Algorytmy rekurencyjne

background image

-HU]\3HMD $OJRU\WP\LVWUXNWXU\GDQ\FK

$/*25<70<

5(.85(1&<-1(

background image

-HU]\3HMD $OJRU\WP\LVWUXNWXU\GDQ\FK

$/*25<70<5(.85(1&<-1(

5HNXUHQFMDZVW S

” 5HNXUHQFMD ]ZDQD UyZQLH UHNXUVM MHVWMHGQ ]QDMZD QLHMV]\FK

PHFKDQL]PyZX \ZDQ\FKZLQIRUPDW\FH

” 0LPR L X \FLH UHNXUHQFML QLH MHVW RERZL ]NRZH DOJRU\WP\

UHNXUHQF\MQH PRJ E\ü SU]HNV]WDáFRQH ] PQLHMV]\P OXE

ZL NV]\PZ\VLáNLHPQDSRVWDüNODV\F]Q LWHUDF\MQ MHM]DOHW\

V RF]\ZLVWH GOD ND GHJR NWR FKRü UD] VSUyERZDá WHJR VW\OX

SURMHNWRZDQLDDOJRU\WPyZ

'HILQLFMDUHNXUHQFML

” 3U]\ GHILQLRZDQLX QRZ\FK RELHNWyZ OXE SRM ü SRZLQQR

SU]HVWU]HJDüVL ]DVDG\DE\GHILQLFMD]DZLHUDáDZ\á F]QLHWHUPLQ\

ZF]H QLHM ]GHILQLRZDQH OXE RF]\ZLVWH 'HILQLRZDQLH RELHNWX ]D

SRPRF MHJR VDPHJR MHVW SRZD Q\P QDUXV]HQLHP WHM UHJXá\

Eá GQ\PNRáHP

” -H OL MHGQDN VSHáQLRQH V IRUPDOQH RJUDQLF]HQLD QDNáDGDQH QD

GHILQLFMH WDNLH MDN LVWQLHQLH RUD] MHGQR]QDF]QR ü GHILQLRZDQHJR

RELHNWX ZyZF]DV QLH GRFKRG]L GR ]áDPDQLD UHJXá SRSUDZQHM

GHILQLFML'HILQLFMHWDNLHQRV] QD]Z UHNXUHQF\MQ\FKLX \ZDQH

V JáyZQLHGRGHILQLRZDQLD]ELRUyZQLHVNR F]RQ\FK

” 3RZVWDá\ Z Z\QLNX GHILQLFML UHNXUHQF\MQHM RELHNW OXE SRM FLH

]ZDQ\ MHVW ] NROHL UHNXUHQF\MQ\P L VNáDGD VL F] FLRZR ] VLHELH

VDPHJROXEMHJRGHILQLFMDRGZRáXMHVL GRQLHJRVDPHJR

'HILQLFMDUHNXUHQF\MQDVNáDGDVL ]GZyFKF] FL

” :SLHUZV]HM]ZDQHMSU]\SDGNLHPEU]HJRZ\POXESRF] WNRZ\P

Z\OLF]DQH V HOHPHQW\ SRGVWDZRZH VWDQRZL FH F] FL VNáDGRZH

SR]RVWDá\FKHOHPHQWyZ]ELRUX

” :GUXJLHMF] FLV SRGDQHUHJXá\XPR OLZLDM FHNRQVWUXRZDQLH

QRZ\FK RELHNWyZ ] HOHPHQWyZ SRGVWDZRZ\FK OXE RELHNWyZ

