&" WMFCk ulah Rt EMFD!?f   ah% %    '% Ld&9&9p!??% (      '% Ld&+e&s!??% (      '% Ldes!??% (      '% Ld&f&fp!??% (   !&?   '% Ld,e,ds!??% (    Rp@Times New Roman  RObj  x $Obj  oh  l roh XG*Ax Times ew Romanf < 9h!x x zh! l rdv% % %  TX,d@^@,ML&?P1522TTd@^@ML&?P 2"    '% Ld9:>9!??% (      '% Ld??!??% (      '% Ld5?:5?!??% (      '% Ld:!??% (   !?;   '% Ld?4?s!??% (    % % %  T?@^@L?;pRozwa|my tablic C2-H,-O/,2,,!?;F(GDICJ FTFTNPPhttps://edu.pjwstk.edu.pl/tex/ASDEgzaminPop/tex/pyt59158_1.gif!b K  FTNPPQK K P00eN(   ]]MM ! 1`1`0`QK K PH`eN( TTT888FFFbbbnnn 2AVe15awS0B1V" FTNPP" FGDIC" % % % T ?k@^@ L?;lreprezentujc !,2",-,22,,,!?;F(GDICkJFTFTNPPhttps://edu.pjwstk.edu.pl/tex/ASDEgzaminPop/tex/pyt59158_2.gif!b K  FTNPPQlKlK P00eN( >|  ]]MM  ``8p0`QlKlK P8`eN( bbb01 FTNPP" FGDIC" % % % TT?@^@L?;P-!TP?@^@+L?;elementowy cig r|nych liczb naturalnych: ,,N,22J0,-1!2-40,2,-22,2!,41,2   '% Ld43!??% (    !?;F(GDICZFTFTNPPhttps://edu.pjwstk.edu.pl/tex/ASDEgzaminPop/tex/pyt59158_3.gif!b K  FTNPPQXP0m(0 `000 `00@ 0 `00>3τg>3?>~30 !a w07Gso3  c3F0G `CD0 gFpp pG'8!>0C>t!0G 4!`sG0 <!1`c0!F0<80 `wp1p8> `??6QXP``m(bbbnnnTTTFFF888(((111```````       @G@G@G@q0Vq01G@@G0Vq01G@aGa`1DaDa!$F`)Aa`01)Aa``  01 a)AaE01)AaEtI0Da IFDa IF`a`aLtL@1Aa aILG aILqU01AB`AB``a` qU zFGQAwAAA`AEAAEAzp1`! a 01 0a0V010a 0V!&" WMFC UFTNPP" FGDIC" % % % TY3@^@Y>L?;. Do posortowania owej tablicy stosujemy algorytm QuickSort w H222'2!2H,2,2I,,2-0'2'2,P0,12#0NH2,282!H   '% Ld444s!??% (    T4@^@eL?;implementacji rekurencyjnej, z procedur podziaBu zgodn z metod Partition. Ktre z poni|szych zdaD N2,N,2,,!,22!,3.12,-2!2,,22!,222-,2-1222,-N,22,8,!22H2!,-222-'./,2-2,2   '% Ld4s!??% (    Tr@^@ L?;djest prawdz,'2!,H2-Tds/@^@sL?;Tiwe?H,-TT0a@^@0L?;P 2"    '% Ld&&p!??% (      '% Ld&9>&9p!??% (      '% Ld:!??% (      '% Ld9:>9!??% (      '% Ld&-.&-p!??% (   !&3)   '% Ld, ,ds!??% (    % % %  TT,]@^@,L&3)P 2"    '% Ld-t2-!??% (      '% Ld3(3!??% (      '% Ldo3t(o3!??% (      '% Ld)t.)!??% (   !3u)   '% Ld3n3s!??% (    % % %  Td3@^@YL3u)W rozwa|anym przypadku liczba wykonanaD algorytmu Partition jest rwna dokBadnie liczbie _!2-H,-,3/N3!.02,322,-2,I0222,3,2,22"0N28,!22,'!2I2,222,22,,-2,   '% Ldn(!??% (    T '@^@5L3u)wykonaD rozwa|anego algorytmu dla danych wej[ciowych I0223,2!2-H,-,2-12,12#0N22,2,40-2H,(,2I0-2!3u)F(GDIC FTHTNPPhttps://edu.pjwstk.edu.pl/tex/ASDEgzaminPop/tex/opc1087139_1.gif!b K  FTNPPQ  P0m(000000000000>3>|3>3?10n0Cyw07@q3pC8c3@90@C@0@8g@8p?@xp@w@>0@ta@80@4A@s@a<cpBc0!@c88w1wp1Àw `> ??>Q  P``m(bbbnnnTTT888FFF(((AAAA000000      PWP1WPWPq@cq@AWPPW@cqPqPW!%S10A U1  U1 @10A*Q10@A*Q@A0  u1*Q1V@A*Q@A%aZ@U1 ZSU1@ť101PA\u\u1 1Z\W 1W5Af&" WMFC 5@AQR0Qe!0xS10 qfqf QwQxpAQQ0QVQQQ@1%a@A @1 @c@A@1 @A1!FTNPP" FGDIC" % % % TT'@^@L3u)P 2"    '% Ld-t-DH!??% (      '% Lduus!??% (      '% Lduus!??% (      '% Ld.DG!??% (   !3)   '% Lduu8s!??% (    % % %  TTu@^@L3)P02TTu@^@L3)P 2"    '% Ld-.-K!??% (   !3)   '% Ld ?s!??% (    % % %  TT@^@L3)P 2"    '% Ld+-:.+-!??% (   !+3;)   '% Ld14 1s!??% (    % % %  TT3:@^@3L+3;)P 2"    '% Ld&).&)p!??% (      '% Ld&.3&.p!??% (      '% Ld)t.)!??% (      '% Ld.t3.!??% (      '% Ld).)D!??% (      '% Ld.3.D!??% (      '% Ld).)K!??% (      '% Ld.3.K!??% (      '% Ld+):.+)!??% (      '% Ld+.:3+.!??% (      '% Ld&<-&<p!??% (   !&B(   '% Ld,',ds!??% (    % % %  TT,]&@^@,L&B(P 2"    '% Ld<tA<!??% (      '% LdB'B!??% (      '% LdoBt'oB!??% (      '% Ld(t-(!??% (   !Bu(   '% LdBnBs!??% (    % % %  TXB@^@WLBu(W rozwa|anym przypadku wyskok[ drzewa wywoBaD rekurencyjnych algorytmu QuickSort jest _!2-H,-,3/N3!.02,322I0'222',3!-,H,J1H2,2!,22",2.040,2,12#0N2H2,282!,'   '% Ldn's!??&" WMFC % (    T&@^@ LBu(drwna dokBad!2H2,222,2Td^&@^@LBu(Tnie 2,!Bu(F(GDIC^FTHTNPPhttps://edu.pjwstk.edu.pl/tex/ASDEgzaminPop/tex/opc1087129_1.gif!b K  FTNPPQ__ P00/N(   ]]MM t 4`<`p 0`Q__ PH0/N( TTTnnnbbbFFFg !U @3FTNPP" FGDIC" % % % TT&@^@LBu(P 2"    '% Ld<{<D@!??% (      '% Ld||s!??% (      '% Ld||s!??% (      '% Ld-D?!??% (   !B(   '% Ld||8s!??% (    % % %  TT|@^@LB(P02TT|@^@LB(P 2"    '% Ld<-<K!??% (   !B(   '% Ld'?s!??% (    % % %  TT&@^@LB(P 2"    '% Ld+<:-+<!??% (   !+B;(   '% Ld14'1s!??% (    % % %  TT3:&@^@3L+B;(P 2"    '% Ld&(-&(p!??% (      '% Ld&=B&=p!??% (      '% Ld(t-(!??% (      '% Ld=tB=!??% (      '% Ld(-(D!??% (      '% Ld=B=D!??% (      '% Ld(-(K!??% (      '% Ld=B=K!??% (      '% Ld+(:-+(!??% (      '% Ld+=:B+=!??% (      '% Ld&;&;pe!??% (   !&A   '% Ld,`,ds!??% (    % % %  TT,]_@^@,HL&AP 2"    '% Ld;t@;!??% (      '% LdAAY!??% (      '% LdoAtoAY!??