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N"" "  ;"" "&"" "Q"  O"" "   " "l"  P" " Q" " " "l"  R" " S" " """ ""Q" "& T""" """"("(""":":"""H"H"""0"0"0 """"%"*"* """"9"9 """"B"B """" "  """""""""""#"$""""&"5"6"""""$"""*"*"+###(###-#-#-### ##Q# #&#### #GraphMap####y#9# #####CompactDirection#Outgoing# #Incoming# $%#&#'(#Nodes###)#####iVf2State## #mapping##ins#out_size#ins_size#0# generation#_etype## #OpenList#Out# #In# #Other# ###Frame##Outer# #Inner#y# # open_list#Unwind#y# ########Format###sep#######)#Z#*$Z$+$Z$,$Z$-$Z$.$Z$/$Z$0$Z$1$Z$2$Z$3$Z$4$Z$ MatrixGraph$$$$$ $$$y$nb_edges$ $5$$$$$ $ IdStorage$$elements$$6$$ UnionFind$$parent$rank$$$$ Direction$$ $ $ζ$ $  $  $ $ $$$$$Directed$$ Undirected$$77777727376777;7<7A7B7K7K7K7K7O7f7j7k7x7z7{77777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 777777777777777777777777777777777777777777777777777777777777777777777 '77777 '777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777 77777777777777777777777777777777777777777777777777777777777777777777777777777777 777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7!7!7!7!7!7!7!7!7!7!7!7!7!7!7!7!7!7!7!7!7!7!7!7!7!7!7!7!7!7!7!7!7!7!7!7!7!7"7"7"7"7"7"7"7"7"7"7"7"7"7"7"7"7"7"7"7"7"7"7"7"7"7"7"7"7"7#7#7#7#7#7#7#7#7#7#7#7#7#7#7#7#7#7#7#7#7#7#7#7#7#7#7#7#7#7#7#7#7#7#7#7#7#7$7$7$7$7$7$7$7$7$7$7$7$7$7$7$7$7$7$7$7$7$7$7$7$7$7$7$7$7$7$7$7$7$7$7$7$7$7$7$7 0  (~fG _3GI          3=BGlc !)9G000   'wdHkˈS Gʬt&$kG]7P7օPP]\E_PP'&ЂdG9 HkˈS ʬt&$k]7P7օPP]\E_     cK]_ ̟$awf3  ###y#9# fM{5{7    y y 9   1"         y y 9   1"  ̟$awf3     ''  ###y#9# fM{5{7 چ߈     FixedBitSetElength!!!^!  #$' !!!_!  M3   base /ϥY], چچچ߈߈ ߈ %7 %7    /ϥY],  bG   b934CN$   9645X_т 978_fB 99848}  =&͎G   =& 9<ȭ  9>8/lz9?ajɘ   u5ɗGɗɗɗɗɗɗɗɗɗ9CA:,  SjYCGɗ9Efbxcɗɗɗɗɗɗ  ɗ ɗچچچ߈چ߈&;%  &#{ Gڛڛڛڛڛڛچ߈9NN2VQ͎G   P Oj?,֝9POQQf#oB   ٞ(Q G     şx 36GG    y  _' 9X8XXYY$!& 2<   Ϡ   ȧnd< G      d"yN+ {GZG    9  Ϣ a  FOR3'   YG  9  %   }]ˣ G  9  %   }]ˣ!G!!!!%! !&! wZ3P!!!!!%! !&! wZ3P !!!!%! !&! wZ3P !!!!%! !&! wZ3P 9  9  %   }]ˣ      9  Ϣ a  FOR3'9  * g  g  9   xa  !! !OMڡ! G!! !OMڡ!ެ9!! !OMڡ ެ 9  # l  D | G!!!!!!!!!ŧ!!ݧ!!! ו'vdG  o 8 o o o <0S                  Less~Greater0^" "  "  `         `     `      ݡ   h  {-P      h                                                                                                                                                                             a b                                                                                                               I                                                                                                                           __self_0 __self_1                   Finish  !  !         Discover             TreeEdge               BackEdge          CrossForwardEdge             "Ԟ  ۟                                                      c                                           c    Break         H        Continue     H      Prune            Ԟ    ۟                      .C lc !)9 C     c       /   {-P          64    4    74    4   :9  9     ;                  <         1   @;   ;        2   c  A (      c         3   d  B (          E6  6  ; ; ; ; ;  ; ; < < <  < < <  < <  < <   < < <   <  <  8  <  <   <  <  <  <  98 <  <   < < = = =C =  Kd  =C  <  >      2       >       3     DZZ A*Z(internal error: entered unreachable code((DZ  > >  1> >  > > >  > > >    > >  > > : > > F: ; < <  < <  : : : : ; ; < <  < < < <  < <  <  {-P <   <  < < =C =  =          DZ>  8: starts: visitor: time; < <   <  < x : Q@? S@? @ @  @ @   @ @ @  1dG@ @' A A  O A A*  A3  A3 A  ͎          3=B A3  S        2N     S    E       3 N     5A A   NA  A  A  8 N A  A  A  A  A  A  9M A  A   A A A B A B  MB  F 5NA   A "B  B   B!  B! B MB!  ! #!  #"L   " !D  %!   %$L    $4  !MC 'C: C  K͎'&MC: ! (&! *(! ! *)K!   )! (D!  ,(!  ! ,+K!    +! $DZ$Z$*Z(internal error: entered unreachable code((-K$DZ!  (MD 0D 1D D 01/#MD D . / D .+$D 5D 4 5D! 3 4D! D 32%MD! & 62& 86& & 87&J&   7('& 6D&  :6&  & :9)J&    9*3&  6ME >E = >E) < =E) E <;,ME) ( ?;( A?( ( A@-I(   @/.( ?D(  C?(  ( CB0I(    B12(  ?M(  ?M&  6M  !M   6  S  F F D7F *?YE*?Y ?YE:8F GD+?YF G ?YF:9+?Y+?Yassertion failed: first_finishH+?YG G L;G F( K LF1 J KF1 F JI<F1 . MI. OM. . ON=H.   N?>. MG.  QM.  . QP@H.    PBA2, 2, 9G5 3Pruning on the `DfsEvent::Finish` is not supported!33RH2,.  MCG G GG  F EN  SFP  S  GH .  MO(  ?M&  6M!  (M  !M F N   O>    FK >   A A  ! & ( F . T? > > ͎> > ? ?  @ @ A3 A3 A* A        ɜ   A A  A  A   A  A A  A A  A B B! B! B B    ɜ   ɜ  C: C !   ɜ!   ɜ!  $DZ D D D D D! D! D D &   ɜ&   ɜ&  E) E) E E (   ɜ(   ɜ(  F  ?Y ?YF +?YF1 F1 F( G .   ɜ.   ɜ.  2,  8> u> > > ? ?    A vA  !! (& 6( ? first_finishF D. M> 3  444040bW`(666Global 7C\ w3  3   3  3  3  3   3  3 3 3 3 3 3 3 3  3  3  3  3 3 4 4 Dfs4  4  stack4  4  4  4   discovered 4  4   4   4 4  H4 4 4 Ԟ4 4 ۟4 4 4  4  Ũ4  4  4  4  4  4 4 4     4      U     z _ z     z    h     j      c  N           8    ٞ     eb      b %  %        5  f    %  %       8          Y    h     ޴ 8          5  jg           g      5                      8                  9ۼ            !  !          "   "     ظ            k      {-P          ۼ  ۼ ۼ     ۼ      " ! !      8 Q    succ  5 5 5 ߦ5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 Ũ5 5 5 5 5 5 5  6 6  DfsPostOrder 6 6 stack6 6 6 6  discovered 6 6  6 6 finished6 6  6  6 6  H  6 6 6 Ԟ6 6 ۟6 6 6 6 Ũ6 6 6 6 6 6 6 6 6 6 6      ĭ   ĭ      p      " "  v" " " "  z" # # # ! t! "O ! ! ! 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K K I K K< N N N N N N N NY N N M M M M N ޴N N 8M M P" P P" P P Q Q Q Q Q Q Q  Q Q O O O O P" ޴P" P Q Q Q Q O 8O O U U U V غV U  U U V V  V V ̾ V  V V) V  W  V V ٻ  V W W W W  W  W ռ   W  W   W   W  W  W   W  W   W  W X  X1 Y   u5Y  Z Xk Y Y    Xk Y  :چY$ Y  Xk  Y Y Z ظZ Z Z  Z Z Z Z Y  Z T Y  T V  W W T T T U U U U  V V V V V W ۼ W ۼW W ۼ W  W  W  W W  Xk ܈Xk چX1 X Y Y Y Y Z T T nixU  W neighW T Y Y Y Y Y Y ̾Y Y Y Y  Y Y Y Y Y Y Y T Y  _ref__self_E k` ^ PP'&Ђ^ ^ ^ ^ ^ ^ 9` 9` 9`  9` 9a 9a 9a  9a 9` 9` 9` 9` 9` 9` 9` 9` 9` 9a 9a 9` 9` :` :`  WalkerIter :` :` walker:` :` :a :a context:a :a  :a  :` :` :` :` :` Ԟ:` :` ۟:` :` :` :` :` :a :a Ϣ:a Ϣ:a :` :` :` b b b b b a? a a Ϣb a a? b b b: b b b b: c c bF  c b b bF d+ d d d d d+ d  d d dd  {-Pd ̩d d+ d Ϣd d dd f f f  f f ee  {-Pf  e e e e e ee h h  kh h g\ g g g g g g\ i i  {i j i\ i i i i i i\ k k  k k j\ k k k k k j\ m m  m m l\ m l l l l l\      [  95cz#    n [      X   `     X  )             ' '  ' ' &t      9  UI}& & & & & &t )% )  )% * ( ) ( ) ) ( ) ) ( ,+ ,  ,+ - + , , , , , , , + / /  / / .| " LJu/ շ/ / / / / / .|  ) 4     4        ) <     <          ) >     >     A A  A A @] """l "  sz~@ @ @ @] B B  B B B? 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U    ɗ    (        @@ OO 9+ ?9  SjY d {-P ͘  {-P  d    ReversedEdgeReferenceԞ۟ --88 @ @ @ @ A  ˭A   8  8 N Efbxcɗˠ+d ڙ  d) ) g    g  )   ) ) g    h   )    ) ) h    h   )    ) >     > ɗ   ) S     S ɗ   ) ) j    j  )   ) )       {-P     &  ) )       {-P     &  ) ) )         )   &  ) ) )     ɿ  )   &  ) )       )  &  ) )       )  &  ) )      {-P      &  ) )      {-P     &  ) )      {-P  ɗ   )  &  ) )      {-P   )  &       $    {-P          &    i&i  i {-P &i y {-P    &y y {-P   &y  i&i  i&i y چ  &y y  &y f   &f !  {-P  &!!  !!        & ## ##"f" " "" &""f$$ $$! $#$# ###$# ##&##&&  &&$% % %%%% %%&%$'' '('f'  ߈' '' &''f ) ) ) )))) އ) )) ) ***** *?Y ?Y ?Y *  * * >  * ?Y   ?Y ?Y?Yassertion failed: r.is_none()  ?Y* *  * * **(* * * ()o {-P)( ((( )) {-P)* ?Y ?Y*  * ?Y**( ((&(l)(,,,,, ,*+ + +++,+ ++&+*-!- -!.-f---y-9--f/!/ /!//fچ///y/9//f1!1 1!10f߈111y1910f3 34 ;5 ;5 ;4 5  5 5   5 34 4 4 4 3 33   33 333 ڛ3 ڛ334 4 4 5 5 4 5 5 34 4 5 __self_25 33 3 4  ;5  ;5  ;3 3Edge4  4 source4  5 5 target5  5 5 weight5  5 33 334 33Node4 4 weight4 4 33 H33 333Ԟ3 3۟334 34 4 4 4 5 5 34 4 5 5 5 5  5 334 4  5  Ё 5  33  3  3 3 3 3 3 3  3  3  3  33  3  3 3 3  3  3  4  4  4  4  4 4   4 4   4   ;5 ! 5 !;5 " 5 ";4 # 4 #;5 $ 5 $;5 % 5 %;4  4 4 5  5 5 5 5 5  5 5 5 5  5 5 5 5 5  5  5 5 3 3  3 3 3 3 3 3 &3  3  3 3 3 3 3  3 3 3 3 4 4 4 5 5 4 5 5 5 4 4 4 5 5 5 5  3  3  3  3  3  3  3  3  3  3  3  3 3  __self_tag3  __arg1_tag3 4  __arg1_04  4  5 Ё 5 ˘ 4 __arg1_15 __arg1_25 3 3 33333 3337777777777 777778 8 48 888 8 8 8 8 8 8 8 8 8 8  8 8 &;%  &#{ 8 8    8 ;9 ;: ;::: ;:-:: :  444040bW`( : 8   9999   999 5 9: :: :   : : ;;;:-: :*;;;;;;;;;; ;;6;;;;;;9677 888b9 667 7 88 8 {-PΟ 8 8 8Ο 88 89  9999:::-:-:  :   ::  :  :;;;; iterable6gr77 8element8 &8 %9 :&:6< <<<< <== ==== == = = = = = = = = = =  = = &;%  &#{ = =    = @ ? ;? ;??? ;??? ??  %7 %7 ?>  >>>  >@@@ @@  @@@@@@@@@  @@@@@@ @@;@@@@ > ;<= ==>P>?@W!<;< = == = {-P° = = =° =>>>>????  ? ??@ @ @@ {-P@@@@@@@  ; <=  =ث = &> %? ?&??to@;== = === === ===C!C C!CAB A AAE!E چ E!FDچD D DDH!H ߈H!HG߈G G GGOO O 4O ONy OOOOMMNN2VQMMMO444040bW`(O OMMM"TTTTˠTT TU&;%  &#{ UU͎U U  TU  W ;W;W; Wu      XV  V    VU  UU ͎&;%  &#{     UY YZZ Z ZZZ ZZ  Z Z ZZZ 5!Z ZZ[Z[ZZ@[[  [\ \ \;\;`! ``  ! `` a"``  W"``# `$#a$a  %$a  %$a  %b) bb )(bb'(b*bb  '*&bb+ &b$+c,&c  -,c  -,c  -cd.d   .dddd TZ TTUUV<VX Y$\ab/ {-P T T  T TTU UUU U UV  VWW WXY ZZZZ  ZZZ [[\ \ \   'w`  ` `  `aaa a  b b b bbbc c  d T eltT UkeepU&V %W  W&Wis_nodeX%\ \a $c ,T Dominators root dominators  :QF     Ԟ ֝۟          ֝    1 1          r       #  ?              Q   #  #    #  v  | POQQf#oB       {-P    # #  v Q  # #   #  b h        # # b Q {-P ?   )    P Oj?,) 5 gN  POQQf#oB      )   +++::std::usize::MAXH#x##w## # 444040bW`(x:QF    /ϥY] 5G?Y ?Y ?Y     ?Y   ?Y ?Y?Yassertion failed: length > 0 G?Y?Y?Y ?Y   G VG       {-P  G ?Y  ?Y ?Y?Y2assertion failed: post_order.last() == Some(&root)22G?Y! !!   G!!!! V G!!/!  9NNIterNMNMN_markerMjg(+G! !X! 9 Enumerate))məA3  ۃ  G!!k! :-/8X  :QFG! # $# #  $#A# # "##%#x##&#T# "%&!A#T$( !  5$ ('@ ! w $)$ *)$$ *)$E$ ,'$.$ /.$$ /.$E$ -/$$  ,-+E$$#+*$0$$ $10 $12%0%%6% 76%% 76%E% 57%4 %5%% ; J;((m43E% % % 8Rev0Nпd] 32E % %82 %  %:8 % % 9 :9E % %; 9 %;%<9?Y=?Y ?Y=$  %& B&&  B<A!E&&@A&C&& @C?"E&?Y> ? ?Y>$#?Y?Y)assertion failed: post_order[idx] != root))DE?Y(L!(( 444040bW`( L<K%E((7JK(7(7 JI&E(7(7HI(7( VHG'E() N') M    N(u( 9NN NMNMNǁ Mjg(+  GMF(E(() QF) ) 9»͂)`L ,!.  QP)E)) R)Because the root is initialized to dominate itself, and is the first node in every path, there must exist a predecessor to this node that also has a dominator) ) >PRO*E)+  SF+  TO,~ V',~ U   V+ + : Θ  STUE+E+?Y W?Y ?Y W.,-  ZE- [- YZ[?Y X Y ?Y X.-?Y ?Y'assertion failed: new_idom_idx < length''\E?Y-  ^E-  a'- -  a<`/E-- _`- ]^_ - ]0.  bE.  d'. .܉ d<c1E.. cb. 0.- ?Ye?Y ?Ye83/m'// ml4E//kl// kj5E//.ij/./ :   i h6E///g h?Yf g ?Yf87?Y?YAassertion failed: !dominators.iter().any(|&dom| dom == UNDEFINED)AAnE?Y0o0 w0 0 t'0#0  8 ts9E0 0<0  911IntoIter101phantom01cap0101010+qg Asr:E0 07v07u    v00 9 ))məA3ڡ    ruq;E0<01 :-/8Xƣ  :QFqp<E1 /  op1w11!=A1>G1x11?11!A1G1C1'@1w@D1B1xBF  "# $  % %'() y   P Oj?,    #  ?Y ?Y ?Y ?Y ?Y            ?Y  !X !/ ! ! ! ! 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ZKcur_scc[ R [SQ Q v`vv_vv^vv]vv\vv[vvZvvYvv`vvvv  Nvv_vw w w 5444040bW`(Lww ww   Lw w0w Lw0w^wxx  Jxx xx  Jx  !  5  J !x_xx x x 8444040bW`( < x x x  x x x 911 101 01 0101010+qg A  ; x x  x x]xx xy yHy  x y<xy Hyy]yy y y 8 H y y yH y y y 911 101 01 0101010+qg A: y y  y yyy! y y":y yHyy  !" :yy  yHy]y x z`zz&zz &%<zz\zz#%444040bW`(!!!&! ;ԅG5oz[zz$%444040bW`("";"&" "Q rژR~/7{ \{{ *#{ {  8 *)E{ { {  911 101 01 0101010+qg A )(E{  {  { 8 ))məA3 ('E { { +' zl  { -+ {  { 9 -,8 { { . , { .  z /, z Zzz 0,  {  4{ 7 {  {   7/6!C{  { +$E{  56{ {   y y 9   1"453"C{{* 23{  Z{ {  80{* {ظ281#C{{ Z{ zl { [{{ :$ {  { 8 :9%E { { ;9 { & { =; {  { 911 101 01 0101010+qg Aһ =<'7 { { > < { >)( { Y{{ ?<һ | B |  E?|  | ED*A| ~ ;5E| |DC+A|| | BCA,A|| @A|H | K?| | KJ-A|||JI.A||| HIG/A||FG | 30}M@}NF}} MNL1A} }L42}2P}Q@}RF} Y} } S?}2}  PQRSOOA}(~/U~V@~WF~ Y~ ~ X?~/~ UVWXTPA~%~ Y>?~  ^~ ~  ~[~~\~~ 6J~^~~_~~ ~ ;E { +E~\7~ ?7~ Y7@{ 08{ Z8B~$9~[9D~#<y;y];G~L~^LI~N~_NK~=~`=M}24~/4u vvx xxx yHy8z zl {; { { | |a vuu а vv v w  а w ww x xxx xа x x {-P x   x x xx  xy  y y y {-P y   y yHyy y  yy  z z zz { { { { {  {-P {   { zlz z {*{*{ { {  {   {{  { { {  {-Pһ {   { {һ { |  | |||  һ | | | |||  |  } } }}2 }2}}} ~/ ~/~~~ ~{~~y~~~u make_acyclicu v condensedv Yx   xcompxnew_nixx yښyyz #9z $ { +ښz /Qz 0 { ;{ ?%|@ |Fu   '  &  %   ' &   9   ؆.؆   (~f ؆.%&                     tχ χ ԇ   ԇ   χχ݇  ݇       c  t  iʈ!! ߈ º  '  " %  #  $ "#$׉%&'މ#މ"މ  %&'tÆ (٠  `E2H dž        t  t cχχχ  χ        ʈ {-Pº߈º    :QFX 9Ydž  ێ      º  9º    ُ<           ُ<   .      ِT ԐZ °  ºБ   Б   Б     ˔ ˔    ڔ       " "!  !ו&$ %&& $%&# &#, - ,-+ / 0 /0. :* +.:2 * @2,,Edge references unknown node5,:1 * @1 3* 4*  ) 34ٖ8)ٖ'89)(976 '(7 ° 6   °   ӎ ǏҕӖݗ(:  ٠ ׎ º  {-P     ُ<  ُ<     ° ِT     {-P  ˔ڔו      & &ٖ :      ޗ ,°   ׎ Qscoreڔa_indexוb_indexa_orderٖ'b_order(a_id3b_id4     Cycle Ԟݓ ۟    ݓ  ݓ     ŜќPݓ P  ܝܝܝܝ ܝ       ܝܝ   O    !  5 !ҰҰ  MҰ   M  !  5 M !          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M!M L  MLOOO  O  OP P DirectedObP P  Undirected P ObPPGraphPP  HPQ Q QTyQ Q  QQ E  QQ2Q Q  node_count QQQ Q QQQ2QQ'Q2Q Q  edge_count RRR   R RRQ2Q Q'RRR   R RR R R R!RedgesS;) S;S;  )( S;S;'(S;S Vһ '&SSS 9NN NMNMNǁ Mjg(+һ  AV    ٹ&%S;T*T, ST -/8X%*$T S#$S"#RR !"RUU   +U U+U-U.U node weights U33U32    ))məA3-/8XNN NMNMNǁ Mjg(+      3U=1  ο2U>01U>/0UU-./,UVV   4V V4V6W7W edge weights W3<W3;    ))məA3-/8X  ο<W=:  ο;W>9:W>89VV6785VX=XX E=XX O OP>ԞO O۟OO OOP EE DebugStructEEE EE has_fieldsED˄PP QQQQQQ2Q2Q QQQQQ2Q2Q RRRR RRRRRRS ###߻#6:ۦ*USSSS;  һ S;S;S;TUUUUU>  uQKl,U>U=U3пU3VVVWW>  uQKl,W>W=W3пW3XOOetypeO fmt_structPO S S SSSSS S SSTTS( S2  T S6ٹS S6 S S(SS SS SS6UпUU UU  UUUU V UU$V 9׾VU0V  9V V U3 U U3U$׾U  UUͬUпU3U3OпU3V V V V V VVV WпWW WWWWWW޸WW$W 9WW0W  9W W W3 W W3W$WWWWпW3W3OпW3W W W W W  WWW  Y YY Z Z Y YZ    Y Z ZZ Z Z Z Z  Z  Z  Z   Z [[ V[[[*˩[* [* [*[*[* [*[*[* \\*˩\* \* \*\*\* \*\*\* \\*\   Z [* \\ \ Y[[\]   {      {    ٛA@nY   YYY YY Z  Z  ZZZ ZZ[ [$[\\$\˩\*\*\*\*\*\*˩[*[*[*[*[*[*slcYYYar[ br\Y_ _ 4!!!&! ;ԅG5o_ _ _ 4"";"&" "Q rژR~/7_ _l  ִ<ɏ`_^ ^  y y 9   1"_444040bW`(_ 444040bW`(_ ^b bb b bb bl  ִ<ɏccb b  y y 9   1"bb b bee 4 eee 4һ ee  ffd dddd e eyd9ddg gg 5 gg gBggͬgggBh hh 5һ hh hBhhhhhBiiii iCiiiiClllmm mmmmm$ l\l\l\ !m  mm mm m m nn nnF nFnFnn  nnO   nO  n n n nn nn& nF nonn  nnF nFnOnOXassertion failed: ::max().index() == !0 || NodeIndex::end() != node_idxXXnOo ooooo 5 o oooomloo llml l l llm$mmmmͬm nOnFn&n n nnn nn onOoo ool &lQlnode_idxmlp ppppq qqpq V qp,q ? qq pvp pp {-Ppppͬpq pppvq q q qq qqq r rr  rrs ssrs V sr4s ?    ss rrr r {-Pr rˈrrs r rrs s ssssss#xAxx@xxAxx xx"xx x "x xx "xxF xFxFyy"yxO   xO x   x y "yy yx&  xF yyyy  "yxF xFxOxOXassertion failed: ::max().index() == !0 || EdgeIndex::end() != edge_idxXX"xOyAyyz zz zzyg@ygyg "z zzȅ  zzz z zz { {z2z    z2z2 z8}+{},{}.}} /} } 0./} 0/. z2,,{-+Graph::add_edge: node indices out of bounds++  ,{!{|"!|"|#|$|| %| | &$%| &%$ |!$#|'|(|| )| | *()| *)( |!('|} -+.~2~} 3} } 423} 432 } 1,2}$ -1~5~6~~ 7~ ~ 867~ 876 ~+65~9~:~~ ;~ ~ <:;~ <;: ~,:9~~> @?~ 5һ >?=  @z"w"@"A! wxy{}Bx w wxxxxx xOxFx&x x xyy yyyxOһ yyzzz   {      {    ٛA@nz2ˈzˈzzz z { ,{|||| | ||| | }}} }} } } ~} } ~~~ ~ ~~~ ~ ~ϯ~һ  w wx&xedge_idxxyan{!}+bn},wzzz zzz2     ˃Ѓ  Ѓ  Ń      ߄   ӄӄӄ Ą   Ą߄ ߄  H  ̂ނ˃Ńӄ߄ ̂&ނedŃ     Vһ . ?  رȆ Ѕx  {-P  Ѕx  ر ܮ     Vһ 6 ? һ   ш Ň܇  {-P ޸ϯ ܇ Ňʈ ܮ& &&&& &X ?   $̊  {-P&߲&&&&      Ŋ    ܮ8           lݐ Uݐ    ݐ  ݐ  8U  ݐ    ɐ  {-P3  ݐ    Ԑ  ݐ   ݐ  ݐ  9NN NMNMNǁ Mjg(+   ݐ  ݐ   ݐ  ؐ     !& • ĕ'ĕ          ?Y ?Y ?Y    #   >#"5 ?Y ! " ?Y !?Y ?Yassertion failed: ret.is_some()$5?Y !  4 &'% ,  ,+4 *+  -4 *-)4 . ) .ח 0)ޗ (0Ř 3 Ř И32 4И  /% /3  21!4 ϙ Tϙ   ϙ  ϙ T4"4 ϙ  ϙ 54 ř# ϙ 75 ϙ  ϙ 76$4 ϙ  ϙ 8 6 ϙ 8&%ʙV6ʙ9V 9:'4 S% S3> ʵ>=(4<=Ś@: A  B@A BA@)4 ?(@3 <?9;743D;  DC+4  E C E,#FC?YG?Y ?YG1-K:LMKLMLK.4JFK N1 JNI/4?YH I ?YH10?Y?Y.assertion failed: curedge.node[k] == old_index..O4?YP:ԛQԛԛRPQԛRQP24ԛFPٚ*%66 3*   ɐ ɐ Ԑzړ  җ   řۙyW  l c uty ͬ  ɐ ݐ  ݐ  {-P ݐ   ݐ  Ԑؐ ͬ    ?Y ?Y  ?Y !•   ͬ  ח   ŘͬŘ ϙ  ϙ  ϙ  ϙ  řʙ   9   sb ޸޸ϯ Ś     ?Y ?Y   ?Yԛԛ ϙ ݐ  ϙ   ɐ   ݐ  ؐk Q % swap_edges  (ܮח 0 old_index 1 new_index  ϙ 5ʙ9:9 ;curedgeF ސ  Й  Й Й  ϙ ϙ  ϙ Й ϙ ސ ސ  ݐ ݐ   ݐ ސ ݐ #ž Mž   ž  ž M ž  ž   ž  ž  ž  ž  ž   ž  "N N    ž ( ((ȅ((       (  ( . ?Y?Y ?Y" ̟ (  )  *() *)(?Y  ?Y"ɠ/Lɠ/ ɠ/L! ޠޠ G! ޠ$  %  &$% &%$ #$ G#"*, ˚ "*,*,*,*,ۛ*,A,, AA, '(,'-,-+ +ţ/  0  1/0 10/ ./2  3  423 4322.8 ʵ87679': )69:5)Ӥ<5Ӥ٤ <;٤ ä = ;ä =Ȥ>;A BCABCBA@>AD@D? ?ɥF  G  HFG HGF  EFI JKIJKJI!>IE   Ξܞǟ O ȝ   ž  ž  ž  ž  (ˈ(ˈ((   ǟ̟ ?Y ?YA,ڨ*,ɠ/*,*,*,˚ޠ˚        ţ     ޸޸ϯӤӤä Ȥ  ɥ  ɠ/ž  ž    edge_nodeȝ  edge_next  ž   Ql̟fst'9 5Ȥ> Þ  ɠ/ ɠ/Edge's endpoint dir=ɠ/ index=ɠ/ not found ɠ/ɠ/ ܞɠ/ɠ/ɠ/Þ Þ  ž ž   ž Þ ž  2 2 ϫ  ϫϫ ϫϫޫ  ϫګ ګϫ ɫ         /­ ­*ϫ "      ɫu߲ϫϫϫϫޫ  /    !  !  4һ ԰  ԰԰  ԰԰    ԰߰  ߰԰ ΰ ޱ    ԰      Ћ   γ ٳ /  *    ðٱ ® ͮһ ϯ! ǰ߲԰԰԰԰   ޱ /γ ٳ ® ͮswapǰܮޱ swapped_e ȸ $$ ׸ r     9  UI}ȸr                  # "                        $         ͬ  $   j  9 9     =j                   $        ͬ  $+&  Ȍ 9   +SO?+  >  v v      1 ?               *   %   8  {-Pͬ Q                                             ߲            Qedix     ,  '  : "ͬ Q  %      %                  & &                                   "  #  $"# $#" !" !   '"           ߲              Q                   9׾ t     ܆      H$ ))məA3׾׾ͬ   Y "ִ<ɏ  """l "  sz~  ȅ V  D  y =P NNNMNMNǁ M-bD ˈˈ     Y " """l "  ڨ@H  ޸  9 K  * *V`C ))məA3 ʵ Vһ  D  9 jcI4 NNNMNMNǁ M-bDһ ޸޸ϯ ΀  ΀ ΀ ΀ ΀ ߀ E΀ ͬ΀ E      ҁ E  E      n $    n̈́ ̈́̈́̈́̈́܄ ބބ̈́؄؄̈́ DŽ  ą ȅ ȅ̈́              ˆ Ɔ    ̈́̈́̈́ͬ̈́܄ ą  ˆQ   Έ ЈЈʈʈ             ׉ ߉߉ ߉߉׉׉ ׉ ׉  ԉ    ԉ  ܇߲Έ    ׉׉߉߉Q  ܇ BBB    Ô K  K  (B        B BKKTassertion failed: T::is_node_index() != U::is_node_index() || i.index() != j.index()TTK˩  ! " !#"#  3ј˩ј ј јјј јјј 3ٗ ј3   33  Ô 3 ߓ$ Ô Y Ô KB(  Ô    K ϝ3ϝ3Ô33ј˩јјјјјј˩ ª self_mutߓ ؚ  ؚ ؚ 8ϯ ؚ ؚ ̚k ؚ ؚ ؚ 9 ؚ ؚ  ؚК     V    ؚ̛  ̛ ̛ 8 ̛    V    ̛ I  ̛ ̛ ̛ 9  ̛ ̛  ̛ ěͦ    ̚kO Iܛ-͙™  ؚϯؚ ؚ ؚ  ؚ ̚kКˤ   ̛̛ ̛ ̛  ̛ Iě۫™  ؚК ̛Qěڜ ڜ 5   5һ  WМŜ ڜڜϯŜ W ֝ ֝ܮ      e   ާ        ݞ  0     e  eI ̝ ֝ϯ֝     e  Q ן ן 4    4һ  ֟.  g ןͬןg  4 ֢ b    additional b  4һ  bդ  ϯդ  b$ $  4 ͨ ߧn  $$  ߧnͫ$ ͫ$ث  4һ ث në  ͫ$ϯͫ$  n   4  ӬQ  ӬQ   4һ Ю Q ϯ Q ʯ ʯ   o ϯ o³  ³ѳ ;ѳ   8 0Nпd]        9              cK]_            ?Y?Y ?Y ״ ״ ۴ > ۴ ?Y  ?Y?Y?Yassertion failed: ret.is_some()?Y  ׳{Ȳ Ӳ           ?Y ?Y״ ״ ?YȲ Ӳ   ڸڸ߸  ߸ڸ ; ڸ ڸ 8 0Nпd] ڸ ڸ ͸ ڸ  ڸ ڸ 9  ڸ ڸ  ڸ Ѹ         ڸ     ¹   ¹?Y?Y ?Y     ?Y  ?Y?Y?Yassertion failed: ret.is_some()?Yη η ͸{   ڸڸڸڸ ڸ ڸ  ڸ ͸Ѹ   ?Y ?Y  ?Y   ڸѸ η   ] ־  ־!('&%  8  (  9 8  Ժ (    8            9        8     '&%'   &            " "! %$%$# %&' (&'  %(    )    ϯ   {-P         %   low   % &%        : ߅ :444040bW`(!!!