]EXGRZDQ\FKZF]H QLHM5HJXá\WHPR QDVWRVRZDüZLHORNURWQLH

WZRU] FQRZHRELHNW\

background image

-HU]\3HMD $OJRU\WP\LVWUXNWXU\GDQ\FK

$/*25<70<5(.85(1&<-1(

3U]\NáDG

'RVNRQVWUXRZDQLD]ELRUXOLF]EQDWXUDOQ\FK1MHVWSRWU]HEQ\HOHPHQW

SRGVWDZRZ\]HURRUD]RSHUDFMD]ZL NV]DQLDRMHGHQ

ž1

MH OLQž1WRQž1

QLHPD DGQ\FKLQQ\FKRELHNWyZZ]ELRU]H1RSUyF]W\FKNWyU\FK

LVWQLHQLHZ\QLND]UHJXáL

'HILQLFMDWDSURZDG]LGRGR üQLHSRU F]QHMOLVW\HOHPHQWyZ'ODWHJR

Z\JRGQLHM MHVW X \ZDü SRQL V]HM GHILQLFML RSDUWHM QD DUDEVNLP

V\VWHPLH]DSLVXOLF]E

ž1

MH OLQž1WRQQQQQQQQQQž1

QLHPD DGQ\FKLQQ\FKRELHNWyZZ]ELRU]H1RSUyF]W\FKNWyU\FK

LVWQLHQLHZ\QLND]UHJXáL

” 6SUyEXM ]DVWRVRZDü SRZ\ V] GHILQLFM GR UHNXUHQF\MQHJR

Z\JHQHURZDQLDQSOLF]E\

” 'HILQLFMH UHNXUHQF\MQH VáX GZyP FHORP WZRU]HQLX QRZ\FK

HOHPHQWyZRUD]VSUDZG]DQLXF]\GDQ\HOHPHQWQDOH \GR]ELRUX

: W\P RVWDWQLP SU]\SDGNX UR]ZL ]\ZDQ\ SUREOHP SUyEXMH

VSURZDG]LüVL GRSUREOHPXSURVWV]HJRDMH OLWHQSURVW\MHVWQDGD

]áR RQ\UHGXNXMHVL JRGRMHV]F]HSURVWV]HJRLWDNGDOHMGRSyNL

QLH GRMG]LH VL GR SUREOHPX Z\PLHQLRQHJR Z SU]\SDGNX

EU]HJRZ\P 1D SU]\NáDG VSUDZG F]\ OLF]ED MHVW OLF]E

QDWXUDOQ

3U]\NáDG

'HILQLFMLUHNXUHQF\MQ\FKX \ZDVL F] VWRGRGHILQLRZDQLDIXQNFMLL

FL JyZ OLF]E )XQNFM VLOQLD PR QD QD SU]\NáDG ]GHILQLRZDü Z

QDVW SXM F\VSRVyE

Q MH OLQ SU]\SDGHNEU]HJRZ\

Q QQMH OLQ!NURNLQGXNF\MQ\

background image

-HU]\3HMD $OJRU\WP\LVWUXNWXU\GDQ\FK

$/*25<70<5(.85(1&<-1(

3U]\NáDGFG

àDWZR VSUDZG]Lü H VWRVXM F W GHILQLFM PR HP\ RWU]\PDü

QDVW SXM F\FL JOLF]E

'HILQLFMH UHNXUHQF\MQH QLH ]DZV]H V Z\JRGQH àDWZR WR ]DXZD \ü

GHILQLXM FUHNXUHQF\MQLHFL JRSRVWDFL

J Q

J Q

MH OL Q

=

=

-

>

Å

­

®

MH OL Q