% (      '% Ldt!??% (   !Au   '% LdAnAs!??% (    % % %  TPA@^@VLAuW rozwa|anym przypadku liczba wykonanaD rekurencyjnych algorytmu QuickSort jest rwna _!2-H,-,3/N3!.02,&" WMFC 322,-2,I0222,3,2!,32!,2.040,2,13#0N2H2,282!,'!2H2,   '% Ldn&s!??% (    TPK%@^@VLAudokBadnie liczbie wywoBaD rekurencyjnych rozwa|anego algorytmu dla danych wej[ciowych 222,22,,-2,I0H2,2!,22",2.040,2!2-H--,2,12,13#/N22,3-30,2H,',2J0-2   '% Ld'n's!??% (    !AuF(GDIC+ZFTHTNPPhttps://edu.pjwstk.edu.pl/tex/ASDEgzaminPop/tex/opc1087135_1.gif!b K  FTNPPQ,X,P0m(0 `0`00 `0`0@  0 `0`0>3ϟ|g>3>|g30 !fq0a3!p9p 00 pp 8 |p|t p4 0a< 0c0808wp8c `~>~ Q,X,P``m(nnnbbbTTT888FFF(((AA00000000        `g`g`1g`1gq1g``g`g`qg!&c&c@10A&c 10A@10A0@A0@A v&Q@A&Qi&c@Ɩ1&c@@Ɩ100101`Av@Aa6Ag16A1qUvV!vV!0xc qU10 A@AgQawaaxpAa!@1&Q!aaa@1&Q0! 1 S1S@A@A1 `FTNPP" FGDIC" % % % TTY?@^@YLAuP 2"    '% Ld;;Dy!??% (      '% Ld&s!??% (      '% Ld&s!??% (      '% Ld''Dy!??% (   !A   '% Ld&8s!??% (    % % %  TT%@^@LAP12TT%@^@LAP 2"    '% Ld;;Ky!??% (      '% Ld&s!??% (      '% Ld&s!??% (      '% Ld''Ky!??% (   !A   '% Ld&?s!??% (    % % %  TT%@^@LAP+8TT%@^@LAP 2"    '% Ld+;:+;e!??% (   !+A;   '% Ld14`1s!??% (    % % %  TT3:_@^@3HL+A;P 2"    '% Ld&&p!??% (      '% Ld&<A&<p!??% (      '% Ldt!??% (  &" WMFC     '% Ld<tA<!??% (      '% LdD!??% (      '% Ld<A<D!??% (      '% LdK!??% (      '% Ld<A<K!??% (      '% Ld+:+!??% (      '% Ld+<:A+<!??% (    Rp@"Calibri H RObjH @  , $ObjH @ oh@ H rohhX%7.@ Calibr@ (h X@ t 9h! zh! rdv% % %  TT,a@^@,LahP 6   '% Ld&G&!??% (      '% Ld&H+&Hs!??% (      '% LdHHs!??% (      '% Ld&t &!??% (   !&o    '% Ld,H,Hs!??% (    % % % TXOH@^@OL&o P1522TTH@^@L&o P 2"    '% Ld:Q!??% (      '% Ldn !??% (      '% Ld5:n 5!??% (      '% Ldo :t o Q!??% (   !;o    '% Ld4Es!??% (    % % %  T@^@L;o pRozwa|my tablic C2-H,-O/,2,,!;o F(GDICTFTFTNPPhttps://edu.pjwstk.edu.pl/tex/ASDEgzaminPop/tex/pyt59160_1.gif!b K  FTNPPQR P00eN(   ]]MM ! 1`1`0`QR PH`eN( TTT888FFFbbbnnn 2AVe15awS0B1V" FTNPP" FGDIC" % % % TS@^@SL;o lreprezentujc !,2",-,22,,,!;o F(GDICFTFTNPPhttps://edu.pjwstk.edu.pl/tex/ASDEgzaminPop/tex/pyt59160_2.gif!b K  FTNPPQ P00eN( >|  ]]MM  ``8p0`Q P8`eN( bbb01 FTNPP" FGDIC" % % % TT8@^@L;o P-!T9p @^@9L;o elementowy cig r|nych l,,N,22J0,-1!2-40,2Tq =@^@q L;o piczb naturalnych: ,-22,2!,41,2   '% Ld4E!??% (    !;o F(GDIC<rFTFTNPPhttps://edu.pjwstk.edu.pl/tex/ASDEgzaminPop/tex/pyt59160_3.gif!b K  FTNPPQ:pP0Km(00000000@@0000>3ϟ1>13Cq3q3w1Gp3@98cF0 @CD  gDpb @ D8r@>D:@D@asDccc pF08waw 1pc > ?  ?0Q:pP`Km(bbbnnnTTT&" WMFC 888FFF(((AAAA000000      Pq1WWPPW@AqWPWq@AWq@A!%S @10A@A@A1010 pu @A1V1\ 0 \SPA01u@10Q@Aܱ01W1\[afR0@A xS0qfA@A 107qxpAwQ@10AQ@10AV0 @A P  @c @A!FTNPP" FGDIC" % % % T;}@^@;q>L;o . Do posortowania owej tablicy stosujemy algorytm QuickSort w H222'2!2H,2,2I,,2-0'2'2,P0,12#0NH2,282!H   '% Ld4Es!??% (    T7@^@eL;o implementacji rekurencyjnej, z procedur podziaBu zgodn z metod Partition. Ktre z poni|szych zdaD N2,N,2,,!,22!,3.12,-2!2,,22!,222-,2-1222,-N,22,8,!22H2!,-222-'./,2-2,2   '% Ld4n Es!??% (    Tvm @^@V L;o ljest prawdziwe?,'2!,H2-H,-TTwm @^@wV L;o P 2"    '% Ld&o t &o !??% (      '% Ld&&!??% (      '% Ldo :t o Q!??% (      '% Ld:Q!??% (      '% Ld& Y & !??% (   !& T    '% Ld,n  ,n s!??% (    % % %  TT,n ] @^@, L& T P 2"    '% Ld ,  C !??% (      '% Ld S  !??% (      '% Ld' , S ' !??% (      '% LdT , Y T C !??% (   ! - T    '% Ld &  7 s!??% (    % % %  T 0 @^@ 8L - T W rozwa|anym przypadku wyskok[ drzewa wywoBaD rekurency_!2-H,-,3/N3!.02,322I0'222',3!-,H,J1H2,2!,22",2.0Tp) ( @^@1 L - T Xjnych 40,2   '% Ld & m  7 s!??% (    T , l @^@U BL - T algorytmu QuickSort jest rwna dokBadnie wysoko[ci drzewa wywoBaD ,12#0N2H2,282!,'!2H2,222,22,J/'232',2!-,H,J0H2,2   '% Ldn & n 7 s!??% (    Tn C @^@ <L - T rekurencyjnych rozwa|anego algorytmu dla danych wej[ciowych !,22!,3.040,2!2-H,--2,12,12#0N22,2,41,2H,',2J0-2   '&" WMFC % Ld & S  7 s!??% (    ! - T F(GDIC <T FTHTNPPhttps://edu.pjwstk.edu.pl/tex/ASDEgzaminPop/tex/opc1087213_1.gif!b K  FTNPPQ :R  P0Km(` 000` 000 ` 000>g>1>13f7C@3w1Gp3pA@cF00@@CD0@p@gDpp@8b@D8;@r@>D0@:@`tD C@p4sD1CF8<c pF08;øw 1pc `   ?Q :R  P`Km(bbbnnnTTT888FFF(((AAAAAA0000    Pq1W@AqqPqWWq@AWq@A!%S0@10A@A1010@A up 1V1 010\ \SPA@10QQ@A01ܱq011\[afR0@AxSWa A@A0 10QxpA@10A0! 17qw@10AV0    P @c @A!FTNPP" FGDIC" % % % TT; lS @^@;S L - T P 2"    '% Ld: t4 : ;!??% (      '% Ld: 5 ? : 5 s!??% (      '% Ldo5 t o5 s!??% (      '% Ld: tY : ;!??% (   !: uT    '% Ld@ 5 n @ 5 /s!??% (    % % %  TT 5 @^@ L: uT P12TT 5 ! @^@ L: uT P 2"    '% Ld >4  !??