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Mirkowska, ASD_9 KopiecO =h ALGORYTMY I STRUKTURY DANYCH pWYKAAD 09 Kopiec Gra|yna Mirkowska PJWSTK, 2003/2004 9  Plan wykBadu Kopiec (sterta) Definicja Operacja wkBadania elementu do kopca Usuwanie elementu minimalnego Koszty operacji Zastosowanie - algorytm Heap_sort Implementacja kopca w tablicy Konstrukcja kopca w tablicy PrzykBad Koszt konstrukcji kopca `]@=]@=& ^)Kopiec czyli sterta, czyli heap&5PrzykBad kopca ( Wstawianie elementu 7LPrzykBad - doBczanie nowego elementu '*Usuwanie minimum +6PrzykBad - usuwanie minimum ,Koszty operacji - Zastosowanie .Implementacja kopca w tablicy 6PrzykBad 1*Operacja insert w implementacji tablicowej& :!Delmin w implementacji tablicowej/Konstrukcja kopca w tablicy ;Algorytm tworzenia kopca > 8PrzykBad - konstrukcja kopca 2Koszt konstrukcji kopca /=  ` @ ff3Ιd332z` @ ff3Ιd332z` 999MMM` fffPP3f>?" dd@ ?4Zd@ d " @ ` n?" dd@   @@``@n?" dd@  @@``PV    @ ` ` p>>  K0  D(  F   `  0PPf  c 6AminispirlB  <g   H 1Ȝ? p`  TKliknij, aby edytowa styl tytuBu z Wzorca++  c $D p  Kliknij, aby edytowa style tekstu z Wzorca Drugi poziom Trzeci poziom Czwarty poziom Pity poziom,  c  c $ p    X* 2    c $     Z*(2    c $    Z*(2 XB   0D`Z  BsZ޽h))?? @ ff3Ιd332z Notatnik&  K0 @ <(   FF       XA StationeryPP`   S 0AminispirH  <P ?^~  ALGORYTMY I STRUKTURY DANYCHKliknij, aby edytowa styl tytuBu z WzorcaGG  c $hS 3    ZKliknij, aby edytowa styl podtytuBu z Wzorca..  c $$X ^#  X* 2f   c $\ ^~#   Z*(2f   c $` ~#  Z*(2f Z  BsZ޽h))?? @ ff3Ιd332z| 0 `( F0E,   0, P    T*   0     V* d  c $ ?    0  @  Kliknij, aby edytowa style wzorca tekstu Drugi poziom Trzeci poziom Czwarty poziom Pity poziom*  a  6 `P   T*   6 `   V* H  0޽h ? ̙3380___PPT10.0k7y K0 0(  l  C k ^~  l  C l 3    H  0޽h ? @ ff3Ιd332zy___PPT10Y+D=' = @B +  K0 P@4(  @l @ C P p`    @ S   " PpH @ 0޽h ? @ ff3Ιd332zy___PPT10Y+D=' = @B +#  K0 F > `( q@G@ l  C l p`     3 ZwG UNd)?DefinicjaArial Black$ k !2 0 x  0 0,$  0 Kopcem nazywamy etykietowane, doskonaBe drzewo binarne cz[ciowo uporzdkowane.P 2P PH  VtAPapeteria`,$D  0 2Etykietowane drzewo binarne D = <V, E, et> jest kopcem wtedy i tylko wtedy, gdy (1) D jest drzewem cz[ciowo uporzdkowanym: et(v) < et(v.lewy) i et(v)< et(v.prawy) dla wszystkich wierzchoBkw v V, (2) D jest drzewem doskonaBym: wszystkie poziomy drzewa, z wyjtkiem co najwy|ej ostatniego poziomu, s maksymalnie zapeBnione, a na ostatnim poziomie wszystkie li[cie s zgrupowane maksymalnie na lewo., 2 >l @ p  p,$D   0`R  0@ @Z  s * pH  0޽h ? @ ff3Ιd332zme___PPT10E+ZD' = @B Dt' = @BA?%,( < +O%,( < +D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*PD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*PD' =%(D|' =%(D$' =A@BB BB0B%(E' =4 B`BPB`B?<* %( /%,( < +D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*DL' =%(D' =%(D' =4@BBBB%(E' =4 B`BPB`B?<* %(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =+K4 8?CBB#ppt_x+(cos(-2*pi*(1-$))*-#ppt_x-sin(-2*pi*(1-$))*(1-#ppt_y))*(1-$)CB?B*Y3>B ppt_x<*D' =+K4 8?CBB#ppt_y+(sin(-2*pi*(1-$))*-#ppt_x+cos(-2*pi*(1-$))*(1-#ppt_y))*(1-$)CB?B*Y3>B ppt_y<*+p+0+ ++0+ +P  K0 u)m)pAS)(  R l  C % p`  % d l p @  pp ,$D  02  6%p G1 2  6 % 0 G5 2  6%`P G2 2  6 %pp  Q4  2  6`%pp  G3 2  6%00  G7 2   6%pp  G8 2   6t%  @  G9 2   6|% `@  H10 `B  0D p``B   0DP0`B B 0Dp`B  0D `B B 0DP`B  0Dp`B B 0D  `B  0D@   0X'% @ ,$  0 To nie jest kopiec , bo nie jest to drzewo doskonaBe(chocia| jest to drzewo cz. uporzdkowane)_ 2_ _d l `   '0  ,$D  02  6+%  p G1 2  6/%`  G7 2  6P.