&" WMFC[ ;[lah Rt EMF[ #p   ah% % Rp@Times New Roman RObj   $Obj  oh \<ohMZ sXG*Ax Times ew Roman E~L 9h! zh! \<dv% % % Rp@"Arial RObj   $Obj  oh @ohMZ sX3.*Cx Arialbj9bjl.F|@`~L 9h! zh! @dv% % % % % %   TX,Pj}@w@,LahP1.*% % % TTkN}@w@kLahP W% % % TTP}@w@LahPB8TTP}@w@LahP-TxP3}@w@Lah\drzewo:.%%%=)TT4P`}@w@4LahP -!ah"  TT,X }@w@,LahP -Rp@Times New Roman d RObj L $Obj oh AohMZ sXG*Ax Times ew RomanW~ 9h!L L zh!t Adv% % % Rp @Times New Roman d RObj L $Obj oh AohMZ sXG*Ax Times ew omanW~ 9h!L L zh!t Advdv% % ( Rp@Times New Roman d RObj L $Obj oh AohMZ sXG*Ax Times ew omanW~ 9h!L L zh!t Advdv% Rp@Times New RomanhM wݩd w00Gj *Ax j qu`,1 H0luB`,1 ) 8008?: 0 8 wIE wr w w! 8?: J0"~08?: J08?: j w lu7ludv% ( Rp @Times New Roman j qu`,1 H0lu wݩd w0008?: k 0 k ^$H0luBH  H w \  >u0?u&C\  qu \ \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0 k ^$H0lu wݩd w00 w l  0  l ^$H0luBH  H w  >= m >u0?u&C>= m  qu \ >= m8 ^uC?ulu  إe ! إe lu7ludv% ( Rp@Times New Roman0  l ^$H0lu wݩd w00 w  m  0 m ^$H0luBH  H w \  >u0?u&C\  qu \ \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp @Times New Roman0 m ^$H0lu wݩd w00 w n  0  n ^$H0luBH  H w  >= n >u0?u&C>= n  qu \ >= n8 ^uC?ulu  إe ! إe lu7ludv% ( Rp@Times New Roman0  n ^$H0lu wݩd w00 w  o  0 o ^$H0luBH  H w \  >u0?u&C\  qu \ \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0 o ^$H0lu wݩd w00 w p  0  p ^$H0luBH  H w  >= o >u0?u&C>= o  qu \ >= o8 ^uC?ulu  إe ! إe lu7ludv% ( Rp @Times New Roman0  p ^$H0lu wݩd w00 w  q  0 q ^$H0luBH  H w \  >u0?u&C\  qu \ \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0 q ^$H0lu wݩd w00 w r  0  r ^$H0luBH  H w  >= p >u0?u&C>= p  qu \ >= p8 ^uC?ulu  إe ! إe lu7ludv% ( Rp @Times New Roman0  r ^$H0lu wݩd w00 w  s  0 s ^$H0luBH  H w \  >u0?u&C\  qu \ \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0 s ^$H0lu wݩd w00 w t  0  t ^$H0luBH  H w  >= q >u0?u&C>= q  qu \ >= q8 ^uC?ulu  إe ! إe lu7ludv% ( Rp @Times New Roman0  t ^$H0lu wݩd w00 w  u  0 u ^$H0luBH  H w \  >u0?u&C\  qu \ \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0 u ^$H0lu wݩd w00 w v  0  v ^$H0luBH  H w  >= r >u0?u&C>= r  qu \ >= r8 ^uC?ulu  إe ! إe lu7ludv% ( Rp @Times New Roman0&" WMFC [  v ^$H0lu wݩd w00 w  w  0 w ^$H0luBH  H w \  >u0?u&C\  qu \ \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0 w ^$H0lu wݩd w00 w x  0  x ^$H0luBH  H w  >= s >u0?u&C>= s  qu \ >= s8 ^uC?ulu  إe ! إe lu7ludv% ( Rp@Times New Roman0  x ^$H0lu wݩd w00 w  y  0 y ^$H0luBH  H w \  >u0?u&C\  qu \ \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp @Times New Roman0 y ^$H0lu wݩd w00 w z  0  z ^$H0luBH  H w  >= t >u0?u&C>= t  qu \ >= t8 ^uC?ulu  إe ! إe lu7ludv% ( Rp@Times New Roman0  z ^$H0lu wݩd w00 w  {  0 { ^$H0luBH  H w \  >u0?u&C\  qu \ \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0 { ^$H0lu wݩd w00 w |  0  | ^$H0luBH  H w  >= u >u0?u&C>= u  qu \ >= u8 ^uC?ulu  إe ! إe lu7ludv% ( Rp@Times New Roman0  | ^$H0lu wݩd w00 w  }  0 } ^$H0luBH  H w \  >u0?u&C\  qu \ \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0 } ^$H0lu wݩd w00 w ~  0  ~ ^$H0luBH  H w  >= v >u0?u&C>= v  qu \ >= v8 ^uC?ulu  إe ! إe lu7ludv% ( Rp@Times New Roman0  ~ ^$H0lu wݩd w00 w    0  ^$H0luBH  H w \  >u0?u&C\  qu \ \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  ^$H0lu wݩd w00 w   0   ^$H0luBH  H w  >= w >u0?u&C>= w  qu \ >= w8 ^uC?ulu  إe ! إe lu7ludv% ( Rp@Times New Roman0   ^$H0lu wݩd w00 w    0  ^$H0luBH  H w \  >u0?u&C\  qu \ \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  ^$H0lu wݩd w00 w   0   ^$H0luBH  H w  >= x >u0?u&C>= x  qu \ >= x8 ^uC?ulu  إe ! إe lu7ludv% ( Rp@Times New Roman0   ^$H0lu wݩd w00 w    0  ^$H0luBH  H w \  >u0?u&C\  qu \ \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp @Times New Roman0  ^$H0lu wݩd w00 w   0   ^$H0luBH  H w  >= y >u0?u&C>= y  qu \ >= y8 ^uC?ulu  إe ! إe lu7ludv% ( Rp@Times New Roman0   ^$H0lu wݩd w00 w    0  ^$H0luBH  H w \  >u0?u&C\  qu \ \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  ^$H0lu wݩd w00 w   0   ^$H0luBH  H w  >= z >u0?u&C>= z  qu \ >= z8 ^uC?ulu  إe ! إe lu7ludv% ( Rp@Times New Roman0   ^$H0lu wݩd w00 w    0  ^$H0luBH  H w \  >u0?u&C\  qu \ \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  ^$H0lu wݩd w00 w   0   ^$H0luBH  H w  >= { >u0?u&C>= {  qu \ >= {8 ^uC?ulu  إe ! إe lu7ludv% ( Rp@Times New Roman0   ^$H0lu wݩd w00 w    0  ^$H0luBH  H w \  >u0?u&C\  qu \ \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp @Times New Roman0  ^$H0lu wݩd w00 w   0   ^$H0luBH  H w  >= | >u0?u&C>= |  qu \ >= |8 ^uC?ulu  إe ! إe lu7ludv% ( Rp@Times New Roman0   ^$H0lu wݩd w00 w    0  ^$H0luBH  H w \  >u0?u&C\  qu \ \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roma&" WMFC [n0  ^$H0lu wݩd w00 w   0   ^$H0luBH  H w  >= } >u0?u&C>= }  qu \ >= }8 ^uC?ulu  إe ! إe lu7ludv% ( Rp @Times New Roman0   ^$H0lu wݩd w00 w    0  ^$H0luBH  H w \  >u0?u&C\  qu \ \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  ^$H0lu wݩd w00 w   0   ^$H0luBH  H w  >= ~ >u0?u&C>= ~  qu \ >= ~8 ^uC?ulu  إe ! إe lu7ludv% ( Rp @Times New Roman0   ^$H0lu wݩd w00 w    0  ^$H0luBH  H w \  >u0?u&C\  qu \ \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  ^$H0lu wݩd w00 w   0   ^$H0luBH  H w  >=  >u0?u&C>=   qu \ >= 8 ^uC?ulu  إe ! إe lu7ludv% ( Rp@Times New Roman0   ^$H0lu wݩd w00 w    0  ^$H0luBH  H w \  >u0?u&C\  qu \ \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp @Times New Roman0  ^$H0lu wݩd w00 w   0   ^$H0luBH  H w  >=  >u0?u&C>=  qu \ >= 8 ^uC?ulu  إe ! إe lu7ludv% ( Rp@Times New Roman0   ^$H0lu wݩd w00 w    0  ^$H0luBH  H w \  >u0?u&C\  qu \ \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp @Times New Roman0  ^$H0lu wݩd w00 w   0   ^$H0luBH  H w  >=  >u0?u&C>=  qu \ >= 8 ^uC?ulu  إe ! إe lu7ludv% ( % (  '% Ld#mb`!??% ( T`l}@w@YLahTa) %T#l}@w@YLahjest drzewem zrwnowa|onym% *%%:&?%+;),:%%+*)ATT$Hl}@w@$YLahP % T`o}@w@LahTb) *To)}@w@Lahxjest drzewem binarnym% *%%:&@*)%*)ATT*oN}@w@*LahP % T`,}@w@LahTc) %T3,}@w@Lahjest drzewem binarnym peBnym% *%%:&?*)%**@*%*)ATT4X,}@w@4LahP % T`/}@w@yLahTd) *T/}@w@yLahljest drzewem AVL% *%%:&@;=3TT/}@w@yLahP % T`}@w@LahTe) %T<}@w@(Lahma operacj sumowania elementw w czasie?%**%%%% *?+;&)%%&@%*+::%%& &TT}@w@LahP % TTK}@w@8LahP %Rp@Times New Roman d RObj L $Obj oh ,ohMZ sXG*Ax Times ew RomanHN~ 9h!L L zh!t ,dv% % % Rp @Times New Roman d RObj L $Obj oh ,ohMZ sXG*Ax Times ew omanHN~ 9h!L L zh!t ,dvdv% % ( Rp@Times New Roman d RObj L $Obj oh ,ohMZ sXG*Ax Times ew omanHN~ 9h!L L zh!t ,dvdv% Rp@Times New RomanhM wݩd w00G *Ax  qu` H0luB` ) 8008?: 0 8 wIE wr w w! 8?: J0"~08?: J08?:  w lu7ludv% ( Rp @Times New Roman  qu` H0lu wݩd w0008?:  0  %H0luBH  H w \  >u0?u&C\  qu \ \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  %H0lu wݩd w00 w   0@  %H0luBH 8 H w@ M8 >u0?u&C M@ qu \ M8 ^uC?ulu@ إe ! إe &" WMFC [ lu7ludv% ( Rp@Times New Roman0@  %H0lu wݩd w00 w@  8 0  %H0luBH  H w \  >u0?u&C\  qu \ \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp @Times New Roman0  %H0lu wݩd w00 w   0@  %H0luBH 8 H w@ N8 >u0?u&C N@ qu \ N8 ^uC?ulu@ إe ! إe lu7ludv% ( Rp@Times New Roman0@  %H0lu wݩd w00 w@  8 0  %H0luBH  H w \  >u0?u&C\  qu \ \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  %H0lu wݩd w00 w   0@  %H0luBH 8 H w@ O8 >u0?u&C O@ qu \ O8 ^uC?ulu@ إe ! إe lu7ludv% ( Rp @Times New Roman0@  %H0lu wݩd w00 w@  8 0  %H0luBH  H w \  >u0?u&C\  qu \ \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  %H0lu wݩd w00 w   0@  %H0luBH 8 H w@ P8 >u0?u&C P@ qu \ P8 ^uC?ulu@ إe ! إe lu7ludv% ( Rp @Times New Roman0@  %H0lu wݩd w00 w@  8 0  %H0luBH  H w \  >u0?u&C\  qu \ \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  %H0lu wݩd w00 w   0@  %H0luBH 8 H w@ Q8 >u0?u&C Q@ qu \ Q8 ^uC?ulu@ إe ! إe lu7ludv% ( Rp @Times New Roman0@  %H0lu wݩd w00 w@  8 0  %H0luBH  H w \  >u0?u&C\  qu \ \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  %H0lu wݩd w00 w   0@  %H0luBH 8 H w@ R8 >u0?u&C R@ qu \ R8 ^uC?ulu@ إe ! إe lu7ludv% ( Rp @Times New Roman0@  %H0lu wݩd w00 w@  8 0  %H0luBH  H w \  >u0?u&C\  qu \ \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  %H0lu wݩd w00 w   0@  %H0luBH 8 H w@ S8 >u0?u&C S@ qu \ S8 ^uC?ulu@ إe ! إe lu7ludv% ( Rp@Times New Roman0@  %H0lu wݩd w00 w@  8 0  %H0luBH  H w \  >u0?u&C\  qu \ \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp @Times New Roman0  %H0lu wݩd w00 w   0@  %H0luBH 8 H w@ T8 >u0?u&C T@ qu \ T8 ^uC?ulu@ إe ! إe lu7ludv% ( Rp@Times New Roman0@  %H0lu wݩd w00 w@  8 0  %H0luBH  H w \  >u0?u&C\  qu \ \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  %H0lu wݩd w00 w   0@  %H0luBH 8 H w@ U8 >u0?u&C U@ qu \ U8 ^uC?ulu@ إe ! إe lu7ludv% ( Rp@Times New Roman0@  %H0lu wݩd w00 w@  8 0  %H0luBH  H w \  >u0?u&C\  qu \ \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  %H0lu wݩd w00 w   0@  %H0luBH 8 H w@ V8 >u0?u&C V@ qu \ V8 ^uC?ulu@ إe ! إe lu7ludv% ( Rp@Times New Roman0@  %H0lu wݩd w00 w@  8 0  %H0luBH  H w \  >u0?u&C\  qu \ \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  %H0lu wݩd w00 w   0@  %H0luBH 8 H w@ W8 >u0?u&C W@ qu \ W8 ^uC?ulu@ إe ! إe lu7ludv% ( Rp@Times New Roman0@  %H0lu wݩd w00 w@  8 0  %H0luBH  H w \  >u0?u&C\  qu \ \ 8 &" WMFC [^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  %H0lu wݩd w00 w   0@  %H0luBH 8 H w@ X8 >u0?u&C X@ qu \ X8 ^uC?ulu@ إe ! إe lu7ludv% ( Rp@Times New Roman0@  %H0lu wݩd w00 w@  8 0  %H0luBH  H w \  >u0?u&C\  qu \ \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp @Times New Roman0  %H0lu wݩd w00 w   0@  %H0luBH 8 H w@ Y8 >u0?u&C Y@ qu \ Y8 ^uC?ulu@ إe ! إe lu7ludv% ( Rp@Times New Roman0@  %H0lu wݩd w00 w@  8 0  %H0luBH  H w \  >u0?u&C\  qu \ \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  %H0lu wݩd w00 w   0@  %H0luBH 8 H w@ Z8 >u0?u&C Z@ qu \ Z8 ^uC?ulu@ إe ! إe lu7ludv% ( Rp@Times New Roman0@  %H0lu wݩd w00 w@  8 0  %H0luBH  H w \  >u0?u&C\  qu \ \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  %H0lu wݩd w00 w   0@  %H0luBH 8 H w@ [8 >u0?u&C [@ qu \ [8 ^uC?ulu@ إe ! إe lu7ludv% ( Rp@Times New Roman0@  %H0lu wݩd w00 w@  8 0  !%H0luBH  H w \  >u0?u&C\  qu \ \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp @Times New Roman0  !%H0lu wݩd w00 w   0@  "%H0luBH 8 H w@ \8 >u0?u&C \@ qu \ \8 ^uC?ulu@ إe ! إe lu7ludv% ( Rp@Times New Roman0@  "%H0lu wݩd w00 w@  8 0  #%H0luBH  H w \  >u0?u&C\  qu \ \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  #%H0lu wݩd w00 w   0@  $%H0luBH 8 H w@ ]8 >u0?u&C ]@ qu \ ]8 ^uC?ulu@ إe ! إe lu7ludv% ( Rp @Times New Roman0@  $%H0lu wݩd w00 w@  8 0  %%H0luBH  H w \  >u0?u&C\  qu \ \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  %%H0lu wݩd w00 w   0@  &%H0luBH 8 H w@ ^8 >u0?u&C ^@ qu \ ^8 ^uC?ulu@ إe ! إe lu7ludv% ( Rp @Times New Roman0@  &%H0lu wݩd w00 w@  8 0  '%H0luBH  H w \  >u0?u&C\  qu \ \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  '%H0lu wݩd w00 w   0@  (%H0luBH 