PiQdZddgZddlmZddlZejdddZejd d Zedd Z edd Z dd Z dZ dZ dZdZdS)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#zK|dkrtd|dkrdS|dkrtjdVdStt |dzdztt d|dzdzz}|5t |}| t |Vt|}|3dSdS)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 {/home/jaya/work/projects/VOICE-AGENT/VIET/agent-env/lib/python3.11/site-packages/networkx/generators/nonisomorphic_trees.pyrrsX qyy5666 zz zznQ % Q'' ( (4a%!)9I0J0J+K+K KF  F##  "6** * * *&v..F      )rcJ|dkrtdt|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*> qyy5666 E " ""rcd}t|dzD]'}|t|t||z zz }(|dzdkr|t|dzz}t||dzz S)z4Implements OEIS A000055 (number of unlabeled trees).rr r r _rooted_trees)nvalueks rrrts E 1q5\\99 q!!M!a%$8$8881uzz qAv&&&   eqj ((rc|dkr|Sd}td|D]F}td|D]3}||zdkr(||t|zt||z zz }4G||dz zS)z;Implements OEIS A000081 (number of unlabeled rooted trees).r rr r)rrjds rrrs 1uu E 1a[[EEq! E EA1uzz]1--- a!e0D0DDD E QU rc`|/t|dz }||dkr|dz}||dk|dkrdS|dz }||||dz kr|dz}||||dz kt|}t|t|D]}|||z |z||<|S)z0One iteration of the Beyer-Hedetniemi algorithm.Nr r)lenrr) predecessorpqresultis rrrs y   q !n!! FA!n!!Avvt AA a.KNQ. . . Q a.KNQ. . . +  F 1c&kk " "&&1q519%q Mrct|\}}t|}t|}||k}|rQ||krKt|t|krd}n(t|t|kr||krd}|r|St|}t||}||dkrIt|\}} t|} t d| dz} | |t|  d<|S)zGOne iteration of the Wright, Richmond, Odlyzko and McKay algorithm.Fr r N) _split_treemaxr$rr) candidateleftrest left_height rest_heightvalidr& new_candidatenew_leftnew_restnew_left_heightsuffixs rrrsY''JD$d))Kd))K ; &E  ++ t99s4yy EEYY#d)) # #t E  II))Q77 Qz_split_tree..s! / / /aF1IM / / /rrc g|] }| Sr:r:r;s rr=z_split_tree..s;;;&);;;r)rr$)r one_foundmr)r.r/s` rr+r+s I A 3v;;  !! !9>> ! y KK / / / /5A;; / / /D 3;;;;U1c&kk%:%:;;; ;D $<rcfdttD}g}ttD]w}|}|rV|d}|}||kr*||d}|}||k*dx|||<|||<||x|S)z\Create the adjacency matrix for the tree specified by the given layout (level sequence).c6g|]}dgtzS)r)r$r;s rr=z%_layout_to_matrix..s& < < rSs7 !"A BT222;/;/32;/| # # #F 4))) 4   &$$$N.(     r