%p  P G4 2  6,2%  `  Q2  2  65%  `  G3 2  6>% p  G5 2  6=% `  G8 2  6D%` @  G9 2  6A% @  H10 `B  0D @ `B   0D @`B !B 0D P `B " 0D P `B #B 0D@  `B $ 0D` `B %B 0D` ` P p `B & 0D ` @ @  ( 0PN% J,$D  0 To nie jest kopiec , bo nie jest to drzewo cz[ciowo uporzdkowane (chocia| jest to drzewo doskonaBe)f 2f f ) s *PpP ,$D  0 * s *P  ,$D  0 z P  = P ,$D  0k N P  > P p 2 ? 6S% G1 2 @ 6|W%0p G5 2 A 60V%` G2 2 B 6 Z%pp  Q4  2 C 6p]%9p  G3 2 D 6lf%^0  G7 2 E 6d%K p  G8 2 F 6`l%P   G9 2 G 6h% 5p  H10 `B H 0D^``B I 0D0`B JB 0D'p`B K 0D^p`B LB 0D'`B M 0Dp p`B NB 0D  `B O 0D  2 P 60v% Up  G6 `B QB 0D   R 0Pz%@  TKopiec 2 Z S 0}%  ,$D  0 hWBasno[ci: 1. Etykiety na dowolnej drodze od korzenia do li[cia tworz cig uporzdkowany rosnco. 2. Element najmniejszy w[rd etykiet wierzchoBkw znajduje si w korzeniu drzewa.. 2 f H  0޽h ? @ ff3Ιd332z4&,&___PPT10 &+^KDH%' = @B D%' = @BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D' =%(DG' =%(D' =A@BBBB0B%(E' =1B B`BPB1:Bhidden*3>+B#style.visibility= `B<*_D' =1:Bvisible*o3>+B#style.visibility<*_%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*_D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*_D' =%(Do' =%(D' =4@BB BB%(E' =4 B`BPB`B?<* %(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*)%(D' =-o6Bdissolve*<3<*)Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*'%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*'D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*'D' =%(D' =%(D`' =A@BBB B0B%(E' =1B B`BPB1:Bhidden*3>+B#style.visibility= `B<*(E' =4 B`BPB`B?<* %(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =-6B+checkerboard(across)*<3<*(Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<**%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<**D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<**Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*=%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*=D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*=D' =%(D|' =%(D$' =A@BB BB0B%(E' =4 B`BPB`B?<* %(-/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*S%(D' =-o6Bdissolve*<3<*S++0+% ++0+(% ++0+S% +-  K0    T (  l  C % p`  %   s *%G,$D  0 6Insert : Heap Et Heap` 2fffffN   0%pz,$D  0 h(1) Dowiza nowy wierzchoBek x do pierwszego z lewej wierzchoBka na przedostatnim poziomie drzewa, ktrego rzd jest <2. (2) Nada nowemu wierzchoBkowi etykiet e. (3) Je|eli tak otrzymane drzewo nie jest cz[ciowo uporzdkowane, to przechodzc wzdBu| drogi od li[cia x do korzenia, poprawi etykiety zamieniajc etykiet ojca z etykiet syna, je[li etykieta ojca jest wiksza ni| etykieta syna. 2   V%APapeteriaj,$D  0 ,Zadanie: Do zbioru etykiet danego kopca D doBczy now etykiet e, czyli wykona operacj insert(D,e)g 2g&[ Lz @ p  ` ,$D   0`R  0@ @Z   s * pJl P     P ,$D  0fB   6D8cP  `2   0f8c  r   BxCDE|F4 8c5KVR x;tasa!O(>./A&CH)v>Sn,5* ^K: ( @            ,$D  0H  0޽h ? @ ff3Ιd332z___PPT10+ĬyD' = @B D' = @BA?%,( < +O%,( < +D' =%(D|' =%(D$' =A@BB BB0B%(E' =4 B`BPB`B?<* %(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D' =%(D' =%(D4' =A@BBBB0B%(E' =4 B`BPB`B?<* %(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B#blinds(vertical)*<3<*DL' =%(D' =%(D' =4@BBBB%(E' =4 B`BPB`B?<* %(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =+K4 8?CBB#ppt_x+(cos(-2*pi*(1-$))*-#ppt_x-sin(-2*pi*(1-$))*(1-#ppt_y))*(1-$)CB?B*Y3>B ppt_x<*D' =+K4 8?CBB#ppt_y+(sin(-2*pi*(1-$))*-#ppt_x+cos(-2*pi*(1-$))*(1-#ppt_y))*(1-$)CB?B*Y3>B ppt_y<*DR' =%(D' =%(D' =4@BBBB%(E' =4 B`BPB`B?