rorder must be non-negativeN) ValueErrornx empty_graphlistrange _next_tree_layout_to_graph_next_rooted_tree)orderlayouts d/home/rose/Desktop/poly/venv/lib/python3.12/site-packages/networkx/generators/nonisomorphic_trees.pyrrsX qy566 z znnQ % Q' (4a%!)9I0J+K KF  F#  "6* *&v.F  s BBB)rc8|dkr tdt|S)aKReturns the number of nonisomorphic trees of the specified `order`. 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 trees with `order` number of nodes. Raises ------ ValueError If `order` is negative. Examples -------- >>> nx.number_of_nonisomorphic_trees(10) 106 See Also -------- nonisomorphic_trees rr )r _unlabeled_trees)rs rrrPs"> qy566 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 rrrtsj E 1q5\ q!M!a%$8881uz qAv&&  eqj ((rc|dkr|Sd}td|D]<}td|D]+}||zdk(s ||t|zt||z zz }->||dz zS)z;Implements OEIS A000081 (number of unlabeled rooted trees).r rr r)rrjds rrrss 1u E 1a[q!A1uz]1-- a!e0DDD QU rc|$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)lenrr) predecessorpqresultis rrrs 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$rr) candidateleftrest left_height rest_heightvalidr& new_candidatenew_leftnew_restnew_left_heightsuffixs rrrsY'JD$d)Kd)K ; &E  + t9s4y EY#d) #t E  I))Q7 Q   y K#(A; /;aF1IM;D / 3U1c&k%:;%:&)%:; ;D $< 0;s B 4 BcPtt|Dcgc]}dgt|z}}g}tt|D]Y}||}|r?|d}||}||k\r |j|d}||}||k\r dx|||<|||<|j|[|Scc}w)z\Create the adjacency matrix for the tree specified by the given layout (level sequence).rr )rr$popappend)rr)r(stacki_levelr!j_levels r_layout_to_matrixrBs*/s6{); <);AqcCK);F < E 3v; ) b AQiGW$ "I )W$+, +F1IaL6!9Q< Q  M=sB#ctj}g}tt|D][}||}|rA|d}||}||k\r |j |d}||}||k\r |j |||j |]|S)zVCreate a NetworkX Graph for the tree specified by the given layout(level sequence)r<)r Graphrr$r=add_edger>)rGr?r)r@r!rAs rrrs  A E 3v; ) b AQiGW$ "I )W$ JJq!  Q  Hr)N)__doc____all__ functoolsrnetworkxr _dispatchablerrrrrrr+rBrrrrMs !"A BT2;/3;/| # #F 4)) 4  &$N.( r