% (      '% Ld5  5 s!??% (      '% Ld95 > 95 s!??% (      '% Ld >Y  !??% (   ! ?T    '% Ld5 8 5 s!??% (    % % %  TTD5 { @^@D L ?T P+8TT|5  @^@| L ?T P m2"    '% LdL :Y L !??% (   !L ;T    '% LdRn 4 Rn s!??% (    % % %  TTCn t @^@C LL ;T P 2"    '% Ld&T Y &T !??% (      '% Ld&  & !??% (      '% LdT , Y T C !??% (      '% Ld ,  C !??% (      '% Ld: T tY : T ;!??% (      '% Ld: t : ;!??% (      '% LdT >Y T !??% (      '% Ld >  !??% (      '% LdLT :Y LT !??&" WMFC u% (      '% LdL : L !??% (      '% Ld&g X &g !??% (   !&m S    '% Ld, R , s!??% (    % % %  TT, ]Q @^@,: L&m S P 2"    '% Ldg , l g C !??% (      '% Ldm R m !??% (      '% Ld' m , R ' m !??% (      '% LdS , X S C !??% (   !m - S    '% Ldm & m 7 s!??% (    % % %  Tm @^@ 7Lm - S W rozwa|anym przypadku liczba wykonanaD rekurencyjnych _!2-H,-,3/N3!.02,322,-2,I0222,3,2!,32!,2.040,2   '% Ld & R  7 s!??% (    TD Q @^@: )Lm - S algorytmu QuickSort jest rwna dokBadnie ,12#0N2H2,282!,'!2H2,222,22,!m - S F(GDIC  ; FTHTNPPhttps://edu.pjwstk.edu.pl/tex/ASDEgzaminPop/tex/opc1087189_1.gif!b K  FTNPPQ  9   P00eN( | ނ ]]MM<  ``p0`Q  9   PT`eN(  nnnbbbFFFTTT0E fQ'a'afQi Qaa 0QFTNPP" FGDIC" % % % TT H Q @^@ : Lm - S P 2"    '% Ld: g t : g ;@!??% (      '% Ld: ?  : s!??% (      '% Ldo t o s!??% (      '% Ld:  tX :  ;?!??% (   !: m uS    '% Ld@ n @ /s!??% (    % % %  TT  @^@  L: m uS P0`2TT ! @^@  L: m uS P 2"    '% Ldg >X g !??% (   !m ?S    '% Ld 8R  s!??% (    % % %  TT` Q @^@`: Lm ?S P N2"    '% LdLg :X Lg !??% (   !Lm ;S    '% LdR 4R R s!??% (    % % %  TTC tQ @^@C: LLm ;S P C2"    '% Ld&S X &S !??% (      '% Ld&h m &h !??% (      '% LdS , X S C !??% (      '% Ldh , m h C !??% (      '% Ld: S tX : S ;!??% (      '% Ld: h tm : h ;!??% (      '% LdS >X S !??% (  &" WMFC U    '% Ldh >m h !??% (      '% LdLS :X LS !??% (      '% LdLh :m Lh !??% (      '% Ld&f W &f !??% (   !&l R    '% Ld, Q , s!??% (    % % %  TT, ]P @^@,9 L&l R P 2"    '% Ldf , k f C !??% (      '% Ldl Q l !??% (      '% Ld' l , Q ' l !??% (      '% LdR , W R C !??% (   !l - R    '% Ldl & l 7 s!??% (    % % %  Tl  @^@ Ll - R dW rozwa|anyh_!2-H,-,3/TTl @^@ ,Ll - R m przypadku liczba wykonanaD rekurencyjnych N3!.02,322,-2,I0222,3,2!,32!,2.040,2   '% Ld & Q  7 s!??% (    TD P @^@9 )Ll - R algorytmu QuickSort jest rwna dokBadnie ,12#0N2H2,282!,'!2H2,222,22,!l - R F(GDIC : FTHTNPPhttps://edu.pjwstk.edu.pl/tex/ASDEgzaminPop/tex/opc1087186_1.gif!b K  FTNPPQ 8   P04/N(    $ UI s  `Q 8   PD4/N( bbbA`a@P!FTNPP" FGDIC" % % % TT  P @^@9 Ll - R P 2"    '% Ld: f t : f ;@!??% (      '% Ld: ?  : s!??% (      '% Ldo t o s!??% (      '% Ld:  tW :  ;?!??% (   !: l uR    '% Ld@ n @ /s!??% (    % % %  TT  @^@ L: l uR P12TT ! @^@ L: l uR P 2"    '% Ldf > f @!??% (      '% Ld   s!??% (      '% Ld9 > 9 s!??% (      '% Ld >W  ?!??% (   !l ?R    '% Ld 8  s!??% (    % % %  TTD { @^@D Ll ?R P+8TT|  @^@| Ll ?R P 2"    '% LdLf :W Lf !??% (   !Ll ;R    '% LdR 4Q R s!??% (    % % %  TTC tP @^@C9 LLl ;R P 2"    '% Ld&R W &R !??% (      '% Ld&g l &g !??&" WMFC 5% (      '% LdR , W R C !??% (      '% Ldg , l g C !??% (      '% Ld: R tW : R ;!??% (      '% Ld: g tl : g ;!??% (      '% LdR >W R !??% (      '% Ldg >l g !??% (      '% LdLR :W LR !??% (      '% LdLg :l Lg !??% (    % % %  TT,d a @^@, LahP 6   '% Ld&F&Fq!??% (      '% Ld&+r&s!??% (      '% Ldrs!??% (      '% Ld&s-&sq!??% (   !&L(   '% Ld,r,ds!??% (    % % % TX,q@^@,ZL&L(P1522TTq@^@ZL&L(P 2"    '% LdF:KF!??% (      '% LdL'L!??% (      '% Ld5L:'5L!??% (      '% Ld(:-(!??% (   !L;(   '% LdL4Ls!??% (    % % %  TL@^@LL;(pRozwa|my tablic C2-H,-O/,2,,!L;(F(GDICW Fh[TNPPC:\Users\Piotr\AppData\Local\Temp\Rar$EX01.912\edu\result2.asp_files\pyt59145_1.gif!b K  FTNPPQX X P00eN(   ]]MM ! 1`1`0`QX X PH`eN( TTT888FFFbbbnnn 2AVe15awS0B1V" FTNPP" FGDIC" % % % T Lk@^@ LL;(lreprezentujc !,2",-,22,,,!L;(F(GDICkWFh[TNPPC:\Users\Piotr\AppData\Local\Temp\Rar$EX01.912\edu\result2.asp_files\pyt59145_2.gif!b K  FTNPPQlXlX P00eN( >|  ]]MM  ``8p0`QlXlX P8`eN( bbb01 FTNPP" FGDIC" % % % TTL@^@LL;(P-!TPL@^@+LL;(elementowy cig r|nych liczb naturalnych: ,,N,22J0,-1!2-40,2,-22,2!,41,2   '% Ld4A!??% (    !L;(F(GDIC*Fh[TNPPC:\Users\Piotr\AppData\Local\Temp\Rar$EX01.912\edu\result2.asp_files\pyt59145_3.gif!b K  FTNPPQ(P0Km(0  00  0@@@@0  0~3ϟ|ϟϟϟ3o3q ;!3g8 11   0 p #   8p  # 1 8# ; ! ?   0!Cc 18!cap;c? `0|`0Q(P\Km( nnnbbbFFFTTT888111&" WMFC PPPPPPP       Qi01i`Qi`i`01i`01i`Qi``&e!&e0QP1!P1&ev01vPPQPv01Qv v01&ePg!P&e0QPa01`1PQ`QP1Q1iD!101eP01QPD!v0QP1a1aa0QP10QPaa!vaE`0101E01FTNPP" FGDIC" % % % T6@@^@)>LL;(. Do posortowania owej tablicy stosujemy algorytm QuickSort w H222'2!2H,2,2I,,2-0'2'2,P0,12#0NH2,282!H   '% LdB4Bs!??