shNSrSS/rSSKJr SSKr\R "SSS9S5r\R "SS 9S 5r\"S5S 5r \"S5S 5r SS jr Sr Sr SrSrg)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## US:a[e[[US-S-55[[SUS-S-55-nUb,[U5nUb[ U5v [ U5nUbM+gg7f)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 {/Users/tiagomarins/Projetos/claudeai/copy_bank/venv/lib/python3.13/site-packages/networkx/generators/nonisomorphic_trees.pyrrsx qy % Q' (4a%!)9I0J+K KF  F#  "6* *&v.F  s A/A53A5)rc0US:a[e[U5$)a1Returns 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 ""cSn[US-5HnU[U5[X- 5-- nM! US-S:XaU[US-5-n[U5US-- $)z4Implements OEIS A000055 (number of unlabeled trees).rr r r _rooted_trees)nvalueks rrrBsh E 1q5\ q!M!%$8881uz qAv&&  eqj ((rcUS:aU$Sn[SU5H>n[SU5H+nX#-S:XdM X[U5-[X- 5-- nM- M@ XS- -$)z;Implements OEIS A000081 (number of unlabeled rooted trees).r rr r)rrjds rrrNsk 1u E 1a[q!Auz]1-- ae0DDD U rcUc%[U5S- nXS:XaUS-nXS:XaMUS:XagUS- nXXS- :waUS-nXXS- :waM[U5n[U[U55HnX4U- U-X4'M U$)z0One iteration of the Beyer-Hedetniemi algorithm.Nr r)lenr r ) predecessorpqresultis rrr\s y  q n! FAn!Av AA .KNQ. . Q .KNQ. . + F 1c&k "q519% # Mrc[U5up[U5n[U5nXC:nU(a?XC:Xa:[U5[U5:aSnO[U5[U5:XaX:aSnU(aU$[U5n[X5nXS:a5[U5up[U5n [ SU S-5n X[U 5*S&U$)zCOne 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'JDd)Kd)K  &E + t9s4y EY#d) # E  I))7 SnSn[[U55HnXS:XdM U(aUn OSnM Uc [U5n[SU5Vs/sH o0US- PM nnS/[U[U55Vs/sHo0UPM sn-nXE4$s snfs snf)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.FNr Tr)r r!)r one_foundmr&r+r,s rr(r(s I A 3v;  9>   y K#(A; /;a1IM;D / 3U1c&k%:;%:)%:; ;D < 0;s B?Bc\[[U55Vs/sHnS/[U5-PM nn/n[[U55H[nXnU(a<USnXnXd:a UR5 USnXnXd:aM S=X!U'X%U'URU5 M] U$s snf)zXCreate the adjacency matrix for the tree specified by the given layout (level sequence).rr )r r!popappend)rr&r%stacki_levelrj_levels r_layout_to_matrixr?s*/s6{); <);AqcCK);F < E 3v; ) b AiG$ "I )$+, +FIaL69Q< Q  M=sB)c [R"5n/n[[U55H^nXnU(a?USnXnXd:a UR 5 USnXnXd:aM UR X55 UR U5 M` U$)zRCreate a NetworkX Graph for the tree specified by the given layout(level sequence)r9)nxGraphr r!r:add_edger;)rGr<r&r=rr>s rrrs  A E 3v; ) b AiG$ "I )$ JJq  Q  Hr)N)__doc____all__ functoolsrnetworkxrA _dispatchablerrrrrrr(r?rrrrKs !"A BT2/3/4##* 4)) 4  &$N.( r