1DSLHUZV]\U]XWRND]DEDUG]RQLHZLDGRPRFRWDGHILQLFMDRSLVXMH

-H OL MHGQDN VSUyERZDü SR]E\ü VL WHJR ]DSLVX UHNXUHQF\MQHJR

NRU]\VWDM F ] LQGXNFML PDWHPDW\F]QHM WR SU]HGVWDZLRQ GHILQLFM

PR QDSU]HGVWDZLüZSRVWDFLUyZQRZD QHJRSURVWHJRZ]RUX

J Q

Q

=

5HNXUHQFMDZSURJUDPRZDQLX

6WRVRZDQLHUHNXUHQFMLZSURJUDPRZDQLXZ\QLND]IDNWX HSU]HM FLH

] PDWHPDW\F]QHM GHILQLFML UHNXUHQF\MQHM QD NRQNUHWQ\ M ]\N

SURJUDPRZDQLDOXEQDZHWSVHXGRNRGMHVWRSHUDFM EDUG]RQDWXUDOQ

3RSDWU]P\MDNWRPR QD]URELüZSU]\SDGNXGHILQLFMLIXQNFMLVLOQLD

6LOQLD9QLQWHJHU

LIQ WKHQ

UHWXUQ

HOVH

UHWXUQQ6LOQLD9Q

HQGLI

HQG

5(.85(1&-$ : 352*5$02:$1,8 72 ='2/12 û

32'352*5$08352&('85<'2:<:2à$1,$6$0(*2

6$0(-6,(%,(%(=32 5('1,2/8%32 5('1,2

background image

-HU]\3HMD $OJRU\WP\LVWUXNWXU\GDQ\FK

$/*25<70<5(.85(1&<-1(

)RUPDOQDGHILQLFMDSURFHGXU\UHNXUHQF\MQHM

3URFHGXUD UHNXUHQF\MQD 3 PR H E\ü Z\UD RQD MDNR ]áR HQLH 3

LQVWUXNFML SRGVWDZRZ\FK 6

L

QLH ]DZLHUDM F\FK 3 RUD] VDPHM

SURFHGXU\3

[

]

3

6 3

L

Ù 3

” -H OLSURFHGXUD3]DZLHUDEH]SR UHGQLHRGZRáDQLHGRVDPHMVLHELH

WR3QD]\ZDVL SURFHGXU EH]SR UHGQLRUHNXUHQF\MQ MH OL]D 3

]DZLHUD RGZRáDQLH GR LQQHM SURFHGXU\ 4 NWyUD ]DZLHUD

EH]SR UHGQLH OXE SR UHGQLH RGZRáDQLH GR 3 WR 3 QD]\ZD VL

SURFHGXU SR UHGQLRUHNXUHQF\MQ

” 3URFHGXU\ UHNXUHQF\MQH GRSXV]F]DM PR OLZR ü Z\NRQ\ZDQLD

QLHVNR F]RQ\FK REOLF]H =DVDGQLF]\P Z\PDJDQLHP Z WDNLHM

V\WXDFML MHVW X]DOH QLHQLH UHNXUHQF\MQHJRZ\ZRáDQLDSURFHGXU\3

RG ZDUXQNX % NWyU\ Z SHZQ\P PRPHQFLH SU]HVWDMH E\ü

VSHáQLRQ\'ODWHJRWH VFKHPDWDOJRU\WPyZUHNXUHQF\MQ\FKPR QD

GRNáDGQLHMZ\UD]LüZSRVWDFL

[

]

3 LI % WKHQ 6 3

L

Ù

3

OXEZSRVWDFL

[

]