<* %(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* D' =%(D' =%(D-' =4@BBB*B%(E' =4 B`BPB`B?<* %(#/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B)barn(outHorizontal)*<3<*++0+% ++0+% ++0+% +]R  K0 H#@#7< "( x l  C % p`  %   P  # P p ,$D 02  6|% G1 2   6%0p G5 2   6h%` G2 2   6%pp  Q4  2   6$%9p  G3 2   6%^0  G7 2  6%K p  G8 2  68%P   G9 2  6@% 5p  H10 `B  0D^``B  0D0`B B 0D'p`B  0D^p`B B 0D'`B  0Dp p`B B 0D  `B  0D  2  6% Up  G6 `B B 0D  "  6% 0 z,$  0 BPo doBczeniu nowego wierzchoBka" 2" "l  @   @ ,$D  0`B  0D 2  0%fpP @  E0  l  `  5 ` ,$D  02   <%N@ G1 2 ! <%;` G5 2 " <|%`  G2 2 # <y 0  Q4  2 $ <yN0  G3 2 % < y)`  G7 2 & <Hy`0  G8 2 ' <4 y @ d  G9 2 ( <y   H10 fB ) 6DNfB * 6Dr`fB +B 6DN fB , 6D fB -B 6DrfB . 6D)fB /B 6D 0 @ fB 0 6Dp0 K 2 1 <hy    G6 fB 2B 6D0  `B 3 0D0 0 2 4 6y u  G0 ( 6 0X"y p 0z,$  0 NZero  wdruje wzdBu| drogi do korzenia( 2( (2 7 6|y u ,$D  0 G3 2 8 0*yfU0 ,$D  0 G0 2 9 6@-yU0 ,$D  0 G2 2 : 0/yf` ,$D  0 G0 2 ; 64y` ,$D  0 G1 2 < 0 8yf@@,$D  0 G0 H  0޽h ? @ ff3Ιd332z..___PPT10}.+tjوD,' = @B D\,' = @BA?%,( < +O%,( < +D' =%(D' =%(D3' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*D' =%(D|' =%(D$' =A@BBB B0B%(E' =4 B`BPB`B?<* %( /%,( < +D' =1:Bvisible*o3>+B#style.visibility<*"%(D' =-o6Bbox(out)*<3<*"D' =%(Do' =%(D' =4@BB BB%(E' =4 B`BPB`B?<* %(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bdissolve*<3<*DR' =%(D' =%(D' =4@BBBB%(E' =4 B`BPB`B?<* %(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*5%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*5D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*5D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*6(%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*6(D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*6(D' =%(D|' =%(D$' =A@BBB B0B%(E' =4 B`BPB`B?<* %( /%,( < +D' =1:Bvisible*o3>+B#style.visibility<*7%(D' =-o6Bbox(out)*<3<*7D' =%(D|' =%(D$' =A@BBB B0B%(E' =4 B`BPB`B?<* %(%/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =-o6Bbox(out)*<3<*8D' =%(D|' =%(D$' =A@BBB B0B%(E' =4 B`BPB`B?<* %(*/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*9%(D' =-o6Bbox(out)*<3<*9D' =%(D|' =%(D$' =A@BBB B0B%(E' =4 B`BPB`B?<* %(//%,( < +D' =1:Bvisible*o3>+B#style.visibility<*:%(D' =-o6Bbox(out)*<3<*:D' =%(D|' =%(D$' =A@BBB B0B%(E' =4 B`BPB`B?<* %(4/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*;%(D' =-o6Bbox(out)*<3<*;D' =%(D|' =%(D$' =A@BBB B0B%(E' =4 B`BPB`B?<* %(9/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-o6Bbox(out)*<3<*<++0+y ++0+6y ++0+7y ++0+8y ++0+9y ++0+:y ++0+;y ++0+<y +V@  K0    f ( ,mz3 l  C Wy p`  y   3 ZwG UNd)?AlgorytmArial Black$ k !2pp   s * 2fffZN  04`y ,$  0 tNiech e bdzie etykiet li[cia x znajdujcego si najbardziej na prawo na ostatnim poziomie kopca. (1) Usun wierzchoBek x z drzewa d. (2) Zastpi etykiet w korzeniu drzewa przez e. (3) Je[li tak otrzymane drzewo nie jest kopcem, to zaczynajc od korzenia i idc w kierunku li[cia, zamienia etykiet ojca z etykiet tego z jego synw, ktrego etykieta ma mniejsz warto[, tak dBugo a| zostanie otrzymane drzewo cz[ciowo uporzdkowane. 2 Lz @ p  ` ,$D   0`R  0@ @Z   s * p2  s *f`  ,$D  04  3 BPCDE@F f8c``00@ Pp8pP`8 @      p ,$D   0  # BBCDEF<8c%%quM0yo@DDMn[[I E \-%(>Tj^][  @            3P ,$D  0H  0޽h ? @ ff3Ιd332z33___PPT102+:D\2' = @B D2' = @BA?