% (    TB@^@LL;(pimplementacji rekuN2,N,2,,!,22T@B@^@SLL;(rencyjnej, z procedur podziaBu zgodn z metod Partition. Ktre z poni|szych zdaD !,3.12,-2!2,,22!,222-,2-1222,-N,22,8,!22H2!,-222-'./,2-2,2   '% Ld4's!??% (    T/&@^@LL;(ljest prawdziwe?,'2!,H2-H,-TT0a&@^@0LL;(P 2"    '% Ld&',&'p!??% (      '% Ld&FK&Fp!??% (      '% Ld':,'!??% (      '% LdF:KF!??% (      '% Ld&;,&;q!??% (   !&A'   '% Ld,&,ds!??% (    % % %  TT,]%@^@,L&A'P 2"    '% Ld;@@;!??% (      '% LdA&A!??% (      '% Ld:A@&:A!??% (      '% Ld'@,'!??% (   !AA'   '% LdA9As!??% (    % % %  TPA@^@VLAA'W rozwa|anym przypadku liczba wykonanaD rekurencyjnych algorytmu QuickSort jest rwna _!2-H,-,3/N3!.02,322,-2,I0222,3,2!,32!,2.040,2,13#0N2H2,282!,'!2H2,   '% Ld9&s!??% (    TK%@^@ LAA'`dokBadnie 222,22,!AA'F(GDICK|Fl]TNPPC:\Users\Piotr\AppData\Local\Temp\Rar$EX01.912\edu\result2.asp_files\opc1086661_1.gif!b K  FTNPPQLz L P04/N(    $ UI s  `QLz L PD4/N( bbbA`a@P!FTNPP" FGDIC" % % % TT{%@^@{LAA'P 2"    '% LdM;yM;B?!??% (&" WMFC       '% LdMzRMzs!??% (      '% Ldzzs!??% (      '% LdM,MB@!??% (   !MA'   '% LdSzSz6s!??% (    % % %  TTUz@^@ULMA'P12TTz@^@LMA'P 2"    '% Ld;y;I?!??% (      '% Ldzzs!??% (      '% Ldzzs!??% (      '% Ld,I@!??% (   !A'   '% Ldzz=s!??% (    % % %  TTz@^@LA'P+8TTz@^@LA'P 2"    '% Ld;:y;I?!??% (      '% Ldzzs!??% (      '% Ld5z:5zs!??% (      '% Ld:,I@!??% (   !A;'   '% Ldz4z=s!??% (    % % %  TTz1@^@LA;'P+8TT2z:@^@2LA;'P 2"    '% Ld&&+&&p!??% (      '% Ld&;@&;p!??% (      '% Ld&?+&!??% (      '% Ld;?@;!??% (      '% LdM&+M&B!??% (      '% LdM;@M;B!??% (      '% Ld&+&I!??% (      '% Ld;@;I!??% (      '% Ld&:+&I!??% (      '% Ld;:@;I!??% (      '% Ld&:&:qt!??% (   !&@   '% Ld,f,ds!??% (    % % %  TT,]e@^@,NL&@P 2"    '% Ld:@?:!??% (      '% Ld@@h!??% (      '% Ld:@@:@h!??% (      '% Ld@!??% (   !@A   '% Ld@9@s!??% (    % % %  Tt@ @^@1L@AW rozwa|anym przypadku&" WMFC  wyskok[ drzewa wywoBaD re_!2-H,-,3/N3!.02,322I0'222',3!-,H,J1H2,2!,T0 @@^@ &L@Akurencyjnych algorytmu QuickSort jest 22",2.040,2,12#0N2H2,282!,'   '% Ld9%s!??% (    Td$@^@ YL@Arwna dokBadnie wysoko[ci drzewa wywoBaD rekurencyjnych rozwa|anego algorytmu dla danych !2H2,222,22,J/'223',2!-,H,J0H2,2!,23!,2.040,2!2-H,-,2-12,12#0N22,3,40,2   '% Ld&9&!??% (    T6@^@ L@Adwej[ciowych H,',2J0,2!@AF(GDIC"Fl]TNPPC:\Users\Piotr\AppData\Local\Temp\Rar$EX01.912\edu\result2.asp_files\opc1086687_1.gif!b K  FTNPPQ##P0Km(` 0` 0 @@@` 0|g?ϟϟϟ|3f7; 3rp#11 80  0   #p< 1#8px ;#  ?!Ѐ  0 0 18 pp;pc0| |`0`Q##P\Km( bbbnnnTTT888FFF11111PPPPP     H0eQH@01H@01H@QH@PqQP1DQq$E0QP1!P1q$E*APPQP01PQQA PQ0p Q$E!P$EJA@QP1PQQp101!fHaQPQ01QPPP! QPp!A0QP10QPAA!A 01 !Pe0101e!FTNPP" FGDIC" % % % TT6H@^@L@AP 2"    '% LdM:M:B!??% (      '% LdMR,Ms!??% (      '% Ld,s!??% (      '% LdM-M-B!??% (   !M@   '% LdS,S6s!??% (    % % %  TTU+@^@ULM@P02TT+@^@LM@P 2"    '% Ld::It!??% (   !@   '% Ldf=s!??% (    % % %  TTe@^@NL@P 2"    '% Ld:::I!??% (      '% Ld,s!??% (      '% Ld5:,5s!??% (      '% Ld-:-I!??% (   !@;   '% Ld4,=s!??% (    % % %  TT1+@^@L@;P+8TT2:+@^@2L@;P 2"    '% Ld&&p!??% (      '% Ld&:?&" WMFC &:p!??% (      '% Ld?!??% (      '% Ld:??:!??% (      '% LdMMB!??% (      '% LdM:?M:B!??% (      '% LdI!??% (      '% Ld:?:I!??% (      '% Ld:I!??% (      '% Ld::?:I!??% (      '% Ld&9&q!??% (   !&4   '% Ld,3,d9!??% (    % % %  TT,]3@^@,UL&4P 2"    '% Ld@!??% (      '% Ld3s!??% (      '% Ld:@3:s!??% (      '% Ld4@94!??% (   !A4   '% Ld93s!??% (    % % %  T4d2@^@QLA4W rozwa|anym przypadku liczba wykonanaD algorytmu Partition jest rwna dokBadnie _!2-H,-,3/N3!.02,322,-2,I0222,3,2,22"0N28,!22,'!2I2,222,22,!A4F(GDICdFl]TNPPC:\Users\Piotr\AppData\Local\Temp\Rar$EX01.912\edu\result2.asp_files\opc1086669_1.gif!b K  FTNPPQee P00/N( |  ]]MM|  ``p~0`Qee PP0/N(  nnnbbbFFF((( A@!V1 vAFp!6Q AV1AFTNPP" FGDIC" % % % TT2@^@LA4P 2"    '% LdMMB!??% (      '% LdMR3Ms!??% (      '% Ld3s!??% (      '% LdM49M4B!??% (   !M4   '% LdS3S6s!??% (    % % %  TTU2@^@ULM4P02TT2@^@LM4P 2"    '% Ld9I!??% (   !4   '% Ld3=9!??% (    % % %  TT3@^@UL4P 2"    '% Ld:I!??% (      '% Ld3s!??% (      '% Ld5:35s!??% (      '% Ld4:94I!??% (   !;4   '%&" WMFC  Ld43=s!??% (    % % %  TT12@^@L;4P+8TT2:2@^@2L;4P 2"    '% Ld&49&4p!??% (      '% Ld&&p!??% (      '% Ld4?94!??% (      '% Ld?!??% (      '% LdM49M4B!??% (      '% LdMMB!??% (      '% Ld494I!??% (      '% LdI!??% (      '% Ld4:94I!??% (      '% Ld:I!??% (    % % %  TT,Fa@^@,LahP 6   '% Ld&(&(p!??