~iQSrSS/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#D# US:a [S5eUS:XagUS:Xa[R"S5v g[[ US-S-55[[ SUS-S-55-nUb,[ U5nUb[ U5v [U5nUbM+gg7f)a|Generate 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/mande/repo/quber/.venv/lib/python3.13/site-packages/networkx/generators/nonisomorphic_trees.pyrrsX qy566 z znnQ % Q' (4a%!)9I0J+K KF  F#  "6* *&v.F  s BB B )rc:US:a [S5e[U5$)aReturns 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 ""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 rrrtsh E 1q5\ q!M!%$8881uz qAv&&  eqj ((rcUS:aU$Sn[SU5H>n[SU5H+nX#-S:XdM X[U5-[X- 5-- nM- M@ XS- -$)z;Implements OEIS A000081 (number of unlabeled rooted trees).r rr r)rrjds rrrsk 1u E 1a[q!Auz]1-- ae0DDD U rcUc%[U5S- nXS:XaUS-nXS:XaMUS:XagUS- nXXS- :waUS-nXXS- :waM[U5n[U[U55HnX4U- U-X4'M U$)z0One iteration of the Beyer-Hedetniemi algorithm.Nr r)lenrr) predecessorpqresultis rrrs 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$rr) candidateleftrest left_height rest_heightvalidr& new_candidatenew_leftnew_restnew_left_heightsuffixs rrrsY'JDd)Kd)K  &E + t9s4y EY#d) # E  I))7 SnSn[[U55HnXS:XdM U(aUn OSnM Uc [U5n[SU5Vs/sH o0US- PM nnS/[U[U55Vs/sHo0UPM sn-nXE4$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)rr$)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$s snf)zXCreate the adjacency matrix for the tree specified by the given layout (level sequence).rr )rr$popappend)rr)r(stacki_levelr!j_levels r_layout_to_matrixrBs*/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)r<)r Graphrr$r=add_edger>)rGr?r)r@r!rAs rrrs  A E 3v; ) b AiG$ "I )$ JJq  Q  Hr)N)__doc____all__ functoolsrnetworkxr _dispatchablerrrrrrr+rBrrrrMs !"A BT2;/3;/| # #F 4)) 4  &$N.( r