3

6 LI % WKHQ 3

L

Ù 3

5HNXUHQF\MQHZ\ZRáDQLDSURFHGXU\

3UDF SURFHGXU UHNXUHQF\MQ\FK ]LOXVWUXMHP\ QD SU]\NáDG]LH IXQNFML

SRGQRV]HQLDGRZROQHMOLF]E\GRSRW JLQDWXUDOQHM

[

[ [

MH OL Q

Q

Q

=

=
>

Å

­

®

-

MH OL Q

background image

-HU]\3HMD $OJRU\WP\LVWUXNWXU\GDQ\FK

$/*25<70<5(.85(1&<-1(

5HNXUHQF\MQHZ\ZRáDQLDSURFHGXU\FG

)RUPXOHSRGQRV]HQLDGRZROQHMOLF]E\GRSRW JLQDWXUODQHMRGSRZLDGD

QDVW SXM FDSURFHGXUDUHNXUHQF\MQD

3RWHJD[QIORDW

LIQ WKHQ

UHWXUQ

HOVH

UHWXUQ[3RWHJD[Q

HQGLI

HQG

” .RU]\VWDM F]SRZ\ V]HMGHILQLFMLUHNXUHQF\MQHREOLF]DQLHZDUWR FL

[

SU]\SRPRF\NROHMQ\FKZ\ZRáD SURFHGXU\3RW JDPDSRVWDü

Z\ZRáDQLHZ\ZRáDM3RW JD3URFHGXUH][

Z\ZRáDQLHZ\ZRáDM3RW JD3URFHGXUH][

Z\ZRáDQLHZ\ZRáDM3RW JD3URFHGXUH][

Z\ZRáDQLHZ\ZRáDM3RW JD3URFHGXUH][

Z\ZRáDQLHZ\ZRáDM3RW JD3URFHGXUH][

Z\ZRáDQLH

Z\ZRáDQLH[

Z\ZRáDQLH[[

Z\ZRáDQLH[[[

Z\ZRáDQLH[[[[

” &R G]LHMH VL SRGF]DV Z\NRQ\ZDQLD SURFHGXU\" :V]\VWNLH

Z\PLHQLRQH SRZ\ HM Z\ZRáDQLD RGQRWRZ\ZDQH V QD VWRVLH

SURJUDPX.D GHPXZLHUV]RZLNRGXSU]\SLVXMHVL QXPHUDMH OL

ZLHUV] MHVW Z\ZRáDQLHP SURFHGXU\ WR MHJR QXPHU MHVW DGUHVHP

SRZURWX $GUHV WHQ V\VWHP Z\NRU]\VWXMH GR ]DSDPL WDQLD RG

NWyUHJR PLHMVFD QDOH \ Z]QRZLü Z\NRQ\ZDQLH SURJUDPX SR

]DNR F]HQLXG]LDáDQLDSURFHGXU\

” ,OH UD]\ UHNXUHQF\MQLH SURFHGXUD 3RW JD PXVL Z\ZRá\ZDü VLHELH

VDP GOD GRZROQHJR Q GOD [

QDOH DáR WR ]URELü F]WHURNURWQLH

LQDF]HM LOH Z\QRVL SR]LRP ]DJá ELHQLD UHNXUHQFML" 6SUyEXM

SROLF]\ü &R PR HV] SRZLHG]LHü R ZLHONR FL VWRVX SRSWU]HEQHJR

GR]UHDOL]RZDQLDQZ\ZRáD UHNXUHQF\KQ\FK"

background image

-HU]\3HMD $OJRU\WP\LVWUXNWXU\GDQ\FK

$/*25<70<5(.85(1&<-1(

.LHG\QLHVWRVRZDüUHNXUHQFML"

” 3URFHGXU\ UHNXUHQF\MQH V SDPL FLR HUQH 0R H WR VWDQRZLü

RVWU]H HQLH HLVWQLHM ZSUDNW\FHSUREOHP\NWyU\FKUHNXUHQF\MQH

UR]ZL ]DQLH MHVW PR OLZH DOH SURZDG]L Z LVWRWQ\ VSRVyE GR

VSRZROQLHQLDZ\NRQ\ZDQLDSURFHGXU\LOXEGRSU]HSHáQLHQLDVWRVX

DQJVWDFNRYHUIORZ

” 5]HF]\ZL FLH WDN E\ZD 1LH QDOH \ VL MHGQDN W\P IDNWHP

SU]HUD Dü 7U]HED SR SURVWX PLHü ZLDGRPR ü H LVWQLHM

SUREOHP\E\üPR H]QDWXU\UHNXUHQF\MQHGRUR]ZL ]DQLDNWyU\FK

MHGQDN DEVROXWQLH QLH PR QD VWRVRZDü UHNXUHQFML QDOH \ MHM

XQLNDü

3URFHGXU\ZNWyU\FKPR HP\XQLNQ üUHNXUHQFMLDQDZHWQDOH \MHM

XQLNDüPR QDVFKDUDNWHU\]RZDü]DSRPRF QDVW SXM FHJRVFKHPDWX

XZLGDF]QLDM FHJR]DVDG LFKEXGRZ\

(

)

3 LI % WKHQ 6 3

L

Ù

OXEZSRVWDFL

(

)