8 H w@ _8 >u0?u&C _@ qu \ _8 ^uC?ulu@ إe ! إe lu7ludv% ( Rp@Times New Roman0@  (%H0lu wݩd w00 w@  8 0  )%H0luBH  H w \  >u0?u&C\  qu \ \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp @Times New Roman0  )%H0lu wݩd w00 w   0@  *%H0luBH 8 H w@ `8 >u0?u&C `@ qu \ `8 ^uC?ulu@ إe ! إe lu7ludv% ( Rp@Times New Roman0@  *%H0lu wݩd w00 w@  8 0  +%H0luBH  H w \  >u0?u&C\  qu \ \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp @Times New Roman0  +%H0lu wݩd w00 w   0@  ,%H0luBH 8 H w@ a8 >u0?u&C a@ qu \ a8 ^uC?ulu@ إe ! إe lu7ludv% ( % (   fTNX}@w@Lah* wg niektrych zrdeB 'b' w 'b$6%&!%&$!&!&&! & 5 &TTYNq}@w@YLahP-THrN }@w@r*Lahdrzewie' znaczy balanced (zrwnowa|one). B&!"5! !&"!"$&!!&!!&!&" WMFC [&5&&6!!&&!2TT N }@w@ LahP-T N }@w@ Lahpdrzewo z definicji&!!5&!&!&!TT N }@w@ LahP TD NA}@w@ )Lahjest zrwnowa|one. Szczegln wBasno[ci !!&5&&5"!&&!*!!!!%&&!5!&&!!   fTT}@w@LahPb&TT}@w@LahP-TTR}@w@,Lahdrzewa jest jego szeroko[/rozBo|ysto[c. W b&!!5!!!%&!!&%&!&!&!$&!F&TTSk}@w@SLahP-T li}@w@lNLahdrzewie ka|dy wierzchoBek poza korzeniem musi mie n...2n+1 wzBw potomnych. &!!5!&!!'$5"!!&&!%&&!!%&!!&!99&9!!&%&*&5!!&5&&&9&%!& Rp@Times New Roman d RObj L $Obj oh ,ohMZ sXG*Ax Times ew RomanH~ 9h!L L zh!t ,dv% % %  % % %  fTd O}@w@>YLahWierzchoBek drzewa binarnego z definicji ma <= 2 wzBy potomne, a drzewo AVL z definicji F!!!&&!%&!"5!&&!&!%&!&!&!9!+*&5!!%&&&9&!!&!!5&57-!&"&!T O}@w@ >Lahxjest drzewem binarnym!&!!6"9&&!&%:% % % TT K}@w@>LahP   % % % TTQ}@w@LahP % % % % TX,j}@w@,LahP2.*% % % TTk}@w@kLahP W% % % T}@w@ LahdDrzewo AVL:<%%%=*<<7TT}@w@LahP -!ah" Rp@Times New Roman d RObj L $Obj oh |ohMZ sXG*Ax Times ew Roman@L~ 9h!L L zh!t |dv% % %  TTm}@w@ZLahP % '% Ldo% od`!??% ( T`p}@w@LahTa) %Ttp }@w@1Lahkoszt pesymistyczny wyszukiwania elementu wynosi )* %*%!)@ (%&*(;)!%*);&)%%&@%))<))+ Tx p% }@w@ Lah\O(logn)<*))TT& pJ }@w@& LahP % '% Ld.`!??% ( T`-}@w@LahTb) *T-}@w@Lahpjest drzewem BST % *%%:&@8.4TT-}@w@LahP % '% Ld/$/c`!??% ( T`0}@w@zLahTc) %T0$}@w@zLahxjest drzewem binarnym% *%%:&?*)%**@TT%0:}@w@%zLahP TT;0_}@w@;zLahP % % % % TT}@w@LahP %% % %   fTTD }@w@3 LahP*$TD }@w@3 Lah`Drzewo AVL7!"5&57-TD }@w@3 Laht, nazywane rwnie| &!"%5!&!'5&!!TD }@w@3 Lahxdrzewem dopuszczalnym&!!6"9&&&&!!!!&%9T- D }@w@3 Lahp, to zrwnowa|one &!&5&&6!!&&!T. vD }@w@. 3 Lahbinarne drzewo poszukiwaD&&!&!&!!5&&&!&%5!&TTwD }@w@w3 LahP TlED }@w@3 LahX(BST)2*-TTFgD }@w@F3 LahP "   fTF B }@w@ LahdAlgorytmy p5%&&" WMFC {[$:%&TCF  }@w@C vLah8odstawowych operacji na drzewie AVL przypominaj te z binarnych drzew poszukiwaD, ale s poprzedzane lub nastpuj po &&!5'6$!&&&!!!&!&!!5!57-&"$&'9&!!!!&&!&$!&&!!5&&!&%5!&!!!&&&!!&!!&!&%&!!&%!&&   fT<  }@w@ }LahHnich jedna lub wicej "rotacji". Wszystkie algorytmy s zazwyczaj realizowane poprzez rekurencj. Koszt ka|dej operacji to O(&!&!%&!&&5!!!&!!G"$%!!%&$:$!!""6%!!!!!!&5!&!&&&!!!!%&!&!!6&!%!!&!&&!!!&6Tx  }@w@ Lah\log n).&%&TT  }@w@ LahP "  % % % TT O }@w@< LahP %% % % Rp@Times New Roman RObj   $Obj  oh \<ohMZ sXG*Ax Times ew oman E~L 9h! zh! \<dvdv% Rp@Times New RomanhM wܩd w00G *Ax  qu`,1 H0luB`,1 ) 8008?: 0 8 wIE wr w w! 8?: J0"~08?: J08?:  w lu7ludv% ( Rp @Times New Roman  qu`,1 H0lu wܩd w0008?:  0  j/%H0luBH x T w ex >u0?u'C e qu h e8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  j/%H0lu wܩd w00 w  x 0  j0%H0luBH  T w \  >u0?u'C\  qu h \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  j0%H0lu wܩd w00 w   0  j1%H0luBH x T w fx >u0?u'C f qu h f8 ^uC?ulu إe ! إe lu7ludv% ( Rp @Times New Roman0  j1%H0lu wܩd w00 w  x 0  j2%H0luBH  T w \  >u0?u'C\  qu h \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  j2%H0lu wܩd