&! ;ԅG5o     ͬ  x x      9    } 8-/8X  444040bW`("";"&" "Q rژR~/7           9   8-/8X        y y 9   1"  Á ͬ xx  Y edge_map   ) )  )  l !  xl  x )͆)  xYQx_ref__node_map  Ћ ) )  )     "       ))   _ref__edge_map:ECD,E 8 8  !  8 !     +   8 +          9 +        +    + ) )Æ +)C 2C +  +"2   8+    !   9! +  "  " # $  '  $)+E(8)(+%% '(&+%%%&,  $.+.-+%% ,-++%%*+ 1%  3 +8 /88  5*  7"+ 8 /$ 23  120!+8 0 67  564#+8 /48  9 Ћ#;%+  <$) : ;<) 9:8&+) D = 8 ='6 D >8 @ A% B*  @AB>?9+E)-*8-. C C/1/+F F0/ D  D35 83+ G 8 G43,E,7 6   C G HÁ  Á  ͬ   {-P     {-P)͆)  Á      {-P      %   %   8     {-P))  Y  node_index_map  Qnw #$%%  *ew >     l  φִ<ɏ   y y 9   1"     ))məA3NN NMNMNǁ Mjg(+!!!&! ;ԅG5o 9            w ww w           w ;;;w w; $$$;;      ܆      H$  {-P  w    ;$  Q 2$.  "";"&" "Q rژR~/7     !!!_!  M3 $ V.$ *             $              !!!^!  #$' $/       $/            ! "  #!" #"!!& '  (&' ('& %&) %)$ $ + ,  -+, -,+ *+ *  u0 {-P      9  UI}  {-P$           $                        zp  "T g ]  ]T _    ='( GE #  Եެ ˁ   9   sbԵެ  9ˁ   ?     ݃\ {-P    9   sb  {-P  ݃\ t  Յ%  Յ% VՅ% υ+ ن φ  φ φ   φ   Յ% φ   Æ     pՄ)DŽ  Յ% φ نφ φ DŽ DŽ  this_index     L  9 9     =߈ ňˈňˈL  {ÊɊڊÊɊڊ{ٍٍٍٍٍٍ2,ޔޔޔ ޔ   ۔ ĕ ĕӕ ӕ   '   ۔”  {-PД  $   > V,, V , , ĖĖ      ǖ ǖWW ! !  X XY YZ Z   ! "  #!" #"!!&   &% )U  )U( (*  *''ߗ$ "%'ڗ """ "Q "& +$+ ./ $  ./- ,-ŚTŚ,,,T+, ,+*$[3 4  534 543 2321$[10!6 0!6* \0 7\]0 8]^0 9^ܛ;ܛқ <қ қ =;<қ =<;қ :;?@A?@A@?>9?B C  DBC DCBB>G >GF" 4E44!JKLJKLKJ# 4E%4F I7JMIMH$4EH4!QSQSP& P('R7 RO)O7)N ":O8 N+۠ + _ {-P  ” Д۔ ޔĕĕ ,    Ė  ߲!    ߗ   ,   ߲$   !ݕś ܛқ қ    4   Ś      $ $ $   iterate_over” ДQ&Q7&89wś : $ Ś $ŚŚ ŚŚŚƘ $ Ƙ $   9                    ߥ ڥ    n            ߥ Ħ Ħ Ħ Ʀ V˦ΦƦ ֦٦ئDDĦ Ħ  Ħ D22 è   ҧ ȧè ȧȧNNNMNMNǁ M-bD!!!&! ;ԅG5o 9. ?   ūf {-P۫ y =Pͫ  {-P ͫ ūfQ  9 T Ȭ  T߯NNNMNMNǁ M-bD߯ 9߯. ? ڷfï 9 jcI4 ߯ ߯ fڷѰѰܰ  9ܰ T  ̸ ѰT   !]ͬ  ]     %mӵ    m  Ƹ ̸̸  !]  Ƹ ]     %ĺmѺ ܺϯ  Ѻ ܺĺmؼؼؼ>ɼ>@@Ŀ/ڿĿ/@@002 _   !444040bW`("";"&" "Q rژR~/7!! !!            ! V! '        !                     !!!!!  !! $ %  &$% &%$  #$#"!" '  '(* +  ,*+ ,+* )*. /  0./ 0/. -(.1 2  312 3211-6 7  867 876 5(69 594 4 < =  ><= >=< ;(<: ); : ? {-P&     y y 9   1" {-P!  !! !             !!!!                    ܮ(ܮ)   ?   {-P     ?   {-P    ִ<ɏ   ""    NodeIndices r ty    " Ԟ۟      ?  V       V   P P   9  " `    `  ""ھ ھ  EdgeIndices r ty    " Ԟ۟     ?  V ھ      V   P P   " `    `"2  EdgeReference indexnode     weight          "Ԟ """ "Q "& +۟         --   444   444e        e444040bW`(!!!&! ;ԅG5o ߖ V  9NN NMNMNǁ Mjg(+ K 5 >/s f ))məA3ݘݘ   ߖ ))məA3NN NMNMNǁ Mjg(+ 9Y ?  ͝؝. {-P؝ 5 >/s f  {-P͝  ѝ      )؝)͝ ѝ  Q)  9 S   S""  9 ^ ?͝؝.Ğ ӟ"" ѝ     )؝)͝ ѝ  Q) 9 """ "Q "& +ެ9     =   =     =   = 22 7 7 ))məA3NN NMNMNǁ Mjg(+ 9 ? Ͳٲ {-P * *V`C  {-PͲ        z "zٲͲ      9 S   S  9  ?Ͳ ̴      z "zͲ      <  cK]_ <, ؿ, C  C       S   ؿ      S      w   cK]_      ª     ؿ ) )    "   )   &     ) )    " ɿ  )   &  ) )   "     &  ) )   "     &     ) ) ԏ   "   )       ) )    " ֑  ΅   )            cK]_  ) Z    " Z   ޴       ) 4    " 4    ޴        ) <    " <     ޴         )    " ۼ    ޴        ) $   " چ$     ޴         ) > Ձ  " ɂ>   ޴       ) S    " S   ޴      ) ) j   " j  )       ) ) g   " g  )       ) ) g   # h   )        ) ) h   # h   )           ) ) }   # }  )           ) ) ~   #    )            Directedb   Undirected  b   StableGraph    Ty     0   node_count 0%0   edge_count 0%  y y 9   1"444040bW`("";"&" "Q rژR~/7   V // :NN NMNMNǁ Mjg(+    /     edges R) R R)( R R'( R!'&! ! 9  &%! ! 9»͂)`L ,!.ٹ ٹ%$!;"*",  " -/8X$*#"  "# !"   ! ## ż+# #+#-#.# node weights $3$2  ǻǻʻ*˻*Au ))məA3-/8XNN NMNMNǁ Mjg(+!!!&! ;ԅG5o    {-P 3$1 ӂ2$01$/0##-./,#&& 4& &4&6'7' edge weights '<';  ǻǻʻ*˻*Au ))məA3-/8X   {-Pӂ<': ӂ;'9:'89&&6785&).>) ?)  free_node *A*@A).)>?@=)#*.C* D*  free_edge *F*EF*.*CDEB*#*G**G**  HԞ ۟   00 00  / /        ###߻#6:ۦ*U ӏ    R R R R"####$  uQKl,$ˑ$$Ղ$&&&''  uQKl,'''Ղ').).) * **.*.* ***        !!!!! !!! ! !!!!!" " """"" " """""( "2  "!6ٹ" !6! "("" "" !!6$EՂ$E $E 444040bW`($E$E $E$E$E$ V$$y% 9%$%  9% $%  9‚݁݁%-&$ $ $$$y$E  $E$E $EՂ$$Ղ$%%% >%%%% %́%%%%%%&   ‚%% ?‚%&%!%% ݁%!%%%&%wo%%!&& &&‚&&&& &%&'EՂ'E 'E 'E'E'E'E'E(('y( 9ʆʆ('(  9( ')  9օ؇)-)' ' 'օ''y'E'E'E'EՂ''Ղ'((( >(((( ʆ((((()))  ؇)) ?؇)))!)) )!)))Ҭ))))!)) ))؇)Ҭ))) )))-- ----->̟$awf3-->/"/ /"00 0000/ 0011//چ////"00y/9//222 2 21J 11 211J233333 33!3333!444 44222 334 42 2 445555!555 556 6 6 8  6 6 6 6  6 6 9NNNMNMNǁ M-bD  6 6  6 6  6  66  6  67 6  66 666 660  6j4 6644 55 5 66 6 {-P 6  6 66 66664  6Q6 4888A8888A999A9999A:::;:C::::C=#==#==>> >>="=" =" =">>  >? ?>>   >># ? ?#???  ?,?   ?, ?Y ?Y ?Y ? ???  ?Y  ?Y  ?Y ?Y assertion failed: _old.is_none()  ?Y@@@@@@ @ @@   @ @/@@ @@@@@@@@$ @A AA#AA!A  !AA  AA"AA"AA"AAA =AA#A==>>?$= = == =" = >>>> >> >? ?? ? ?Y ?Y?? ?Y@@@@@@@@@AA A AA= &==> node_slot>  _old? =CC CCCC C CC CCC CC#D DD   D D DDDD D D*  DDDBBCBB  B CCCC CC CCDDDDDDB B CC B'I II  II I I III V  I I  I   I  I   I  I lI.I.I ?I I  I  I" I  I/ I/   I/ I/  I/ I/lI/ J 4J  J  J 4 $ J  I/ I" I/ J  I  J   J   J $ J  J    J  I J  J  J&$JM -M M.$MK  K  K$KK K $KK K KK K $K K !K K#$KK "#K K!" $K K   L %L L  %$$L ?Y& ?Y ?Y&L )$L L)(#L  ?Y' ( ?Y' ?Y ?Yassertion failed: ret.is_some()*# ?YM $$MM-.,$MM+,O0OO 0/$O OO1 $OO@+ /1OP2PP2P!$P2P 3P 3P"PM $$P%HJ  HI I II I  I II/I/ IJ J K Lz MM5I H II l c uty I/I.I.l c uty I I IIII  II  II/ J  J  J  J  II J J K ́KܟK K KKK KKKKL L ?Y ?YL L  ?YM MM M OOO PP J  H I:I  I I  I I/ J  I J K L$M +HJ  J J  J J IJ J J PQ Q PPQ >́Q QP`PPP  {-ṔPPPPP`R5R5R5ҜR5R5R RRR5R VRR{R ?́́ ˁR8SQRQQR5R5R5ܟR5R QQQSSSڠSS    ́ˁS'S ?́ˁSSR.SR.́RSSS QRR.ŚSS ́SS SQŔS QOWzWWyWWzWWyWW X XX LXX  X"X"  LX" X" Y Y Y YYYLYYY LYY# Y* ZZzZZZ  Y'Y  LY' ?Y ?Y ?Y ZZZDZ  ?Y  ?Y  ?Y ?Y assertion failed: _old.is_none() D ?YZZZ Z Z Z  DZ Z[ [L[![[ 5!  L[["[Ћ L["[-\\'L\\F#\F\F\\+L\ \O" # \O"\ &'\ \&%L\\( \\&$%(\F$\*+\,\\*,)L\\F#)\F \O \OXassertion failed: ::max().index() == !0 || EdgeIndex::end() != edge_idxXX-L \O]z]]1] 0 1]2 ]]4C]]34\/ "032\. /\\y\\.^8^^ >87L^\y\\.\L^^ > 76L^^56^!5X_=__=<L__;<_ _>L__ _? L_^4^  ;>?:!L^4^4@ :^:@"($#bQ:{bR:{cTQccTS/Lc ^4_ _B%L__ _C&L___BCA'L__$9 A_;`D:{`FD``FE)L`  `E,*` `G+L``9 G`;aHDaHaIaJaa Ka a LJKa LKJ-LaDJIbMbNba Oa a PNOa PON.LaDNMb9 `; cS20c dU1Ldc9 Uc;dWRddWV3Ld  dV64d dX5Ldd9 Xd;eZee [e e \Z[e \[Z7Le YQZe^ee _e e `^_e `_^8Le ]R^e$ Y]eaebee ce e dbce dcb9LeQbafeffff gf f hfgf hgf:LfRfef9 d;gi 9giL *, A, ,lkL A,hshhsh@Lhsh  t h  tABi yii ui wi i 5wuvNLi ii{ i{HG^0L[LizFMViyiiiyGIiGEiyEKiEi| i|JEiFi B VWWXY^ `bgi0}W V WWWW {-PW X X"XXXYY#YY YYY ZZ Z ?Y ?YZZ ?YZ ZZ Z ["[[ \O\F\&\ \ \\\\\\ \O\\] ]]]]^^ {-P^ ^ ^    {      {    ٛA@n^4____ _ _ __ _ ` ``` aaaa a bba a bb ccc  ddd e ee e e ee e eee e fff f gg A,ڨ *,gA *, *, *,˚ g h hh i iigAiiiiV WW&WҥWnew_edgeW XY wrong_index^ 9`DbQbRgji uVgA gA"StableGraph::add_edge: node index ""gA is not a node in the graphgAgAggAgAgA]]]]]]2jjkkkkj"jЋj" ?Y ?Y?Yk kk kk  kk  k ?Y ?Y ?Y ?Y.assertion failed: edge_idx != EdgeIndex::end()..  ?Yk ll  llll  llk|k|k| "l lll l l l  l mmmmmm mm m mmml jm  m jjkjj  j jkk?Y?Ykkkk ?Ykklllll ll l mmmmmj j ҥjk jllllll2llllll2qh qhqh qhqh qhqqq   qq qqq qq qq qq چ  qq q qq  q qrrq qq  q r rr rr   rrpq q  rr  rpqAq p ppqqqqqqqrqrp pp&qqpv vv vv v v vvv V vv v! w w www vv w w w$ vv v w w w x1x1x  x*y z z zyy yyzzz zz. zz zzz zz0 {{{{{{{{{ ?{{tvw/yu t tvv v v {-Pvvvvv vwwwwwwx1x1yyy z zzzz {{t tis_edgevv v w yt}}}Ҝ}}} }}}}}} }!} }}} ́}  }}ڠ }~|} | ||}}}ܟ}} }́}}||} |  %     > Ԁ     ׂ&ׂ& ׂ` :y =P>/q ,' ׂ&ׂ&  ? " "  maybe_node "   ܄܄  ܄F 6gd ))məA3܄†††††ӆ ՆՆ†φφ† ! †      ††††ӆ ܮ    V %    ˉ > ˉ Ȉ ӈ  Ȉ ӈܮ && ` :9 jcI4>/q ,'ڋ̋ &&̋ ˌ֌ ?֌ "ˌ "  maybe_edge "   !      ʎ ʎ   ݎ Ҙ    ܎ ׎    CӍ& ܎ݎ   ܮ ܮ _otherwise ѐ֐  ֐ ǐǐ  ǐF bp ))məA3ǐѐ ݾ ĒvْѿْĒv     1 ? ؖݖݖ ؖ Җ ́, ,   %ؖ  : ؖ́,Q      ޛ́.. ' Ț<"́.QȚ $$ ¡Рr 95cz#Рr      ި ڨ ڨ ڨ ڨ ڨ Ш ШШ  Ш  Ш# "  ֧ڧڨި ڨШШڧ      ïȯȯ ï  ́ ï  $    հ Ǯ   ḯ Գ $ ³ ³j99 -tԳj         κ ́Ժ ٺ  $    ɺ Ը   ́κκ   #  9 z ܆ .M cſ#BBB     K K (B       B B K KTassertion failed: T::is_node_index() != U::is_node_index() || i.index() != j.index()TT K˩  چ! " !#"#  3˩  چ  3 3  چ 33  چÔ 3$ چÔ چY ÔKB(     K چ33Ô33˩˩ ª                     2 22   چ     cK]_چ 2 2  2 2           2                  Ā     : ::   چ   :  >  :  : :          :        ]چ چ  .   .                ̟$awf3    y y 9   1"..Y   ڠ     " ? . .   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G!   *, ˚ *, *, *, *,ۛ *, A, , A, ?Y$ ?Y?Y$ ?Y% ̖?Y%Ӗ!Ӗ!֧Ӗ!( //. -.  -,  *,+ ˚, *,*+ *,)* *, *,ۛ()' *, A, ,'& A, GY0 GYGY0  3  Y23ŗ 8ŗ 7867ٗ 9&:69&:69 &5:  Y45 Y1 24  Y;1  Y<1  Y?;  Y@<  Y>?@  Y= > Y=   !YA   YC ڨ  ]Y  Y AA;<CB  ]YDE!ǘ GEԘԘI"ԘԘHIǘǘGHF#ǘǘF9$#M##ML%##KL OEON&#KNJ'P JP(3QJSQƙSR)ƙ R-*U V  WUV WVU+ TQUETXDXD,DX! ?YY ?Y?YY3. ?YZ ?YZ3/..֧.] ddc0 bc ̛ ̛ba1 ̛ *,` ˚a *,_` *,^_ *, *,ۛ]^\2 *, A, ,\[ A, ?Ye ?Y?Ye!4 ?Yf ?Yf!5!!֧!iޜ pEޜpo6 ޜno ל ל nm7 ל *,l ˚m *,kl *,jk *, *,ۛijh8 *, A, ,hg A, GYq GYGYq?:  t;  Yst ܆y< xywx zD&{wz&{wz= &v{  Yuv Yr su  Y|r  Y}r  Y |  Y }  Y   Y ~  Y ~?>  !Y    Y  ڨ  ]Y   Y|}  ]Y֝ ؑ     Y  Y  Y  Y  Ғ Ғ  ߒߒ###ܟ# ́ȓȓ    ?Y?Y A,ڨ *,. *, *, *,˚   ?Y?Y A,ڨ *,Ӗ! *, *, *,˚   GY Y Y  Y&ٗ  &  Y  Y Y  Y  Y  Y  Y  ]Y  Y ǘǘ ԘԘ####     ?Y?Y A,ڨ *,. *, *, *,˚ ̛  ?Y?Y A,ڨ *,! *, *, *,˚ ל ޜޜޜ GY Y Y  Y&  &  Y  Y Y  Y  Y  Y  Y   ]Y  Y֧Ӗ!֧.֧!֧.   free_node_len  Y;а  Y<  YA free_edge_lenD EQ  Y |а  Y }  Y ؑ Ӗ! Ӗ!Corrupt free list: missing Ӗ!Ӗ! ֧Ӗ!اӖ!Ӗ!. .(Corrupt free list: pointing to existing ((..֧.ا..! !Corrupt free list: missing !!֧!ا!!. .(Corrupt free list: pointing to existing ((..֧.ا..ȟȟϟ ϟ چȟȟΡá  áߡ  Ģ   ۢ   ΡĢ      ϥ >ϥ ݥ\ \$ >$̧l٧ $٧ ̧l   > \ªɪ ªɪ\ƭ˭˭ƭ$ >ƭ$l ƭ$ƭ l¯>چ>  Ҽ  kIJ 9   IJW    ų 9  һ ųq    9-/8X      9-/8X  ƵƵƵƵ̵ : ̵  :                 چ          ƵƵy9 ̲N !ȲR̲ ȲR ɲɲȲR ͳh "ɳlͳ ɳlһ ʳʳɳlB  G  F  I  D  H  E  H  I  A üüɼ Aɼ <A<ռGռ =ɽ ɽϽ  =Ͻ   !    =  ! I      . 8 ))məA311 101 01 0101010+qg A .   9 -  Dʗ 3.D- ϾϾϾ -ϾϾ)h3 H     8.      911 101 01 0101010+qg A,     E տ # տ ڿҘ#";ڿ*.տ"!; &  &%;%$; '  ') E F (  +  ,!  +,*8 )* /  0$  /0.8 -. ?Y 1 ?Y?Y 1" 4)  68 56  453 8 ?Y 2 3?Y 2"! ?Y  ?Y,assertion failed: source != NodeIndex::end(),,78 ?Y ?Y 8 ?Y?Y 8'# ;-  =$8 <=  ;<:%8 ?Y 9 :?Y 9'& ?Y  ?Y,assertion failed: target != NodeIndex::end(),,>8 ?Y% @ A) B- F C(% @ABC?(8 F )K K54G+=G..=˻D D020-J J10EE46 4, (; F;7E,: ,L L9,AGA<H/?/>I>@ ˻J¿   Mچӻ üü ɽɽ  {-Pʗ  Ͼ Ͼ      ƿ տ տ             ?Y?Y   ?Y?Y?Y   ?Y%%8ӻ Q  gƿ ! target_index  $ı (% )  -˻       !!!&! ;ԅG5o I 5>!i ))məA3NN NMNMNǁ Mjg(+e ))məA3NN NMNMNǁ Mjg(+!!!&! ;ԅG5o e  ѽ  ̾Ğ؝NĞ 5>!i  ѽe   >  ؝5 ?؝ A5Ğ A  {-P  QA    ؝  ѽ  9ѽ   r:     ѽhirfѽf  ѽ؝OĞ f   5 ?؝ A5Ğ A QA    ؝  #2   EdgeReference   index    node         weight                # Ԟ  ####Q#&e$ ۟                   --  444  444e        e 9 ####Q#&e$ެ9     =   =     =   = 22 7 7  L99 -t L {{23         '      $   ^,,^ ,,        __ l l l`l `l  aabbcc ! ! " #  $"# $#""'  Ā'& *]*]))+  +((% #&( ī%2 /0 $  /0. -.\,,-\,,,,1$d4 5  645 654 3432$d21!7 1!71e18ef19fg1:g ?Y; ?Y?Y; 9=  ?Y< =?Y<  ?Y ?Y"assertion failed: weight.is_some()""> ?Y@ A  B@A BA@! ?@DEFDEFED"C:DG H  IGH IHG#GCLLK' 4J44&OPQOPQPO(4J*4K$%N8ORNRM)4JM4&V[V[U+U-,W8 WT.T8.9Z/ZY0XYS #?TX īS2 ī2 h   ,       lݕ  ī ,   $   !ݕ?Y?Y ?Y     4  ī  $$$   Q&Q8&9:w ? $  $  $  $     DD  ު D22  y y 9   1"  {-P444040bW`("";"&" "Q rژR~/7  V  9NN NMNMNǁ Mjg(+ M *8eew$R ))məA3    ))məA3NN NMNMNǁ Mjg(+"";"&" "Q rژR~/7     {-P *8eew$R      ?       | #  &      ?       | #  & ))məA3NN NMNMNǁ Mjg(+!!!&! ;ԅG5o  9  ޷   >      σσσ Q QQ       Q       Q  Q ΃;΃;΃; ΃;$$$΃;΃;ĄĄĄ    ܆ .M c  {-P޷ Q    ΃;σ$ Ą Q2׋ r  ͊V}Ki  95cz#ۊr׋ ۊ͊$8       $ V8$ * ˎ  ?Y  ?Y?Y  $     ?Y  ?Y   ?Y ?Y'assertion failed: edge.weight.is_some()'' ?Y            ߏߏՏ Տ Տ Տ  Տ  Џ $9     $9    ! ?Y" ?Y?Y"%!Ȓ%$Ȓ  ?Y# $?Y# ?Y ?Y'assertion failed: edge.weight.is_some()''& ?Y( )  *() *)( '!(+ ,  -+, -,++'0 1  201 210 /!03/3.. ԓ5ԓʓ 6ʓ ʓ 756ʓ 765ʓ 4!5œ 4 Ǝ:   {-P$   ˎ?Y?Y ?Y     Տ ߏՏ Տ $    ?Y?Y ?Y        ʓ ԓʓ ʓ    ˎ !      zp  # T g  ]   ] T¢Ң  y y 9   1" ¢͢  ͢ ݢ& ֡  ̟$awf3¢ Ң֡    ? ̣     ?  Ҥ  Ҥѽ  ѽ ͧ 6gdէ է ͧ     ۨ v v   Qѽ    r: ԩ ʩ  ʩrѽū  ѽū  ԫ׫      vЬ vҫޫޫ ҫӫ ԫ׫ ԫQ׫ҫήӮ  Ӯήή  9 ή< ? j ή ήήj       ί ѯѯޯIIR R    {-P ɲ ߲ bpѲ Ѳ ɲ ܳ ܳ ܳ ׳ v v    ܳ Q  9   r: д  ƴ   ƴr        жӶ     v̷ vζڶ ڶ  ζ϶ жӶ жQӶζ .IndexMap hash_builder>uaSK 9444040bW`( . .   .   >uaSK 9           #    # ߈   .  .         G VԞ ۟ V  #               #                            ߈4߈4    #߈  y9       . g   g      a        a     !!!! C!   C'' 8߈ 8 ''&߈& & &&( ((  (((B(( (((B) )) )))B)) )))B* **  ** ** **)W** *  **  ** )W+ ++  ++ + 4 + +)+   +++*j++ +  +)    u&^9 +ĭ + + + +*j--- ---   -- - . ...... .. 8  .---000.  ..  .. 911 101 01 0101010+qg A  .. . .  /// $.,/  /'0 /0 00//  ///0/   /%00000000 ,00,-...-- - - {-P -ĭ --- . . . . {-P .  ....,////0 /0 //000- -links-sus.. .,1 111   110U111 11110U8/#8/8/"8/8/#8/8/ 99 88  89#99 8/8  8$9"98 8 8"88 9 8:$ ::$: ::^:     :(::: #: :: 5  :%;;;; ;; ;( <;(<  <;f<     <(;< =! #<  !;< <%= 8="===8= =" ==#; 89$8 8 8888/ 8/899988: : :^ :$ĭ :$: :::;;;; ; ;f ;(ĭ ;(< <<===8 88&8old8 8:: 4 :::: : ::<< <<<< < <<? ??  ? ? >? ?? ??????  @#@#@#  @#@# @#@ V  @@v  @/@/@/    @v@ :NN NMNMNǁ Mjg(+      @9@v @| BBBA AA  4  ABBBC C C  C C C C CC&CC  C&C :   CC& C,EEECDD   DDDDE>?AC!>> >>> {-P ?ĭ ?? ?? @v  @v @#  @# @#  @# @/@/@/A A A C& C& C  C  C  C  CCC C D> >>> ?AC>@@ @  @ A A @@  @@! @"@"@)@)   @)A@/ @  @/ @  @ @" @" @!@@A@/@/@/ @>>@/_ref__b _ref__dirCCCC C  C CCC  C CCCC C>C JJJ $J)J J$J J JJ   JJ K K K $J)K  K$KJoK( LLKK KKK(K K ?Y ?Y?YLLLL. L.L.L. LLLL L  ?Y ?Y LL.L.  ?Y ?Y@assertion failed: exist1 == exist2 && exist1 == weight.is_some()@@ ?YLLLIIJJK J I IIJJJJJJJJKKKK K( KKLL?Y?YL.LLLLLLL ?YI IIexist1Jexist2J&KIN. NN NNN.N  N#NMnMMMM N. NNMMMMnO OO  OOO ;Keys>=`,ӛ OO? #POo###ށOO'[oN{ c O O OOOoS SSS  SS SS  S   S   S S  SSS S S   S S  S S  SR TRS   `RRR Sx {-P S SSS  S S  S  S  S RRSRS S S R S  SS Y YYY YY YY Y  Y   Y Z  ZYY  Y Y   Y Y  Y Y  YZ X  ZXY" LJuXXXX Yx Y YYY  Y Y  Y  Y Z Y XXXY XY Y Y X Y  YY ^^  ^^  ^k ^]99^9a;.]]] ^ ^ ]]]`% `` ```%` ```i` ``` `% ``````ib) bb bbb)b bbaybb bb b) bbb bbayd dd ddS ed ;FJ*|Ddd >  kd dddg gg g gZ gf S|)ff >J*ړg gf f!m)mm*mm*mmmm m nnn  n m:mm:n  n n  8 n n  nHn   n n  9 >  k  n n  n   n(  n (nnn  nn o *o o  o o  8  o o n o o o  9 >b o o  o  no՜!o )o o ՜!o ooo  o po o > ooo! p"op!!" p o pǞ! pop8$pp %ppp &pp )p p 'p8p$%&'#p5p)pn pp pplqpp)p*p p nlmnHn*nooo+l߈lmmmnn˘!n  n ˘!n  {-P˙!n  ˘!n nHnnn֛!o  o ֛!o  {-P՜!o  ֛!o nnoo o͞!o  {-P͞!o ooo͞!o !o opp8p8ppp n pp l mn  Qn o no:o aiobiol s sss s s ssss s stttttt tt tt 8߈ t tt tttrtt rssytP ߈r rss ss߈ttttt rsstrwwwwww w wwwww w wx xx x xxx xx xx  xx  xx xx x x xx  xxy xxxxxyyyy%y y y yyxyyyy vyyyyvwwxxxuwv  vww wwx xxxx {-Pxxxxxxxxy%yyy v  vwwx  x%x x&xv }'[oN{ c >=`,ӛ444040bW`( } } 9½! } }# |Y } ###ށ |  ½! } |  |Y ~½! ~ ~  9½! ~  ~# }c } ſ! } ½! ~ } }cłNN NMNMNǁ Mjg(+־!łf  9 !  ־! !Dł~ł~ 9ǻǻʻ*˻*Au!!! 9!! ?! !!     `  !ł~!łf!ł {-P!!   , ,8,  !8!  8 $, ! ! ч! !  9!!! 9ǻǻʻ*˻*Au!! !! ! ?!! !ӊΆ    " LJuֆ ć  !!!!!!ֆ self_dirć Ά ň̈ňň!ňň"ň"ň"؈ ݈  ؈؈   ؈ň"ň"ň" ň"   ˆ ˆ   !! ň"ň ň̈؈؈݈ !ć !Š ! !  ˍˍՍ 9Սˍ ō ʎ5   >uaSK 9ڎ$ڎ  ڎ$ˍ  َ% ʎ5Վ Վ*ʎ5 Ď; Ǐ Տ   Џ    DZ Z *Z(internal error: entered unreachable code((  DZ  {-P 99^9a;.  ˍ ˍ {-Pʎ5 َ%ڎ$ DZǏՏ !  Ǐ    Q ;FJ*|DշQ >  k 9! ӕ !!ӕ ֕ !!֕ ڕ!    ؔ˕% ! !  {-P! !ӕ֕ڕ !! ӕ֕ϣڕؔ!ʖ  9!ʖ ۖT  ! !T ! 9!:!! :ݗ!ݗ 9!ݗW ?! !!+!! !ݗ!ݗ !! &!&!!!n1n2&& ! 9!W ?!!!+˙!ј!Ș!! Ș!! ę&!&!!!!!&&#!#  9! \ ?!!!+њ!!ޚ !#!#ޚ њ›!›ƛ!ƛ˛ԛ &ԛԛ!&!›ƛ˛!!!›!ƛ&˛&Ξ>J*ړΞ 9ɀ"ΞW ?! ́" ȁ"ԁ""+ {-Pԁ"  S|)  {-Pȁ"Ξ ɀ"Ξ !!́" &ԁ""&ȁ"́"!!!!&&ɀ"  9ɀ" T ȟ " ɀ"T ɀ" 9ɀ"Š:"ɀ" :ɀ" 9ɀ"W ?ȁ"ԁ"""+ˠǂ""Ҡ ݠ""Ҡ ݠˠ!!ġ́"͡ ݡ&͡ԁ"͡"&ȁ"́"ġ!!!!&ġ& ɀ" 9ɀ"WĢ ?ȁ"ԁ"""Ģ+ǂ"""ɀ" ̢!̢Т!Тբ́"ޢ Ȣ&ޢԁ"ޢ"Ȣ&ȁ"ɢ̢Т́"բ!ɢ!ɢ!̢!Т&բȢ&#ɀ"#Τ  9ɀ"Τ \ ?ȁ"ԁ"""+ǂ"" "#"# !!́" &ԁ""&ȁ"́"!!!!&&  L!զ շL    "   ҩ ҩGraphMap::index: no such edgeW˩ > ˩'W بƨW"ҩƨ    &  !ʬ ʬGraphMap::index: no such edge[ì > ì'[٫ ȫ ݫ[&ʬ ݫB߈B- G{ "-Dzϲ= "= ʳP"г"׳ "г׳г׳ʳP "  ʴc"ٴ"ٴʴc   "T2 Ҷ"""" " ",",Ϲ Ϲ ӹ I" ӹp:"ܖ""Ϲ stpܺ ܺ  GRԞƺ "۟R  >uaSK 9! !{ ִ<ɏ# <շ >  k! "  ƾB޾ԾԾƾB" 9"! ? ! ""Z  "  {-P" " Z " " ""z "5 nwuշ"۷""Ź"& ?" """_ {-P" ؾ" "߻" _ """  ?? ! !Ǟ!zB͞!!! z     ! >˙!~D ˙!!! !key~  #ެ  444040bW`(                      ִ<ɏ        ι  Vf2State     #   Ԟ   ۟ ι   "   "                " "   "     #ެ"    out   ins   out_size    ins_size     adjacency_matrix       generation      _etype    mapping    # " "                    ެ     4     4        ެ                3 "  3     y y 9   1"  ެ   #ެ   "                      $"   ެ     $  5                              " "     3                  $ " $      c0  " 5%W""W "  ެ  "     ެ  8     9  UI} ެ     9"       "  " Λ     "܉ z $$   ެ"$$"$$$$$"$$ $  !$  "!%Λ $%#"#"'  "!(܉ '(&&)))*  "  "  """ {-P "      "$"$"$"$"$           $! " " " " - " "    "      "  " Λ    "܉ z $$""$$"$$$ $$" $$! $! "&  ""'Λ &'%$%#$#)  ""*܉ )*((+++," " ""  """""      "$"$"$"$"$         $"        ** C  9  u ެ  ј " : ))məA3 ެ## { ?ј ެ ј #   "  {-Pј  ##C * *   #u+ @@@@ "  "           "     "44 4@@u` #u ј  4  Ğ# "   Ğ#"u"+  u+#ј     "      "      #    *  *     C! ߔ#!  !u ެ## ! :#ެ## !{ " ?ј ެ##""  "   # ˜# # C * *   #!u+ !!!!!!@!@!@!@! "!  "!  !  !  "!  ! ! #  ! !  !!"!!!4!4#!4!@!@!u!`! #!u#! !!!!!4Ğ#! Ğ#! "! !!  !Ğ#!!"!u"+ ! !!u+"""""#"ј " ""#  "#  ## "  ##.#.# V##G$  9NN NMNMNǁ Mjg(+$ ##$ : ))məA3#ެ  Ğ##$*#$ ?б#ެ б##$$#  # "##  {-Pб## ####G##.  #.##"# # #+# #$Ğ#$$"$$$$#$$$$$$ #$$ б#$ Ğ#$Ğ#$$ $$$$$$$$#$б#$ $$)) ) )H)H)H))  ) )H )) ) )")H))   ) )" )H)H))+))    )** #  *)& ########0#и#A \c  * ***F*    *F*W*  > * *+ ++ * '')((()H)")))"))л#)л#)л#* {-P*F #* **#**g0(g1(") '// / /H/H/H//   / /H // / /"/H//   / /"   /H /H//100 #  000 # 00& л# 0 000<0   0<0M1 #1 11 11111 0 11--0.---#./H/"///"//#0л#0л#0#0<#00 #0#-#- node_match- edge_match."0 -2232*22*3333;3#3 333 3;4444)44)5  5 5 ͎5 54A54 45#5 4 454A5888 88  8  888  8 88  8,8"8 9 9999 9N N N  # (7 (7# P P P  # (7 (7##S% S% S% S%S%S%  # )7 )7##  # "  #####y##Ѻ#y#^`A "  # "  "  " "!  #y " #  !ɧǁ EO+7##CC8f# #  ˩      #             /y  $y  y 5#$# -yy  % #y  % +y &##y ' &y  '  L& M& OQQP L   ####OPN-z (&Ѻz )&Ѻz  +z -z -z , (z z   ####+,* -z{  /{ 1{ 1{ 3{{ 4{{ 534{ 543-{ 2(3{# 0 2){# {   # (7 (7# #/0.-{#{# 6 .{) 6| 7.| ;|| <|| =;<| =<;-| :(;| 9 7:| 8 #9)} ?} } 5#?8>0-}~ A~ C~ C~ B ~ ~  # (7 (7# {-P#AB@-~~ D @~ D E@# F@# G@#I EFtH #IG K €#KHJ1-€N& SUUT L   ####STR-˂X˂ȂYȂȂZXYȂZYX-ȂWXȂ΂ #WV-΂ ȂV  Ɋ,^_`^_`_^-D[DDghighihg!-D[%#]^bcdbcdcb -ab \]aD\fgklmklmlk"-jk efjD[eDۄwn #LMp#pno$-r s ##rsq2- uwwv L #uvt3- yʇ{ʇ{ه}هӇ~ӇӇ}~Ӈ~}'-Ӈ|L}#z |M# #yzx(-## x))x*-L ˈ #M  #4-Ċ Ɋ,ʊɊ.5T   #" "!  