% (      '% Ld&+P&s!??% (      '% LdPs!??% (      '% Ld&Q&Qp!??% (   !&.   '% Ld,P,ds!??% (    % % % TX,O@^@,8L&.P1522TTO@^@8L&.P 2"    '% Ld(:-(!??% (      '% Ld..!??% (      '% Ld5.:5.!??% (      '% Ld:!??% (   !.;   '% Ld.4.s!??% (    % % %  T.`@^@L.;lRozwa|my tablicC2-H,-O/,2,TXa.@^@aL.;P ,!.;F(GDIC9 F`TTNPPC:\Users\Piotr\AppData\Local\Temp\Rar$EX00.114\Edukacja_files\pyt59154_1.gif!b K  FTNPPQ: : P00eN(   ]]MM ! 1`1`0`Q: : PH`eN( TTT888FFFbbbnnn 2AVe15awS0B1V" FTNPP" FGDIC" % % % T .k@^@ L.;lreprezentujc !,2",-,22,,,!.;F(GDICk9F`TTNPPC:\Users\Piotr\AppData\Local\Temp\Rar$EX00.114\Edukacja_files\pyt59154_2.gif!b K  FTNPPQl:l: P00eN( >|  ]]MM  ``8p0`Ql:l: P8`eN( bbb01 FTNPP" FGDIC" % % % TT.@^@L.;P-!TP.@^@+L.;elementowy cig r|nych liczb naturalnych: ,,N,22J0,-1!2-40,2,-22,2!,41,2   '% Ld4{!??% (    !.;F(GDICF`TTNPPC:\Users\Piotr\AppData\Local\Temp\Rar$EX00.114\Edukacja_files\pyt59154_3.gif!b K&" WMFC u  FTNPPQP0e( 0nn 0@@@ 0ϟϟ3>!!L!&3y7bb !@! 8c @   a @  8Abb   <bxc   x`rw   `:8~  @ `  ! `p;``a  QP`@e(nnnbbbTTT888FFF(((1111@@@@@@      `q01g`Ag``g`Agq`q01g`g0Tq01!&d &d@ fA@01A@)a@A01 Av01pAe)a!@&d@A idfA!@`1vaٱk1gq@Aik A1!vQb@a!xdqUgQ  a0A@axp1aa!@! AGqeaa0A@01T0T 0A FTNPP" FGDIC" % % % T@^@>L.;. Do posortowania owej tablicy stosujemy algorytm QuickSort w H222'2!2H,2,2I,,2-0'2'2,P0,12#0NH2,282!H   '% Ld4s!??% (    T@^@veL.;implementacji rekurencyjnej, z procedur podziaBu zgodn z metod Partition. Ktre z poni|szych zdaD N2,N,2,,!,22!,3.12,-2!2,,22!,222-,2-1222,-N,22,8,!22H2!,-222-'./,2-2,2   '% Ld4s!??% (    T/@^@L.;ljest prawdziwe?,'2!,H2-H,-TT0a@^@0L.;P 2"    '% Ld&&p!??% (      '% Ld&(-&(p!??% (      '% Ld:!??% (      '% Ld(:-(!??% (      '% Ld&&p!??% (   !&   '% Ld,,ds!??% (    % % %  TT,]@^@,L&P 2"    '% Ld9!??% (      '% Ld!??% (      '% Ld393!??% (      '% Ld9!??% (   !:   '% Ld2s!??% (    % % %  T@^@u L:dW rozwa|any_!2-H,-,3/T@^@uKL:m przypadku liczba wykonanaD rekurencyjnych algorytmu QuickSort jest rwna N3!.02,322,-2,I0222,3,2!,32!,2.040,2,13#0N2H2,282!,'!2H2,   '% Ld2s!??% (    TK@^@ L:`dokBadnie 222,22,!:F(GDICKFdVTNPPC:\Users\Piotr\AppData\Local\Temp\Rar$EX00.114\Edukacja_files\opc1086980_1.gif!b K  FTNPPQLL P00eN( &" WMFC U| ނ ]]MM<  ``p0`QLL PT`eN(  nnnbbbFFFTTT0E fQ'a'afQi Qaa 0QFTNPP" FGDIC" % % % TT@^@L:P 2"    '% LdFSFD?!??% (      '% LdFTKFTs!??% (      '% LdTTs!??% (      '% LdFFD@!??% (   !F   '% LdLTLT8s!??% (    % % %  TTOT@^@OLFP02TTT@^@LFP 2"    '% LdL!??% (   !   '% Ld@s!??% (    % % %  TT@^@LP 2"    '% Ld:SL?!??% (      '% LdTTs!??% (      '% Ld5T:5Ts!??% (      '% Ld:L@!??% (   !;   '% LdT4T@s!??% (    % % %  TTT/@^@L;P+8TT0T:@^@0L;P 2"    '% Ld&&p!??% (      '% Ld&&p!??% (      '% Ld8!??% (      '% Ld8!??% (      '% LdFFD!??% (      '% LdFFD!??% (      '% LdL!??% (      '% LdL!??% (      '% Ld:K!??% (      '% Ld:K!??% (      '% Ld&x&pe!??% (   !&s   '% Ld,8,ds!??% (    % % %  TT,]7@^@, L&sP 2"    '% Ld9!??% (      '% LdrY!??% (      '% Ld39r3Y!??% (      '% Lds9xs!??% (   !:s   '% Ld2s!??% (    % % %  TP@^@tVL:sW rozwa|anym przypadku liczba wykonanaD reku&" WMFC 5rencyjnych algorytmu QuickSort jest rwna _!2-H,-,3/N3!.02,322,-2,I0222,3,2!,32!,2.040,2,13#0N2H2,282!,'!2H2,   '% Ld2s!??% (    T@^@LL:sdokBadnie liczbie wywoBaD rekurencyjnych rozwa|anego algorytmu dla danych we222,22,,-2,I0H2,2!,22",2.040,2!2-H--,2,12,13#/N22,3-30,2H,TK@^@ L:s`j[ciowych ',2J0-2   '% Ld2rs!??% (    !:sF(GDIC sFdVTNPPC:\Users\Piotr\AppData\Local\Temp\Rar$EX00.114\Edukacja_files\opc1086991_1.gif!b K  FTNPPQ q P0e( 00nn 00 00?13> CCy8CyL33y7bb @1B8C8@8c @0@@a @ @@888Abb @1A8@xxc @;A@w @?A@8t8~ @0A0@@4` @8A1B<p;;`    Q q P`@e(nnnbbbTTT888FFF(((111111@@@@    `gq0Tqq0Tq`ggqg0Tq01!@1fA@ fA 0A@1 fA@)a)a01)a@01Aa)a01 &Q)a A@AfAi0AfA!@`A@1akv@Ak q AgF1 A1aUV!a!01AgQqU@ a@! Aaw0A&Qa0A@ 01 !@  0A01A 0A FTNPP" FGDIC" % % % TTr@^@rL:sP 2"    '% LdFFDy!??% (      '% LdFKFs!??% (      '% Lds!??% (      '% LdFxFDy!??% (   !Fs   '% LdLL8s!??% (    % % %  TTO@^@OLFsP12TT@^@LFsP 2"    '% LdLy!??% (      '% Lds!??% (      '% Lds!??% (      '% LdxLy!??% (   !s   '% Ld@s!??% (    % % %  TT@^@LsP+8TT@^@LsP 2"    '% Ld:xLe!??% (   !;s   '% Ld48@s!??% (    % % %  TT:7@^@ L;sP 2"    '% Ld&rw&rp!??% (      '% Ld&&p!??% (      '% Ldr8wr!??% (      '&" WMFC % Ld8!??% (      '% LdFrwFrD!??% (      '% LdFFD!??% (      '% LdrwrL!??% (      '% LdL!??% (      '% Ldr:wrK!??% (      '% Ld:K!??% (      '% Ld&&p!??% (   !&z   '% Ld,u,ds!??% (    % % %  TT,]t@^@,]L&zP 2"    '% Ld9!??% (      '% Ldy!??% (      '% Ld39y3!??