w00 w   0  j3%H0luBH x T w gx >u0?u'C g qu h g8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  j3%H0lu wܩd w00 w  x 0  j4%H0luBH  T w \  >u0?u'C\  qu h \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp @Times New Roman0  j4%H0lu wܩd w00 w   0  j5%H0luBH x T w hx >u0?u'C h qu h h8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  j5%H0lu wܩd w00 w  x 0  j6%H0luBH  T w \  >u0?u'C\  qu h \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp @Times New Roman0  j6%H0lu wܩd w00 w   0  j7%H0luBH x T w ix >u0?u'C i qu h i8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  j7%H0lu wܩd w00 w  x 0  j8%H0luBH  T w \  >u0?u'C\  qu h \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp @Times New Roman0  j8%H0lu wܩd w00 w   0  j9%H0luBH x T w jx >u0?u'C j qu h j8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  j9%H0lu wܩd w00 w  x 0  j:%H0luBH  T w \  >u0?u'C\  qu h \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp @Times New Roman0  j:%H0lu wܩd w00 w   0  j;%H0luBH x T w kx >u0?u'C k qu h k8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  j;%H0lu wܩd w00 w  x 0  j<%H0luBH  T w \  >u0&" WMFC [[?u'C\  qu h \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  j<%H0lu wܩd w00 w   0  j=%H0luBH x T w lx >u0?u'C l qu h l8 ^uC?ulu إe ! إe lu7ludv% ( Rp @Times New Roman0  j=%H0lu wܩd w00 w  x 0  j>%H0luBH  T w \  >u0?u'C\  qu h \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  j>%H0lu wܩd w00 w   0  j?%H0luBH x T w mx >u0?u'C m qu h m8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  j?%H0lu wܩd w00 w  x 0  j@%H0luBH  T w \  >u0?u'C\  qu h \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  j@%H0lu wܩd w00 w   0  jA%H0luBH x T w nx >u0?u'C n qu h n8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  jA%H0lu wܩd w00 w  x 0  jB%H0luBH  T w \  >u0?u'C\  qu h \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  jB%H0lu wܩd w00 w   0  jC%H0luBH x T w ox >u0?u'C o qu h o8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  jC%H0lu wܩd w00 w  x 0  jD%H0luBH  T w \  >u0?u'C\  qu h \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  jD%H0lu wܩd w00 w   0  jE%H0luBH x T w px >u0?u'C p qu h p8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  jE%H0lu wܩd w00 w  x 0  jF%H0luBH  T w \  >u0?u'C\  qu h \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  jF%H0lu wܩd w00 w   0  jG%H0luBH x T w qx >u0?u'C q qu h q8 ^uC?ulu إe ! إe lu7ludv% ( Rp @Times New Roman0  jG%H0lu wܩd w00 w  x 0  jH%H0luBH  T w \  >u0?u'C\  qu h \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  jH%H0lu wܩd w00 w   0  jI%H0luBH x T w rx >u0?u'C r qu h r8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  jI%H0lu wܩd w00 w  x 0  jJ%H0luBH  T w \  >u0?u'C\  qu h \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  jJ%H0lu wܩd w00 w   0  jK%H0luBH x T w sx >u0?u'C s qu h s8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  jK%H0lu wܩd w00 w  x 0  jL%H0luBH  T w \  >u0?u'C\  qu h \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  jL%H0lu wܩd w00 w   0  jM%H0luBH x T w tx >u0?u'C t qu h t8 ^uC?ulu إe ! إe lu7ludv% ( Rp @Times New Roman0  jM%H0lu wܩd w00 w  x 0  jN%H0luBH  T w \  >u0?u'C\  qu h \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  jN%H0lu wܩd w00 w   0  jO%H0luBH x T w ux >u0?u'C u qu h u8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  jO%H0lu wܩd w00 w  x 0  jP%H0luBH  T w \  >u0?u'C\  qu h \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp @Times New Roman0  jP%H0lu wܩd w00 w   0  jQ%H0luBH &" WMFC ;[x T w vx >u0?u'C v qu h v8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  