l* #     )#  }  & 5T8Q8Q9Q=MGBN<P:R7x "y z { | ~   ҄È#7 #6666 #7 8 л#8888#8 8 9#=#H #N N#N#P P#P#RS%#S% S%#S%#S%444040bW`(#x # " " " "  l*# "#y  {-P#y  #y y #y zSz z z #z #z #z {# #{ #{#${{{{{{| #| |||||} $} #~ #~#~$~~   # $    # #$ # #$Ȃ#Ȃ˂ȂȂD  #ք$$# $ #$ #ǂ$ ##$ʇӇهӇӇ#Lj $ ##z#{#~###ʇ# "˩            "6#6#6#6 #7 8 graph_indices8  9 next_candidate=# next_from_ixH # pop_stateN  push_stateP  is_feasibleRx  framey &yz (olz )| 7|8EmxF$GHyL$Mf0քnLj5T6666662 ; ;# ; ;  ; ; ; ;   ;   ;  ;# ;  ;  ;  ; $ ; $ ;  ;  ;  ;  ;  ;  ;  ; <<<#<<<2===#===2  ;  ; < Ѻ =Ѻ <  <  ʗ$  <  ; ; # ;  < ʗ$ < <  < $ <  < <  < ; # ;  = =ՙ$  = ; #   ;  ;# ; ; ;  ;  ; ; ʗ$ < $ <ʗ$ <  <؛$ < $ =ʗ$ <  = ; <  < <  = ; ;   ;   ;  ;  ;  ;  ;  ;   ; $ ;   ;   ; ;  ;  ;  ; $ ;   ;  ; $ ;   ;    < $ <  ʗ$ <$ <  < $ <  ʗ$ <$ < <  <  ʗ$ʗ$  <  < < < < <   < <  < < < $ < Ѻʗ$ =$ =Ѻ <  $ <  Ѻʗ$ =!$ =!Ѻ <  < ߡ$ <  = = = = =$ = =  = = ;  ; # ;  ;  ;  ;  ; " ; $ ; $ ;  ;  ;  ;  ; $$ ;  ;  ;  ; ؛$ < $ <؛$ < $ < <  <؛$ < $ =؛$ < $ = <  =$ ; $ ; $ ; $ ; $ ; $ ; $ ; $ ; $ ; $ ; $ ;   ;  ;  ;  ;  <   < ˘ <   < <  =˘ <  = ;  ;  ; <  Ѻʗ$ =Ѻ ; ;Unwind <  < nodes <   = = open_list  = = ; ; ; ; ; ;Outer ; ; ; < ʗ$ < ; ;Inner <  < nodes <   <  < open_list  <  <   ; ;   ; <# ; ; ;Ԟ ;$ ;۟ ; ; ;؛$ < $ < ; <  <  < < $ <؛$ < $ = ; <  <  = =̳$ = ; ; <  < <   = ;(> ?  #??? ??  ?  ??? ???"? ?@  @ ? @@@@@@@@@$@ @@$ @  #@?AAA > A A*A*A* AAA$ A A* A* A*A* AAAAAAAAA  BAA!BBB B BB!BB"BB#!"B#"!B !BB $ BBB#C $ #B$BD'DD$'&D D*%D*D*D)DD$)(D D*%!D*&D*%(D*D,DD-DD.,-D.-,D+,DD +D*DD#*D0DD 0/D D/!E3EE4EE534E543E23EE$2E1 EE%1E6 #E6D!F 8F9F7 89F; 7 F;#"G #G'F: 7 F:$"F<7 F=7 FF<?%FGG=@&GG AF1> ?@AF7 #>G'G= > > > FMB#=0$= #= >  >>  ?#????? ? @#@@@@@ A*A AA A A#AAAAB B B#BBBBC D*D DD D D#DDDDD D E#EEEEE F F  FFFFF#F1FGG "=*> +>> F<σF== ======2J JJJJJJJJ  J KKKKKK J J JJ JJ J J  JJJ$   JKKKKKKKKKK $  KKKKK$  KL L   #  JL ? #$   LL L  M ?Y ?Y?YL LM!M  ! ?Y  ?Y ?Y ?Yassertion failed: ix >= start" ?YMM#MM #MNHIJMp$ Iǂ$H#HHH JJ  J J JJ #JJJJJ#KKKKK#KKKKK$L L LM?Y?YM M ?YM"HHH  Jcand0JMHHHHHHH2LLL L L LL L$L LL L L L JL  _ref__start OOOOOO OOOYOOO OO O O O OO O OPO!  OOO O O OOO O O#O O!O    ONOYO:O$N#NN O O O O OOYOO! л#O!OOOOOOON#NN"NyN$8 8#Oª O N_ref__graph_indicesު NNNNNN2OOOOOO2 QQQQQQ QQQhQQQ QQ Q Q Q QQ Q QRQ0  RRR R R RR RR RR R R R  R RRR R R#R Q0Q    Q*PQhQIQ$P#PP Q Q Q Q QQhQQ0$Q0QQRRRR R RR R RRP#PP"PyP$8 8#Qª Q P$ު PPPPPP2QQQQQQ2Y YYZZZZZZ ZZZZ ZZ  ZZ Z Z ZZZ Z Z_A__ B_ _ CAB_ CBA%Z#Z ZZZ Z Z ZZ    ZZZ 8  ZZ Z ZZZ 9 ZZ ZZZ Z Z  Z  Z ZZ ZZ [[[ [ [ [ [[  [[\#\\$ #\$# \ "  \&\\&%\\\ "%!\\![\(\ \(\ \'(\ )\ \ *')\ *)'\ '[],] ]],+]]+ ^/^ ^/^ ^./^0^^1.0^10.^H#^H.^4^ ^4^ ^34^ 5^ ^ 635^ 653 ^23^9^ ^9^ !^89^ :^ ^ ;8:^ ;:8"^ 78^<^H^  27<-#^?^>-^ = >^ = $___ @A_E__ F_ _ GEF_ GFE&_ DE_?@D_?('__`I``J``KIJ`KJI)`#`I`` H*` `HK+`L ````aN,a`` NM-``OM` .` QO` ` QP/`` R P` R10` SPa Vaa WSVa WVS2ffe e e e Ha+ #a+ Sa Yaa ZSYa ZYS3a XSa [ $a+ aX[U4a&a+ a+$UT5a+a+ \Ta 6a+ ^\a+ a+%^]7a+a+ _ ]a+ _.8a `]a  aa a  bSaa  baS9a cLSba cLSb:a LScb gbb hSgb hgS;b  fS b c`i<cb b fie=bb dec kdc  c ckj>cc j?6d ndSd ndS@d mnd odd pmod pomAdH #dH md sdSd sdSBd rsd  td d  urtd  utrCd qrd vdd ydSd ydSDd xyd  zd d  {xzd  {zxEd  wxdH d %qvwlFd?e}le | }e |6Geee Lfff f f f If Le~e~KJffg g  Og g@g@g@Ng/#g/ggggggPg@XWg@LMg#gggggggQggg RggggggggSg#gggggggTggg%Uggg/g Vg$g0 g@g@Nggh h  #Yh h Ziii[iii \iii]iii ^ii i`_iiiiiaqqqqqqi#iiiiibiii $cii!i!i dijjjjjej#jjj fj j jg]jj%kkkkhkkkk ikknjkkkkkk  kkklkkk mkkkqlllloll l l l pl kqll llrllsdmmmmtmmmmmum)#m)mmmmvmm m m m wm mm)m xm m) m/yz DZ Z *Z(internal error: entered unreachable code(( DZnn/#n/nnnn{n#nn n  |n n nnnn}nnnnn~n#nnn%nnn/n #n$n0 n0dooq#qqq q qqqqqqq qqqqqq qq qqqqqqq+#q+rrrrrr $q+qq&q4q4r%rrrrrrr#rrrϲ%r r rr%r%sssss  sssss sstt ttttuuuuuuuuuu)#u)uuuuuuu u u u u u)u u u) u/ DZ Z *Z(internal error: entered unreachable code(( DZuv/#v/vvvvv#vv v %v v vvvvvvvvvv#vvv%vvv/v%v$v0 v0vvxxxxS%YZZZZ[]``a a a b c iiijknqqqrsuS$S%#SSY Z Z Z Z ZZZZZZZZZZZ Z ZZZZ Z Z[[ [[[ [ \ \ \\\\\ \\ \ ] ]]^ ^^^^^ ^^ ^ ^ ^ ^^ ^ ^^ ^__ __ _ _ __ _ ````%` ` ` ` ` ``` a+a+aaaaaaa+  a+%a+aa a a %ab  b b bbbc cd d ddddd dd d dd d dd d e eee fe e f ff f g@g g0g/ggggggggggggggggggh  i i i i iii  ='( GEi  i!iiiiii {-P%j %jjjjjjkk kkk k k k kkkkl ll l l lm)m mmmm m mm m mn nn0n/n n nnnnn nnn DZqqqq q q q q qqq%q %q4q+qqrrrr%r%rrrrrrs s s ssst tu)u uuuuu u uu u u uv0v/v v vvvvv vvv DZS%#S%S% S%#S%S%#S%S%S%#S%S% S%#S%S%#S%S%#S%S%#S%S%S%#S%S%#S%S% S%#S%S%#S%#S%#S%S%#S%S%#S%S%S%#S%S%#S%S% S%#S%S%#S%#S%#S%S%#S%S%#"SyS$8 8#9 #6 ##7 # succ_countYZª Z Zn_neighZm_neigh[]- pred_count`L` Oª ` Sa+ \%a `%b ddliª i9i n_edgej%j%km_edgenqª q9q &r%r%s&uS%$ު _ref__end_ref__node_match_ref__edge_matchSSSSSS2SSSSSS2   H !͎  ͎ ! F ** Fo Ԟ  ۟ FFFEF EFEFhas_keyEF EIgEE*Շ&!Շ&!ׇ&  Еo ֧      G   Y ˚ Y Y Y Yۛ Y .Y  Y )Y^ Ԟ  ۟ڨ Y Y Y Y˚  ֧^ ^֧ا            !!!borrow!amZ {-P   &   # # ###߻#6:ۦ*U  &       &  &        ! {-P  [ # ###߻#6:ۦ*U  !!!Ž&!amZ& &  separator 6 -  ,   &   !& )      ""RefMut""Ž&"=Cզ&(     ?(    $  , , $"Format: was already formatted once"" ( ,    -     2    92  ,     . ,         ۟ '   ˜ '      -    '   3'      ٚ&&      *  ^* % '     +  +"% ˜"!% # ! # 4% & (  ' (  &&'%%    ˜%$%   ) $  )& 5% .2-$ &!'"2,-#0-$&'2  )* , -/,+-+2. .,+)#))-)1 !                    /Ԟ & ۟   &  & &  & & &    , Ţ    Ԟ  &       Ţ   Ԟ Ԟ &         ͊                $   G &  # Ԟ  & ۟      8 w 9  9   ͎&                wg. {-P   ͎ {-P& w&¶&&¶&       9     & &            g. ¶&  ͎ŷ& &¶&&¶&            >   A    {-P& &   A  44  >H {-P H  >P {-P   P    7 7       "assertion failed: !value.is_zero()""  ZZ Z& : :     Z Z&&&    ^ ^&  &   &    Y Y &## ###D!!!^!  #$'# #ax##D -444040bW`( - - & - - - -$$$$$OȱlQ) - - & - -  -  .  . .  . .  . .   . , $ , , , ,$ , ,  ,& - & - - -& - & - - - . . .  . , ,      4  3'3  3'2 $33 ?Y ?Y?Y44   44   4 4   441 ?Y ?Y ?Y ?YCassertion failed: node_capacity <= ::max().index()CC   ?Y59 55  5595     57555 4 22222 2&  &3'?Y?Y414  4 4 ?Y59 5952 σ226 6 66 6&666M6# 6M756&5666 6 65665 7 &7 7  &7 7 7 7 V7 7 7  8NNNMNMNǁ M-bD7 7 7`7  7 7  9& 7 7  7  7  88   87 8&88   88   8  7`8  788877`837&7 &7 &7   7 &7  &7 &7  {-P&7  &7 7`&788 &87 7 7 7:&:: ::9B:&:&::9B; ;;?;&;;;?<<<<M     M>NNNNN  N N NNNN NNC N N N NN   NNNNLNN N N LMML &L LLLL#M&MM &M&M&MMNNN N NN NNL LL&LѼ M old_weightM LTT  TTTTT  T T T T'assertion failed: old_edge_id.is_none()''  TUUUSST_ T&S STTT TTT TS ST&T old_edge_idT S WWWWW&WW &W WW&  WW WW& WW?W '  W?WSX'XWiX >XX XX XXXXYXY XY Y Y YYܛ'  YYYYVY Y VWWXlW&V VVW&WW WSW?&W&W&WWWX X  XY YV VVѼ W'W 'X V[[&[[&[ [[ & [["["['[ [# [ZZV Z&ZZZ[["'["'[&[[ZZZѼ [Z] &] ]&]]] &]]]\X]&]]]&] ] ]]\X_ &_ _&___ &____h_&_ __&_ _ _ __haa&ab &b bb'  bb!b!b bb*bbb*baa] a&aaaab*b!'b!'b&bbaaaѼ aaddd&de &e ee&  ee! e!e ee*eee*edd] d&d ddd&de*e!&e!&e&eed ddѼ ddi i&ii&ii &iiihwh hwh ih    hiSNh&hh9 ;khwi  &i'i&iihhhl l&lm&mm'mmmlHl'lHml'l&lll 'm'm&mmlllssssss  sssssss stttqttqsSr'qss&s'st qsqx xxxxxxx 8'xxxxxx 9'8xx xx'8xx ' xx{x xx  'xxx  'xxx  y yy y y 'yyyy y y' yy y yyyۆ' yyy y& yzzz   z yy z z z zz z{{{ z%z  z {{{{{ {x{{{ {v{ {{ { y z vxxxyy!v&v 'v'x'x {-P'x 'xx'x'x'xx''xyyyy 'yy 'yyyy yz&zzz z%{{{{ v  vx x%x  x &x %y  yyvрր րр р  р р    Ɓ ȁȁ 444040bW`( '      ΀    hiSN $$$$$y$$ ${gqU7р р9 ;kƁ   ' 'րր $րրրրր        ц ӆӆ܆ '܆܆' ܆܆ †E†' †E 'ԅ'Å ц '܆'܆'܆Å $ъ? ެִ<ɏެt#B@v tެŠ&t&&$ ? ެŌ'ڌ]" '  ' ]  n ִ<ɏ5y*/| $$$$$OȱlQ)&yʒ&ʒ&''  ؝  'ʒW ?؝'',Ğ'  ʒ'ʒ''''   '  '   ' # ' ؝'' '''''''' ˘ִ<ɏִ<ɏЙŗ* XuI!'̗ ̗ ŗ  ћ֛              u  u   Ѡ        p šDš#  šD'!'!!  '0 6 '̛ʢ^  {-P' ' ћ֛       Ѡ   {-P'! !''0' '  ћ֛max_column_len Ѽ  9 ;k  9'  ?' 'р(Y ȧ    hiSN '  '  Y р( '   ˭ '''' :p`] ð  '''ʯ'ٯ (ðʯٯ Ŵ    9999   9 99 ',ܵ (ֵ  öö           D#' D̷'̷̷̷̷! '̷! ̷!'· ·Ƿ' (  Ÿ  Ѹƹƹƹ) / '!'ɳ(  Ŵ 9   '̷!'̷!̷̷·'Ƿ ')ƹ' '  Ѽ Ƿ"2 2׻0׻# ׻0ĺӺĺ ӺŽŽ"ŽŽQ QȾCȾ ȾC 444040bW`(ּŽּold_node_capacitymin_node_capacity   pͿܿ    Ϳ ܿp+ ) )     4         ?    ?       ) 6   444040bW`()(6 .. 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" $*%˶*$%##"  '& +ǃ* ,   ǃ*+,*  -*  -*  *- a!!!!.*    * * **  **  * *     ǃ*     xrepyrep xrepuyrepuxrankyrank"*""* "" """  """"""  "" " " # *# # * # "$ *$ǃ*#  ## ۙ*   ##  ###*   #$$!*$!$!*  $!$!$!$*   $$)"$!$!""###o*"" " ""څ*" " " """##*# *# څ*# #*#$*$!*$!*$!*$!""" # *#!r{  8{ r   98  ))məA3*4$*r $      *  9*33333U`q**8#** *ª 666$6660777$7771 5   5   5  5$ 5 5  5  5  5  5  5  5  5  5  5  5  5  5   5   5  5  5  5  5  5$ 5 5  5  5  5  5  5  5  5  5  5  5  5  5  5  5  5  5 5 5 5 5 5$ 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5$ 5 5 5 5 5 5  5 5 5 5 5$ 5 5 5 5ͻ 5 5 5 5 5 5 5 4 4$ 4= 4 4 4 4=8 8 9 $989 $9988 8888: :::: : :::A:::::::A 4$ 4= 4  4 4 4= 4$ 4= 4  4 4 4=>>>>->>-???>.?>.BBBBB B  B B CCCBjBjB5B BBBBBB B BBBjDDC?C CCC?EެEެEEEE E EE EEEEjEjE5E ެެEެEެEEެEެEE EEEEEjGެGެG G  G G GFkG6G FެGެGG F GGFkI I IIHGH HHHG                                                                                                              ͎    ͎    ͎    ͎  @ ͎@@@@͎@@@ ͎@@@@͎@@ ɗ ɗ# ###### #####      Ý  Ý ÝÝÝÝÝ  Ý ÝÝÝÝ  ! !      ! !    .  . .̱....  . .̱...3  3 33333  3 33335  5 55555  5 5555$ !$!$$$$$ !$!$$$$$ !$!$$$$$ !$!$$$$X  X X   {      {    ٛA@nXXXXX  X X+XXXXX  X X+XXXX  X X+XXX ؿ ؿ " "` `` uQKl,```` ``+```    ҥ? ҥ?ҥ?ǁ(ҥ?'ҥ?ҥ?ҥ? ҥ?ҥ?ǁ(ҥ?'ҥ?ҥ?  $$$ ' (y) ζ*$ζ*$*$*$͝3  EdgeDirection: $I. `petgraph` is a graph data structure library.12E Graphs are collections of nodes, and edges between nodes. `petgraph`6HN provides several [graph types](index.html#graph-types) (each differing in theQ3 tradeoffs taken in their internal representation),6P [algorithms](./algo/index.html#functions) on those graphs, and functionality toS7 [output graphs](./doc/petgraph/dot/struct.Dot.html) in:E [`graphviz`](https://www.graphviz.org/) format. Both nodes and edgesHT can have arbitrary associated data, and edges may be either directed or undirected.W # Example  ```rust + use petgraph::graph::{NodeIndex, UnGraph};.3 use petgraph::algo::{dijkstra, min_spanning_tree};6" use petgraph::data::FromElements;%" use petgraph::dot::{Dot, Config};%T // Create an undirected graph with `i32` nodes and edges with `()` associated data.W* let g = UnGraph::::from_edges(&[- (1, 2), (2, 3), (3, 4), (1, 4)]);P // Find the shortest path from `1` to `4` using `1` as the cost for every edge.S> let node_map = dijkstra(&g, 1.into(), Some(4.into()), |_| 1);A> assert_eq!(&1i32, node_map.get(&NodeIndex::new(4)).unwrap());A M // Get the minimum spanning tree of the graph as a new graph, and check that P // one edge was trimmed. A let mst = UnGraph::<_, _>::from_elements(min_spanning_tree(&g)); D< assert_eq!(g.raw_edges().len() - 1, mst.raw_edges().len()); ? . // Output the tree to `graphviz` `DOT` format 1B println!("{:?}", Dot::with_config(&mst, &[Config::EdgeNoLabel])); E // graph {  // 0 [label="\"0\""]  // 1 [label="\"0\""]  // 2 [label="\"0\""]  // 3 [label="\"0\""]  // 1 -- 2  // 3 -- 4  // 2 -- 3  // }  ```   # Graph types  ) * [`Graph`](./graph/struct.Graph.html) - ,: An adjacency list graph with arbitrary associated data.=< * [`StableGraph`](./stable_graph/struct.StableGraph.html) -?C Similar to `Graph`, but it keeps indices stable across removals.F2 * [`GraphMap`](./graphmap/struct.GraphMap.html) -5T An adjacency list graph backed by a hash table. The node identifiers are the keysW into the table.< * [`MatrixGraph`](./matrix_graph/struct.MatrixGraph.html) -? An adjacency matrix graph. # * [`CSR`](./csr/struct.Csr.html) -&B A sparse adjacency matrix graph with arbitrary associated data.E ### Generic parametersS Each graph type is generic over a handful of parameters. All graphs share 3 commonVQ parameters, `N`, `E`, and `Ty`. This is a broad overview of what those are. EachTA type's documentation will have finer detail on these parameters.DO `N` & `E` are called *weights* in this implementation, and are associated withRY nodes and edges respectively. They can generally be of arbitrary type, and don't have to\Y be what you might conventionally consider weight-like. For example, using `&str` for `N`\S will work. Many algorithms that require costs let you provide a cost function thatVX translates your `N` and `E` weights into costs appropriate to the algorithm. Some graph[2 types and choices do impose bounds on `N` or `E`.5_ [`min_spanning_tree`](./algo/fn.min_spanning_tree.html) for example requires edge weights thatb[ implement [`PartialOrd`](https://doc.rust-lang.org/stable/core/cmp/trait.PartialOrd.html).^[ [`GraphMap`](./graphmap/struct.GraphMap.html) requires node weights that can serve as hash^I map keys, since that graph type does not create standalone node indices.LO `Ty` controls whether edges are [`Directed`](./petgraph/enum.Directed.html) orR0 [`Undirected`](./petgraph/enum.Unirected.html).3O `Ix` appears on graph types that use indices. It is exposed so you can controlRV the size of node and edge indices, and therefore the memory footprint of your graphs.YR Allowed values are `u8`, `u16`, `u32`, and `usize`, with `u32` being the default.U ### Shorthand typesO Each graph type vends a few shorthand type definitions that name some specificRX generic choices. For example, [`DiGraph<_, _>`](./graph/type.DiGraph.html) is shorthand[8 for [`Graph<_, _, Directed>`](graph/struct.Graph.html). ;G [`UnMatrix<_, _>`](./matrix_graph/type.UnMatrix.html) is shorthand for J] [`MatrixGraph<_, _, Undirected>`](./matrix_graph/struct.MatrixGraph.html). Each graph type's!`: module documentation lists the available shorthand types."=" # Crate features"" * **serde-1** -"G Defaults off. Enables serialization for ``Graph, StableGraph`` using#JS [`serde 1.0`](https://crates.io/crates/serde). May require a more recent version#V of Rust than petgraph alone.$" * **graphmap** -$F Defaults on. Enables [`GraphMap`](./graphmap/struct.GraphMap.html).$I * **stable_graph** -%P Defaults on. Enables [`StableGraph`](./stable_graph/struct.StableGraph.html).%S * **matrix_graph** -&P Defaults on. Enables [`MatrixGraph`](./matrix_graph/struct.MatrixGraph.html).&S''''' ' 'https://docs.rs/petgraph/0.4/''8  $$$ ' (y) ζ*$ζ*$*$*$͝3 +: $'' (())*&***** * * * *  E ! "& ',./<0 16 7= >@ACB DGJ  T W\b ] ^d glz {      * *     4        -  $7$7 $7 $7     - + + +     5 + + +     B  $7$7 $7 $7    . + + +     2  $7$7 $7 $7    + + + + # Graph traits and graph traversals.& '  ### The `Into-` Traits+ F J Graph traits like [`IntoNeighbors`][in] create iterators and use the sameJM J pattern that `IntoIterator` does: the trait takes a reference to a graph,M J and produces an iterator. These traits are quite composable, but with theM ; limitation that they only use shared references to graphs.>   ### Graph Traversal  D [`Dfs`](struct.Dfs.html), [`Bfs`][bfs], [`DfsPostOrder`][dfspo] andG J [`Topo`][topo] are basic visitors and they use “walker” methods: theM I visitors don't hold the graph as borrowed during traversal, only for theL A `.next()` call on the walker. They can be converted to iteratorsD ! through the [`Walker`][w] trait.$  H There is also the callback based traversal [`depth_first_search`][dfs].K   [bfs]: struct.Bfs.html " [dfspo]: struct.DfsPostOrder.html%  [topo]: struct.Topo.html " [dfs]: fn.depth_first_search.html%  [w]: trait.Walker.html   ### Other Graph Traits  K The traits are rather loosely coupled at the moment (which is intentional,N K but will develop a bit), and there are traits missing that could be added.N   F Not much is needed to be able to use the visitors on a graph. A graph I = needs to define [`GraphBase`][gb], [`IntoNeighbors`][in] and @ ! [`Visitable`][vis] as a minimum. $    [gb]: trait.GraphBase.html   [in]: trait.IntoNeighbors.html "  [vis]: trait.Visitable.html    +&P     BuildHasher I I I8 ( ^ ! #̟  $y   u  ͝ ȸ  1 36"7*91:; <J>U?YC E+ +  0: F\  ,    D `   @ @                                    methods         =          σ    extra        σ       +          +                            +  "                                                                  escape    _x                                                                                     section                                                                                                       tail                                              ,                                                       ,                            ,                          ,                            ,                                                      rest                   !       !        ,             param       self_type     self_wrap      self_map               sup          more_sup            +    "  assoc_name_ext         + "           _assoc_attr    "  assoc_name        assoc_bound             +            _method_attr       method_name            self_selftype          marg     marg_ty          mret             + nodelegate     ,                ,       , %  ,             "  ,   ,   ,       "  ,   ,   ,             ,          ,       ,   ,       ,     ,         ,       ,        0FKO &'+4 &)Տ> &*  %# 4 4 > >             Ѽ                  Ѽ               Ѽ       q                                                Ѽ         ,     -- ./    ,, .% 2 Get the value in `Control::Break(_)`, if present.5  ,, /   Control flow for callbacks.  7 The empty return value `()` is equivalent to continue.:  000123123  00 1  $7 $70 0 2   $7 $70 0 3  567  44 5  $7 $74 4 6   $7 $74 4 7 " 99, :;<    88 :  $7 $78 8 ;   $7 $78 8 < 4 d>?>?  0 @AB      == @  $7 $7= = A   $7 $7= = B   The default is `Continue`. DD, E    CC E:  A recursive depth first search.#  I Starting points are the nodes in the iterator `starts` (specify just oneL & start vertex *x* by using `Some(x)`).)  K The traversal emits discovery and finish events for each reachable vertex,N M and edge classification of each reachable edge. `visitor` is called for eachP 1 event, see [`DfsEvent`][de] for possible values.4  U The return value should implement the trait `ControlFlow`, and can be used to changeX  the control flow of the search.#  U `Control` Implements `ControlFlow` such that `Control::Continue` resumes the search.X K `Control::Break` will stop the visit early, returning the contained value. N L `Control::Prune` will stop traversing any additional edges from the current!O 4 node and proceed immediately to the `Finish` event.!7 " N There are implementations of `ControlFlow` for `()`, and `Result` where"Q L `C: ControlFlow`. The implementation for `()` will continue until finished."O X For `Result`, upon encountering an `E` it will break, otherwise acting the same as `C`.#[ $ D ***Panics** if you attempt to prune a node from its `Finish` event.$G $  [de]: enum.DfsEvent.html$ %  # Example returning `Control`.%" % G Find a path from vertex 0 to 5, and exit the visit as soon as we reach%J  the goal vertex.