%,( < +O%,( < +D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D' =%(D?' =%(D' =A@BBBB0B@B%(D' =1:Bvisible*o3>+B#style.visibility<*d%(D' ,=+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*dD' ,=+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*dD' =%(D?' =%(D' =A@BBBB0B@B%(D' =1:Bvisible*o3>+B#style.visibility<*d%(D' ,=+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*dD' ,=+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*dD' =%(D?' =%(D' =A@BBBB0B@B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' ,=+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' ,=+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D' =%(D?' =%(D' =A@BBBB0B@B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' ,=+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' ,=+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*DL' =%(D' =%(D' =4@BBBB%(E' =4 B`BPB`B?<* %(#/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =+K4 8?CBB#ppt_x+(cos(-2*pi*(1-$))*-#ppt_x-sin(-2*pi*(1-$))*(1-#ppt_y))*(1-$)CB?B*Y3>B ppt_x<*D' =+K4 8?CBB#ppt_y+(sin(-2*pi*(1-$))*-#ppt_x+cos(-2*pi*(1-$))*(1-#ppt_y))*(1-$)CB?B*Y3>B ppt_y<*D' =%(Do' =%(D' =4@BBB B%(E' =4 B`BPB`B?<* %(+/%,( < +D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bbox(out)*<3<* D' =%(D,' =%(D' =4@BBBB%(E' =4 B`BPB`B?<* %(0/%,( < +D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* D#' =+4 8?nCB!#ppt_y+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* D' =+4 8?\CB#ppt_wBCB#ppt_wB*Y3>B ppt_w<* D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<* D' =%(DH' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* D#' =+4 8?nCB!#ppt_y-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* D' =+4 8?\CB#ppt_wBCB#ppt_wB*Y3>B ppt_w<* D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<* +p+0+y ++0+y +V  K0  *,(  l  C  yy p`  y Sl `  ` ` ,$D  02  <zyR @ G0 2  <y `@  G5 2  <~ye  G1 2  <y@0  Q4  2  <ly 0  G3 2   <y  0  H10 2   <y  0  G8 2   <y`   G9 2   <y@ u  G7 fB  6D.fB  6DR  `fB B 6D fB  6D. @fB B 6D  fB  6D@ ` fB B 6D @ fB  6D0 0@ 2  <dy @   G6 fB B 6D0 @@ fB  6Dp0 @ 2  <Сy@ u  H20 `B B 0D 0 @ 2  6y @ e  H12 Pl    ,$D  0fB  6DԔ 0 fB  6DԔ P @ 2  0yf0 p,$D  0 P12   # B`CpDEF8c`0P`xp@  P0 ,$D  02 ! 0lyf ,$D  0 P12 2 " 0Hyf0 p,$D  0 O1 & $ c BCDE(F| 8P`x80  @    ,$D  0, %@ s BCDE(F| 8P`x80  @     ,$D  02 & 0Hyf p` ,$D  0 F12 2 ' 0 yf ,$D  0 E3 2 ( 0yf p ,$D   0 F12 2 ) 0yf p` ,$D  0 E6  * s * P ,$D  0 + VlyAPapeteria g#Usuwamy najmniejszy element zbioru.$ 2$ $ , <yGP @ @U 0U 0 P pokaz pokaz   H  0޽h ? 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@ ff3Ιd332zJ%B%___PPT10"%+|tD#' = @B Dq#' = @BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D' =%(D|' =%(D$' =A@BBB B0B%(E' =4 B`BPB`B?<* %( /%,( < +D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bbox(out)*<3<*Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D' =%(D|' =%(D$' =A@BBB B0B%(E' =4 B`BPB`B?<* %(./%,( < +D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bbox(out)*<3<*+P+0+| ++0+| ++0+| ++0+| ++0+| ++0+| ++  K0    U (  l  C D| p`  |   3 ZwG UNd)?AlgorytmArial Black$ k !2Pp@   0E|P ,$  0 F(1) Z danego n elementowego zbioru utworzy kopiec. (2) Dopki kopiec nie jest pusty, wypisywa i usuwa element minimalny kopca. 2   s *TL|P 7,$D  0 xAlgorytm Heap_sort 2f&  *  0P|0 P ,$  0 8Koszt sortowania = koszt utworzenia kopca + n * O(lg n)9 29&1B  @ HDjJ` 0 ,$D  0  VU|APapeteriaPY: ,$D  0 O ile wkBadamy kolejno elementy stosujc operacj insert : O(n lg n)E 2E@2  0 [| ,$  0 i = O(n lg n) 2 &H  0޽h ? @ ff3Ιd332z!!___PPT10!+Z,[D\ ' = @B D ' = @BA?