% (      '% Ldz9z!??% (   !:z   '% Ld2s!??% (    % % %  Td@^@YL:zW rozwa|anym przypadku liczba wykonanaD algorytmu Partition jest rwna dokBadnie liczbie _!2-H,-,3/N3!.02,322,-2,I0222,3,2,22"0N28,!22,'!2I2,222,22,,-2,   '% Ld2y{!??% (    T x@^@a5L:zwykonaD rozwa|anego algorytmu dla danych wej[ciowych I0223,2!2-H,-,2-12,12#0N22,2,40-2H,(,2I0-2!:zF(GDIC bFdVTNPPC:\Users\Piotr\AppData\Local\Temp\Rar$EX00.114\Edukacja_files\opc1087000_1.gif!b K  FTNPPQ ` P0e(```nn```   ```gϙ??>c>g>aCy8Cs8gsa 7bbB8F00 c@F0`a@DpCbbA8F0c<AGpwAG~A0F0h0``A1G1x0`p;ð;8p8 `; Q ` P`@e(nnnFFFbbbTTT888(((!!!!!!!!@@PP 4p 4 !xp !xp 4 ! wAwA@@ wAVqVq@A@Vq@ !A !PAVqq`AsVq@wAPA@AQ@@Aa vtwAQ@{qqֱ{PA!@Av{PA!qQ1u@qQAx1x1 Pqq@QPA A@@QPAHsqq A@ APPQ@PP 4P AFTNPP" FGDIC" % % % TTJx@^@aL:zP 2"    '% LdFFDC!??% (      '% LdFK;Fs!??% (      '% Ld;s!??% (      '% LdF<F<DD!??% (   !Fz   '% LdL;L8s!?? &WMFC% (    % % %  TTO:@^@O#LFzP02TT:@^@#LFzP 2"    '% LdL!??% (   !z   '% Ldu@s!??% (    % % %  TTt@^@]LzP 2"    '% Ld:L!??% (   !;z   '% Ld4u@s!??% (    % % %  TT:t@^@]L;zP 2"    '% Ld&y~&yp!??% (      '% Ld&&p!??% (      '% Ldy8~y!??% (      '% Ld8!??% (      '% LdFy~FyD!??% (      '% LdFFD!??% (      '% Ldy~yL!??% (      '% LdL!??% (      '% Ldy:~yK!??% (      '% Ld:K!??% (    % % %  TT,a@^@,LahP 6% % 6h6ah6a66g6`g6`66f6_f6_66e6^e6^66d6]d6]66c6\c6\66b6[b6[66a6Za6Z66`6Y`6Y6 6 _6X_6X 6  6 ^6W^6W 6  6 ]6V]6V 6  6 \6U\6U 6  6 [6T[6T 6 6Z6SZ6S66Y6RY6R66X6QX6Q66W6PW6P66V6OV6O6  KS."System?????????-- - @ !&#-  - @ !<#-  - @ !<0-  - @ !J#- ,`1&# - @ ! <$- @Times New Roman--- 2 G$#&1`15 2 G0#&1` ' - @ !&2-  - @ !:&2-  - @ !:&/-  - @ !`2- ,`0&2 - @ !&3- --- %2 132&0`Rozwamy tablic   ,`0&2,9A  ((   ]]MM ! 1`1`0`aA  (( TTT888FFFbbbnnn 2AVe15awS0B1V" ''---"2 12&0`reprezentujc ,`0&2,9A  (( >|  ]]MM  ``8p0`YA  (( bbb01 ''--- 2 12&0`-L2 1+2&0`elementowy cig rnych liczb naturalnych:    - @ !43- ,`0&2,A  43(0 `000 `00@ 0 `00>3τg>3?>~30 !a w07Gso3  c3F0G `CD0 gFpp pG'8!>0C>t!0G 4!`sG0 <!1`c0!F0<80 `wp1p8> `??6mA  43(bbbnnnTTTFFF888(((111```````       @G@G@G@q0Vq01G@@G0Vq01G@aGa`1DaDa!$F`)Aa`01)Aa``  01 a)AaE01)AaEtI0Da IFDa IF`a`aLtL@1Aa aILG aILqU01AB`AB``a` qU zFGQAwAAA`AEAAEAzp1`! a 01 0a0V010a 0V!''---h2 A>2&0`. Do posortowania owej tablicy stosujemy algorytm QuickSort w        - @ !D3- 2 O3e2&0`implementacji rekurencyjnej, z procedur podziau zgodn z metod Partition. Ktre z poniszych zda     - @ !R3- 2 ]3 2&0`jest prawdz2 ]j2&0`iwe?  2 ]2&0` ' - @ !`#-  - @ !&#-  - @ !`2-  - @ !&2-  - @ !b#- ,1c# - @ ! q$- ---  2 |$#c1 ' - @ !b2-  - @ !c2-  - @ !c-  - @ !2- ,c2 - @ ! c3- --- 2 m3Y2cW rozwaanym przypadku liczba wykonana algorytmu Partition jest rwna dokadnie liczbie      - @ !p3- [2 }352cwykona rozwaanego algorytmu dla danych wejciowych h    ,c2,A  pQ(000000000000>3>|3>3?10n0Cyw07@q3pC8c3@90@C@0@8g@8p?@xp@w@>0@ta@80@4A@s@a<cpBc0!@c88w1wp1Àw `> ??>mA  pQ(bbbnnnTTT888FFF(((AAAA000000      PWP1WPWPq@cq@AWPPW@cqPqPW!%S10A U1  U1 @10A*Q10@A*Q@A0  u1*Q1V@A*Q@A%aZ@U1 ZSU1@ť101PA\u\u1 1Z\W 1W5Af@AQR0Qe!0xS10 qfqf QwQxpAQQ0QVQQQ@1%a@A @1 @c@A@1 @A1!''--- 2 }2c ' - @ ! b-  - @ !j-  - @ !j!-  - @ ! x- ,"c - @ !j- ---  2 uc"0 2 u!c" ' - @ ! b#- ,,c# - @ !q$- ---  2 |(#c, ' - @ !b.- ,0c. - @ !q.- ---  2 |/.c0 ' - @ !#-  - @ !b#-  - @ !2-  - @ !b2-  - @ ! -  - @ ! b-  - @ ! #-  - @ ! b#-  - @ !.-  - @ !b.-  - @ !#- ,1# - @ ! $- ---  2 $#1 ' - @ !2-  - @ !2-  - @ !-  - @ !2- ,2 - @ !3- --- 2 3W2W rozwaanym przypadku wyskok drzewa wywoa rekurencyjnych algorytmu QuickSort jest       - @ !3- 2 3 2rwna dokad 2 t2nie ,2,9A  (   ]]MM t 4`<`p 0`IA  ( TTTnnnbbbFFFg !U @3''--- 2 2 ' - @ ! -  - @ !-  - @ !!-  - @ ! - ," - @ !- ---  2 "0 2 !" ' - @ ! #- ,,# - @ !$- ---  2 (#, ' - @ !.- ,0. - @ !.- ---  2 /.0 ' - @ !#-  - @ !#-  - @ !2-  - @ !2-  - @ ! -  - @ ! -  - @ ! #-  - @ ! #-  - @ !.-  - @ !.-  - @ !+#- ,1# - @ ! $- ---  2 $#1 ' - @ !2-  - @ !)2-  - @ !)-  - @ !2- ,2 - @ !3- --- 2 3V2W rozwaanym przypadku liczba wykonana rekurencyjnych algorytmu QuickSort jest rwna     - @ ! 3- 2 3V2dokadnie liczbie wywoa rekurencyjnych rozwaanego algorytmu dla danych wejciowych      - @ !3- ,2,A  3(0 `0`00 `0`0@  0 `0`0>3ϟ|g>3>|g30 !fq0a3!p9p 00 pp 8 |p|t p4 0a< 0c0808wp8c `~>~ mA  3(nnnbbbTTT888FFF(((AA00000000        `g`g`1g`1gq1g``g`g`qg!&c&c@10A&c 10A@10A0@A0@A v&Q@A&Qi&c@Ɩ1&c@@Ɩ100101`Av@Aa6Ag16A1qUvV!vV!0xc qU10 A@AgQawaaxpAa!@1&Q!aaa@1&Q0! 1 S1S@A@A1 `''--- 2 2 ' - @ ! -  - @ ! -  - @ ! !-  - @ ! - ," - @ ! - ---  2 "1 2 !" ' - @ ! #-  - @ ! #-  - @ ! +-  - @ ! #- ,,# - @ ! $- ---  2 $#,+ 2 +#, ' - @ !