jQ%H0lu wܩd w00 w  x 0  jR%H0luBH  T w \  >u0?u'C\  qu h \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp @Times New Roman0  jR%H0lu wܩd w00 w   0  jS%H0luBH x T w wx >u0?u'C w qu h w8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  jS%H0lu wܩd w00 w  x 0  jT%H0luBH  T w \  >u0?u'C\  qu h \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  jT%H0lu wܩd w00 w   0  jU%H0luBH x T w xx >u0?u'C x qu h x8 ^uC?ulu إe ! إe lu7ludv% ( Rp @Times New Roman0  jU%H0lu wܩd w00 w  x 0  jV%H0luBH  T w \  >u0?u'C\  qu h \ 8 ^uC?ulu إe ! إe lu7ludv% ( Rp@Times New Roman0  jV%H0lu wܩd w00 w   0  jW%H0luBH x T w yx >u0?u'C y qu h y8 ^uC?ulu إe ! إe lu7ludv% ( Rp @Times New Roman0  jW%H0lu wܩd w00 w  x 0  jX%H0luBH  T w \  >u0?u'C\  qu h \ 8 ^uC?ulu إe ! إe lu7ludv% ( % ( Rp @Times New Roman RObj   $Obj  oh \<ohMZ sXG*Ax Times ew oman E~L 9h! zh! \<dvdv% % (  TX,S j }@w@, LahP3.*% % % TTkQ  }@w@k LahP W% % % TdS z }@w@ LahTWstaS *T{S a }@w@{ Lahtwiamy do pustego dr=+C*.*.. %**.%TbS }@w@b !Lahzewa BST kolejno: 1 0 3 4 6 2 5. %%=*8.7-*%.********TX S Y }@w@ LahPWyS*TxZ S W }@w@Z Lah\pisujc. .*%TTX S l }@w@X LahP T<m S ? }@w@m (Lahwarto[ci wzBw przy przej[ciu drzewa w =*$* %=%%)=.%%*.%%% %..%%%=*=!ah"  Tp  }@w@ LahXporzd.*%%*.T` , }@w@ LahTku ..T-  }@w@- Lahtinorder, otrzymamy:.*%.%%*%%+C+D*TT C }@w@ LahP -!ah"  % % % TT o }@w@\ LahP % T`r  }@w@ LahTa) %Tdr  }@w@ LahT0 2 **TXr  }@w@ LahP5 *Txr  }@w@ Lah\6 4 3 1***)TTr  }@w@ LahP % T` . }@w@ LahTb) *Td . }@w@ LahT0 2 **TX . }@w@ LahP5 *Tx . }@w@ Lah\6 4 3 1***)TT . }@w@ LahP % '% Ld0  0 `!??% ( T`1  }@w@{ LahTc) %T1  }@w@{ Lahh0 1 2 3 4 5 6******)TT1  }@w@{ LahP % TT  }@w@ LahP % % % %  fT E }@w@4 !Lah* inOrder jest zawsze posortowany$&6&!!!"5"!&&&&5!&&% % % TT G }@w@4 LahP %  TTG  }@w@ LahP % % % % TX, j}@w@, LahP4.*% % % TTk }@w@k LahP W% % % T, }@w@ %LahWstawiamy do pustego drzewa BST kolejS *=+C*.*.. %**.%&" WMFC [%%=*8.7-*%TX }@w@ LahPno.*T }@w@ Lahl: 6 4 3 5 2 0 1*******T ?}@w@ 4Lah. Wypisujc warto[ci wzBw przy przej[ciu drzewa w S*. .*%=*$* %=%%)=.%%*.%%% %..%%%=*=!ah"  Tpd}@w@SLahXporzd.*%%*.T`,d}@w@SLahTku ..T-d}@w@-SLahtinorder, otrzymamy:.*%.%%*%%+C+D*TTCd}@w@SLahP -!ah"  % % % TTg}@w@LahP % T`#}@w@LahTa) %T#}@w@Lahh1 0 2 3 5 4 6 *******TT#}@w@LahP TT#}@w@LahP % T`&}@w@pLahTb) *T&}@w@pLahh1 0 2 3 5 4 6 *******TT&}@w@pLahP TT&}@w@pLahP % '% Ld`!??% ( T`}@w@LahTc) %T}@w@ Lahh0 1 2 3 4 5 6******)TT}@w@LahP % TTC}@w@0LahP % % % %  fTF}@w@!Lah* inOrder jest zawsze posortowany$&6&!!!"5"!&&&&5!&&TTF}@w@LahP "  % % % TT}@w@LahP % % % % TX,jY}@w@,HLahP5.*% % % TTkZ}@w@kHLahP W% % % TDY}@w@H)LahWstawiamy do pustego drzewa BST kolejno: S *=+C*.*.. %**.%%%=*8.7-*%.*TT:Y}@w@HLahP0*TT;OY}@w@;HLahP TTPyY}@w@PHLahP4*TTzY}@w@zHLahP TXY}@w@HLahP1 *TTY}@w@HLahP2*TT Y}@w@HLahP Td  Y}@w@ HLahT3 6 **T l Y}@w@ H Lahh5. Wypisujc *S*. .*%T<m ?Y}@w@m H(Lahwarto[ci wzBw przy przej[ciu drzewa w =*$* %=%%)=.%%*.%%% %..%%%=*=!ah"  Tp]}@w@LahXporzd.*%%*.T`],}@w@LahTku ..T-]}@w@-Lahtinorder, otrzymamy:.*%.%%*%%+C+D*TT]C}@w@LahP -!ah"  TT}@w@LahP - '% Ldy`!??% ( % % % T`x}@w@eLahTa) %Tx}@w@e Lahh0 1 2 3 4 5 6*******TTx}@w@eLahP TTx}@w@eLahP % T`{}@w@LahTb) *T{}@w@ Lahh3 2 1 5 6 4 0******)TT{}@w@LahP % T`8}@w@%LahTc) %T8}@w@% Lahh3 2 1 5 6 4 0******)TT8}@w@%LahP % TT;}@w@LahP % % % %  fT}@w@!Lah* inOrder jest zawsze posortowany$&6&!!!"5"!&&&&5!&&TT}@w@LahP "  % % % TTN}@w@;LahP % % % % TX,Rj}@w@,LahP6.*% % % TTkP}@w@kLahP W% % %  &WMFC [T<R}@w@(LahWstawiamy do pustego drzewa BST kolejno:S *=+C*.*.. %**.%%%=*8.7-*%.*TTR}@w@LahP TR }@w@ Lahh4 0 6 1 3 5 2*******TT R}@w@ ,Lah. Wypisujc warto[ci wzBw przy przej[ciu dS*. .