3

6 LI % WKHQ 3

L

Ù

3U]\NáDG
6SyMU]P\ QD GREU]H ]QDQ\ SU]\NáDG REOLF]DQLD NROHMQ\FK ZDUWR FL

IXQNFML VLOQLD I

L

L :DUWR ü ]HURZ ]GHILQLRZDOL P\ EH]SR UHGQLR

MDNRI

SRGF]DVJG\NROHMQHOLF]E\JHQHURZDQHV UHNXUHQF\MQLH

]DSRPRF LFKSRSU]HGQLNyZ

( )

I

L

I

L

L

+

= +

:SURZDG]DM F GZLH ]PLHQQH L RUD] I SURFHV REOLF]DQLD NROHMQ\FK

OLF]EVLOQLPR HP\Z\UD]LüZSRVWDFL

L LI LI

background image

-HU]\3HMD $OJRU\WP\LVWUXNWXU\GDQ\FK

$/*25<70<5(.85(1&<-1(

3U]\NáDGFG
=DVW SXM F6ZVFKHPDFLHIRUPXá ]SRSU]HGQLHMIROLLX]\VNXMHP\

QDVW SXM F\SURJUDPUHNXUHQF\MQ\

(

)

3 LI L Q WKHQ L L

I

L I 3

L

I

3

Ù

<

= +

=

=

=

JG]LHGUXJLZLHUV]WHJRSURJUDPX]DZLHUDLQLFMDFM SURFHGXU\RUD]MHM

SLHUZV]HZ\ZRáDQLH

6LOQLD9LQI

LILQWKHQ

L L

I LI

6LOQLD9LQI

HQGLI

HQG

” $QDOL]XM F SURFHGXU\ 6LOQLD9 L 6LOQLD9 PR QD ]DXZD \ü H

UHNXUHQFM PR QD]DVW SLüLWHUDFM

6LOQLD9QLQWHJHU

L

I

ZKLOHLQGR

L L

I LI

HQGGR

HQG

” 1DRJyáSURJUDP\RGSRZLDGDM FHVFKHPDWRPLSRZLQQRVL

SU]HNV]WDáFDü GR SRZ\ V]HM SRVWDFL LWHUDF\MQHM NRU]\VWDM F ]H

VFKHPDWX

(

)

3

[

[ ZKLOH % GR 6

Ù

=

:1,26(. .$ ' 352&('85 5(.85(1&<-1 02 1$

35=(.6=7$à&,û:352&('85 ,7(5$&<-1
&]\ ]DZV]H ZDUWR WR URELü" 3URVWRWD L F]\WHOQR ü SU]HPDZZLDM ]D

UHNXUHQFM VSRZROQLHQLHZ\NRQ\ZDQLDSURFHGXU\SU]HFLZ

background image

-HU]\3HMD $OJRU\WP\LVWUXNWXU\GDQ\FK

$/*25<70<5(.85(1&<-1(

6FKHPDW\ZNWyU\FKQDOH \XQLNDüUHNXUHQFML

'REU\P SU]\NáDGHP WHJR W\SX VFKHPDWX MHVW REOLF]DQLH NROHMQ\FK

OLF]E)LERQDFFLHJR]GHILQLRZDQHSU]\SRPRF\UHODFMLUHNXUHQF\MQHM

ILE

ILE

ILE

GOD Q

Q

Q

Q

+

-

=

+

Ë

JG]LH ILE

ILE

%H]SR UHGQLH QDLZQH SRGHM FLH GR WHJR

]DGDQLDPR QD]DSLVDüZSRVWDFL

)LERQDFFLQLQWHJHU

LIQWKHQ

UHWXUQQ

HOVH

UHWXUQ)LERQDFFLQ)LERQDFFLQ

HQGLI

HQG

3URFHGXUDIXQNF\MQD)LERQDFFLMHVWSURVWDLáDWZDGR]UR]XPLHQLDDOH

QLHVá\FKDQLHQLHHIHNW\ZQD'ODF]HJR"3RND]XMHWRSRQL V]\U\VXQHN

)

)