+.- ,0. - @ ! .- ---  2 /.0 ' - @ !#-  - @ !#-  - @ !2-  - @ !2-  - @ ! -  - @ ! -  - @ ! #-  - @ ! #-  - @ !.-  - @ !.- @"Calibri---  2 $SL  - @ !#-  - @ !#-  - @ !8-  - @ ! #- ,#9# - @ !$- ---2 (#9#15 2 4#9# ' - @ !;-  - @ !:;-  - @ !:/-  - @ !#;- ,#0; - @ !;- --- %2 ;;0#Rozwamy tablic   ,#0;,9A  (   ]]MM ! 1`1`0`aA  ( TTT888FFFbbbnnn 2AVe15awS0B1V" ''---"2 ;0#reprezentujc ,#0;,9A  ( >|  ]]MM  ``8p0`YA  ( bbb01 ''--- 2 ;0#-12 ;0#elementowy cig rnych l  &2 ~;0#iczb naturalnych:  - @ !;- ,#0;,A  ;(00000000@@0000>3ϟ1>13Cq3q3w1Gp3@98cF0 @CD  gDpb @ D8r@>D:@D@asDccc pF08waw 1pc > ?  ?0)A  ;(bbbnnnTTT888FFF(((AAAA000000      Pq1WWPPW@AqWPWq@AWq@A!%S @10A@A@A1010 pu @A1V1\ 0 \SPA01u@10Q@Aܱ01W1\[afR0@A xS0qfA@A 107qxpAwQ@10AQ@10AV0 @A P  @c @A!''---h2 >;0#. Do posortowania owej tablicy stosujemy algorytm QuickSort w       - @ !;- 2 ;e;0#implementacji rekurencyjnej, z procedur podziau zgodn z metod Partition. Ktre z poniszych zda      - @ !;- "2 ;;0#jest prawdziwe?  2 ;0# ' - @ !##-  - @ !#-  - @ !#;-  - @ !;-  - @ !9%#- ,]9&# - @ !A$- ---  2 L$#&9] ' - @ !Y%;-  - @ !7&;-  - @ !7&-  - @ !Y];- ,]&; - @ ! Y&;- --- _2 0;8;&]W rozwaanym przypadku wyskok drzewa wywoa rekurency      2 0v;&]jnych  - @ !Y3;- n2 >;B;&]algorytmu QuickSort jest rwna dokadnie wysokoci drzewa wywoa      - @ !YA;- e2 L;<;&]rekurencyjnych rozwaanego algorytmu dla danych wejciowych     - @ !YO;- ,]&;,A  P;(` 000` 000 ` 000>g>1>13f7C@3w1Gp3pA@cF00@@CD0@p@gDpp@8b@D8;@r@>D0@:@`tD C@p4sD1CF8<c pF08;øw 1pc `   ?)A  P;(bbbnnnTTT888FFF(((AAAAAA0000    Pq1W@AqqPqWWq@AWq@A!%S0@10A@A1010@A up 1V1 010\ \SPA@10QQ@A01ܱq011\[afR0@AxSWa A@A0 10QxpA@10A0! 17qw@10AV0    P @c @A!''--- 2 ];&] ' - @ !&%-  - @ !:-  - @ !:-  - @ !&H- ,]& - @ !$:- ---  2 E&]1 2 E&] ' - @ !6%-  - @ !:-  - @ !:-  - @ !6H- ,]& - @ !4:- ---  2 E&]+ 2 E&] ' - @ !9<%- ,]0& - @ !:A- ---  2 L&0] ' - @ !]#-  - @ !%#-  - @ !Y];-  - @ !Y%;-  - @ !&]-  - @ !&%-  - @ !6]-  - @ !6%-  - @ !<]-  - @ !<%-  - @ !_#- ,|9`# - @ !n$- ---  2 y$#`9| ' - @ !Y_;-  - @ !`;-  - @ !`-  - @ !Y|;- ,|`; - @ !Y`;- --- ^2 k;7;`|W rozwaanym przypadku liczba wykonana rekurencyjnych     - @ !Yn;- I2 y;);`|algorytmu QuickSort jest rwna dokadnie  ,|`;,9A  o ( | ނ ]]MM<  ``p0`gA  o (  nnnbbbFFFTTT0E fQ'a'afQi Qaa 0Q''--- 2 y;`| ' - @ !&_-  - @ !g-  - @ !g-  - @ !&u- ,|` - @ !$g- ---  2 r`|0 2 r`| ' - @ !6_- ,|` - @ !4n- ---  2 y`| ' - @ !<_- ,|0` - @ !:n- ---  2 y`0| ' - @ !|#-  - @ !_#-  - @ !Y|;-  - @ !Y_;-  - @ !&|-  - @ !&_-  - @ !6|-  - @ !6_-  - @ !<|-  - @ !<_-  - @ !~#- ,9# - @ !$- ---  2 $#9 ' - @ !Y~;-  - @ !;-  - @ !-  - @ !Y;- ,; - @ ! Y;- --- 2 ; ;W rozwaany  M2 ~,;m przypadku liczba wykonana rekurencyjnych   - @ !Y;- I2 ;);algorytmu QuickSort jest rwna dokadnie c ,;,;A   (    $ UI s  `IA   ( bbbA`a@P!''--- 2 ; ' - @ !&~-  - @ ! -  - @ ! -  - @ !&- , - @ ! $- ---  2 1 2  ' - @ !6~-  - @ ! -  - @ ! -  - @ !6- , - @ ! 4- ---  2 + 2  ' - @ !<~- ,0 - @ !:- ---  2 0 ' - @ !#-  - @ !~#-  - @ !Y;-  - @ !Y~;-  - @ !&-  - @ !&~-  - @ !6-  - @ !6~-  - @ !<-  - @ !<~- ---  2 $SL  - @ !#-  - @ !#-  - @ !0-  - @ !#- ,1# - @ ! $- ---2 $#115 2 0#1 ' - @ !2-  - @ !:2-  - @ !:/-  - @ !2- ,02 - @ !3- --- %2 320Rozwamy tablic   ,02,9A  (   ]]MM ! 1`1`0`aA  ( TTT888FFFbbbnnn 2AVe15awS0B1V" ''---"2 20reprezentujc ,02,9A  ( >|  ]]MM  ``8p0`YA  ( bbb01 ''--- 2 20-L2 +20elementowy cig rnych liczb naturalnych:    - @ !3- ,02,A  3(0  00  0@@@@0  0~3ϟ|ϟϟϟ3o3q ;!3g8 11   0 p #   8p  # 1 8# ; ! ?   0!Cc 18!cap;c? `0|`0'A  3( nnnbbbFFFTTT888111PPPPPPP       Qi01i`Qi`i`01i`01i`Qi``&e!&e0QP1!P1&ev01vPPQPv01Qv v01&ePg!P&e0QPa01`1PQ`QP1Q1iD!101eP01QPD!v0QP1a1aa0QP10QPaa!vaE`0101E01''---h2 >20. Do posortowania owej tablicy stosujemy algorytm QuickSort w       - @ !3- &2 320implementacji reku  2 S20rencyjnej, z procedur podziau zgodn z metod Partition. Ktre z poniszych zda c  - @ !3- "2 320jest prawdziwe?  2 20 ' - @ !#-  - @ !#-  - @ !2-  - @ !2-  - @ !#- ,1# - @ ! $- ---  2 $#1 ' - @ !2-  - @ !2-  - @ !-  - @ !2- ,2 - @ ! 3- --- 2 3V2W rozwaanym przypadku liczba wykonana rekurencyjnych algorytmu QuickSort jest rwna     - @ !3- 2 3 2dokadnie ,2,;A  e(    $ UI s  `IA  e( bbbA`a@P!''--- 2 k2 ' - @ !-  - @ !-  - @ !-  - @ ! - , - @ !- ---  2 1 2  ' - @ !-  - @ !-  - @ !%-  - @ ! - ,% - @ !- ---  2 %+ 2 $% ' - @ ! '-  - @ !'-  - @ !/-  - @ ! '- ,0' - @ !(- ---  2 ('0+ 2 /'0 ' - @ !#-  - @ !#-  - @ !2-  - @ !2-  - @ !-  - @ !-  - @ !-  - @ !