& & +&  use petgraph::prelude::*;& & use petgraph::graph::node_index as n;&) ) use petgraph::visit::depth_first_search;&, * use petgraph::visit::{DfsEvent, Control};'- ' - let gr: Graph<(), ()> = Graph::from_edges(&['0  (0, 1), (0, 2), (0, 3),'  (1, 3),(  (2, 3), (2, 4),(  (4, 0), (4, 5),(  ]);( ( 2 // record each predecessor, mapping node → node(5 ? let mut predecessor = vec![NodeIndex::end(); gr.node_count()];)B  let start = n(0);)  let goal = n(5);) / depth_first_search(&gr, Some(start), |event| {*2 . if let DfsEvent::TreeEdge(u, v) = event {*1 $ predecessor[v.index()] = u;*'  if v == goal {+ & return Control::Break(v);+)  }+  }+  Control::Continue+  });, ,  let mut next = goal;,  let mut path = vec![next];,  while next != start {, * let pred = predecessor[next.index()];,-  path.push(pred);-  next = pred;-  }-  path.reverse();- . assert_eq!(&path, &[n(0), n(2), n(4), n(5)]);-1 +. .  # Example returning a `Result`..# +. ,.) ,. ,/, ' use petgraph::visit::{DfsEvent, Time};/* / N let gr: Graph<(), ()> = Graph::from_edges(&[(0, 1), (1, 2), (1, 1), (2, 1)]);/Q ,0  let mut back_edges = 0;0  let mut discover_time = 0;0 > // Stop the search, the first time a BackEdge is encountered.1A < let result = depth_first_search(&gr, Some(start), |event| {1?  match event {2 2 // In the cases where Ok(()) is returned,25 O // Result falls back to the implementation of Control on the value ().2R J // In the case of (), this is to always return Control::Continue.3M " // continuing the search.4% , DfsEvent::Discover(_, Time(t)) => {4/  discover_time = t;4"  Ok(())4 ,5 & DfsEvent::BackEdge(_, _) => {5)  back_edges += 1;5 = // the implementation of ControlFlow for Result,5@ 8 // treats this Err value as Continue::Break6;  Err(event)6 ,7  _ => Ok(()),7 ,7 ,7 7 2 // Even though the graph has more than one cycle,75 F // The number of back_edges visited by the search should always be 1.7I  assert_eq!(back_edges, 1);8 / println!("discover time:{:?}", discover_time);82 = println!("number of backedges encountered: {}", back_edges);9@ % println!("back edge: {:?}", result);9( +9 : GHIdJHJGI : : : : : : 8; 8; ; ; 0; F8: : : : : : : : : : : > > &$7$7$7$7 $7͎ $7 $7 $7LMdNLMN> ,> ͎> > ,? ,? ͎? ͎@ 0@ ȉ8> բ> > > ? ? > > > > > > H& H &$7 $7H H   PR PS+ PT+ PTB PVQ PW+h PXՏr PYζ $PZζ $PZ !P[0      + + :B B B Q Q h h r r     " ]^]^      _       \\ _  abab,  ,      cefhjk     j G Create a new **Dfs**, using the graph's visitor map, and put **start** J  in the stack of nodes to visit. #  `dd`         c8      8 - Create a `Dfs` from a vector and a visit map0  `` e  e  Clear the visit state  %7 %7`gg `, , , , , f 8   b B Create a new **Dfs** using the graph's visitor map, and no stack.E  `ii`, , , , , 8   # ? Keep the discovered map, but clear the visit stack and restartB  the dfs from a particular node.#  %7 %7` `ɯ   ` G Return the next node in the dfs, or **None** if the traversal is done.J  %7 %7`ll `,  , k 8   + nono, , , p      mm p rsrs,  ,  ,  , , tvxz{     !j C Create a new `DfsPostOrder` using the graph's visitor map, and put F ( `start` in the stack of nodes to visit.!+ ! quuq,! ," ," ," ," t8!  ! ! ! #b I Create a new `DfsPostOrder` using the graph's visitor map, and no stack.#L # qwwq,# ,$ ,$ ,$ ,$ 8# # # &e ,% & %7 %7qyy& q,& ,& ,& ,& ,& x& 8& & & )# L Keep the discovered and finished map, but clear the visit stack and restart(O ,(# ) %7 %7q) q)  ) *` K Return the next node in the traversal, or `None` if the traversal is done.)N * %7 %7q||* q,* ,+ ,+ {* 8* * * 8" ~~,8 ,8 ,8 8 8 8 8 9 9 }} : ,: ,: ,: ,: ,: : : : : ;j G Create a new **Bfs**, using the graph's visitor map, and put **start**:J ,;# ; ,; ,< ,< ,< ,< 8;  ; ; ; >` G Return the next node in the bfs, or **None** if the traversal is done.>J > %7 %7> ,> ,? ,? > 8> > > D# ,D ,D ,D D D D D D E  E ,F ,F ,F ,F ,F F F F F G @ Create a new `Topo`, using the graph's visitor map, and put allFC $ initial nodes in the to visit list.G' G ,G G H ,H ,H ,H 8G G G Iy I P%7 %7I ,I -I -J! ,J I I I I K !!!ԂM^ M P,M ,M ,M ,M ,N 8M M M O E Clear visited state, and put all initial nodes in the to visit list.OH O %7 %7O ,O -P -P ,P ,P ,P O 8O O O Tz D Return the next node in the current topological order traversal, orQG ' `None` if the traversal is at the end.R* R J *Note:* The graph may not have a complete topological order, and the onlyRM N way to know is to run the whole traversal and make sure it visits every node.SQ T %7 %7T ,T -T ,T ,T ,T T T T T Y !!!\ ? A walker is a traversal state, but where part of the traversalZB 4 information is supplied manually to each next call.[7 [ I This for example allows graph traversals that don't hold a borrow of the[L  graph they are traversing.\ \ k\ \ \ \ \ ] ]@  Advance to the next item] ] %7 %7 {-P-]  ] ] ^s : Create an iterator out of the walker and given `context`.]= ^ _ _ ^ ^ a da a a a a a a a a a %7 %7a  a b b %7 %7 %7b  b b% b %7 %7 %7b  b c( d-c ѩ-c -c -c c c c c d d d( d %7 %7 {-P9d  d e. dѩ-e e e e e e e e e e e9 e %7 %7 {-Pe  e e f, ,f ,g ,g f f g g g9 g %7 %7 {-Pg  g g h5 ,h ,h ,h h h i i i9 i %7 %7 {-Pi  i i j, ,j ,j ,j j j j j j9 j %7 %7 {-Pk  k k k- ,k l ,l k k l l l9 l %7 %7 {-Pl  l l                        "           "     $ ! A copyable reference to a graph.$    - -    ߁    ' - -         J        ͝                       95cz#6     ?        ȸ  - - -    I -             `6     %D  -% -% -% -% % -% -% % % % % % % % % % % % &      9  UI}&J & - & & 'L  -' -' -' -' ' -( -( ' ' ' ' ' ' ' ' ' ' ( (      9  UI}( ( - ( ) ) *R * * * *  * * ͝* *  -* -* -* -* * -+ -+ * * * * * * * * * * + +  95cz#+] ,  , , , -G - - - -  - - ȸ- - -- -- -- - -. -. -. -. - - - - - - - - . . " LJu.L /  / / / ?J  -? -? -? -? ? -@ -@ ? ? ? ? ? ? ? ? ? ? @ @ @3 @  @ A4  ,A ,A A A B B A A A A A A A A B B %7 %7B  B CP B B B C  B B ͝B B  -C -C -C -C C -C -C ȆC C C C C C C C C C D D 6gdD2 D ȆȆ D E: E E E E  E E ͝E E  ,E ,E -E -E -F -F چE E E E E E E E F F %7 %7چF  F J  An edge reference.I I I Edge references are used by traits `IntoEdges` and `IntoEdgeReferences`.IL J -J -J J J J J J J J J J J!  The source node of the edge.J J %7 %7-K  K K!  The target node of the edge.K K %7 %7-K  K L" ' A reference to the weight of the edge.K* L %7 %7 %7-L  L L  The edge’s identifier.L L %7 %7-L  L M( -M -M -M M M M M M M M M M M M M N N %7 %7N  N N N %7 %7N  N N N %7 %7 %7N  N O O %7 %7O  O O  A node reference.O O -P -P P P P P P P P P %7 %7-P  P P" P %7 %7 %7-P  P S 'T T T T T T T T T T %7 %7T  T U! U %7 %7 %7U  U U U U' 'U V V U U U U V V V V V V V V %7 %7V  V W! W %7 %7 %7W  W [* [ [ [ [  [ [ ȸ[ [ ,[ ,[ -[ ,[ ,[ -[ ߈[ [ [ [ [ [ \ \ \ \ _4  ,_ ,_ -_ -_ -_ -_ _ _ _ _ _ _ _ _ _ _ `: ` ` ` `  ` ` ͝` _  ,` ,` -` -` -` -` چ` ` ` ` ` ` ` ` a a a/ a a a a  a a ȸa a ,a ,a -a a -b ߈a a a a a a b b bM  -b -b -b -b b b -c -c ؉b b b b b b b b b b c c """ "Q "& +c c * *V`Cd0 d ؉؉ d m8  ,m ,m -m -m -m -m m m m m m m m m m m %7 %7m  m n. n %7 %7n  n n n/ n %7 %7o  o o o?  ,o ,o -o -o -p -p o o o o o o o o p 9 A mapping for storing the visited status for NodeId `N`.p< q -q q q r"  Mark `a` as visited.q q = Return **true** if this is the first visit, false otherwise.q@ r %7 %7r  r r r$ , Return whether `a` has been visited before.r/ r %7%7 %7 %7r  r r s7  s s s s s4 s %7 %7s  s s t6 t %7%7 %7 %7t  t t u7  .u ͛.u u u u4 u %7 %7v  v v v6 v %7%7 %7 %7v  v v w%  .w ͛.w w w w" x %7 %7x  x x x$ x %7%7 %7 %7x  x x y( ,,y y Iy y Iy y y y y y! y %7 %7y  z z z# z %7%7 %7 %7z  z z ~4  ,~ ,~ -~ -~ - ~ ~ ~ ~ ~ ~ ~ ~     4  , , - - -Ā -ր           "  %7 %7   (  %7%7 %7 %7    : ق ق ܂   ݂  ͝ ׂ  , , - - - چ        ҃ ׃   „:        ͝   ,DŽ ,ʄ -̈́ -ф - - چDŽ DŽ ʄ ʄ ̈́ ̈́ ф ф   ʅ" ͅ %7 %7چׅ  ؅ (  %7%7 %7چ %7چ   Æ 5        ͝   ,Ç ,Ƈ -ɇ -͇ - - چÇ Ç Ƈ Ƈ ɇ ɇ ͇ ͇    È / ؈ ؈ ۈ   ܈  ȸ ֈ , , - , , ߈      ȉ ͉ ݉  /        ȸ  , , - ,Њ ׊ .݊ - ߈        !  %7 %7߈   (  %7%7 %7߈ %7߈    ߒ8        ȸ  5 The `GraphMap` keeps an adjacency matrix internally.8 , , - , . . - ߈      Г Փ   %7 %7߈   1  %7%7 %7߈ %7   Ŕ ˔   ) L ִf ִf    ٌ   &+Տ   %zu y z  ̟  # $ $ζ$ζ$$$ $_~ !^ !) :LYf x5               A graph filter for nodes. -(2 Return true to have the node be part of the graph5 %7 %7 Q- $ %7 %7 %> This filter includes the nodes that are contained in the set.A, $ %7 %7 *.A,,. $ %7 %7  &7%%-     $ %7 %7  %7   +7%,%-  ؍ Ѝ     $ %7 %7Ѝ  %7   )- - ) .     +< Create an `NodeFiltered` adaptor from the closure `filter`.? 80+,,   7-,  34CN$3  . A filtered neighbors iterator.",,.34CN$CN$ ;,,9 (%7 %7 {-P9 !!!?-,.34CN$T =-,.34CN$2 <-,. 645X_т 0   "*% A filtered node references iterator."(",","".#645X_т5X_т""""""""""## #7,#,#.#.##$(Ő######$ $$($%7 %7Ő {-PŐ9$ $%!!!̯&<-&,&&.'&&&&&&' '''78_fB(0( (*6 A filtered edges iterator.)*-****/*78_fB_fB**********ȵ**** +F9,/+/++.+9,-+++++++++, ,9,(,%7 %7 {-P9, ,- !!!޸.3-.,.. ......... /9848}/+/ //1-.11-1/1/11ċ/29848}8}1111111111ȵ222222 2=Ƀ/3/2/2/3/3 /3-2222222223 3/3(3%7 %7 {-P94 45 !!!5),5,56͎655556D6 %7 %7 {-P %76 ͎6&68D8 %7 %7 {-P %78 ͎8&88999999 99 99999 99 99; A graph filter for edges;; ;;;;;<+2 Return true to have the edge be part of the graph<5< %7 %7/< /<<<.=-<.= .<<<<<=$= %7 %7= ==@A-A.AA.AAAAAB+< Create an `EdgeFiltered` adaptor from the closure `filter`.A?B 8B0BC+,C,C.C CCCCC CC CD7-D,D/D DDDDDDDDD <ȭE3E  EEF?-F,FGȡ/G̔FFFFFFGG?ajɘHTH̔̔ HHHJ..J"J-J,JJ/J ާ/K<ȭȭJJJJJJJJKK K;-K,Kȡ/K/L ޔKKKKKKL LL(L%7 %7ޔ {-Pޔ9L LM !!!N<-O,O.Oȡ/ONNOOOOO PPP>8/lzP0P PR3-R,R/R ȡ/RRRRRRRS S>8/lzS+S SSU-.UU-U/U/UU/V>8/lz/lzUUUUUUUUUUȵUUVV V=Ƀ/W/V/VV.V/W-V˕VVVVVVVVW W/W(W%7 %7˕ {-P˕9W WX !!!Y6( A filtered neighbors-directed iterator.X+Y-Y,YY/Y/Y?ajɘajɘYYYYYYYYYY ZZZC-Z,Zȡ/Z/[ZZZZZZ[ [[([%7 %7 {-P9[ [\ !!!   $ζ$ζ$;%AJ U `ٌj~    Տ   ';;AAJ J U U ``jj~ ~         ,,. ɗ  *,ɗ%,-ɗ 8 ɗ -,-ɗOɗ  !,  ɗ     . ɗɗɗ    ), / ɗ     G ɗ//     ,, , ɗ   %7 %7ɗ ( %7%7 %7ɗ %7ɗ  A reversed edges iterator. ͘A:,%/9͘ (%7 %7͘ {-P͘9  C!0 Return the original, unreversed edge reference.3 %7 %7 %7 !C Consume `self` and return the original, unreversed edge reference.F , An edge referenceC/   ͭ %7 %7  %7 %7/ !%7 %7 %7 %7 %7 *,ɗ   SjY ް0ɗɗ $% A reversed edge references iterator.(/ڙfbxc.///ڙ (%7 %7ڙ {-Pڙ9     + + + 4+ 9 Graph traits for associated data and graph construction.<+uP  # ̟   (y BP |&    8          !: A graph that can be extended with further nodes and edges =   / /  A %7 %7    &  B Add a new edge. If parallel edges (duplicate) are not allowed and E( the edge already exists, return `None`. + %7 %7     & F Add or update the edge from `a` to `b`. Return the id of the affected I edge.  %7 %7&! A graph that can be created//5 ܜ y9/ ,,---   2 ,,---- D %7 %7. {-P %7 &D %7 %7 {-P %7 &5 ,,---- P%7 %7. {-P %7/ &P%7 %7/ {-P %7/ &86 ͝  ,,---- چD %7 %7چچ {-P %7چ &D %7 %7چچ {-P %7چ &;7 ͝  ,,---- چP%7 %7چ0 {-P %70 &P%7 %7چ0 {-P %7݄0 &0 ,,---- @%7 %7/. &%7 %7../ {-P/ & %7 %7..//     & !6!!8!! !!͝!!  ,!,!-!-!-"-" چ!!!!!!!!"@"%7 %7چ00" "&"##%7 %7چ00݄0 {-P0# ###&#$$ %7 %7چ00݄00% %%%&%&+&&9&& &&ȸ& &,&,&-&-'.' ߈&&&&&&'@'%7 %7߈߈߈' '&'((%7 %7߈00߈ {-P߈( (((&(** %7 %7߈0000+ +++&+,1 ,,,,-,-,-,-- ,,,,,,,,-4-  y-9-.7..;.. ..͝..  ,.,.-.-.-.-/ چ......../4/ چ y/9/0,00;00 00ȸ0 /,0,0-0-0.0 ߈000000040 ߈ y1915- Create a graph from an iterator of elements.505 50566 ,6ʨ-6,6@8Ο 62  666;;,;,;<< ,<:8° <,  ;;;;;= !!! @7 ,A,A-A-A-A-A AAAAAAAAAA   AB8 B@ 8&;%  &#{ //B2   AAAC=CC>CC CC͝CC  ,C,C-C-C-D-D چCCCCCCCCDD  چά0DچE0E@ 8&;%  &#{ 0݄0E2   DDDF2FF>FF FFȸF F,F,F-F-F.G ߈FFFFFFGG  ߈ G߈G8 G@ 8&;%  &#{ 00G2   GGGI?. Iterator adaptors for iterators of `Element`.H1I9I9&;%  &#{ I-I-I0I0IIIIIM8 Create an iterator adaptor that filters graph elements.I;JE The function `f` is called with each element and if its return valueJH@ is `true` the element is accepted and if `false` it is removed.JCD `f` is called with mutable references to the node and edge weights,KG> so that they can be mutated (but the edge endpoints can not).LAL= This filter adapts the edge source and target indices in theL@4 stream so that they are correct after the removals.M7M /Mʨ-N%7%7&;%  &#{  %7 %7N&%7%70N MMMMO19ڛP,O/P,OOOOOOOQ) An iterator that filters graph elements.P,P4 See [`.filter_elements()`][1] for more information.P7Q7 [1]: trait.ElementIterator.html#method.filter_elementsQ:R/R,R2VQRRRRRRRR RR RR͎R29 S%7%7͎&;%  &#{  %7  %7 S R R/S/R%7%7͎0S&,RRRRRRRRRS S T(T%7 %7 {-P9T ͎  T+  Graph algorithms.M It is a goal to gradually migrate the algorithms to be based on graph traitsPL so that they are generally applicable. For now, some of these still requirekO the `Graph` type.+ min ` u   $ ٌ    +Տ (  &[ m     pGpGAdd  %zu y z  ̟  # $ $ζ$ζ$$$ $_~ !^ !, Compute dominators of a control-flow graph./0 # The Dominance Relation4QQ In a directed graph with a root node **R**, a node **A** is said to *dominate* aUT> node **B** iff every path from **R** to **B** contains **A**.AQ The node **A** is said to *strictly dominate* the node **B** iff **A** dominatesT **B** and **A ≠ B**.N The node **A** is said to be the *immediate dominator* of a node **B** iff itQM strictly dominates **B** and there does not exist any node **C** where **A**P+ dominates **C** and **C** dominates **B**..   II   Տ $I        ,,..֝? Get the root node used to construct these dominance relations.B%7 %7֝  7/ Get the immediate dominator of the given node.2 I Returns `None` for any node that is not reachable from the root, and for L the root itself.  %7 %7֝   Q  E1 Iterate over the given node's strict dominators. 4 A If the given node is not reachable from the root, then `None` is D returned.  %7 %7֝ {-PPOQQf#oB%7   Q >E Iterate over all of the given node's dominators (including the givenH node itself).0D0  %7 %7֝ {-PPOQQf#oB%7 Q " Iterator for a node's dominators.%---0POQQf#oBQf#oB    .--0- (%7 %7 {-P9  E This is an implementation of the engineered ["Simple, Fast DominanceH+ Algorithm"][0] discovered by Cooper et al..R This algorithm is **O(|V|²)**, and therefore has slower theoretical running timeUJ than the Lengauer-Tarjan algorithm (which is **O(|E| log |V|)**. However,ML Cooper et al found it to be faster in practice on control flow graphs of upO to ~30,000 vertices.1 [0]: http://www.cs.rice.edu/~keith/EMBED/dom.pdf4  ,, , I 8P!!!! )!!! , !!! 0!!! 1S1 %7 %7 1 O1 finger11finger2244%7&7 %7 &7 4,4,5.5.5  4  4 5446!!! 6!!! 7!!! 99 ,9,: ,: 0:0: 89P999 '                 1;  %eD \[Generic\] Return the number of connected components of the graph.GA For a directed graph, this is the *weakly* connected components.Dգ+ +  use petgraph::Graph;* use petgraph::algo::connected_components;-,  5 let mut graph : Graph<(),(),Directed>= Graph::new(); 83 let a = graph.add_node(()); // node with no weight 6 let b = graph.add_node(());  let c = graph.add_node(());  let d = graph.add_node(());  let e = graph.add_node(());  let f = graph.add_node(());  let g = graph.add_node(());  let h = graph.add_node(());   graph.extend_with_edges(&[  (a, b),  (b, c),  (c, d),  (d, a),  (e, f),  (f, g),  (g, h),  (h, e) ,  // a ----> b e ----> f  // ^ | ^ |  // | v | v  // d <---- c h <---- g , assert_eq!(connected_components(&graph),2);/ graph.add_edge(b,e,());, assert_eq!(connected_components(&graph),1);/+,/ ]? \[Generic\] Return `true` if the input graph contains a cycle.B0 Always treats the input graph as if undirected.3,٨0 / < \[Generic\] Perform a topological sort of a directed graph.?I If the graph was acyclic, return a vector of nodes in topological order:L, each node is ordered before its successors./G Otherwise, it will return a `Cycle` error. Self loops are also cycles.JG To handle graphs with cycles, use the scc algorithms or `DfsPostOrder`J instead of this function.M If `space` is not `None`, it is used instead of creating a new workspace forP2 graph traversal. The implementation is iterative.5&7 {-P &7  ,-,   !!!ȅ +hH \[Generic\] Return `true` if the input directed graph contains a cycle.)K*F This implementation is recursive; use `toposort` if an alternative is*I needed.* +,+1+,+ ,+  ++++,,,,,,!!! -- ,- --/,/,/,/,/ ,/ /////\/,/,0,0,0 ,0 ///0',0,0,1 ,1000011 33&7 {-P &7 ͎ C3,3,3 3/3,4 &7͎ &74(&7͎1 4 ͎ 3 333333337O \[Generic\] Check if there exists a path starting at `from` and reaching `to`.5R6: If `from` and `to` are equal, this function returns true.6=717P graph traversal.77&7 {-P &7 8,8,9 ,9  88 8 8889!!! :!!! :p Renamed to `kosaraju_scc`.:: : N:: ::renamed to kosaraju_scc::/;ʧ1 ,;-;,; 1; ;;;@yY \[Generic\] Compute the *strongly connected components* using [Kosaraju's algorithm][1].<\<: [1]: https://en.wikipedia.org/wiki/Kosaraju%27s_algorithm<==L Return a vector where each element is a strongly connected component (scc).=OE The order of node ids within each scc is arbitrary, but the order of=H8 the sccs is their postorder (reverse topological sort).>;?G For an undirected graph, the sccs are simply the connected components.?J?E This implementation is iterative and does two passes over the nodes.?H@  ,@-@,@ 1A @@@MsW \[Generic\] Compute the *strongly connected components* using [Tarjan's algorithm][1].HZIV [1]: https://en.wikipedia.org/wiki/Tarjan%27s_strongly_connected_components_algorithmIYJЪ1JO1JH1K;KȬ1KJLC This implementation is recursive and does one pass over the nodes.LFM  ,M1M,M ٨0M  MMMQkQ &7&7 &7    y  _'&7Q,Q,Q ٨0Q  ϣQQEQQQRRRRRRR QRR RRRR ERR yRRR RR *RRRR QRRu^ [Graph] Condense every strongly connected component into a single node and return the result.babU If `make_acyclic` is true, self-loops and multi edges are ignored, guaranteeing thatbX the output is acyclic.cգ+c +c 1c" use petgraph::algo::condensation;d%,dd6 let mut graph : Graph<(),(),Directed> = Graph::new();d91e61e1e1f1f1f1fކ1gg1g1gЇ1g1g1h (b, e),h1h1hȈ1h1h,hh // a ----> b ----> e ----> fh 1i ։1i 1i i1 let condensed_graph = condensation(graph,false);i4 let A = NodeIndex::new(0);j let B = NodeIndex::new(1);j- assert_eq!(condensed_graph.node_count(), 2);j0- assert_eq!(condensed_graph.edge_count(), 9);k0P assert_eq!(condensed_graph.neighbors(A).collect::>(), vec![A, A, A, A]);kSS assert_eq!(condensed_graph.neighbors(B).collect::>(), vec![A, B, B, B, B]);lV+lC If `make_acyclic` is true, self-loops and multi edges are ignored:lFm+m  # use petgraph::Graph;m$ # use petgraph::algo::condensation;m' # use petgraph::prelude::*;n #n8 # let mut graph : Graph<(),(),Directed> = Graph::new();n;5 # let a = graph.add_node(()); // node with no weightn8 # let b = graph.add_node(());o! # let c = graph.add_node(());o! # let d = graph.add_node(());o! # let e = graph.add_node(());p! # let f = graph.add_node(());p! # let g = graph.add_node(());p! # let h = graph.add_node(());p!1q # graph.extend_with_edges(&[q  # (a, b),q # (b, c),q # (c, d),q # (d, a),q # (b, e),r # (e, f),r # (f, g),r # (g, h),r # (h, e)r # ]);r 9 let acyclic_condensed_graph = condensation(graph, true);r<߽1s1s5 assert_eq!