)

)

)

)

)

)

)

)

)

)

)

)

)

)

)

)

)

)

)

)

)

)

)

'U]HZRZ\ZRáD GOD)LERQDFFL

background image

-HU]\3HMD $OJRU\WP\LVWUXNWXU\GDQ\FK

$/*25<70<5(.85(1&<-1(

6FKHPDW\ZNWyU\FKQDOH \XQLNDüUHNXUHQFMLFG

” =DXZD P\ H ND GHZ\ZRáDQLHWHMSURFHGXU\]QËSRZRGXMH

GZD GDOV]H Z\ZRáDQLD WM FDáNRZLWD OLF]ED Z\ZRáD UR QLH

Z\NáDGQLF]R $E\ VL R W\P SU]HNRQDü REOLF]P\ ZJ WHJR

DOJRU\WPX )LERQDFFL R]QDF]P\ WR GOD XSURV]F]HQLD SU]H]

)2GE\ZDVL WRQDVW SXM FR

) ))

)))

))))

))

)))

)))

)

LWG

” 2EOLF]HQLDV EDUG]RQLHHIHNW\ZQHJG\ SURFHGXUD)LERQDFFLMHVW

Z\ZRá\ZDQDD UD]\SU]\REOLF]DQLXV]yVWHJRHOHPHQWXFL JX

)LERQDFFLHJR UyGáHP WHM QLHHIHNW\ZQR FL MHVW SRZWDU]DQLH W\FK

VDP\FK REOLF]H QS SURFHGXUD MHVW D NURWQLH ZRáDQD ]

SDUDPHWUHPQ

” /LF]EDGRGDZD SRWU]HEQ\FKGRREOLF]HQLDILE

Q

]X \FLHPGHILQLFML

UHNXUHQF\MQHMMHVWUyZQDILE

Q

” /LF] F GZD Z\ZRáDQLD QD MHGQR GRGDZDQLH SOXV Z\ZRáDQLH QD

VDP\P SRF] WNX R]QDF]D WR H SURFHGXUD )LERQDFFL MHVW

Z\ZRá\ZDQDILE

Q

UD]\ZFHOXREOLF]HQLDZDUWR FLILE

Q

7DEOLFD /LF]ED RSHUDFML GRGDZDQLD Z\ZRáD UHNXUHQF\MQ\FK SU]\

REOLF]DQLXOLF]E)LERQDFFLHJR

Q

ILE

Q

/LF]EDGRGDZD

/LF]EDZ\ZRáD

background image

-HU]\3HMD $OJRU\WP\LVWUXNWXU\GDQ\FK

$/*25<70<5(.85(1&<-1(

,WHUDF\MQ\VFKHPDWREOLF]DQLDOLF]E\)LERQDFFLHJR

” 3U]\REOLF]DQLXOLF]E\)LERQDFFLHJRPR QDSRVáX \üVL VFKHPDWHP

LWHUDF\MQ\P 8QLND VL ZWHG\ SRQRZQHJR REOLF]DQLD W\FK

VDP\FKZDUWR FLG]L NLZSURZDG]HQLX]PLHQQ\FKSRPRFQLF]\FK[L

\ WDNLFK H [ ILE

L

L \ ILE

L

3URZDG]L WR GR QDVW SXM FHJR

DOJRU\WPX

)LERQDFFLQLQWHJHU

^REOLF][ ILE

L

GODQ!`

L

[

\

ZKLOHLQGR

] [

L L

[ [\

\ ]