%,( < +O%,( < +D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D' =%(D?' =%(D' =A@BBBB0B@B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' ,=+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*4D' ,=+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*4D' =%(D?' =%(D' =A@BBBB0B@B%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' ,=+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*4D' ,=+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*4D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*9%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*9D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*9D' =%(Do' =%(D' =4@BBB B%(E' =4 B`BPB`B?<* %(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bbox(out)*<3<* D' =%(D|' =%(D$' =A@BBB B0B%(E' =4 B`BPB`B?<* %("/%,( < +D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bbox(out)*<3<* D_' =%(D' =%(D' =A@BBBB0B%(E' =4 B`BPB`B?<* %('/%,( < +D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* ++0+| ++0+| ++0+| ++0+ | ++0+ | +  K0 9(  l  C q| p`  | f  0s| `@,$  0 ZReprezentujemy kopiec jako par Tab + idx . 2.@#  0x|@x,$  0 TOrganizacja elementw w tablicy: Tab[1] = etykieta korzenia Tab[2i] = etykieta lewego syna wierzchoBka i-tego o ile 2i idx Tab[2i+1] = etykieta prawego syna wierzchoBka i-tego o ile 2i+1 idxV 2 ff\J@H   H|G}H 00 ,$D  0 ]tablica etykiet   H\|G@Ha  ,$D  0 r$aktualna liczba elementw w tablicy%$ %H  0޽h ?/  @ ff3Ιd332z___PPT10{+NzD' = @B D:' = @BA?%,( < +O%,( < +D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*.%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*.D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*.D' =%(D|' =%(D$' =A@BBB B0B%(E' =4 B`BPB`B?<* %( /%,( < +D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bbox(out)*<3<*D' =%(D|' =%(D$' =A@BBB B0B%(E' =4 B`BPB`B?<* %(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bbox(out)*<3<*D' =%(D?' =%(D' =A@BBBB0B@B%(D' =1:Bvisible*o3>+B#style.visibility<*!%(D' ,=+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*!D' ,=+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*!D' =%(D?' =%(D' =A@BBBB0B@B%(D' =1:Bvisible*o3>+B#style.visibility<*!%(D' ,=+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*!D' ,=+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*!++0+| ++0+| ++0+| ++0+| +NL  K0 1K(  l  C | p`  |  F P       k N P   P p 2  6| G1 2  6|0p G5 2  6Ԡ|` G2 2   6$|pp  Q4  2 ! 6|9p  G3 2 " 64|^0  G7 2 # 6|K p  G8 2 $ 6|P   G9 2 % 6| 5p  H10 `B & 0D^``B ' 0D0`B (B 0D'p`B ) 0D^p`B *B 0D'`B + 0Dp p`B ,B 0D  `B - 0D  2 . 6| Up  G6 `B /B 0D   0 0|@   TKopiec 2  l 0 0P  @ `,$D  0 1 B|̙A)0 0P  <  2 6| p  E1  3 6| p  E2  4 6H| p  E5  5 6$| pp  E4  6 6|p `p  E3  7 6xG|` Pp  E7  8 6||P @p  E8  9 6X|@ 0p  E9  : 64|0 p  F10  ; 6|  p  E6  < 0|  VTab: 2 = 0| P  M n : 10 2   ? 04| `   j& 1 2 3 4 5 6 7 8 9 10' 2' ' B 0|  pt,$  0 qReprezentacja tablicowa kopca$ 2f  C 6GT;` @ ,$D  0 D 6GT;p ,$D  0 E 6GT;`  ,$D  0 F 6GT;`  ,$D  0 G 6G = P ,$D  0 H BGH?HMI@ P ,$D  0 I <G=I ,$D  0 J 6GV? @,$D  0 K 6Gq?pp ,$D  0H  0޽h ? @ ff3Ιd332z,,___PPT10,+DF,' = @B D,' = @BA?%,( < +O%,( < +D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*B%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*BD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*BDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*@D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*@D' =%(Do' =%(D' =4@BBB B%(E' =4 B`BPB`B?<* %(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*C%(D' =-o6Bbox(out)*<3<*CD' =%(Do' =%(D' =4@BBB B%(E' =4 B`BPB`B?