(acyclic_condensed_graph.node_count(), 2);s85 assert_eq!(acyclic_condensed_graph.edge_count(), 1);t8O assert_eq!(acyclic_condensed_graph.neighbors(B).collect::>(), vec![A]);tR+uu   ,u,u-u-u-v-v  u u uuuuuuuu: \[Generic\] Compute a *minimum spanning tree* of a graph.~=- The input graph is treated as if undirected.0G Using Kruskal's algorithm with runtime **O(|E| log |E|)**. We actuallyJR return a minimum spanning forest, i.e. a minimum spanning tree for each connectedU component of the graph.[ The resulting graph has all the vertices of the input graph (with identical node indices),^Q and **|V| - c** edges, where **c** is the number of connected components in `g`.T͂C Use `from_elements` to create a graph from the resulting iterator.тF٠, /٨0Ȅ  < An iterator producing a minimum spanning forest of a graph.?,Ί1Պ٠!& 2<#   NjHNj    Ќ',Ռ1٨0 11֍ ٠ՌՌ ° (&7 &7٠ {-P٠9 ,50 Return a node id that participates in the cycleɛ3&7 &7, D \[Generic\] Compute shortest paths from node `source` to all other.GB Using the [Bellman–Ford algorithm][bf]; negative edge costs areEC permitted, but the graph must not have a cycle of negative weightsF( (in that case it will return an error).+I On success, return one vec with path costs, and another one which pointsLA out the predecessor of a node along a shortest path. The vectorsD) are indexed by the graph's node indices.,C [bf]: https://en.wikipedia.org/wiki/Bellman%E2%80%93Ford_algorithmFգ+ + 1" use petgraph::algo::bellman_ford;%,Ң let mut g = Graph::new();/ let a = g.add_node(()); // node with no weight2 let b = g.add_node(());ţ let c = g.add_node(()); let d = g.add_node(()); let e = g.add_node(()); let f = g.add_node(()); g.extend_with_edges(&[Ѥ (0, 1, 2.0), (0, 3, 4.0), (1, 2, 1.0), (1, 5, 7.0), (2, 4, 5.0), (4, 5, 1.0),ե (3, 4, 1.0),,2 // Graph represented with the weight of each edge5 // // 2 1Ȧ // a ----- b ----- cݦ // | 4 | 7 | // d f | 5 // | 1 | 1 | // \------ e ------/çܧ let path = bellman_ford(&g, a);#L assert_eq!(path, Ok((vec![0.0 , 2.0, 3.0, 4.0, 5.0, 6.0],OK vec![None, Some(a),Some(b),Some(a), Some(d), Some(e)]ԨN )) );@ // Node f (indice 5) can be reach from a with a path costing 6.ΩCZ // Predecessor of f is Some(e) which predecessor is Some(d) which predecessor is Some(a).]4 // Thus the path from a to f is a <-> d <-> e <-> f7G let graph_with_neg_cycle = Graph::<(), f32, Undirected>::from_edges(&[J (0, 1, -2.0), (0, 3, -4.0), (1, 2, -1.0), (1, 5, -25.0),Ŭ (2, 4, -5.0), (4, 5, -25.0), (3, 4, -1.0),,J assert!(bellman_ford(&graph_with_neg_cycle, NodeIndex::new(0)).is_err());M+  , 1¯ ٨0ί   %!!! ` Return `true` if the graph is bipartite. A graph is bipartite if it's nodes can be divided into͹c[ two disjoint and indepedent sets U and V such that every edge connects U to one in V. This^F algorithm implements 2-coloring algorithm based on the BFS algorithm.Iڻ1޻3 ,- /,  ,1 - G½ ۽     R@ Associated data that can be used for measures (such as length).CG  /11 11 /1Zߢߢߢ Gߢߢߢ ߢߢߢߢߢߢ& A floating-point measure. -1-      + + ( ( 2 2`R ^xIxI%  +Տ   Z5((22?'R R ^^mxB       ( \[Generic\] A* shortest path algorithm.+T Computes the shortest path from `start` to `finish`, including the total path cost.W[ `finish` is implicitly given via the `is_goal` callback, which should return `true` if the^ given node is the finish node."Z The function `edge_cost` should return the cost for a particular edge. Edge costs must be] non-negative.] The function `estimate_cost` should return the estimated cost to the finish for a particular`` node. For the algorithm to find the actual shortest path, it should be admissible, meaning thatc] it should never overestimate the actual cost to get to the nearest goal node. Estimate costs` must also be non-negative.; The graph should be `Visitable` and implement `IntoEdges`.>գ+ +1 use petgraph::algo::astar;1 let a = g.add_node((0., 0.)); ! let b = g.add_node((2., 0.)); ! let c = g.add_node((1., 1.)); ! let d = g.add_node((0., 2.)); ! let e = g.add_node((3., 3.)); ! let f = g.add_node((4., 2.)); !1  (a, b, 2),  (a, d, 4),  (b, c, 1),  (b, f, 7),  (c, e, 5),  (e, f, 1),  (d, e, 1), ,  1 50 // Edges with '*' are part of the optimal path. 31 1 1  // | 4* | 7 | 1  // | 1* | 1* | 1 G let path = astar(&g, a, |finish| finish == f, |e| *e.weight(), |_| 0);J/ assert_eq!(path, Some((6, vec![a, d, e, f])));2+Z Returns the total cost + the path of subsequent `NodeId` from start to finish, if one was] found.  ͎ \\,,   1 ,     00͎͎         ͎   8 ӟ  !! ,!.! 0"0"˃!\w!!"("  ","." 0#0#""## $C$&7 &7$$Q$$%@%&7 &7 % %%+ @ Compressed Sparse Row (CSR) is a sparse adjacency matrix graph.C+ !!uT Y t ִ ִ IndexIndexMut ٌ %    Տ  u   u   $ (  ̀  SliceIterƃ N ITTYYht t  ">    K        D  $    -"& Csr node index type, a plain integer.)   .& Csr edge index type, a plain integer.) !0        ,,----    C       ,,-- &7 &7  $       ,,----   Create an empty `Csr`.  Aa Create a new [`Csr`] with `n` nodes. `N` must implement [`Default`] for the weight of each node.dO [`Default`]: https://doc.rust-lang.org/nightly/core/default/trait.Default.htmlR [`Csr`]: #struct.Csr.htmlգ+ +  use petgraph::csr::Csr;,) let graph = Csr::::with_nodes(5);," assert_eq!(graph.node_count(),5);%" assert_eq!(graph.edge_count(),0);% assert_eq!(graph[0],0); assert_eq!(graph[4],0);+     ! ! !   &      ,,   "3 Create a new `Csr` from a sorted sequence of edges6I Edges **must** be sorted and unique, where the sort order is the defaultL8 order for the pair *(u, v)* in Rust (*u* has priority).;# Computes in **O(|E| + |V|)** time.&գ+ + ҳ2 ,  / let graph = Csr::<(),()>::from_sorted_edges(&[ 2$ (0, 1), (0, 2),!', (1, 0), (1, 2), (1, 3),!/ (2, 0)," (3, 1),","+""&7 &7 ;  # "##+#2$ 9#""$ ! ! !   4 ! ! !   9$       ,9,9-9-:-:-:  999999:::!: &7 &7 : :;!; &7 &7 ; ;\25 Iterator element type is `EdgeReference`.]8]&7 &7  9  %   }]ˣ&7 ] ]]c@       ,c-c-cc cccccccccc&7 &7 c  cc?       ,d-d-d2ḑccddddddd0       d-d-dd!!!!%! !&! wZ3P  ddddddddf Access the edge’s weight.ee3 **NOTE** that this method offers a longer lifetimee65 than the trait (unfortunately they don't match yet).e8f&7 &72  f  ff<       ,f-f-f-g-g  ffffffffg g  g h  h h  h h&7 &7 h  hh h&7 &72 h  hii&7 &7 &7 i  iii&7 &7 i  ij5       ,j-j-j-j-j  jjjjjjjjk k  !!!!%! !&! wZ3P k(k&7 &7 {-P9 k  kk ! ! !   ώn-       ,n,n-n-n-n-n  nnnnnnnnoo   oo   oC         -o-o-o-o-p-p  oooooooooop p  !!!!%! !&! wZ3P pp    * g  g  9   xa q0q   qs0s       ,t-t-t t t2u2t  * g  g  9   xa xa sstt tttt tt   t t  t*t    ))məA3ϣM M^6 tt  uu  u9u  33333U`qNN NMNMNǁ Mjg(+ NN NMNMNǁ Mjg(+ uu  v>       ,v-v-v-v-v  vvvvvvvvv v  !!!!%! !&! wZ3P w(w&7 &7 {-P9 w  w}:         -}-}-}-}-}-}  }}}}}}}}}}~ ~    9  %   }]ˣ ~.~   ~~2       ,,----        ̀ ۀ2       ,,----  ā  ہ"ށ &7 &7  ( &7&7 &7 &7 ͂ ΂Ԃƃ Ą+   ެ̈́ ެ  ɄɄ̈́̈́   ެ(&7 &7 {-P9   ެ- &7 &7    ެކ>          ------ ޭ ·Ӈ   !! !OMڡ 6, Return an iterator of all neighbors of `a`./2 - `Directed`: Targets of outgoing edges from `a`.5B - `Undirected`: Opposing endpoints of all edges connected to `a`.E22* Iterator element type is `NodeIndex`.- ޭޭޭ   6        ,,‹-ŋ-ɋ--  ‹‹ŋŋɋɋ &7 &7  ,&7 &7  / &7 &7ԙ3  ƍ=        ,,---̎-ގ =       ,,----̏  ݏ   (&7 &7 &7  ΐ@       ,Ӑ,֐-ِ-ݐ--  ӐӐ֐֐ِِݐݐ4Ñ &7 &7 &7 ͑ ґؑ*  .ƒD | ƒƒܒܒ    ִ<ɏ)  .͛.  ғ ד  (&7 &7 {-P9  ˔-Δ &7 &7  ؔ ٔD          ------ Ԯ   Ŗ2ȖԮԮ   ٖ2        ,,----  ͘И &7 &7 ۘ ܘ2       ,,---ԙ-     + +  (   (   2   2  `R   ^  xI  xI  %     +  Տ   Z        5((22?'R R ^^mx7     0 \[Generic\] Dijkstra's shortest path algorithm.3H Compute the length of the shortest path from `start` to every reachableK node. H The graph should be `Visitable` and implement `IntoEdges`. The functionKH `edge_cost` should return the cost for a particular edge, which is usedK8 to compute path costs. Edge costs must be non-negative.;N If `goal` is not `None`, then the algorithm terminates once the `goal` node'sQ cost is calculated.5 Returns a `HashMap` that maps `NodeId` to path cost.8գ+ + 1 use petgraph::algo::dijkstra;!, use std::collections::HashMap;"181611111 1 ކ1 , // z will be in another connected component / let z = graph.add_node(());  1 1 Ї1 1 1 1 1 1 Ȉ1 1 , Ǽ1 1 ։1 1  0 let expected_res: HashMap = [ 3 (a, 3),  (b, 0),  (c, 1),  (d, 2),  (e, 1),  (f, 2), (g, 3), (h, 4)! ].iter().cloned().collect();$* let res = dijkstra(&graph,b,None, |_| 1);- assert_eq!(res, expected_res);"> // z is not inside res because there is not path from b to z.A+͎      ,,1 , 002͎ ͎8  + ( Simple graphviz dot file format output.+, !<%  xBG  WriteKG  l  %r  {        ٌ       &  1 <6BBKKXllrr{ {      = `Dot` implements output to graphviz .dot format for a graph.@B Formatting and options are rather simple, this is mostly intendedE( for debugging. Exact output may change.+ # Examples+1+%' let mut graph = Graph::<_, ()>::new();* graph.add_node("A"); graph.add_node("B"); graph.add_node("C"); graph.add_node("D");1, (1, 2), (1, 3), (2, 3),,D println!("{:?}", Dot::with_config(&graph, &[Config::EdgeNoLabel]));G, // In this case the output looks like this:/1 // digraph { // 0 [label="\"A\""] // 1 [label="\"B\""] // 2 [label="\"C\""] // 3 [label="\"D\""] // 0 -> 1 // 0 -> 2 // 0 -> 3 // 1 -> 2 // 1 -> 3 // 2 -> 3+I // If you need multiple config options, just list them all in the slice.L+     - . .    8  8  8  8  o 8 o o o <0 Create a `Dot` formatting wrapper with default configuration. A 3   8 := Create a `Dot` formatting wrapper with custom configuration.@  ́3   8o ! ! !   ΄ ! ! !   3    3   8ooo   -- ..  o 8 o o o <0S&7Ԟ q q q q       .. - &&7&7 &7 &7&7&7Ԟ&7F&7&73Ԟ &7&7 &7 &7&7&7Ԟ&7F&7&73Ԟ   ؃  ! ! !   & ! ! !   ('   -(.).)3) 3) G) G)  ((((*4*&7&7&7 &7 &7GGGEGEGEG EGEGEQ ! >S&7Ԟ *  *** ! ! !   ۢ* ! ! !   +%   -+.+.+3+ 3, G, G,  ++++,4,&7&7&7 &7 &7GGGEGEGEG EGEGEQ ! >S&7Ԟ ,  ,,- ! ! !   - ! ! !   ..   -.̱1s| ̱.. ̱  ....   .!  -.G/ ̱ ../// &7&7 &7̱ &7Ԟ / / /000 &7 &7̱Ԟ 0 0033   3k`<T4 33   3333   3#  33G3  33343&7&7&7 &7 &7GGGEGEGEG EGEGEQ ! >S&7Ԟ 3 3355   35. 55   5555   6$  36G6  66646&7&7&7 &7 &7GGGEGEGEG EGEGEQ ! >S&7Ԟ 6 66,,  "!!!""!!"   %  +I  +I  :%  ִQ   ִQ    l    2  2     (  $   $  (  ζ$  ζ$    $  $   $                 %         uX     +5 :DQ bly" X    7   @  , The default integer type for graph indices./H `u32` is the default to reduce the size of the graph's data and improveK performance in the common case.#B Used for node and edge indices in `Graph` and `StableGraph`, usedE for node indices in `Csr`. ND Trait for the unsigned integer type used for node and edge indices.G< Marked `unsafe` because: the trait must faithfully preserve? and convert index values.   -/I1  -/4ό41 4   &7 &7           &7 &7               &7 &7              &7 &7       &7 &7    !  .͛.        $    .  .͛.    1  .G  4&7&7&7 &7 &7GGGEGEGEG EGEGEQ ! >S&7Ԟ  ?" Short version of `NodeIndex::new`%   .͛. ?" Short version of `EdgeIndex::new`%   .͛. !  .͛.      F An invalid `EdgeIndex` used to denote absence of an edge, for exampleI to end an adjacency list.  $    .  .͛.    1  .4  4&7&7&7 &7 &7GGGEGEGEG EGEGEQ ! >S&7Ԟ  # #  #%!   Ե%3%Ե%ެ&"%%%%&"   ,&3&3&  &&&&'8N Accessor for data structure internals: the first edge in the given direction.&Q' &7 &7 ' ެ''*!   4*3*4*4*"****+"    4+3+3+  ++++,8N Accessor for data structure internals: the next edge for the given direction.+Q, &7 &7 , Եެ,,-% Return the source node index.-!-&7 &7 - Եެ-.% Return the target node index.-!.&7 &7 . Եެ.E5W `Graph` is a graph datastructure using an adjacency list representation..Z/ `Graph` is parameterized over:/"/E - Associated data `N` for nodes and `E` for edges, called *weights*./H0 The associated data can be of arbitrary type.03U - Edge type `Ty` that determines whether the graph edges are directed or undirected.0XC - Index type `Ix`, which determines the maximum size of the graph.1F2K The `Graph` is a regular Rust collection and is `Send` and `Sync` (as long2N% as associated data `N` and `E` are).2(3M The graph uses **O(|V| + |E|)** space, and allows fast node and edge insert,3P- efficient graph search and graph algorithms.30M It implements **O(e')** edge lookup and edge and node removals, where **e'**4P% is some local measure of edge count.4(0 Based on the graph datastructure used in rustc.535E Here's an example of building a graph with directed edges, and below5H? an illustration of how it could be rendered with graphviz (see6B" [`Dot`](../dot/struct.Dot.html)):6%6+6167+ let mut deps = Graph::<&str, &str>::new();7.$ let pg = deps.add_node("petgraph");7'' let fb = deps.add_node("fixedbitset");7*& let qc = deps.add_node("quickcheck");8)" let rand = deps.add_node("rand");8%" let libc = deps.add_node("libc");8% deps.extend_with_edges(&[9 (pg, fb), (pg, qc),9* (qc, rand), (rand, libc), (qc, libc),9-,9+::K ![graph-example](https://bluss.github.io/ndarray/images/graph-example.svg):N: ### Graph Indices::C The graph maintains indices for nodes and edges, and node and edge:FJ weights may be accessed mutably. Indices range in a compact interval, for;M: example for *n* nodes indices are 0 to *n* - 1 inclusive.<=<Q `NodeIndex` and `EdgeIndex` are types that act as references to nodes and edges,H4 removing an edge shifts the index of the last edge.>7. * Adding nodes or edges keeps indices stable.?1?W The `Ix` parameter is `u32` by default. The goal is that you can ignore this parameter?ZI completely unless you need a very big graph -- then you can use `usize`.@LAT * The fact that the node and edge indices in the graph each are numbered in compactAWN intervals (from 0 to *n* - 1 for *n* nodes) simplifies some graph algorithms.AQBQ * You can select graph index integer type after the size of the graph. A smallerBT" size may have better performance.C%CG * Using indices allows mutation while traversing the graph, see `Dfs`,CJ and `.neighbors(a).detach()`.D!DF * You can create several graphs using the equal node indices but withDI& differing weights or differing edges.E)EC * Indices don't allow as much compile time checking as references.EFEF       ,F,F-F -F1" FFFFF FFFFF   FF   FF   H& A `Graph` with directed edges.G"GJ For example, an edge from *1* to *2* is distinct from an edge from *2* toGM *1*.GH     ,H,H2H  y y 9   1"HHHHHHI&! A `Graph` with undirected edges.H$HJ For example, an edge between *1* and *2* is equivalent to an edge betweenHM *2* and *1*.II     ,I,I2I  y y 9   1"IIIIIIJ;A The resulting cloned graph has the same graph indices as `self`.JD       ,J,J-J-J-J 2K2K JJJJJJJJKK&7 &7 K KL$L &7&7 &7 &7 L L MN5       ,N,N-N-NGN GN -N-O  NNNNNNNNO4O&7&7&7 &7 &7GGGEGEGEG EGEGEQ ! >S&7Ԟ O OOS ! ! !   U ! ! !   V ! ! !   W ! ! !   W ! ! !   X X   3X+ٛA@n  + + XXXX   XX +  XX   XX   XX   XX +  XX   XX   +XX   +X XYDY  &7 &7   {      {    ٛA@n &7  Y3Y YYYYY\    ,\,\ \\\\^* Create a new `Graph` with directed edges.]-]Q This is a convenience method. Use `Graph::with_capacity` or `Graph::default` for]TE a constructor that is generic in all the type parameters of `Graph`.^H^  `"   ,`,` ````b, Create a new `Graph` with undirected edges.`/`4`T4aHb  c&       ,c,c-c-c-c-c  ccccccccd8. Create a new `Graph` with estimated capacity.d1d   yd9dg!4 Return the number of nodes (vertices) in the graph.f7f2fg &7 &7 g gh!) Return the number of edges in the graph.g,g2hh &7 &7 h hi!- Whether the graph has directed edges or not.h0i &7 &7 i il6L Add a node (also called vertex) with associated data `weight` to the graph.iOj2jj" Return the index of the new node.j%kH **Panics** if the Graph is at the maximum number of nodes for its indexkK type (N/A if usize).ll&7 &7 l l&lp9 Access the weight for node `a`.o#o2 Also available with indexing syntax: `&graph[a]`.o5p &7 &7 {-P &7 p ppq ! ! !   rE) Access the weight for node `a`, mutably.q,q6 Also available with indexing syntax: `&mut graph[a]`.q9r&7 &7 {-P &7 r rrs ! ! !   wZ> Add an edge from `a` to `b` to the graph, with its associatedsA data `weight`.tt" Return the index of the new edge.t%t2tt0 **Panics** if any of the nodes don't exist.
t3H **Panics** if the Graph is at the maximum number of edges for its indexuK4vvN **Note:** `Graph` allows adding parallel (“duplicate”) edges. If you wantvQP to avoid this, use [`.update_edge(a, b, weight)`](#method.update_edge) instead.wSw&7 &7 w wwx&xz  ]' Add or update an edge from `a` to `b`.*3 If the edge already exists, its weight is updated.6' Return the index of the affected edge.*ɀ@ Computes in **O(e')** time, where **e'** is the number of edgesрC? connected to `a` (and `b`, if the graph edges are undirected).B, **Panics** if any of the nodes don't exist./ &7 &7  ̂&ނЅ9 Access the weight for edge `e`.#2 Also available with indexing syntax: `&graph[e]`.5ׅ &7 &7 {-P &7   ! ! !   رŇE) Access the weight for edge `e`, mutably.Ά,6 Also available with indexing syntax: `&mut graph[e]`.9̇&7 &7 {-P &7 ܇  ! ! !   X, Access the source and target nodes for `e`.׈/&7 &7   ! ! !   <? Remove `a` from the graph if it exists, and return its weight.ҊB1 If it doesn't exist in the graph, return `None`.4ҋB Apart from `a`, this invalidates the last node index in the graphڋE@ (that node will adopt the removed node index). Edge indices areC@ invalidated as they would be following the removal of each edgeC with an endpoint in `a`.ՍC Computes in **O(e')** time, where **e'** is the number of affectedݍFG edges, including *n* calls to `.remove_edge()` where *n* is the numberJB of edges with an endpoint in `a`, and including the edges with anE endpoint in the displaced node.# &7 &7   &7 &7  ȝ  <I Remove an edge and return its edge weight, or `None` if it didn't exist.LB Apart from `e`, this invalidates the last edge index in the graph§E/ (that edge will adopt the removed edge index).2èX Computes in **O(e')** time, where **e'** is the size of four particular edge lists, for˨[? the vertices of `e` and the vertices of another affected edge.B &7 &7  G &7 &7 ® Ǯͮ=@ Return an iterator of all nodes with an edge starting from `a`.Cϴ2״** - `Undirected`: All edges from or to `a`.-: Produces an empty iterator if the node doesn't exist.