*%=*$* %=%%)=.%%*.%%% %..T|R?}@w@Lah\rzewa w %%%=*=!ah"  Tp }@w@LahXporzd.*%%*.T`, }@w@LahTku ..T- }@w@-Lahtinorder, otrzymamy:.*%.%%*%%+C+D*TTC }@w@LahP -!ah"  TT,Xm}@w@,\LahP - % % % T`p}@w@LahTa) %Tp}@w@ Lahh2 3 1 0 5 6 4******)TTp}@w@LahP % T`-}@w@LahTb) *T-}@w@ Lahh2 3 1 0 5 6 4******)TT-}@w@LahP % '% Ld//`!??% ( T`0}@w@zLahTc) %T0}@w@z Lahh0 1 2 3 4 5 6******)TT0}@w@zLahP % TT}@w@LahP % % % %  fTC}@w@2!Lah* inOrder jest zawsze posortowany$&6&!!!"5"!&&&&5!&&TTC}@w@2LahP "  % % % TTF}@w@LahP % % % % TX,j}@w@,LahP7.*% % % TTk}@w@kLahP W% % % TD}@w@)LahWstawiamy do pustego drzewa BST kolejno: S *=+C*.*.. %**.%%%=*8.7-*%.*T }@w@Lahh2 0 6 4 3 1 5.*******Tx *}@w@ 2LahWypisujc warto[ci wzBw przy przej[ciu drzewa w S*. .*%=*%* %=%%)=.%%*.%%% %..%%%=*=!ah"  Tpb}@w@QLahXporzd.*%%*.T`,b}@w@QLahTku ..T-b}@w@-QLahpinorder, otrzymam.*%.%%*%%+C+DTXb}@w@QLahPy:*TTCb}@w@QLahP -!ah"  TT,fX}@w@,LahP -% % 6h6ah6a66g6`g6`66f6_f6_66e6^e6^66d6]d6]66c6\c6\66b6[b6[66a6Za6Z66`6Y`6Y6 6 _6X_6X 6  6 ^6W^6W 6  6 ]6V]6V 6  6 \6U\6U 6  6 [6T[6T 6 6Z6SZ6S66Y6RY6R66X6QX6Q66W6PW6P66V6OV6O6  KS."System?????????--@Times New Roman---@"Arial------ 2 P$SK1.--- 2 P,SK --- 2 P6SKB 2 P=SK-2 P@SKdrzewo:  2 PbSK ,KS' 2 \$SK @Times New Roman--- @Times New Roman--@Times New Roman-@Times New Roman- @Times New Roman-@Times New Roman-@Times New Roman- @Times New Roman-@Times New Roman-@Times New Roman- @Times New Roman-@Times New Roman- @Times New Roman-@Times New Roman- @Times New Roman-@Times New Roman- @Times New Roman-@Times New Roman-@Times New Roman- @Times New Roman-@Times New Roman-@Times New Roman-@Times New Roman-@Times New Roman-@Times New Roman-@Times New Roman-@Times New Roman-@Times New Roman-@Times New Roman- @Times New Roman-@Times New Roman-@Times New Roman-@Times New Roman-@Times New Roman-@Times New Roman- @Times New Roman-@Times New Roman-@Times New Roman- @Times New Roman-@Times New Roman- @Times New Roman-@Times New Roman-@Times New Roman- @Times New Roman-@Times New Roman- @Times New Roman--- @ ! ^6-2 g6SKa) e22 g@SKjest drzewem zrwnowaonym 2 gSK 2 r6SKb) e+2 rASKjest drzewem binarnym 2 rSK 2 ~6SKc) e52 ~@SKjest drzewem binarnym penym 2 ~SK 2 6SKd) e#2 ASKjest drzewem AVL 2 SK 2 6SKe) eG2 @(SKma operacj sumowania elementw w czasie 2 SK  2 6SK @Times New Roman--- @Times New Roman--@Times New Roman-@Times New Roman- @Times New Roman-@Times New Roman-@Times New Roman- @Times New Roman-@Times New Roman-@Times New Roman- @Times New Roman-@Times New Roman- @Times New Roman-@Times New Roman- @Times New Roman-@Times New Roman- @Times New Roman-@Times New Roman-@Times New Roman- @Times New Roman-@Times New Roman-@Times New Roman-@Times New Roman-@Times New Roman-@Times New Roman-@Times New Roman-@Times New Roman-@Times New Roman-@Times New Roman- @Times New Roman-@Times New Roman-@Times New Roman-@Times New Roman-@Times New Roman-@Times New Roman- @Times New Roman-@Times New Roman-@Times New Roman- @Times New Roman-@Times New Roman- @Times New Roman-@Times New Roman-@Times New Roman- @Times New Roman-@Times New Roman- @Times New Roman-- f:2 6SK* wg niektrych rde 'b' w 'b 2 SK-J2 *SKdrzewie' znaczy balanced (zrwnowaone). B 2 LSK-&2 OSKdrzewo z definicji 2 SK I2 )SKjest zrwnowaone. Szczegln wasnoci B  f 2 6SKb 2 ;SK-M2 >,SKdrzewa jest jego szeroko/rozoystoc. W b 2 SK-2 NSKdrzewie kady wierzchoek poza korzeniem musi mie n...2n+1 wzw potomnych.  @Times New Roman------ f2 6YSKWierzchoek drzewa binarnego z definicji ma <= 2 wzy potomne, a drzewo AVL z definicji +2 SKjest drzewem binarnym--- 2 SK  --- 2 6SK ---2 $SK2.