<* %(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*D%(D' =-o6Bbox(out)*<3<*DD' =%(Do' =%(D' =4@BBB B%(E' =4 B`BPB`B?<* %(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*E%(D' =-o6Bbox(out)*<3<*ED' =%(Do' =%(D' =4@BBB B%(E' =4 B`BPB`B?<* %( /%,( < +D' =1:Bvisible*o3>+B#style.visibility<*F%(D' =-o6Bbox(out)*<3<*FD' =%(Do' =%(D' =4@BBB B%(E' =4 B`BPB`B?<* %(%/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*G%(D' =-o6Bbox(out)*<3<*GD' =%(Do' =%(D' =4@BBB B%(E' =4 B`BPB`B?<* %(*/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =-o6Bbox(out)*<3<*HD' =%(Do' =%(D' =4@BBB B%(E' =4 B`BPB`B?<* %(//%,( < +D' =1:Bvisible*o3>+B#style.visibility<*I%(D' =-o6Bbox(out)*<3<*ID' =%(Do' =%(D' =4@BBB B%(E' =4 B`BPB`B?<* %(4/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*J%(D' =-o6Bbox(out)*<3<*JD' =%(Do' =%(D' =4@BBB B%(E' =4 B`BPB`B?<* %(9/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*K%(D' =-o6Bbox(out)*<3<*K+8+0+B +  K0 v=n=V`0 <(  l  C  p`     6p p ,$  0 VKopiec D 2  l   g   p ,$D  02  < l G5 2  < o l H12 2  <" i G7 2   <`!-& H10 2   < *& G8 2   <h%` p   H14 2   <, @  H19 2   <3 g  H16 2  <|2Y 6  G9 fB  6D0 fB  6Dl fB B 6D&fB  6D0NWfB B 6D ` pfB  6DP `@ @fB B 6D2P fB  6D 2  <d< 26  H11 fB B 6D 2  6@@ C  H20 TB  c $D@  l  0 ,P ,$D  0  <D`   G5   <H   G7    < 0 H12 2 e z    @ p ` ,$D   0e N  0 A  0  B <0`   G3  C <    G7  D <  G5  E <` H10  F <`  G8  G <  H12  H < H19  I <p` H16  J <ė`  G9  K <pȗ  H11  L <˗ H20  M 0pϗ` 0 r,1 2 3 4 5 6 7 8 9 10 11- 2- - N 0ח   VTab: 2 O 68֗``  H14  P 0X H12 2  R # BPC DEFP\h   H0@  ` P ,$D  0 S # BpCDEFp`P8 @  ` @ ,$D  0 T # BCDEFXH00@  ` @ ,$D   0l   V ,$D  02  0   G3 TB UB c $D@ 2 X 6\  ,$D   0 H14 2 \ 0t,$D   0 G3 2 ] 0,$D   0 H12 2 ^ 0@c,$D  0 G3 2 _ 0@c,$D  0 G5 2 ` 0 <,$D  0 G3 H  0޽h ? @ ff3Ιd332zGG___PPT10G+DE' = @B DE' = @BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* D' =%(Do' =%(D' =4@BBB B%(E' =4 B`BPB`B?<* %(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =-o6Bbox(out)*<3<*,D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*; %(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*; D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*; DR' =%(D' =%(D' =4@BBBB%(E' =4 B`BPB`B?<* %(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*V%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*VD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*VD' =%(Do' =%(D' =4@BBB B%(E' =4 B`BPB`B?<* %("/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*?%(D' =-o6Bbox(out)*<3<*?D' =%(Do' =%(D' =4@BBB B%(E' =4 B`BPB`B?<* %('/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*R%(D' =-o6Bbox(out)*<3<*RD' =%(Do' =%(D' =4@BBB B%(E' =4 B`BPB`B?<* %(,/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*S%(D' =-o6Bbox(out)*<3<*SD' =%(Do' =%(D' =4@BBB B%(E' =4 B`BPB`B?<* %(1/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =-o6Bbox(out)*<3<*TD' =%(Do' =%(D' =4@BBB B%(E' =4 B`BPB`B?<* %(6/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =-o6Bbox(out)*<3<*@D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*X%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*XD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*XD{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*\%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*\D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*\D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*]%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*]D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*]D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*^%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*^D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*^D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*_%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*_D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*_D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*`%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*`D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*`++0+ ++0+; ++0+X ++0+\ ++0+] ++0+^ ++0+_ ++0+` +Fx  K0 (; ;RW :(  r  S  p`   e z      `,$D  0e N  0   0   < `   G3   <%   G7   <$  G5   <'` H10    <L+`  G8    <\2  H12    <. H19    <5` H16    <L9`  G9   <<  H11   <L@ H20   0C` 0 r,1 2 3 4 5 6 7 8 9 10 11- 2- -  0$L   VTab: 2  6J``  H14   0S H12 2 Al p   , p ,$D  02  <V 2 G3 2  <Z_A G5 2  <8Yno G7 2  <]xd H10 2  <x`d G8 2  <c  H12 2  <hgY  | H19 2  <jpX   H16 2  <hn*   G9 fB  6D<{fB  6D2{fB  B 6Do fB ! 6D<o7 fB "B 6D26 fB # 6D6 fB $B 6DdX fB % 6Dd* 2 & <pw*   H11 fB 'B 6Ddc* 2 ( <L{6 N  H20 ZB ) s *DcM 6 `B *B 0D_ 2 + 6 G  H14  - 0}P 0p,$  0 [ Delmin(D) 2    0 /# 0  ,$D  0 0 <܆`   H14  1 <   G7  2 <l  G5  3 <H` H10  4 <`  G8  5 <  H12  6 < H19  7 <` H16  8 <䚘`  G9  9 <<  H11  : < H20  ; 0` 0 r,1 2 3 4 5 6 7 8 9 10 11- 2- - < 0   VTab: 2 ? # BCDEF0X|0h @   ` x ,$D  0 @ # BpCDEF0dHPp@   P ,$D  0 A 08P ` p,$  0 Q Ostatecznie : 2    0 B# ` ` ,$D  0 C <4`   G5  D <   G7  E <Ļ  H12  F <` H10  G <Xǘ`  G8  H <Ř  H14  I <ɘ H19  J < Ҙ` H16  K <<͘`  G9  L <ט  H11  M <Ԙ H20  N 0ۘ` 0 r,1 2 3 4 5 6 7 8 9 10 11- 2- - O 0   VTab: 22 Q 6 P,$D   0 H14  R 080  < 2  S s * I ,$D   0 G  2 2 T 6X,$D  0 H14 2 U < P,$D   0 G5 2 V 6$@ `,$D   0 H14 2 W 6@ `,$D   0 H12 H  0޽h ? @ ff3Ιd332z<<___PPT10<+6D:' = @B De:' = @BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*,D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*,D' =%(Do' =%(D' =4@BBB B%(E' =4 B`BPB`B?<* %( /%,( < +D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bbox(out)*<3<*D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*- %(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*- D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*- Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*/%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*/D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*/D' =%(Do' =%(D' =4@BBB B%(E' =4 B`BPB`B?<* %(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*?%(D' =-o6Bbox(out)*<3<*?Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*@D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*@D' =%(D|' =%(D$' =A@BBB B0B%(E' =4 B`BPB`B?<* %('/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*A%(D' =-o6Bbox(out)*<3<*ADn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*B%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*BD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*BD' =%(D|' =%(D$' =A@BBB B0B%(E' =4 B`BPB`B?<* %(2/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*S%(D' =-o6Bbox(out)*<3<*SD{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*Q%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*QD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*QD' =%(D|' =%(D$' =A@BBB B0B%(E' =4 B`BPB`B?<* %(=/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*U%(D' =-o6Bbox(out)*<3<*UD' =%(D|' =%(D$' =A@BBB B0B%(E' =4 B`BPB`B?<* %(B/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*V%(D' =-o6Bbox(out)*<3<*VD' =%(D|' =%(D$' =A@BBB B0B%(E' =4 B`BPB`B?