=3-E Use [`.neighbors(a).detach()`][1] to get a neighbor walker that doesH not borrow from the graph.) [1]: struct.Neighbors.html#method.detach, &7 &7     9  UI}&7  $VG Return an iterator of all neighbors that have an edge between them andݸJ! `a`, in the specified direction.$L If the graph's edges are undirected, this is equivalent to *.neighbors(a)*.չO. - `Directed`, `Outgoing`: All edges from `a`.1, - `Directed`, `Incoming`: All edges to `a`./5-ͻߜ5ջ=3-ɼG For a `Directed` graph, neighbors are listed in reverse order of theirѼJE addition to the graph, so the most recently added edge's neighbor isH? listed first. The order in an `Undirected` graph is arbitrary.BS Use [`.neighbors_directed(a, dir).detach()`][1] to get a neighbor walker that doesV5ƞ5¿,&7 &7     9  UI}&7  H5J `a`, in either direction.5O9 - `Directed` and `Undirected`: All edges from or to `a`.<ߜ5=3-P Use [`.neighbors_undirected(a).detach()`][1] to get a neighbor walker that doesS5ƞ5,&7 &7     9  UI}&7  92+2*2/ߜ5=1 Iterator element type is `EdgeReference`.4&7 &7  9 9     =&7  RD Return an iterator of all edges of `a`, in the specified direction.G51٢5/Z - `Undirected`, `Outgoing`: All edges connected to `a`, with `a` being the source of each] edge. Z - `Undirected`, `Incoming`: All edges connected to `a`, with `a` being the target of each]5 > Produces an empty iterator if the node `a` doesn't exist.
A54&7 &7  9 9     =&7  > Return an iterator over all the edges connecting `a` and `b`.A2*2/54&7 &7Ȍ 9   +SO?&7  G, Lookup if there is an edge from `a` to `b`./ȃ5C5B &7 &7  T Lookup an edge from `a` to `b`.#ȃ5C5B &7 &7    ! ! !    &7&7 &7 &7   Q9 Lookup an edge between `a` and `b`, in either direction.<G If the graph is undirected, then this is equivalent to `.find_edge()`.JF Return the edge index and its directionality, with `Outgoing` meaningI, from `a` to `b` and `Incoming` the reverse,/& or `None` if the edge does not exist.)&7 &7   &7&7 &7 &7   Q?? Return an iterator over either the nodes without edges to themB( (`Incoming`) or from them (`Outgoing`).+9 An *internal* node has both incoming and outgoing edges.<= The nodes in `.externals(Incoming)` are the source nodes and@3 `.externals(Outgoing)` are the sinks of the graph.6F For a graph with undirected edges, both the sinks and the sources areI just the nodes without edges.!1 The whole iteration computes in **O(|V|)** time.4 &7 &7  ܆      H$&7  -7 Return an iterator over the node indices of the graph.:I For example, in a rare case where a graph algorithm were not applicable,L< the following code will iterate through all nodes to find a? specific index:+1) # let mut g = Graph::<&str, i32>::new();, # g.add_node("book");A let index = g.node_indices().find(|i| g[*i] == "book").unwrap();D+ &7 &7  ;@ Return an iterator yielding mutable access to all node weights.CB The order in which weights are yielded matches the order of theirE node indices.&7 &7y =P&7  -6 Return an iterator over the edge indices of the graph9 &7 &7  65 Create an iterator over all edges, in indexed order.854&7 &7* *V`C&7  );@ Return an iterator yielding mutable access to all edge weights.C5E edge indices.'7 '79 jcI4'7  ) Access the internal node array.# '7 '7 '7  ) Access the internal edge array.# '7 '7 '7  E? Convert the graph into a vector of Nodes and a vector of Edges؁B   Sܨ4Q '7 '7  ܇R4Q '7 '7  ߓ5 Index the `Graph` by two indices, any combination of8 node or edge indices is fine.!ۋB **Panics** if the indices are equal or if they are out of bounds.E+! use petgraph::{Graph, Incoming};$ use petgraph::visit::Dfs; let mut gr = Graph::new(); let a = gr.add_node(0.); let b = gr.add_node(0.);؍ let c = gr.add_node(0.); gr.add_edge(a, b, 3.); gr.add_edge(b, c, 2.); gr.add_edge(c, b, 1.);؎> // walk the graph and sum incoming edges into the node weightA let mut dfs = Dfs::new(&gr, a);ŏ#' while let Some(node) = dfs.next(&gr) {*5 // use a walker -- a detached neighbors iterator8D let mut edges = gr.neighbors_directed(node, Incoming).detach();ِG2 while let Some(edge) = edges.next_edge(&gr) {57 let (nw, ew) = gr.index_twice_mut(node, edge);ߑ: *nw += *ew;, ,ȒҒ // check the resultڒ assert_eq!(gr[a], 0.); assert_eq!(gr[b], 4.); assert_eq!(gr[c], 2.);+ӓ'7 '7Ô '7ѝ '7      ÔÔ  Ô͕   Ôª # Reverse the direction of all edges&'7 '7 ™ Ǚ Remove all nodes and edges'7 '7 Ŝ ʜ2 '7 '7  Ɲ(8 Return the current node and edge capacity of the graph.;'7 '7   2I Reserves capacity for at least `additional` more nodes to be inserted inLI the graph. Graph may reserve more space to avoid frequent reallocations.L2 **Panics** if the new capacity overflows `usize`.5 '7 '7   2I Reserves capacity for at least `additional` more edges to be inserted inܢL5L55Ǥ '7 '7 դ ڤ ߧ8H Reserves the minimum capacity for exactly `additional` more nodes to beK? inserted in the graph. Does nothing if the capacity is alreadyB sufficient.Ӧ: Prefer `reserve_nodes` if future insertions are expected.ۦ=55'7 '7   8H Reserves the minimum capacity for exactly `additional` more edges to beӨK inserted in the graph.4 Does nothing if the capacity is already sufficient.©7: Prefer `reserve_edges` if future insertions are expected.=Ȫ5Ъ5'7 '7   Ӭ%M Shrinks the capacity of the underlying nodes collection as much as possible.Pڬ'7 '7  %M Shrinks the capacity of the underlying edges collection as much as possible.P'7 '7  7 Shrinks the capacity of the graph as much as possible.֮: '7 '7  p< Keep all nodes that return `true` from the `visit` closure,? remove the others.ΰ< `visit` is provided a proxy reference to the graph, so that?6 the graph can be walked and associated data modified.9. The order nodes are visited is not specified.1 '7 '7   Ȳ Ų'7  cK]_'7*'76 ͲײŲŲηp< Keep all edges that return `true` from the `visit` closure,?55?5Ҷ9. The order edges are visited is not specified.1շ '7 '7    6'7  cK]_'7*'76 0 Create a new `Graph` from an iterable of edges.ĺ3, Node weights `N` are set to default values./6 Edge weights `E` may either be specified in the list,9( or they are filled with default values.+5 Nodes are inserted automatically to match the edges.8+1) let gr = Graph::<(), i32>::from_edges(&[,,ս33,+Ⱦ      ά0Ӿ0 2   ־ӾӾ, Extend the graph from an iterable of edges./6/696+68'7 '7     ά00 6֋62 ) Create a new `Graph` by mapping node and, edge weights to new values.8 The resulting graph has the same structure and the same; graph indices as `self`. Á    ߅         !ؒ6 !6  Y  ! ! !     ! ! !   1 Create a new `Graph` by mapping nodes and edges.4: A node or edge may be mapped to `None` to exclude it from= the resulting graph.9 Nodes are mapped first with the `node_map` closure, then<B `edge_map` is called for the edges that have not had any endpointE removed. K The resulting graph has the structure of a subgraph of the original graph.NA If no nodes are removed, the resulting graph has compatible nodeD@ indices; if neither nodes nor edges are removed, the result hasC" the same graph indices as `self`.%  Á    ߅        6666 )6  )ǝ6   Y_J Convert the graph into either undirected or directed. No edge adjustmentsMH are done, so you may want to go over the result to remove or add edges.K2 φ    >F An iterator over either the nodes without edges to them or from them.I        --- - 6     ܆      H$  H$  3    ))məA3NN NMNMNǁ Mjg(+       =       --- --      +'7 '7    3' Iterator over the neighbors of a node.*3-B Created with [`.neighbors()`][1], [`.neighbors_directed()`][2] orE [`.neighbors_undirected()`][3].#( [1]: struct.Graph.html#method.neighbors+1 [2]: struct.Graph.html#method.neighbors_directed43 [3]: struct.Graph.html#method.neighbors_undirected6      ,2  66     9  UI} UI}             1     ,22     +'7 '7   .     ,22 "$     ,22      9  UI}  )B Return a “walker” object that can be used to step through theE* neighbors and edges from the origin node.-I Note: The walker does not borrow from the graph, this is to allow mixingL0 edge walking with mutating the graph's weights.3'7 '76   ;€      ,Հ2܀ ؀2 6    9   sb sb ррՀՀ ܀܀         ˁ΁ '7 '7   9   sb'7Եެ   4߁33܂  Եެ9߁߁)      ,22̃    9   sb  ݃3  '7 '76 {-P '7    ! ! !   ?„ '7 '76 {-P '7 DŽ  ̄<          ------ ĸ      9 9     = .ĸĸĸ   ňˈD          -----߉- ָ      9 9     = Oָָָ   ÊɊڊ3- Iterator over the edges of from or to a node0     ,--  -- 66  9 9     = =         ÍÍ   ٍюю       5 ,---Ǐ-ُ  """ "Q "& +('7 '7 {-P9 =T Iterator over the multiple directed edges connecting a source node to a target nodeW̡ ,---- 66Ȍ 9   +SO?+SO?ܡܡ  ТТ   9 9     = ? ,---ף- չ """ "Q "& +6'7 '7չ {-P6 (  3 ۦ2 ,--- -§'7 '7ȧ ɧ۩?6 Iterator yielding mutable access to all node weights.9 -22 6((y =P=P- NNNMNMNǁ M-bDӪ6 -ܪ2ߪ2 تتܪܪߪߪ  ū'ȫ'7 '7 {-P6ͫ ҫ!!!- '7 '7  í?6 Iterator yielding mutable access to all edge weights.9έ ,22 6((9 jcI4jcI4ݭݭ- NNNMNMNǁ M-bD6 ,Į2Ǯ2 ۻĮĮǮǮ  ''7 '7ۻ {-P6 !!!ڷ- '7 '7ۻ  ܱ?9 Index the `Graph` by `NodeIndex` to access node weights.<& **Panics** if the node doesn't exist.) ,,---- Ͳ Ҳ+'7 '7 '7 B6ó<6) ,,---- 7 '7 '7 '7 ?9 Index the `Graph` by `EdgeIndex` to access edge weights.<ж& **Panics** if the edge doesn't exist.Զ) ,,---̷-޷  +'7 '7 '7 йB6<6) ,չ,ع-۹-߹-- չչعع۹۹߹߹ĺ7Ǻ '7 '7 '7Ѻ ֺܺջ2 Create a new empty `Graph`. ,ڻ,ݻ---- ڻڻݻݻ ) A `GraphIndex` is a node or edge index., --ܽ˽˽νս Ͻɽ߽'7 '7    0 .͛. '7 '7 Ŀǿ  0 .͛. '7 '7   P A “walker” object that can be used to step through the edge list of a node.SA Created with [`.detach()`](struct.Neighbors.html#method.detach).DG The walker does not borrow from the graph, so it lets you step throughJB neighbors or incident edges while also mutating graph weights, asE in the following example:+5$55555555F // step through the graph and sum incoming edges into the node weightI5#5*' // use a detached neighbors walker*5G55 gr[node] += gr[edge];!, ,5555+  .='( GE   $ .͛. '7 '7 % .͛. G Step to the next edge and its endpoint node in the walk for graph `g`.JD The next node indices are always the others than the starting pointG- where the `WalkNeighbors` value was created.0* For an `Outgoing` walk, the target nodes,-6 for an `Incoming` walk, the source nodes of the edge.9'7'7 '7 '7----x '7'7 '7 '7---- !!!x '7'7 '7 '7---- !!!0 .͛.  ('7 '7 {-P9 - '7 '7  ; .͛. - '7 '77 9 .͛. 0 .͛. ھ ('7 '7ھ {-Pھ9 - '7 '7ھ  ; .͛. ھ- '7 '7ھ7 9 .͛. ھ= ,22 '7 '7 < ,22 A ,22   '7'7 '7 '7  E ------   5 >/s f0 ?$ Iterator over all nodes of a graph.' -22 7  5 >/s f>/s f3  ))məA3NN NMNMNǁ Mjg(+6 -22   ('7 '7 {-P9  !!!- '7 '7  A -22 - '7 '7 {-P9  !!!? -22 ( 3-3 """ "Q "& +ެ22628'7 '77  ެ4 3-3     '7 '7 ެ '7 '77 ެ'7 '7 '7 ެ'7 '7 ެ?$ Iterator over all edges of a graph.' ,22 7  * *V`C*V`C3  ))məA3NN NMNMNǁ Mjg(+6 ,22  """ "Q "& +('7 '7 {-P9  !!!ٲ- '7 '7  A ,22 - '7 '7 {-P9  !!!? ,22   u2244NW yv  u      ٌ Տ  $("- 4@"NNW W hv%    Z    h    P      -  cK]_!; Create a new `Frozen` from a mutable reference to a graph.> 7  #D Deref allows transparent access to all shared reference (read-only)G' functionality in the underlying graph.*- '7 '7 '7 )-/ #'7 '7 '7 ,-/ / '7 '7 '7   6 - - - - - -   cK]_           5 85 ! 5 E '7 '77 '7 '7          ª          ͝ 4 `StableGraph` keeps indices stable across removals.78' Depends on `feature = "stable_graph"`.<*g #u%%ִ ִ replace     22 ($ $(y ζ$ζ$$$ $  |  ;"!{ x  %ٌ  w  N  u  _ ! u  ^ !  pu~   M    7   :    s    e               ;H `StableGraph` is a graph datastructure using an adjacencyK list representation.J The graph **does not invalidate** any unrelated node or edge indices whenM items are removed.% `StableGraph` is parameterized over:( J - Associated data `N` for nodes and `E` for edges, also called *weights*. M4 3Ͳ4 X4 F L The graph uses **O(|V| + |E|)** space, and allows fast node and edge insert O and efficient graph search.  4 P4 ( K - Nodes and edges are each numbered in an interval from *0* to some number NI *m*, but *not all* indices in the range are valid, since gaps are formedL by deletions.Q - You can select graph index integer type after the size of the graph. A smallerT4%G - Using indices allows mutation while traversing the graph, see `Dfs`.JJ - The `StableGraph` is a regular rust collection and is `Send` and `Sync`M. (as long as associated data `N` and `E` are).1C - Indices don't allow as much compile time checking as references.FJ Depends on crate feature `stable_graph` (default). *Stable Graph is stillMG missing a few methods compared to Graph. You can contribute to help itJ achieve parity.*  ,,- -چwf3 &    ,% A `StableGraph` with directed edges.(4M4  ,,2̟$awf3,' A `StableGraph` with undirected edges.*4M4  ,,2̟$awf3; ,,--4 4 -- چ4'7'7'7 '7چ '7GGGEGEGEG EGEGEQ ! >S'7Ԟ !!!!!!!!!!!$!!!%!!!% !!!݁&!!!'!!!(!!!ʆ) !!!)!!!Ҭ*&,*,+**++-0 Create a new `StableGraph` with directed edges.+3+? This is a convenience method. See `StableGraph::with_capacity`+BG or `StableGraph::default` for a constructor that is generic in all the,J" type parameters of `StableGraph`.,%- -, ,-,------.-. چ--------/84 Create a new `StableGraph` with estimated capacity..7/ چy/9/1(51;1'7 '7چ 1 12522'7 '7چ2 24244 '7 '7چ4 48!4777278 '7 '7چ889!48,9299 '7 '7چ99:!490: '7 '7چ::=64;O;2;<4<%<F **Panics** if the `StableGraph` is at the maximum number of nodes for׫ߜ5߫=3-Ӭ5۬S5֭ƞ5ޭ,'7 '7چ 95cz#'792۰+2*2±/ߜ5=54'7 '7چ99 -t'7 R5G51٢5/5]5 5]5 5A5ٷ4'7 '7چ99 -t'7ץ?5B5+5<5ݼ@56ݽ5I5!پ54 '7 '7چ܆ .M c'7 ; Index the `StableGraph` by two indices, any combination of>5!5E'7 '7چÔ '7 '755چÔ چ 5 5  Ôª p5?55?5951G The node indices of the removed nodes are invalidated, but none other.Jе8J. each edge with an endpoint in a removed node.1N Computes in **O(n + e')** time, where **n** is the number of node indices andQQ **e'** is the number of affected edges, including *n* calls to `.remove_edge()`TE where *n* is the number of edges with an endpoint in a removed node.H '7 '7چ6'7  cK]_'7چ*'78 p6?55?5961F The edge indices of the removed edes are invalidated, but none other.IE Computes in **O(e'')** time, **e'** is the number of affected edges,H? including the calls to `.remove_edge()` for each removed edge.B '7 '7چ6'7  cK]_'7چ*'78 6 Create a new `StableGraph` from an iterable of edges.96/696+68+) use petgraph::stable_graph::StableGraph;,/ let gr = StableGraph::<(), i32>::from_edges(&[2,33,+  چά00 6֋62   / Create a new `StableGraph` by mapping node and2ˎ66;ŏ6 چ߅6666 !9 !9  Y  ! ! !   ! ! !    ! ! !   ! ! !  7 Create a new `StableGraph` by mapping nodes and edges.:6=66<6E6 6NE Nodes and edges that are not removed maintain their old node or edgeH8   چ߅6666 )9  )9   Y6/6/696+68'7 '7چ ά00 6֋62 - '7 '7چ '7- '7 '7چ '7܆ '7 '7چ!!!ؑ ۑ'7 '7چA4ڝD ,,--- 22چ'7 '7چچ $ '7'7 '7چ '7چ  E? Index the `StableGraph` by `NodeIndex` to access node weights.Bǣ6ˣ) ,,---ɤ-ۤ چ +(7 (7چ (7 ҦH9B6) ,צ,ڦ-ݦ--- چצצڦڦݦݦ̧7ϧ (7 (7چ (7٧ ާE? Index the `StableGraph` by `EdgeIndex` to access edge weights.B6) ,,---- چ +(7 (7چ (7ª êɪHҠ9Bܫ6) ,,---- چ7 (7 (7چ (7 8" Create a new empty `StableGraph`.% ,,---- چچ J' Convert a `Graph` into a `StableGraph`Ư*# Computes in **O(|V| + |E|)** time.&: The resulting graph has the same node and edge indices as= the original graph.ް ,,---ϱ- چ'چ Ȳ!!!ɳ!!!ϺJ' Convert a `StableGraph` into a `Graph`*9&L This translates the stable graph into a graph with node and edge indices inO= a compact interval without holes (like `Graph`s always are).@M Only if the stable graph had no vacancies after deletions (if node bound wasPM equal to node count, and the same for edges), would the resulting graph have͹P- the same node and edge indices as the input.0 ,Ժ,׺-ں-޺-- ԺԺ׺׺ںں޺޺˻1λچ 8ӻK ------   5>!i0 ?7' -22 9  5>!i>!i; ))məA3NN NMNMNǁ Mjg(+̾6 -22   ((7 (7 {-P9  !!!!!!- (7 (7  A -22 - (7 (7 {-P9  !!!!!!= ,22 (7 (7 < ,22 A ,22 7  (7(7 (7 (7  ( 3-3 ####Q#&e$ެ22628(7 (79  ެ4 3-3     (7 (7 ެ (7 (79 ެ(7 (7 (7 ެ(7 (7 ެB ------  99 -t. J ------  99 -tO 360 ,---- 9 9 99 -t-t    5 ,----  ####Q#&e$((7 (7 {-P9 ( 3 S ------  ####Q#&e$*8eew$R0B Create an iterator over all edges in the graph, in indexed order.E54 87' ,29 9 *8eew$R8eew$R; ))məA3NN NMNMNǁ Mjg(+6 ,22  ####Q#&e$((7 (7 {-P9  !!! !!!A ,22 - (7 (7 {-P9  !!! !!!>6I  ---- 9  ܆ .M c.M c; ))məA3NN NMNMNǁ Mjg(+= -----Ȁ ـ ހ+(7 (7  36*& Iterator element type is `NodeIndex`.)Ȇ  ,ֆ2݆ن: :  95cz#5cz#҆҆ֆֆ݆݆   ߇߇$ ,22  95cz#͊)6E6-˷6ĉL63Ԋ(7 (7ʊ:ۊ ܊1 ,22  +(7 (7 ؎7S۔M See [*.detach()*](struct.Neighbors.html#method.detach) for more information.ߔP7J7E7Ŗ+5 use petgraph::Incoming;8,֗! let mut gr = StableGraph::new();ڗ$5555֘557I5#5*7Ě*5G55Ԕ7!, ,555֜5+  .V}Ki۝/ .͛. #% .͛.ž 7J7G707-79(7(7 (7 (7֡----áۡ~ (7(7 (7 (7---- !!!~ (7(7 (7 (7---- ĤҤ!!!5+ Iterator over the node indices of a graph..  -2: : 6gd6gd; ))məA3NN NMNMNǁ Mjg(+̾> -22  ͧ(Ч(7 (7 {-P9է ڧ !!!- (7 (7 ʩ ˩I -22ê - (7 (7 {-P9 ҫ !!!> ,,---ĭ-֭ چ7 Return an upper bound of the node indices in the graph: (7 (7چ !!!.(7 (7چ / (7 (7چ0 5+ Iterator over the edge indices of a graph..  ,2: : bpbp; ))məA3NN NMNMNǁ Mjg(+> ,22  ɲ(̲(7 (7 {-P9Ѳ ֲ !!! - (7 (7 ƴ ǴI ,22 - (7 (7 {-P9 ζ !!!  `Frozen` is a graph wrapper. : The `Frozen` only allows shared access (read-only) to the=: underlying graph `G`, but it allows mutable access to itsЀ= node and edge weights.= This is used to ensure immutability of the graph's structure@6 while permitting weights to be both read and written.9A See indexing implementations and the traits `Data` and `DataMap`D. for read-write access to the graph's weights.1-:   cK]_cK]_ : ::    :,,,,, ,,ȸ, ,L `GraphMap` is a graph datastructure where node values are mappingO keys.P ,### n IndexMapIter IndexMapIterMut %III 8y9ִ ִ u22 N$ $(ζ$ζ$$$ $N  y ٌ   _nxA  ( "F     C  Q    $ A `GraphMap` with undirected edges.'4M4 ,,###y#9# fM{5{7" A `GraphMap` with directed edges.%4M4 ,,###y#9# fM{5{7^,,-..4 4 -߈4(7(7(7 (7߈ (7GGGEGEGEG EGEGEQ ! >S(7Ԟ &0 A trait group for `GraphMap`'s node identifier.3 -ό44-ό44,,..) .%(7(7 (7 (7  !,,-. -߈ Create a new `GraphMap`߈ 81 Create a new `GraphMap` with estimated capacity.4 ߈y9(5;(7 (7߈  !  !& Whether the graph has directed edges. ) (7 (7߈   &~3 Create a new `GraphMap` from an iterable of edges.!6!. Node values are taken directly from the list.!16"96"+#6#8#+#$ use petgraph::graphmap::UnGraphMap;#'$% // Create a new undirected GraphMap.$(9 // Use a type hint to have `()` be the edge weight type.$<, let gr = UnGraphMap::<_, ()>::from_edges(&[%/,%3%3&,&+&&  ߈0&0&  ' '    &&&(!) Return the number of nodes in the graph.',( (7 (7߈(()!4(,) (7 (7߈)!))5)*(7 (7߈* **% Add node `n` to the graph.*+(7 (7߈+++,+' Return `true` if node `n` was removed.+*,I Computes in **O(V)** time, due to the removal of edges with other nodes.,L, (7 (7߈- --0)5 Return `true` if the node is contained in the graph.080 (7 (7߈1 118>A Add an edge connecting `a` and `b` to the graph, with associated1DC data `weight`. For a directed graph, the edge is directed from `a`2F to `b`.2 2G Inserts nodes `a` and/or `b` if they aren't already part of the graph.2J3? Return `None` if the edge did not previously exist, otherwise,3B= the associated data is updated and the old value is returned4@ as `Some(old_weight)`.44+4A // Create a GraphMap with directed edges, and add one edge to it5D$ use petgraph::graphmap::DiGraphMap;5'5 let mut g = DiGraphMap::new();6" g.add_edge("x", "y", -1);6 assert_eq!