-  - @ ! '-  - @ ! '-  - @ !,#- ,?1# - @ ! )$- ---  2 4$#1? ' - @ !2-  - @ !,2-  - @ !,-  - @ !?2- ,?2 - @ !3- --- U2 312?W rozwaanym przypadku wyskok drzewa wywoa rej     D2 G&2?kurencyjnych algorytmu QuickSort jest   - @ !!3- 2 ,3Y2?rwna dokadnie wysokoci drzewa wywoa rekurencyjnych rozwaanego algorytmu dla danych         - @ !/3- 2 <3 2?wejciowych ,?2,A  /u(` 0` 0 @@@` 0|g?ϟϟϟ|3f7; 3rp#11 80  0   #p< 1#8px ;#  ?!Ѐ  0 0 18 pp;pc0| |`0`'A  /u( bbbnnnTTT888FFF11111PPPPP     H0eQH@01H@01H@QH@PqQP1DQq$E0QP1!P1q$E*APPQP01PQQA PQ0p Q$E!P$EJA@QP1PQQp101!fHaQPQ01QPPP! QPp!A0QP10QPAA!A 01 !Pe0101e!''--- 2 <2? ' - @ !-  - @ !"-  - @ !"-  - @ !0- ,? - @ !"- ---  2 -?0 2 -? ' - @ !,- ,?% - @ !)- ---  2 4!%? ' - @ ! '-  - @ !"'-  - @ !"/-  - @ ! 0'- ,?0' - @ !"(- ---  2 -('0?+ 2 -/'0? ' - @ !?#-  - @ !#-  - @ !?2-  - @ !2-  - @ !?-  - @ !-  - @ !?-  - @ !-  - @ ! ?'-  - @ ! '-  - @ !A#- ,O1B# - @ ! I$- ---  2 S$#B1O ' - @ !A2-  - @ ! B2-  - @ ! B-  - @ !O2- ,OB2 - @ ! B3- --- 2 L3Q2BOW rozwaanym przypadku liczba wykonana algorytmu Partition jest rwna dokadnie     ,OB2,9A  C( |  ]]MM|  ``p~0`MA  C(  nnnbbbFFF((( A@!V1 vAFp!6Q AV1A''--- 2 L2BO ' - @ !A-  - @ ! B-  - @ ! B-  - @ !O- ,OB - @ ! B- ---  2 LBO0 2 LBO ' - @ !A- ,O%B - @ !I- ---  2 S!B%O ' - @ ! A'-  - @ ! B'-  - @ ! B/-  - @ ! O'- ,O0B' - @ ! B(- ---  2 L('B0O+ 2 L/'B0O ' - @ !O#-  - @ !A#-  - @ !O2-  - @ !A2-  - @ !O-  - @ !A-  - @ !O-  - @ !A-  - @ ! O'-  - @ ! A'- ---  2 \$SL  - @ !m#-  - @ ! #-  - @ ! 0-  - @ !#- ,1n# - @ ! $- ---2 $#m115 2 0#m1 ' - @ !m2-  - @ !9m2-  - @ !9m/-  - @ !2- ,0n2 - @ !m3- --- "2 x32m0Rozwamy tablic  2 x2m0 ,0n2,9A  o(   ]]MM ! 1`1`0`aA  o( TTT888FFFbbbnnn 2AVe15awS0B1V" ''---"2 x2m0reprezentujc ,0n2,9A  o( >|  ]]MM  ``8p0`YA  o( bbb01 ''--- 2 x2m0-L2 x+2m0elementowy cig rnych liczb naturalnych:    - @ !{3- ,0n2,A  ~{3( 0nn 0@@@ 0ϟϟ3>!!L!&3y7bb !@! 8c @   a @  8Abb   <bxc   x`rw   `:8~  @ `  ! `p;``a  A  ~{3(nnnbbbTTT888FFF(((1111@@@@@@      `q01g`Ag``g`Agq`q01g`g0Tq01!&d &d@ fA@01A@)a@A01 Av01pAe)a!@&d@A idfA!@`1vaٱk1gq@Aik A1!vQb@a!xdqUgQ  a0A@axp1aa!@! AGqeaa0A@01T0T 0A ''---h2 >2m0. Do posortowania owej tablicy stosujemy algorytm QuickSort w        - @ !3- 2 3e2m0implementacji rekurencyjnej, z procedur podziau zgodn z metod Partition. Ktre z poniszych zda     - @ !3- "2 32m0jest prawdziwe?  2 2m0 ' - @ !#-  - @ !m#-  - @ !2-  - @ !m2-  - @ !#- ,1# - @ ! $- ---  2 $#1 ' - @ !2-  - @ !2-  - @ !-  - @ !2- ,2 - @ !3- --- 2 3 2W rozwaany |2 uK2m przypadku liczba wykonana rekurencyjnych algorytmu QuickSort jest rwna e    - @ ! 3- 2 3 2dokadnie ,2,9A  e( | ނ ]]MM<  ``p0`gA  e(  nnnbbbFFFTTT0E fQ'a'afQi Qaa 0Q''--- 2 q2 ' - @ !-  - @ ! -  - @ ! -  - @ !- , - @ ! - ---  2 0 2  ' - @ ! - ,% - @ ! - ---  2  % ' - @ ! '-  - @ ! '-  - @ ! /-  - @ ! '- ,0' - @ ! '- ---  2 ('0+ 2 .'0 ' - @ !#-  - @ !#-  - @ !2-  - @ !2-  - @ !-  - @ !-  - @ ! -  - @ ! -  - @ ! '-  - @ ! '-  - @ !+#- ,1# - @ ! $- ---  2 $#1 ' - @ !2-  - @ !*2-  - @ !*-  - @ !2- ,2 - @ !3- --- 2 3V2W rozwaanym przypadku liczba wykonana rekurencyjnych algorytmu QuickSort jest rwna     - @ !3- }2 3L2dokadnie liczbie wywoa rekurencyjnych rozwaanego algorytmu dla danych we   2  2jciowych   - @ !3- ,2,A  ~3( 00nn 00 00?13> CCy8CyL33y7bb @1B8C8@8c @0@@a @ @@888Abb @1A8@xxc @;A@w @?A@8t8~ @0A0@@4` @8A1B<p;;`    A  ~3(nnnbbbTTT888FFF(((111111@@@@    `gq0Tqq0Tq`ggqg0Tq01!@1fA@ fA 0A@1 fA@)a)a01)a@01Aa)a01 &Q)a A@AfAi0AfA!@`A@1akv@Ak q AgF1 A1aUV!a!01AgQqU@ a@! Aaw0A&Qa0A@ 01 !@  0A01A 0A ''--- 2 2 ' - @ !-  - @ !-  - @ !-  - @ !- , - @ !- ---  2 1 2  ' - @ ! -  - @ !-  - @ !$-  - @ ! - ,% - @ !- ---  2 %+ 2 $% ' - @ !+ '- ,0' - @ !'- ---  2 +'0 ' - @ !#-  - @ !#-  - @ !2-  - @ !2-  - @ !-  - @ !-  - @ ! -  - @ ! -  - @ ! '-  - @ ! '-  - @ !#- ,1# - @ ! $- ---  2 $#1 ' - @ !2-  - @ !2-  - @ !-  - @ !2- ,2 - @ !3- --- 2 3Y2W rozwaanym przypadku liczba wykonana algorytmu Partition jest rwna dokadnie liczbie      - @ !3- [2 352wykona rozwaanego algorytmu dla danych wejciowych h    ,2,A  ~Q(```nn```   ```gϙ??>c>g>aCy8Cs8gsa 7bbB8F00 c@F0`a@DpCbbA8F0c<AGpwAG~A0F0h0``A1G1x0`p;ð;8p8 `; A  ~Q(nnnFFFbbbTTT888(((!!!!!!!!@@PP 4p 4 !xp !xp 4 ! wAwA@@ wAVqVq@A@Vq@ !A !PAVqq`AsVq@wAPA@AQ@@Aa vtwAQ@{qqֱ{PA!@Av{PA!qQ1u@qQAx1x1 Pqq@QPA A@@QPAHsqq A@ APPQ@PP 4P A''--- 2 2 ' - @ !-  - @ !-  - @ !-  - @ ! - , - @ !- ---  2 0 2  ' - @ ! - ,% - @ !- ---  2  % ' - @ ! '- ,0' - @ !'- ---  2 +'0 ' - @ !#-  - @ !#-  - @ !2-  - @ !2-  - @ !-  - @ !-  - @ ! -  - @ ! -  - @ ! '-  - @ ! '- ---  2 $SL --LLSSLLSSLLSSLLSSLLRRKKRRKKRRKKRRKKRRKKRRKKRRKKRRKKQQJJQQJJQQJJQQJJQQJJQQJJQQ