--- 2 ,SK ---2 6 SKDrzewo AVL: 2 rSK ,KS'@Times New Roman--- 2 6SK - @ ! 6-2 6SKa) eU2 @1SKkoszt pesymistyczny wyszukiwania elementu wynosi 2 SKO(logn)  2 8SK - @ ! U6-2 6SKb) o%2 ASKjest drzewem BST  2 SK - @ ! h6-2 6SKc) o+2 @SKjest drzewem binarnym 2 SK  2 SK --- 2 6SK --- f 2 6SK*2 : SKDrzewo AVL(2 lSK, nazywane rwnie y+2 SKdrzewem dopuszczalnym&2 SK, to zrwnowaone 12 WSKbinarne drzewo poszukiwa 2 SK 2 SK(BST)n 2 SK   f2 %6 SKAlgorytmy p2 %dvSKodstawowych operacji na drzewie AVL przypominaj te z binarnych drzew poszukiwa, ale s poprzedzane lub nastpuj po   f2 /6}SKnich jedna lub wicej "rotacji". Wszystkie algorytmy s zazwyczaj realizowane poprzez rekurencj. Koszt kadej operacji to O(2 /SKlog n).  2 /SK  --- 2 ;6SK ---@Times New Roman-@Times New Roman-  @Times New Roman- @Times New Roman- @Times New Roman-  @Times New Roman- @Times New Roman- @Times New Roman-  @Times New Roman- @Times New Roman-  @Times New Roman- @Times New Roman-  @Times New Roman- @Times New Roman-  @Times New Roman- @Times New Roman- @Times New Roman-  @Times New Roman- @Times New Roman- @Times New Roman- @Times New Roman- @Times New Roman- @Times New Roman- @Times New Roman- @Times New Roman- @Times New Roman- @Times New Roman-  @Times New Roman- @Times New Roman- @Times New Roman- @Times New Roman- @Times New Roman- @Times New Roman-  @Times New Roman- @Times New Roman- @Times New Roman-  @Times New Roman- @Times New Roman-  @Times New Roman- @Times New Roman- @Times New Roman-  @Times New Roman- @Times New Roman-  @Times New Roman- -  @Times New Roman--2 F$SK3.--- 2 F,SK ---2 F6SKWsta (2 FLSKwiamy do pustego dr=2 F!SKzewa BST kolejno: 1 0 3 4 6 2 5. 2 F/SKWy 2 F>SKpisujc  2 F\SK G2 F_(SKwartoci wzw przy przejciu drzewa w ,KS'2 R6SKporzd2 RTSKku z(2 RaSKinorder, otrzymamy: 2 RSK ,KS'--- 2 ]6SK 2 i6SKa) z2 i@SK0 2 2 iOSK5 2 iWSK6 4 3 1  2 irSK 2 t6SKb) 2 tASK0 2 2 tPSK5 2 tWSK6 4 3 1  2 tsSK - @ ! <w6-2 6SKc) 2 @ SK0 1 2 3 4 5 6 2 rSK  2 6SK --- f=2 6!SK* inOrder jest zawsze posortowany--- 2 SK   2 6SK ---2 $SK4.--- 2 ,SK ---C2 6%SKWstawiamy do pustego drzewa BST kolej 2 SKno"2 SK: 6 4 3 5 2 0 1Y2 *4SK. Wypisujc wartoci wzw przy przejciu drzewa w  ,KS'2 6SKporzd2 TSKku z(2 aSKinorder, otrzymamy: 2 SK ,KS'--- 2 6SK 2 6SKa) z 2 @SK1 0 2 3 5 4 6  2 uSK  2 SK 2 6SKb) z 2 ASK1 0 2 3 5 4 6  2 uSK  2 SK - @ ! <6-2 6SKc) z2 @ SK0 1 2 3 4 5 6 2 rSK  2 6SK --- f=2 6!SK* inOrder jest zawsze posortowanyo 2 SK  --- 2 6SK ---2 $SK5.--- 2 ,SK ---I2 6)SKWstawiamy do pustego drzewa BST kolejno:   2 SK0 2 SK  2 SK4 2 SK 2 SK1  2 SK2 2 SK 2 SK3 6 2 % SK5. Wypisujc  G2 _(SKwartoci wzw przy przejciu drzewa w ,KS'2 6SKporzd2 TSKku z(2 aSKinorder, otrzymamy: 2 SK ,KS' 2 *6SK - @ ! <-6----2 66SKa) z2 6@ SK0 1 2 3 4 5 6 2 6rSK  2 6uSK 2 A6SKb) z2 AA SK3 2 1 5 6 4 0 2 AsSK 2 M6SKc) z2 M@ SK3 2 1 5 6 4 0 2 MrSK  2 X6SK --- f=2 c6!SK* inOrder jest zawsze posortowanyz 2 cSK  --- 2 n6SK ---2 z$SK6.--- 2 z,SK ---G2 z6(SKWstawiamy do pustego drzewa BST kolejno:  2 zSK 2 z SK4 0 6 1 3 5 2M2 z*,SK. Wypisujc wartoci wzw przy przejciu d 2 zSKrzewa w ,KS'2 6SKporzd2 TSKku z(2 aSKinorder, otrzymamy: 2 SK ,KS' 2 $SK ---2 6SKa) z2 @ SK2 3 1 0 5 6 4 2 rSK 2 6SKb) z2 A SK2 3 1 0 5 6 4 2 sSK - @ ! <6-2 6SKc) z2 @ SK0 1 2 3 4 5 6 2 rSK  2 6SK --- f=2 6!SK* inOrder jest zawsze posortowanyo 2 SK  --- 2 6SK ---2 $SK7.--- 2 ,SK ---I2 6)SKWstawiamy do pustego drzewa BST kolejno:   2 SK2 0 6 4 3 1 5.V2 ,2SKWypisujc wartoci wzw przy przejciu drzewa w ,KS'2 6SKporzd2 TSKku z%2 aSKinorder, otrzymam2 SKy: 2 SK ,KS' 2 $SK --KKSSJJSSJJSSJJRRJJRRJJRRJJRRJJRRJJRRJJRRIIRRIIRRIIQQIIQQIIQQIIQQIIQQIIQQHHQQ