(g.node_count(), 2);6" assert_eq!(g.edge_count(), 1);6"$ assert!(g.contains_edge("x", "y"));7'% assert!(!g.contains_edge("y", "x"));7(+78(7 (7߈8888&8:!!! <!!! >F>(7(7(7 (7߈ (7 (7> >>>>@!!! C!!! I6G Remove edge from `a` to `b` from the graph and return the edge weight.EJF( Return `None` if the edge didn't exist.F+F+FH // Create a GraphMap with undirected edges, and add and remove an edge.FK:G'G let mut g = UnGraphMap::new();G":HH) let edge_data = g.remove_edge("y", "x");H,! assert_eq!(edge_data, Some(-1));H$ assert_eq!(g.edge_count(), 0);I"+II (7 (7߈I IIIM/M Return `true` if the edge connecting `a` with `b` is contained in the graph.LPM (7 (7߈MއMMMO0 Return an iterator over the nodes of the graph.N3N Iterator element type is `N`.N!O(7 (7߈###ށ(7O OR15PCP2P*5Q-Qߜ5Q=;R!R (7 (7߈  `(7R!RRXR5TJ5U$5UOV5V1٢5V/5V-Wߜ5W=;W!X(7 (7߈" LJu(7X XXX]/C Return an iterator of target nodes with an edge starting from `a`,ZF+ paired with their respective edge weights.[.[2[*5\-\ߜ5\=$ Iterator element type is `(N, &E)`.]'](7 (7߈99^9a;.(7] ]]`3B Return a reference to the edge weight connecting `a` with `b`, or_E0 `None` if the edge does not exist in the graph._3` (7 (7߈ {-P (7`"```a?J Return a mutable reference to the edge weight connecting `a` with `b`, or`M;a3b(7 (7߈ {-P (7b"bbbd-U Return an iterator over all edges of the graph with their weight in arbitrary order.bXc& Iterator element type is `(N, N, &E)`c)d (7 (7߈ ;FJ*|D(7d df8\ Return an iterator over all edges of the graph in arbitrary order, with a mutable referencee_ to their weight.ff* Iterator element type is `(N, N, &mut E)`f-f (7 (7߈ S|)(7f fla6 Return a `Graph` that corresponds to this `GraphMap`.h9hI 1. Note that node and edge indices in the `Graph` have nothing in commonhLK with the `GraphMap`s node weights `N`. The node weights `N` are used asiN/ node weights in the resulting `Graph`, too.i2, 2. Note that the index type is user-chosen.j/j- Computes in **O(|V| + |E|)** time (average).j0k= **Panics** if the number of nodes or edges does not fit withk@" the resulting graph's index type.k%l ߈ -l-l lllq>:q6r ,q-qqr,q.r -r߈qqqqqqqqrTr  ߈ά0r0s 8s    rrru86t/u6u8;v ,u-u;u;v,u.v -v߈uuuuuuuuvTv(7 (7߈ vά0v0w;w   v vvvyy y~yzy yy yzzzzz typarmzz  zz zz %zzzzzzz boundszz  z z zzz zz  zz zzz zz  zzzz~% z zz zz{{{{ ;{{ {{ %{{{{{ ;{ {{{ {{{ {{ {{{{{{ ;{{ {{ { {{ {{{{{{ ;{{ {| %||||| ;| ||~ "| ||| ||||| |  | ||| | | || }} }} }}}} }} }} }}}}}} }  } i} }} } }}}~  ~~ ~~  ~~~~ ~~ ~~ i~ ~~~, ---;   ``%NN NMNMNǁ Mjg(+־!1-- -Ձ (7 (7   !!!! !!!!'--˄-ׄ; " LJuLJu%NN NMNMNǁ Mjg(+־!  х9-څ-݅; -օօڅڅ݅݅ Άц(7 (7 ֆ ۆ!!!! !!!!׊"---; -;;99^9a;.^9a;. !  `3---;Ō ׌-  ((7 (7 {-P9 H---; -   ;FJ*|D0 %Ē-ђ-Ԓ-ےג; ; ;  ;FJ*|D;FJ*|D͒͒ђђԒԒےے" >  k“6-˓-Γ-ѓ; -ǓǓ˓˓ΓΓѓѓ  ؔ(۔(7 (7 {-P9 - (7 (7   1(7 (7; !!!!#Ø; Ș!!!!ϙA-ؙ-ۙ-ޙ; -ԙԙؙؙۙۙޙޙњ-Ԛ (7 (7 {-P9ޚ !!!!( ---; ;(;( S|)S|)%>J*ړ9---ŝ;ʝ ܝ-  ((7 (7 {-P9 !!!"- (7 (7   ˠ1Π(7 (7;Ҡ נݠ!!!"#; Ȣ!!!"D---ˣ;У -- (7 (7 {-P9 !!!"?---; - 99^9a;.. 37 Index `GraphMap` by node pairs to access edge weights.:,§,ŧ-ȧ. -߈§§ŧŧȧȧ $(7 (7߈ (7 ƨ6;:,,-ª. -߈ªª0 (7 (7߈ (7 - Create a new empty `GraphMap`.",,-.ҭ -߈߈ > A reference that is hashed and compared by its pointer value.A8 `Ptr` is used for certain configurations of `GraphMap`,;9 in particular in the combination where the node type for<= `GraphMap` is something of type for example `Ptr(&Cell)`,@1 with the `Cell` being `TypedArena` allocated.4+;  G{G{ ;ɀ<;   ɀ<+ +ñññ(7 (7 .""3 Ѳ$+ڲֲֲڲڲʳ(F Ptr compares by pointer equality, i.e if they point to the same valueIͳ(7(7 (7 (7г ѳ׳%+ʴ=ʹ (7(7 (7 (7ٴ ڴ+-O Ptr is ordered by pointer value, i.e. an arbitrary but stable and total order.ֵR(7(7 (7 (7  +Ʒ··ƷƷ (7 (7 (7 +˸+ԸииԸԸ+(7(7 (7 (7 \2I    "1+G 4(7(7(7 (7 (7GGGEGEGEG EGEGEQ ! >S(7Ԟ E---;ƻ -ٻ# <2 /,,-. -߈ƾɾ (7 (7߈Ծ վ,---ƿ;˿ < # <<ܿ5ܿ >  k!"=---; - ((7 (7 {-P9  !!!"@---; -  5 nwu0 +---; < 5 nwunwu5 >  k!"<---; -  ((7 (7 {-P9 !!!"3,,-. -߈ (7 (7߈ -(7 (7߈0 / (7 (7߈0 :,,-. -߈,, # 'yC uJ  ^U !(mζw$ζw$ " '4+CCJ J U U emmww  33 1(7 (7"00 ެ  ! (7 (7 ެ (7(7 (7 (7"00 ެ   Q (7(7 (7 (7"00 ެ  @(7 (7  ެ+ !!!# !!!#? (7 (7  ެ+ !!!!#" !!!##A#(7 (7 # ެ#+# $ !!!#$ !!!#'B [Graph] Return `true` if the graphs `g0` and `g1` are isomorphic.$E%B Using the VF2 algorithm, only matching graph syntactically (graph%E structure).&&& The graphs should not be multigraphs.&)& **Reference**&&B * Luigi P. Cordella, Pasquale Foggia, Carlo Sansone, Mario Vento;&EA *A (Sub)Graph Isomorphism Algorithm for Matching Large Graphs*'D' (7(7 (7 (7 (,(,(-(-(-(-(  #(#(((((((((-<+E+? Using the VF2 algorithm, examining both syntactic and semantic+BH graph isomorphism (graph structure and matching node and edge weights).,K,<,)-(7(7 (7 (7# - ,-,-----6-#--.-. (7(7 (7 (7.(7(7<.(7(7# (7 (7/(7(7#</ ##-#-#. #. ------------11+11111 1'1(7(7(7 (7 (7 (71 11112Z0K7122.322222 3&3(7(7(7 (7 (7 (73 33#(7(7͎ (7 (74,3(7(7͎<433͎333344 ͎4&4(7(7(7 (7͎ (7 (74 ͎44555 )7)7)7)7)7 )7# )7 )7 )7 )7## 6 ,5,5-5-666<6-7-7 7#8#"6#6#6#6 #7 5555556666666=T!!!#=H!!!#HL!!!$N;!!!#NOP;!!!#PQSC!!!#SS-- #%!7%%27`k.t+uQKl,+`k+ ttww/ ͎8 & 2&͎ ,8/G  G& 4)7)7)7 )7 )7GGGEGEGEG EGEGEQ ! >S)7Ԟ ͎ &3AV "33 4)7)7)7 )7 )7GGGEGEGEG EGEGEQ ! >S)7Ԟ ! 00O)7 )7###߻#6:ۦ*U)7ʨ- &  / /    , . ###߻#6:ۦ*U      )7)7)7 )7< )7GGGEGEGEG EGEGEQ ! >S)7Ԟ , )7)7)7 )7 )7GGGEGEGEG EGEGEQ ! >S)7 3)7)7)7<Ԟ         fmt_trait    !   <   !  %      <                   <   --   00k )7 )7͎¶&C,1͎&͎&¶&  ͎  )7 )7͎¶&C,1== 9 ͎ //----- ---- b `MatrixGraph` is a graph datastructure backed by an adjacency matrix.e- $$ִx ִx 22mem ( $ $($$ $GraphNodeIndex!  ٌ    Տ Fu  kx  N                    " Node identifier.  . $33 Y\ Wrapper trait for an `Option`, allowing user-defined structs to be input as containers when_ defining a null element.  _ Note: this trait is currently *sealed* and cannot be implemented for types outside this crate. b /  {-P& ) / = )ږ= &           %        &   +        )7 )7 {-P )7& &  3        )7 )7 {-P )7&            )7 )7   3  *)7 )7 {-P )7 2)7 )7 {-P )7= H `NotZero` is used to optimize the memory usage of edge weights `E` in aKV [`MatrixGraph`](struct.MatrixGraph.html), replacing the default `Option` sentinel.YG Pre-requisite: edge weight should implement [`Zero`](trait.Zero.html).J` Note that if you're already using the standard non-zero types (such as `NonZeroU32`), you don'tcI have to use this wrapper and can leave the default `Null` type argument.L3픃< $3 %3=  )7 )7 *)7 )7 {-P )7 2)7 )7 {-P )7= ,3= P Base trait for types that can be wrapped in a [`NotZero`](struct.NotZero.html).SX Implementors must provide a singleton object that will be used to mark empty edges in a[* [`MatrixGraph`](struct.MatrixGraph.html).-H Note that this trait is already implemented for the base numeric types.KC Return the singleton object which can be used as a sentinel value.F 6 Return true if `self` is equal to the sentinel value.9)7 )7        z          Z  =                          Z      !!!!!!!! !!  !! !!!!!!! !  !!!! !! !! !#): Short version of `NodeIndex::new` (with Ix = `DefaultIx`)"=# & &#.9% A `MatrixGraph` with directed edges..(. ,.,..-/'......///9' A `MatrixGraph` with undirected edges./*/ ,/,0=0-0$$$$$y$$ ${gqU7//0000000h  0 ,0-00-1-00,0-1 000000001122> Create a new `MatrixGraph` with estimated capacity for nodes.1A2 (2 5G5)7 )75&5667 Remove all nodes and edges.77)7 )77 79!4879299 )7 )7:':;!4:,:2:; )7 )7; ;%>T **Panics** if the MatrixGraph is at the maximum number of nodes for its index type.>W?)7 )7?'?&?A4 Remove `a` from the graph.@@:@L@2A.A )7 )7A AAE?E)7 )7E&E'EGJG)7 )7G'GGGLYQ Update the edge from `a` to `b` to the graph, with its associated data `weight`.ITJ" Return the previous data, if any.J%J& Computes in **O(1)** time, best case.J)M Computes in **O(|V|^2)** time, worst case (matrix needs to be re-allocated).JPK5K/L )7 )7L'LLL&LSI4OA4OO4O%P=P)=PPQ5Q/6 **Panics** if an edge already exists from `a` to `b`.Q9Re **Note:** `MatrixGraph` does not allow adding parallel (“duplicate”) edges. If you want to avoidRhG this, use [`.update_edge(a, b, weight)`](#method.update_edge) instead.SJS)7 )7S'SST&TVF. Remove the edge from `a` to `b` to the graph.U1U5U/2 **Panics** if no edge exists between `a` and `b`.V5V )7 )7V VVVZB5 Return true if there is an edge between `a` and `b`.Y8Y5Y/Z)7 )7Z(ZZZ\14[#\4\5\6\)\ )7 )7 )7](]]_=4],^4^9^6^)_)7 )7 )7_(__aC5_#`5`5`=`5a )7 )7 )7a(aaadO5b,b5c9c=c5d)7 )7 )7d(dddhD5eCf2f*5f-fߜ5f=L Iterator element type is [`NodeIndex`](../graph/struct.NodeIndex.html).gOh )7 )7   hiSN)7h hhl<2i+j2j*2j/kߜ5k=G Iterator element type is [`Edges`](../graph/struct.Edges.html).kJl)7 )79 ;k)7l llq6 Create a new `MatrixGraph` from an iterable of edges.m9m6n/6n96n+o6o8o+o) use petgraph::matrix_graph::MatrixGraph;p,p/ let gr = MatrixGraph::<(), i32>::from_edges(&[p2,p3q3q,q+qq ''q8'r 'r's2s ' qqqv6t/t6t/6u96u+u6u8v)7 )7'v=v=v =w=w2x'v vvv{\ { ,{={-{{,{-{ '{{{{{{{{5{J5|$5|O}" - `Outgoing`: All edges from `a`.}% - `Incoming`: All edges to `a`.}#~ߜ5~==~O)7 )7'   hiSN)7 Y5G=%=#5AW Iterator element type is [`EdgeReference`](../graph/struct.EdgeReference.html).Z)7 )7'9 ;k)7 Å"/ Iterator over the node identifiers of a graph.2·K Created from a call to [`.node_identifiers()`][1] on a [`MatrixGraph`][2].҇NG [1]: ../visit/trait.IntoNodeIdentifiers.html#tymethod.node_identifiersJ [2]: struct.MatrixGraph.html  3#B@v tެB@v t]oԉԉ'/ 33 #B@v tެ$]o= ެ< 33 ݋ ()7 )7 {-P9 ެƎ(7ތ'J Created from a call to [`.node_references()`][1] on a [`MatrixGraph`][2].M؍E [1]: ../visit/trait.IntoNodeReferences.html#tymethod.node_references܍H= ю -2>5y*/|*/| ']o'ď- -͏2ԏЏ5y*/|ɏɏ͏͏ԏԏ' '> yE -22   ()7 )7 {-P9 !!!'D7'ӓJ Created from a call to [`.edge_references()`][1] on a [`MatrixGraph`][2].דME [1]: ../visit/trait.IntoEdgeReferences.html#tymethod.edge_referencesH=  2=-ԕ2ŕ=ʕ>* XuI!XuI!ԕԕޕ ޕ  ' '֖֖'P 2=-2=* XuI!ŗBȗ '> ̗ ԙg 2ݙ=-2=- ٙٙݙݙš ǚ '()7 )7 {-P9 ҥ?6*3-@ Created with [`.neighbors()`][1], [`.neighbors_directed()`][2].C. [1]: struct.MatrixGraph.html#method.neighbors17 [2]: struct.MatrixGraph.html#method.neighbors_directed:ݥ  2=-2=>ɪ   hiSNhiSN9 ;kܞ>ҥ?ݥ >ܞ> >^ 2=Ħ-Ԧ2=ʦ-ئ ĦĦԦԦ ()7 )7 {-P9  !!!р((:p`]((((;6ƨ08 Created with [`.edges()`][1], [`.edges_directed()`][2].;* [1]: struct.MatrixGraph.html#method.edges-3 [2]: struct.MatrixGraph.html#method.edges_directed6 2=ê-ت2ɪ=Ϊ>9 ;k;kêêتت%( ' ɫ ɫ٫ ٫''G 2=-ɬ2=9 ;kɬɬU  '>  U¯IJ>> ʯٯ Z 2=-2=-   '()7 )7 {-P9 `<< ĺ Ӻ)7 )7(<+ż<ȼ ּ((żżS(Ϳ ܿ)7 )7(3 (( J#̘(z)7 )7(3> (6 )7 )7(3>(ϣ 3)  &)7 )7 ث $)7 )7 &)7 )7 )7 )7  )7 )7]o)7 %3 #)7 )7 )7 (3/ )7 )7 )7  ]o]o    ( $ ()7 )7 {-P9 t" Create a new empty `MatrixGraph`.%  = ,-=--=,-  &,,(0 Create a new `MatrixGraph` with directed edges.3] This is a convenience method. Use `MatrixGraph::with_capacity` or `MatrixGraph::default` for`K a constructor that is generic in all the type parameters of `MatrixGraph`.N( (,,(2 Create a new `MatrixGraph` with undirected edges.5>`>N( ? Index the `MatrixGraph` by `NodeIndex` to access node weights.B6)  = ,-=--=,-  ()7 )7 )7 &>B6)  = ,-=--=,- 4 )7 )7 )7 &v  = ,-=--=,-  )7 )7 D Index the `MatrixGraph` by `NodeIndex` pair to access edge weights.G55=5  = ,-=--=,-  ?)7 )7 )7 >G59=5  = ,-=--=,- K )7 )7 )7   = ,-=--=,-  -)7 )7 V )7)7 )7 )7> v  = ,-=--=,- " )7 )7 ( )7)7 )7 )7 v  = ,-=--=,-   v  = ,-=--=,-  Ӏq  = ,ۀ-ހ=--=,؀- ؀؀ۀۀހހˁЁ     ----  #B@v tă2ǃ ؃  ƀ? -„-Ʉ?ׄ?ń-̈́?݄-ف? „„ɄɄׄׄÅȅ    hiSN7 )   -=-=--    hiSNV ňˈ݈ʼn  ƀ? -щ-ԉ??-؉?-Ήف? ʉʉΉΉщщԉԉӊ ؊) 5y*/|0 Ƌ  ƀ?Č --??Ҍ-?-ف?֌ ҌҌ )) * XuI!0 ~  ƀ?̏ --??ڏ-?Ï-ف?ޏ ڏڏ 9 ;kϐ.Ґ ؐސz  =Ց ,-=Ƒ--=̑,- ƑƑ )7 )7 .)7 )7 “/œ )7 )7Г ѓד  = ,-=-Δ-=,-Ҕ ΔΔr  =Ǖ ,-=-Օ-=,-ٕ ՕՕ@)7 )7? &)7 )7?? {-P ŗ&ޗęǙ )7 )7??ۨ??ܙ &.. II& 6/ 8(Pt $$; ;&&/ / FP_R_Rtt   Returns iterator that produces all simple paths from `from` node to `to`, which contains at least `min_intermediate_nodes` nodesS and at most `max_intermediate_nodes`, if given, limited by graph's order otherwiseV( Simple path is path without repetitions+ Algorithm is adopted from https://networkx.github.io/documentation/stable/reference/algorithms/generated/networkx.algorithms.simple_paths.all_simple_paths.html )Ũ) - .I8Ũ) Ũ)8 ))   !!!)!!!)..  (*yH uO  ^Z !̟ %ٌ  #*9+HHO O Z Z   1   =B The adjacency matrix for **Graph** is a bitmap that's computed byE `.adjacency_matrix()`. ,,----  ))7 )7 W )7)7 )7 )7  C       ͝  ? E?  , , - - - - چ           ) )7 )7چ   W )7)7 )7چ )7 .1 `UnionFind` is a disjoint-set data structure.4. $uH  a:H Wa 8 )7 )7* )7 + ۙ**     D )7 )7* )7 + **     +      / Create a new `UnionFind` of `n` disjoint sets. 2   # Return the representative for `x`. & $ **Panics** if `x` is out of bounds. ')7 )7*%?&= Write back the found representative, flattening the internal@9 datastructure in the process and quicken future lookups.<?')7 )7*6)7 )7*'I Returns `true` if the given elements belong to the same set, and returnsL `false` otherwise.)7 )7 ++ Unify the two sets containing `x` and `y`..O Return `false` if the sets were already the same, `true` if they were unified.R+ **Panics** if `x` or `y` is out of bounds..)7 )7 !(< Return a vector mapping each element to its representative.!?! * ".. %  [ */!8^   $!!s**/*? 8*  *ª . Commonly used items.+,%+C/zu _~ !y ^ !z  #  ̟   $ $ζ$ζ$$$ $%f=uu~ ~   3    @      &  <    / 4/Z/w0 N0 u0  z0 ;0"_0 !0 "0 "*1191 Ȍ1܆1  1y1 1 u1   1  1!^2 !2 "522z2 2 00 0 0 0 0 0 00000 0 0 0 0 0 111111111 1 11111 1 1 1 1 1 112 2 2 2 2222222 2 33 33 34333 33 3334 3 i3 33 334444 4  4 444 4 44 444 4 4478"! Return the opposite `Direction`.7$88:2 Return `0` for `Outgoing` and `1` for `Incoming`.95:::: =E A graph's edge type determines whether it has directed edges or not.>  >>>  @5 Convert an element like `(i, j)` or `(i, j, w)` into?8) a triple of source, target, edge weight.?,@4 For `Graph::from_edges` and `GraphMap::from_edges`.@7@,@@ @@@ @@?A?? AA, .A,AAAAAAB BB*B BC/ .C,CCCCCC CC*C CD7 3D-DDDDDDDDD DެE*E ެEE4 3E-F4FFEEEEFFF FެF*F ެFG7 3G-G4H?HGGGGGGH HެH*H ެH  + + (~f               + +           + +         )7 )7       + + G <       )7)7)7 )7 )7GGGEGEGEG EGEGEQ ! >S)7Ԟ     G Strictly monotonically increasing event time for a depth first search.KJ  _3                      )7 )7             )7)7)7 )7 )7GGGEGEGEG EGEGEQ ! >S)7Ԟ                      )7)7 )7 )7               )7)7 )7 )7                          )7 )7         )7)7 )7 )7                 )7)7 )7 )7  I       * A depth first search (DFS) visitor event.-  , 3=B             - An edge of the tree formed by the traversal.0           $ An edge to an already visited node.'            A cross or forward edge.  G For an edge *(u, v)*, if the discover time of *v* is greater than *u*,J . then it is a forward edge, else a cross edge.1           * All edges from a node have been reported.-              , ,       , 2     )7 )7       , 4     )7)7)7 )7 )7GGGEGEGEG EGEGEQ ! >S)7Ԟ     1 Control flow for `depth_first_search` callbacks. 4   ,  !)9    & Continue the DFS traversal as normal. )        G Prune the current node from the DFS traversal. No more edges from this J E node will be reported to the callback. A `DfsEvent::Finish` for this H E node will still be reported. This can be returned in response to any H / `DfsEvent`, except `Finish`, which will panic. 2       6 Stop the DFS traversal and return the provided value. 9                ,               ,           )7 )7             ,  G         )7)7)7 )7 )7GGGEGEGEG EGEGEQ ! >S)7Ԟ        G Visit nodes of a graph in a depth-first-search (DFS) emitting nodes inJ + preorder (when they are first discovered)..  H The traversal starts at a given node and only traverses nodes reachableK  from it.   `Dfs` is not recursive.  H `Dfs` does not itself borrow the graph, and because of this you can runK L a traversal over a graph while still retaining mutable access to it, if youO # use it like the following example:&  + 1 5  & let mut graph = Graph::<_,()>::new();)  let a = graph.add_node(0);  # let mut dfs = Dfs::new(&graph, a);& ( while let Some(nx) = dfs.next(&graph) {+ 0 // we can access `graph` mutably here still3  graph[nx] += 1; ,   assert_eq!(graph[a], 1); +  F **Note:** The algorithm may not behave correctly if nodes are removedI E during iteration. It may not necessarily visit added nodes or edges.H  ,  ,  HkˈS        The stack of nodes to visit      The map of discovered nodes  3 3 3 3 ,  ,  23 3      3 3 )7 )73   4 4 4 4 ,  ,  44 G4      4 4 )7)7*7 )7 )7GGGEGEGEG EGEGEQ ! >S*7Ԟ4   4  F Visit nodes in a depth-first-search (DFS) emitting nodes in postorderI 9 (each node after all its descendants have been emitted).<  ! `DfsPostOrder` is not recursive.$  @K @  , , ʬt&$k     @   ڷ@    The map of finished nodes  5 5 5 5 , , 25 @5     5 5 *7 *75   6 6 6 6 , , 46 @6     6 6 *7*7*7 *7 *7GGGEGEGEG EGEGEQ ! >S*7Ԟ6   6 7 ) A breadth first search (BFS) of a graph.0, 0 @0K @1 1  `Bfs` is not recursive.1 1 H `Bfs` does not itself borrow the graph, and because of this you can run1K @2O @2& 3 +3 13  use petgraph::visit::Bfs;3 3 @3) @4 4 # let mut bfs = Bfs::new(&graph, a);4& ( while let Some(nx) = bfs.next(&graph) {4+ @53 @5 ,5 5 @5 +5 6 ݴ@6I @6H 7 ,7 ,7 ]7P77 7 7 7 7  The queue of nodes to visit7 7 8 ڷ@8 8 77 77 77 77 ,7 ,7 277 @77 7 7 7 7 77 77 *7 *777  7 C + A topological order traversal for a graph.A. B D **Note** that `Topo` only visits nodes that are not part of cycles,BG D i.e. nodes in a true DAG. Use other visitors like `DfsPostOrder` orBG D algorithms like kosaraju_scc to handle graphs with possible cycles.CG D ,D ,D ]\E_D D D D D D PD D P8C 8C 8C 8C ,D ,D 28C @8C D D D D 8C 8C *7 *78C  C ` 3 A walker and its context wrapped into an iterator.`6 ` d-` ѩ-` '&Ђ` ` ` ` ` ` Pa a P9` 9` 9` 9` d-` ѩ-` 9` -9` ` ` ` ` 9` 9` *7 *79`  ` :` :` :` :` d-` ѩ-` G:` G:` ` ` ` ` :` :` *7*7*7 *7 *7GGGEGEGEG EGEGEQ ! >S*7Ԟ:`  ` :` ;  ; ; ; ; ; σ; ; ; ; +; ;  ; ; ; ; ; σ; ; ; ; ; +; ;  ;      +    "    +    "    + , # edge identifier "    m    # node identifier "    m    ; @ @ @ = Base graph trait: defines the associated node identifier and@@ ;     edge identifier types.@ ;            @@       @@   \ -[ -\ [ [ [ [ \3 Z \3 Z _ - -_ ́    _3 ^ _3 ^ `  ` ` ` ` ` σ` ` ` ` +` `  ` ` ` ` ` σ` ` ` ` ` +` `  `        + " "               +  #1 Return an iterator of the neighbors of node `a`.4                       ` ( ( ( % Access to the neighbors of each node@( `     ` < < < 9 The neighbors are, depending on the graph’s edge type:@< `     ` 0 0 0 - - `Directed`: All targets of edges from `a`.@0 ` B B B ? - `Undirected`: All other endpoints of edges connected to `a`.@B `   @ , 9@ @9 +  = 4 4 4 @@4 4  @    - .     +  J      #      σ    +        σ     +    # # # # %  # +# "# "# "# # # # # # # $  $ $ $ $ +$ $  $ "$ $ $ $ $ $ $ $ $  $ $ $ $ $ $ $ $ "$ %  M  M  M J Access to the neighbors of each node, through incoming or outgoing edges.