<* %(G/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*W%(D' =-o6Bbox(out)*<3<*WD' =%(D|' =%(D$' =A@BBB B0B%(E' =4 B`BPB`B?<* %(L/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =-o6Bbox(out)*<3<*T++0+- ++0+A ++0+Q ++0+S ++0+T ++0+U ++0+V ++0+W +  K0    (  l  C " p`   B  3 ZwG UNd)?MetodaArial Black$ k !2`p ,$D  0N  0$`,$D  0 tZaBo|enie: Znamy z gry liczb elementw tworzonego kopca.; 2; ;l    0 ,$D  0R  B*  EA R  Bh.P  EB ZB  s *DZB  s *D`2   B3`@ <    6T7 Gi 2    65 g H2i 2    0=`g J2i+1 2 x  0TA ,$D 0 Z1.Tworzymy tablic zawierajc wszystkie elementy. 2.Je|eli s ju| utworzone kopce A i B o korzeniach w 2itej i 2i+1szej pozycji, to albo tab[i] <tab[2i] oraz tab[i]<tab[2i+1] i wtedy mamy ju| kopiec o korzeniu w i, albo tak nie jest i wtedy poprawiamy [cie|k  w dB tak jak w algorytmie delmin.& 2 -2.@H  0޽h ? @ ff3Ιd332znf___PPT10F+*OD' = @B Du' = @BA?%,( < +O%,( < +D' =%(D' =%(D:' =A@BBB*B0B%(E' =4 B`BPB`B?<* %(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B)barn(outHorizontal)*<3<*D' =%(Do' =%(D' =4@BBB B%(E' =4 B`BPB`B?<* %( /%,( < +D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bbox(out)*<3<*D' =%(D' =%(DV' =A@BBB*B0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B)barn(outHorizontal)*<3<*D' =%(D' =%(D-' =4@BBB*B%(E' =4 B`BPB`B?<* %(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B)barn(outHorizontal)*<3<*+p+0+ ++0+ +  K0 0u(  r  S (* p`   _  V+APapeteria  ,$D  0 +For i:= n div 2 downto 1 do downheap(i) od;, 2,@ \  0,3`j,$D 0 <Procedure downheap (k:integer); /* utwrz kopiec o korzeniu w pozycji k zakBadajc, |e 2k i 2k+1 s korzeniami kopcw w tablicy*/ begin v := tab[k]; while (k n div 2 ) do j := 2*k; if (j<n) then if (tab[j] > tab[j+1] )then j := j+1 fi fi; if v<tab[j] then exit fi; tab[k] := tab[j]; k := j; od; tab[k] := v; end; , 2<  e  4 )H  0޽h ? @ ff3Ιd332z  ___PPT10p +5 D' = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D6' =A@BB BB0B%(E' =4 B`BPB`B?<* %(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B%slide(fromBottom)*<3<*D' =%(D' =%(D8' =A@BBB B0B%(E' =4 B`BPB`B?<*%( /%,( < +D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B'blinds(horizontal)*<3<*+p+0+ ++0+ +  K0 HH@gs0 1H(  r  S T p`    l p  y  $  ,$D  02  <lV 2 G5 2  <[_A G1 2  <XZno G7 2  <]xd G6 2  <ad G2 2   <$hGh G8 2   <dY  | G4 2   <kp x  G3 2   <oP y  G9 fB  6D<{fB  6D2{fB B 6Do fB  6D<o7 fB B 6D6fB  6D6 fB B 6Dd fB  6Dd ! l   ( ,$D  0  Bx  p E5   B| @p E7   By@p E1   Bp E6   Bp E2    BЋ@p E8  ! 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E6  p <Hup@0 E9  q 6$y 0 VTab: 2 r 6| `T r, 1 2 3 4 5 6 7 8 9- 2- -H  0޽h ? @ ff3Ιd332zk?c?___PPT10C?+D'?' = @B D>' = @BA?%,( < +O%,( < +D' =%(Do' =%(D' =4@BBB B%(E' =4 B`BPB`B?<* %(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*$%(D' =-o6Bbox(out)*<3<*$Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*(D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*(D' =%(Do' =%(D' =4@BBB B%(E' =4 B`BPB`B?<* %(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*+%(D' =-o6Bbox(out)*<3<*+Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*,D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*,D' =%(Do' =%(D' =4@BBB B%(E' =4 B`BPB`B?<* %(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =-o6Bbox(out)*<3<*8D' =%(Do' =%(D' =4@BBB B%(E' =4 B`BPB`B?<* %( /%,( < +D' =1:Bvisible*o3>+B#style.visibility<*9%(D' =-o6Bbox(out)*<3<*9Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*:%(D' =+4 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