@ M          Q  Q  Q N Depending on the graph’s edge type, the neighbors of a given directionalityA Q  ! ! !  are:A!  ! ! ! !  !< !< !< 9 - `Directed`, `Outgoing`: All targets of edges from `a`.A!<  ": ": ": 7 - `Directed`, `Incoming`: All sources of edges to `a`.A":  "B "B "B @@"B  # # A# #4 9A# A9# #3 # $^ $ A $ $ $  3      σ    +        σ      +    3 3 ٌ3 3 3 3 4  3 +3 "3 "4 94 4 4 4 4 4 4 4 %4 4 4 4 +4 4  4 94 4 4  4 4 4 4 4 4  4 4 4 4 94 4  0% 0% 0% " Access to the edges of each node.A0%  0 0 0 0  08 08 08 5 The edges are, depending on the graph’s edge type:A08  0 0 0 0  0% 0% 0% " - `Directed`: All edges from `a`.ЎA0%  1/ 1/ 1/ 221/  1 1 1 1  1H 1H 1H E This is an extended version of the trait `IntoNeighbors`; the formerA1H  2D 2D 2D A only iterates over the target node identifiers, while this traitA2D  23 23 23 0 yields edge references (trait [`EdgeRef`][er]).A23  3 3 3 3  3 3 3  [er]: trait.EdgeRef.htmlA3  3 3 A3 A3 A3 4) 9֕A4 ֕A94 4( 4 4/ 4 ֕A 4 4  - /     + 4 J 4   4  :      σ    +        σ      +    : : : ; ; ; <  ; +; "; "; B; ; ; ; ; ; ; ; %; ; ; ; +; ;  ; B< < < < < < < < <  < < < < < < < < B< <  5A 5A 5A > Access to all edges of each node, in the specified direction.A5A  5 5 5 5  5J 5J 5J G The edges are, depending on the direction and the graph’s edge type:A5J  6 6 6 6  6 6 6 6  61 61 61 5561  6/ 6/ 6/ ٢5٢56/  7c 7c 7c ` - `Undirected`, `Outgoing`: All edges connected to `a`, with `a` being the source of each edge.¢A7c  8c 8c 8c ` - `Undirected`, `Incoming`: All edges connected to `a`, with `a` being the target of each edge.ۣA8c  8 8 8 8  8P 8P 8P M This is an extended version of the trait `IntoNeighborsDirected`; the formerA8P  9D 9D 9D AA9D  :3 :3 :3 AA:3  : : : :  : : : AA:  : : ; A: A; ;1 9A; A9A; ;0 ; ;P < A < < <  - /     + ; J <   < <  =      σ    +        σ     +    = = = = ?  = += "= "> #> > > > > > > >  > > > > +> >  > $> > >  > > > > #> >  =6 =6 =6 3 Access to the sequence of the graph’s `NodeId`s.ٱA=6  = @= @= >2 9A> A9> >1 > >3 > A >  - . ΅    + > J > ΅΅   - . ć    + # J $ ćć㠁 $ $  G      σ    +        σ     +    G G G H H  H +H "H "H (H H "H (H H  G. G. G. + Define associated data for nodes and edgesAG.  G -G -G  H H H H H H  - 3 և    + H + H  -I 3 H H I I + H + H  Q      σ    +        σ      +    Q Q Q Q Q Q S , Q +Q "R "R &R R &R R  R R R R  R R %R R R R (R R R "R 5R R R R R R R R &R S S S +S S  S 6S S S  S S S S 5S S  Q1 Q1 Q1 . Access to the sequence of the graph’s nodesAQ1  Q /Q Q /Q AQ RD AR5 AR A R R2 9AR A9AR RC R R1 R S1 S A S  - .     + R + R J S    X      σ    +        σ      +    ٌX X X X X X Z 2 X +X "X "X %X X %X X  X X X Y  Y Y  Y Y Y Y  Y Y %Y Y Y Y (Y Y Y "Y *Y Y Y Y Y Y Y Y %Z Z Z Z +Z Z  Z *Z Z Z  Z Z Z Z *Z Z  W1 W1 W1 . Access to the sequence of the graph’s edgesAW1  X /X @X /X @X AXs AXd AX AY AY Y2 9AY A9AY Xr X Y1 Y Z1 Z A Z  - . ͈    + X + Y J Z ͈͈   ]      σ    +        σ     +    ] ] ] ] ^  ] +] "] # The kind edges in the graph.] "] (] ] (] ] ] +] ,^  ^ a^ ^ ^  ^ ^ ^ ^ ^ ^ ^ ^ ^ (^ ^ ^ a^ ^ ^  \5 \5 \5 2 Edge kind property (directed or undirected edges)A\5  ] -] -] ] ] ] ] ] ] AA] ] ] ^ ^ *7 *7^  ^  - 3     + ]  e      σ    +        σ     +    e e e e h  e +e f #:f: #% (suitable for the size of a bitmap).f(  g *g g g  g g g g g  g g #! Convert `a` to an integer index.g$  g *g g h g g g g g g g g g  g h  h h # Convert `i` to a node indexh  h +h h h  h h h h h h h  h h h h  h h  e* e* e* ' The graph’s `NodeId`s map to indicesAe*  e -e -e g$ f: f: f: ::f: f: f( f( f( AAf( f( g *7 *7g  g g3 g$ g$ g$ AAg$ g$ g *7 *7g  g g h5 h h h AAh h h *7 *7h  h h  - 3     J g *7 *7g   J g *7 *7g   g J h *7 *7Ah   h  i      σ    +        σ     +    i i i i j  i +i j  j $j j j  j j j j j  j j  i$ i$ i$ ! A graph with a known node count.Ai$  i -i -i j$ j *7 *7j  j  - ?     J j *7 *7j    l      σ    +        σ      +    l l l l l l l  jE jE jE B The graph’s `NodeId`s map to indices, in a range without holes.BjE  k k k k  kB kB kB ? The graph's node identifiers correspond to exactly the indicesBkB  k k k  `0..self.node_bound()`.Bk  l l /l Bl /l  -       {      σ    +        σ     +    Տ{ { { | ~  | +| "| # The associated map type| "| -| | +| | | |  | | | | +| | # Create a new visitor map|  } -} } }  } } } } } } } -} } #B Reset the visitor map (and resize to new size of graph if needed)}E  ~ -~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ -~ ~  {N {N {N K A graph that can create a map that tracks the visited status of its nodes.B{N  { -{ -{ |! B| | | | | BB| | | }' | | | ވBވB| | } *7 *7B}  } ~/ }E }E }E BB}E }E ~ *7*7 *7 *7B~  ~ ~  -      + | J } *7 *7}   ? ~ *7*7 *7 *7B~   ~        σ    +        σ     +       Ž ܑ  Ȏ +Ɏ "ю #% The associated adjacency matrix typeڎ( " 0   +  # Create the adjacency matrix  я 0ԏ           0  #B Return true if there is an edge from `a` to `b`, false otherwise.E #Ԑ # Computes in O(1) time.ܐ   0  ё            0         ‘ Ñ ő ɑ  ˑ ӑ ֑ ڑ  ь5 ь5 ь5 2 Create or access the adjacency matrix of a graph.Bь5       K K K H The implementor can either create an adjacency matrix, or it can returnğBK  ׍A ׍A ׍A > a placeholder if it has the needed representation internally.ɠB׍A   - -   ڎ( ڎ( ڎ( ӗBӗBڎ( ڎ(  я4    ҘBҘB  ԏ *7 *7B   ` E E E BBE E Ԑ Ԑ Ԑ Ԑ Ԑ ܐ ܐ ܐ BBܐ ܐ  *7*7 *7 *7B     ‘  -      +  J ԏ *7 *7   J  *7*7 *7 *7BĪB     ‘  A node-filtering graph adaptor. #/ , , b͎  ͎ ͎        ͎    , ,  ͎         , ,  ͎       *7 *7  ͎     , , G G͎       *7*7*7 *7 *7GGGEGEGEG EGEGEQ ! >S*7Ԟ  ͎   ,9,91 9999+ H + H  ,:,:٨0 ::::J g *7 *7g  ͎ J g *7 *7/g  ͎ g J h *7 *7/h  ͎ h  ,:,: ::::+ ]  ,;,;, ;;;;+ | J } *7 *7}  ͎ ? ~ *7*7 *7 *7ҽB~  ͎ ~ @! An edge-filtering graph adaptor.=$>B The adaptor may filter out edges. The filter implements the trait>E@ `FilterEdge`. Closures of type `Fn(G::EdgeRef) -> bool` already>C implement this trait.??L The filter may use edge source, target, id, and weight to select whether to?O include the edge or not.@4@ ,@,@=&͎@@ ͎ ͎@@@@@@@@͎@@@@,@,@B@B@@@@@@@@@,@,@B@B@@@@@@@*7 *7@ ͎@@@@@,@,@ֲB@B@@@@@@@*7*7*7 *7 *7GGGEGEGEG EGEGEQ ! >S*7Ԟ@ ͎@@ ,`,`1 ````+ H + H  ,`,`B ````+ ] B -a,a. aaaaaa+ > J >    -a,a. aaaaaa+ R + R J S    ,b,b1 bbbb ,c,c1 ccccJ j *7 *7j  ͎  ,c,c٨0 ccccJ g *7 *7g  ͎ J g *7 *7g  ͎ g J h *7 *7Bh  ͎ h  ,d,d, dddd+ | J } *7 *7}  ͎ ? ~ *7*7 *7 *7B~  ͎ ~ ! An edge-reversing graph adaptor.$7 All edges have the opposite direction with `Reversed`.:=,ɗ u5ɗɗ ,Bɗ,Bɗ*7 *7ɗɗ ,ֲBɗ*7*7*7 *7ɗ *7GGGEGEGEG EGEGEQ ! >S*7Ԟ  , 1 ɗ  + H + H # A reversed edge reference?C/SjY# C/C/*7 *7 C/G*7*7*7 *7 *7GGGEGEGEG EGEGEQ ! >S*7Ԟ  , ٨0 ɗ  J g *7 *7ɗg   J g *7 *7ɗ/g   g J h *7 *7ɗ/h   h  , 1 ɗ   , 1 ɗ  + > J > ɗɗ   , 1 ɗ  + R  + R ºJ S ɗɗ   , B ɗ  + ] B , 1 ɗ  J j *7 *7ɗj         σ    +        σ     +       +    :     &       (    :     &       (  3330 Access node and edge weights (associated data).B3 //K *7 *7 {-P *7  &K *7 *7 {-P *7 & -      J  *7 *7 {-P *7  &J  *7 *7 {-P *7  & -C ΚJ  *7 *7ΚΚ {-P *7Κ  &J  *7 *7ΚΚ {-P *7Κ  & , / ɗ  J  *7 *7ɗ/ {-P *7ɗ  &J  *7 *7ɗɗ {-P *7ɗ  &       σ    +        σ     +        +    H     &        (    H     &        (  )))& Access node and edge weights mutably.C)  CW*7 *7 {-P *7  &W*7 *7 {-P *7 & -      J *7 *7 {-P *7  &J *7 *7 {-P *7  & ,  ɗ  J *7 *7ɗ/ {-P *7C  &J *7 *7ɗC {-P *7͍C  &4 A graph element.11I A sequence of Elements, for example an iterator, is laid out as follows:1LJ Nodes are implicitly given the index of their appearance in the sequence.2M> The edges’ source and target fields refer to these indices.3AN4,4,4ڛ#{  44444 A graph node.4N4ڛ4 44 A graph edge.4N4ڛ4 45 55 53333    ,4,42323ڛ 444433*7 *7ڛڛ 3 33333    ,4,44343ڛ 444433*7*7*7 *7ڛ *7GGGEGEGEG EGEGEQ ! >S*7Ԟ 3 333 3 3 3     ,4,4ڛ44443 3 3 3    ,4,4,3 73 ڛ 44443 3 *7*7 *7ڛ *7ڛ 3 3 3 3333   ,4,4ڛ44443333   ,4,4.33ڛ 444433333 333333*7 *7ڛ 3 30 The dominance relation for some graph and root.3O   ,,..֝j?,        ,4,..֝ *7*7*7 *7֝ *7GGGEGEGEG EGEGEQ ! >S*7Ԟ    ,2,..֝ *7 *7֝֝  /! ! !   .! Workspace for a graph traversal..$W.   ,.,.(Q  ......  ....   ,.,.2.@. ......*7 *7 . .....   ,.,.4.@. ......*7*7*7 *7 *7GGGEGEGEG EGEGEQ ! >S*7Ԟ . ..NXNx 36 NN  NN  NN  NNNNNNNN NN*7 *7 N NNNNN NN*7*7*7 *7 *7GGGEGEGEG EGEGEQ ! >S*7Ԟ N NNOYO   -O3O  OCP!    y  _' _' OOOOP P  PP  PP  P!P   OOOO   -OGO3O  OGO OOOOOO*7*7*7 *7 *7GGGEGEGEG EGEGEQ ! >S*7Ԟ O  OO4 An algorithm error: a cycle was found in the graph.7j  ,ȧnd<      ـ  ,2 *7 *7    ,4 *7*7*7 *7 *7GGGEGEGEG EGEGEQ ! >S*7Ԟ        ,      ,,    *7*7 *7 *7    ÝH An algorithm error: a cycle of negative weights was found in the graph.ԜKkΝ d"yN+ { ÝΝ   ܝܝ   *7 *7   *7*7*7 *7 *7GGGEGEGEG EGEGEQ ! >S*7Ԟ             *7*7 *7 *7     =D Compressed Sparse Row ([`CSR`]) is a sparse adjacency matrix graph.G `CSR` is parameterized over: 4H43Ͳ4X4F   Using **O(|E| + |V|)** space. ! + Self loops are allowed, no parallel edges. . 2 Fast iteration of the outgoing edges of a vertex. 5 e [`CSR`]: https://en.wikipedia.org/wiki/Sparse_matrix#Compressed_sparse_row_(CSR,_CRS_or_Yale_format) hq        , , - - FOR3'                ޶                       , , - - 4 4 G G           *7*7*7 *7 *7GGGEGEGEG EGEGEQ ! >S*7Ԟ     4 Csr creation error: edges were not in sorted order.7wY    ބ *7 *7   *7*7*7 *7 *7GGGEGEGEG EGEGEQ ! >S*7Ԟ  _>z_       ,`-` -` ` `C C   9  %   }]ˣ }]ˣ __`` ` ``` ` `  ``  `9`  33333U`qNN NMNMNǁ Mjg(+ NN NMNMNǁ Mjg(+ aa  ____    !!  ,`-`-`2_ `_2_ `!__`` ```` __*7 *7 _ ! _____!!! !!!!!,`-`-`4_!`C_C_!`!__``!````!__*7*7*7 *7 *7GGGEGEGEG EGEGEQ ! >S*7Ԟ!_! !!__a;{a !!! !!!!!,a-a-a!a!aCb !!!!%! !&! wZ3P!wZ3P!!!!!aaaa!aaaa!bb!!bb!!bb!!b b!! !bb!!aaaa!!! !!!!!,a-a-a4a!aCaCa!a!aaaa!aaaa!aa*7*7*7 *7 *7GGGEGEGEG EGEGEQ ! >S*7Ԟ!a! !!aa,| ! !!!3ެ!D !! !OMڡ!ެOMڡ!!"!!NN NMNMNǁ Mjg(+!ެۃۃۃ܈ۃ! !!!3ެۃެ!!!ۃۃ*7 *7!ۃ! !!ެۃ! !!!3Gެެ!!!+7+7+7 +7 +7GGGEGEGEG EGEGEQ ! >S+7Ԟ!! !!ެ `Dot` configuration.D This enum does not have an exhaustive definition (will be expanded)G}ו'vd!!!!!!!!!!!!!!!!!!! Use indices for node labels. }!!!! Use indices for edge labels. }!!!!  Use no edge labels.} !!  !!  Use no node labels.} !!  !!' Do not print the graph/digraph string.*}!!!! Ɖ } !! !  !! !!!ˉ!+7+7+7 +7 +7GGGEGEGEG EGEGEQ ! >S+7Ԟ!! !       Š !  +7+7 +7 +7!! !  ! +7 +7!! !$=  !!.#$'!!$  !! ! !!ٌ !!. !!.!+7 +7!! ! !!.!!! !     !!.     !!. !  +7+7 +7 +7!! !       !!. !  +7+7 +7 +7!! !   !!. !!.! +7 +7!! !Î !!.!+7+7 +7 +7!! ! !!.I!+7+7 +7 +7!!!!I ! $ Edge identifier.  !!.M3!!$  !! ! !! !!.D !!.D!+7 +7!! ! !!.D!!! !     !!.     !!.D !  +7+7 +7 +7!! !       !!.D !  +7+7 +7 +7!! !   !!. !!.D! +7 +7!! ! !!.ƬD!+7+7 +7 +7!! !ˑ !!.ǮD!+7+7 +7 +7!!!!DD ! $" The graph's node type.#$! !!!,$3$;ԅG5o!!$$$$$  Associated node data.$$!!%% !!%$$$$" """,$3$4$D$"$$$$$$+7+7+7 +7 +7GGGEGEGEG EGEGEQ ! >S+7Ԟ"$" "ެ$$TW+7 +7 ] "Եެ^(" The graph's edge type.((" """4(3(rژR~/7"""(((()  Associated edge data.()""Ե)) "")** ""*((((" """4(3(GԵ(D("((((((+7+7+7 +7 +7GGGEGEGEG EGEGEQ ! >S+7Ԟ"(" "Եެ((TW+7 +7 ] "Եެ^TW+7 +7 ] " ^&:.  "".sz~"" ""  "" "".D"+7 +7"" " "".4"+7+7+7 +7 +7GGGEGEGEG EGEGEQ ! >S+7Ԟ"" "&:.  "".ھڨ@H"" ""  ""ؖ "".Dھ"+7 +7ھھ"" " "".4ھ"+7+7+7 +7ھ +7GGGEGEGEG EGEGEQ ! >S+7Ԟ"" "3 Reference to a `Graph` edge.  "" """",2"D """ "Q "& +"+"""" "" ""  "" "ٗ"" """",24"G""+7+7+7 +7 +7GGGEGEGEG EGEGEQ ! >S+7Ԟ"" "" """"-3 ""+ H ""+ H "" """"-C ""J  +7 +7 {-P +7"" "" &J  +7 +7 {-P +7"" "" & """"-C ""J +7 +7 {-P +7"" "" &J +7 +7 {-P +7"" "" & """"-B """+  ""J ԏ +7 +7" " "" J  +7+7 +7 +7DD" " ""   ‘  """""", """+ X ""+ Y ""J Z "" """  """""", ""+ 4 ""J 4 "" """ 4  """""", ""+ ; ""J < "" """ < <  """""",, ""+  ""ۼJ  "" """   """""",- ""+ # ""چJ $ "" """ $ $  """""",- ""+ > ""ɂJ > "" """  """""", """+ R ""+ R ""J S "" """  """"-B  """"-? "J j +7 +7"j " ""  """"-3 "##J g +7 +7"g " "" J g +7 +7"g " #" g J h +7 +7ƇE"h " #" h  ####-3 #+ ] ##A ####-B ###+ | ##J } +7 +7#} # ## ? ~ +7+7 +7 +7E#~ # ## ~ 3# Reference to a `StableGraph` edge.& ## ####,2#E ####Q#&e$#e$######## ## #     ## ####,24 #D ##  +7+7+7 +7 +7GGGEGEGEG EGEGEQ ! >S+7Ԟ# # ##  T W+7 +7 ] # ^I `GraphMap` is a graph datastructure using an associative arrayL of its node weights `N`.  ? It uses an combined adjacency list and sparse adjacency matrix BJ representation, using **O(|V| + |E|)** space, and allows testing for edge M existence in constant time.  " `GraphMap` is parameterized over: % 4 HE - The node weight `N` must implement `Copy` and will be used as node HB identifier, duplicated into several places in the data structure. ED It must be suitable as a hash table key (implementing `Eq + Hash`). GG The node type must also implement `Ord` so that the implementation can JL order the pair (`a`, `b`) for an edge connecting any two nodes `a` and `b`.O - `E` can be of arbitrary type.#I - Edge type `Ty` that determines whether the graph edges are directed orL undirected.L You can use the type aliases `UnGraphMap` and `DiGraphMap` for convenience.OF `GraphMap` does not allow parallel edges, but self loops are allowed.I/ Depends on crate feature `graphmap` (default).2######,,-߈fM{5{7###.## ## ##     ######,,-2 2 C ߈#  +7 +7߈߈# # #ġg~##############   ţ     ͣ  #  +7 +7# # #     #  +7+7+7 +7 +7GGGEGEGEG EGEGEQ ! >S+7Ԟ# # #                   #    +7+7 +7 +7# # #    zV~####-#; ȬE ###ށ#ށ#~~# {  {##'[oN{ c >=`,ӛ#! {4####-#; ###~~# |  |## |( |+7 +7 {-P9# |# ## | }- } +7 +7 # }# ## }# ###<3A \c##########"## ## ###### ####"     # ###<3G D #  +7+7+7 +7 +7GGGEGEGEG EGEGEQ ! >S+7Ԟ# # #ެ ; ;R$#########;;##;;##;;##;;##;;##;;## : : :ܦ :  ; ; ; ; # ; ;+7 +7# ;# #; ;  ;  ;  ;   ;  ;  ;  ;  # ;  ; +7+7 +7 +7# ;# #;  ;  ; ; ; ; # ; ;+7+7+7 +7 +7GGGEGEGEG EGEGEQ ! >S+7Ԟ# ;# #; ;<<##,<,< ^`A#########<<<<##<<##<<##< <##ʗ$<<< ##<<##< <##ʗ$=== ## ; ; ; ; ##,<2 ;,< #<< ; ;+7 +7# ;# #; ;  ;  ;  ;  ##,<,< << ;  ;  ;  ;  ##,<, ; ,< #<< ;  ; +7+7 +7 +7# ;# #;  ;  ; ; ; ; ##,<4 ;,< #<< ; ;+7+7+7 +7 +7GGGEGEGEG EGEGEQ ! >S+7Ԟ# ;# #; ;####,###߻#6:ۦ*U#6:ۦ*U## ## ###&     ####, #  +7 +7# # ## -####, . G #     4 +7+7+7 +7 +7GGGEGEGEG EGEGEQ ! >S+7Ԟ# # ##    $$  ## $  +7 +7# # $   $$  $$ $  +7 +7$ $ $   $$  $$ $  +7 +7$ $ $   $$  $$ $  +7 +7$ $ $   $$  $$ $  +7 +7$ $ $   $$  $$ $  +7 +7$ $ $   $$  $$ $  +7 +7$ $ $   $$  $$ $  +7 +7$ $ $   $$  $$ $  +7 +7$ $ $   $$  $$ $  +7 +7$ $ $   $$  $$ $  +7 +7$ $ $   $$  $$ $  +7 +7$ $ $ ,dQ `MatrixGraph` is a graph datastructure using an adjacency matrix#T representation.$$% `MatrixGraph` is parameterized over:$($4$H4%3Ͳ4%X] - Nullable type `Null`, which denotes the edges' presence (defaults to `Option`). You may&`^ specify [`NotZero`](struct.NotZero.html) if you want to use a sentinel value (such as 0)'a" to mark the absence of an edge.(%V - Index type `Ix` that sets the maximum size for the graph (defaults to `DefaultIx`).(Y)` The graph uses **O(|V^2|)** space, with fast edge insertion & amortized node insertion, as well)c@ as efficient graph search and graph algorithms on dense graphs.*C*_ This graph is backed by a flattened 2D array. For undirected graphs, only the lower triangular*b^ matrix is stored. Since the backing array stores edge weights, it is recommended to box large+a edge weights.,, $$$$ $$$$$$,,,,-, =,'--=,=, {gqU7$$$$$$,,,,, ,,',----$$&-- $$--$$&--$$..$$..$$ , , ,ǯ , $$$$ $$$$$$ =, ,,-,=,--2 ,2 ,C , ,=,,, ,$,,,,,,,,-- , ,+7 +7$ ,$ $, $$3OȱlQ)$$$$$( $$ $$(     $$3 $  +7 +7$ $ $Z `UnionFind` is a disjoint-set data structure. It tracks set membership of *n* elementsl]\ indexed from *0* to *n - 1*. The scalar type is `K` which must be an unsigned integer type._; > Too awesome not to quote:K “The amortized time per operation is **O(α(n))** where **α(n)** is theNa inverse of **f(x) = A(x, x)** with **A** being the extremely fast-growing Ackermann function.”d $$+֦ol $$$$* $$ǃ*     $$+? $  +7+7+7 +7 +7GGGEGEGEG EGEGEQ ! >S+7Ԟ$ $ $      $$+? $  +7 +7$ $ $6 Edge direction.56 eY$$$$$$$$6? An `Outgoing` edge is an outward edge *from* the current node.6B6$$66$$67= An `Incoming` edge is an inbound edge *to* the current node.6@7$$77$$7 5 5 5ij 5  5 5 5̳ 5 $ 5 5+7+7+7 +7 +7GGGEGEGEG EGEGEQ ! >S+7Ԟ$ 5$ $5 5 5 5  5  5  5 5  5  5 $ 5 5 +7+7 +7 +7$ 5$ $5  5 5 5  5  5 $ 5 5 +7+7 +7 +7$ 5$ $5  5 5 5 5 5 $ 5 5+7+7 +7 +7$ 5$ $5 5 5 5 5 5  5 5 5 5 $ 5 5 5 5 5  5 5 5 5 5 5+7 +7$ 5$ $5 5 5 5õ 5 $ 5 5+7+7 +7 +7$$$ 5$@ 5@ 5 $5 5 5 5 3$ 4 4+7 +7$ 4$ $ 4;" Marker type for a directed graph.;%;'JY ; ; ; ;  ; ; ; ; $ ; ;+7+7,7 +7 +7GGGEGEGEG EGEGEQ ! >S,7Ԟ$ ;$ $; ; 3$ 4 4,7 ,7$ 4$ $ 4<% Marker type for an undirected graph.;(< _z! < < <ö <  < < <˶ < $ < <,7,7,7 ,7 ,7GGGEGEGEG EGEGEQ ! >S,7Ԟ$ <$ $< < 3$ 4 4,7 ,7$ 4$ $ 4              > > ? ? 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P# IFF4HFF4HFF4HFF4HFF4HFF4HFFFFFFFFFFFFFF4HFF4HFF4HFF4HFF4HFF4HFF4HFF4HFF4HFF4HFF4HFF4HFF4HFF4HFF4HFF4HFF4HFF4HFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFH \X\X\XH \XLFHHDHDHDHDHDHDHDHDHDHDH DH DH DH DH DHDH5DHDHDHDHDHDHDHDHDHDHDHDHDHDHDHDH5DH:DHDHDHDHDHDHDHDHDHDHDHDHDHDHDH DH UW9: 9DH26J:/6/6/6/6/6/7/7/7/*7/67/B7/N7/Z7/f7/r7/~72ZK@ /`K/kK/vK/K/K/K/K/K/K/K/K/K/K/K/K/L 2W%: t%: q%:2:&%/t:2:&3/q:5 : NW: h'\ X:6k /p /x 0P 7^9 Wj>Z uj:2LUk 0L3 k52;l/u"; hl5LL5 ::5 ::5 :: WҐxҐ 8;9 :W$S;aW$6p< $6h\  $7p<<HW$W$\ $H=?F= =?F> =LF? <WcW(c\0cH$ pG!A=";#=#=#=#=#=#=';((<#W'T=p'T><4W']oGp']\x']\<iW'MW'M\ 'MH'F((';(((;W*W (*] 0*H<W%ɉ%u\0%ɉ8%ɉ>W&`SZ> W&cSZ>W&iLZ> W&lLZ;W&UW &U\ &UH oG;HW&W &\  &H;W( (\ (I (I?W(;<4W(oG(I?W(\X<5W(oG(Z?W(H<4W(oG(Z?W(F<5W(oG( [?W(<5W(oG(?W(DH<4W(oG(Z?W(EZ<5W(oG(Z?W(>Z<4W(oG(Z?W(L<5W(oG(Z?W(7Z<5W(oG([?W(SZ<6W(oG(Z?W(LZ<6W(oG(Z S<YW)W)\ )H&H<bW!W!\ !H< W!Wp!]x!H< W!Wp!]x!H88@LFAsFjF;BF  uuF  uu*G bG uuoGG G uuG H uu&HiHLFHH:]HCWHHP#I3I,I@I@AsFDW2 )KH;jF;jF@;AsFD4W pI xI L5DQW  IE 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2023-08-23))/home/steffen/.cargo/registry/src/index.crates.io-6f17d22bba15001f/petgraph-0.5.1/src/lib.rs/@/petgraph.5cf8a40f1173021-cgu.0/home/steffen/.cargo/registry/src/index.crates.io-6f17d22bba15001f/petgraph-0.5.1<&usize as core::fmt::Debug>::{vtable}drop_in_place()*const ()sizeusizealign__method3&usize<&usize as core::fmt::Debug>::{vtable_type}> as core::ops::function::FnMut<(usize)>>::{vtable}__method4hashbrownrawinner{impl#7}find_ref__eqindexmapmapcoreequivalentkeyentriesdata_ptrKVhash__0HashValuevalueBucketlength&[indexmap::Bucket]{closure_env#0}&mut indexmap::map::core::equivalent::{closure_env#0}_ref__selfTallocGlobalAtablebucket_maskctrlptrnon_nullu8pointer*const u8NonNullgrowth_leftitemsRawTableInnermarkerPhantomDataRawTable&hashbrown::raw::inner::RawTable{closure_env#0}>> as 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