HQGGR

UHWXUQ[

HQG

” =DXZD P\ HWU]\SU]\SLVDQLDZDUWR FL]PLHQQ\P[\L]PR QD

Z\UD]Lü ]D SRPRF W\ONR GZyFK SU]\SLVD EH] ZSURZDG]DQLD

]PLHQQHMSRPRFQLF]HM]3RUyZQDQLHREXSRGHM ü]DZLHUD7DE

7DEOLFD3RUyZQDQLHLWHUDF\MQHJRLUHNXUHQF\MQHJRDOJRU\WPXREOLF]DQLD

OLF]E)LERQDFFLHJR

3U]\SLVDQLD

Q

/LF]ED

GRGDZD

$OJRU\WP

LWHUDF\MQ\

$OJRU\WPUHNXUHQF\MQ\

background image

-HU]\3HMD $OJRU\WP\LVWUXNWXU\GDQ\FK

$/*25<70<5(.85(1&<-1(

3U]\NáDG\SURFHGXUUHNXUHQF\MQ\FK

3U]\NáDG 3áDWHN QLHJX YRQ .RFKD 1D U\V ZLGDü SU]\NáDG\

SáDWNyZ QLHJX YRQ .RFKD 3áDWHN QLHJX WUDNWRZDQ\ MHVW MDNR

SRá F]HQLHWU]HFKLGHQW\F]Q\FKáDPDQ\FKQDU\VRZDQ\FKSRGUy Q\PL

N WDPL6SRVyEU\VRZDQLDMHGQHMWDNLHMáDPDQHMMHVWQDVW SXM F\

5\V3U]\NáDG\SáDWNyZ QLHJXYRQ.RFKD

']LHOLP\RGFLQHNGáXJR FLVLGHQDWU]\UyZQHF] FL
3U]HVXZDP\ VL QD RGOHJáR ü MHGQHM WU]HFLHM VL]H Z NLHUXQNX

RNUH ORQ\PSU]H]N WDQJOH

6NU FDP\ZOHZRR

W]QVNU FDP\R

LSU]HVXZDP\VL

QDSU]yGRMHGQ WU]HFL VL]H

6NU FDP\ Z SUDZR R

L SU]HVXZDP\ VL QDSU]yG R MHGQ

WU]HFL VL]H

6NU FDP\ZOHZRR

LSU]HVXZDP\VL QDSU]yGRMHGQ WU]HFL

VL]H

5\VD5\VRZDQLHF]WHUHFKRGFLQNyZMHGQHJRVHJPHQWXSáDWND QLHJX

YRQ.RFKD

background image

-HU]\3HMD $OJRU\WP\LVWUXNWXU\GDQ\FK

$/*25<70<5(.85(1&<-1(

3U]\NáDG\SURFHGXUUHNXUHQF\MQ\FKFG

3U]\NáDG3áDWHN QLHJXYRQ.RFKDFG

” = RSLVX SáDWND QLHJX YRQ .RFKD Z\QLND H QD SURFHVNUH OHQLD

VNáDGDM VL F]WHU\ OLQLH RUD] WU]\ VNU W\ R RGSRZLHGQLR GREUDQH

N W\ MHVW WR QDV] SRGVWDZRZ\ Z]RU]HF .D GD ] OLQLL PR H

UyZQLH E\üQDU\VRZDQD]X \FLHPWHJRVDPHJRZ]RUFD-HVWZL F

WR V\WXDFMD GR NWyUHM GREU]H SDVXMH X \FLH UHNXUVML FR

RG]ZLHUFLHGODSRQL V]\SVHXGRNRG

'UDZ)RXU/LQHVOHYHO

LIOHYHO WKHQ

U\VXMOLQL

HOVH

'UDZ)RXU/LQHVOHYHO

VNU üZOHZR

'UDZ)RXU/LQHVOHYHO

VNU üZSUDZR

'UDZ)RXU/LQHVOHYHO

VNU üZOHZR

'UDZ)RXU/LQHVOHYHO

HQGLI

HQG

3RQL HMSU]HGVWDZLRQRSHáQ\NRGZM ]\NX3DVFDOGODWHJRSU]\NáDGX

SUDFXM FHJR]ELEOLRWHNDPL7XUER3DVFDOD

3URJUDP59RQ.RFK
XVHVGRVJUDSK

FRQVW

0B3,
YDU

JUERDUGJUPRGHJUUHVXOWLQWHJHU

DQJOHGRXEOH
SURFHGXUH5LJKW[GRXEOH

EHJLQ

DQJOH DQJOH[

HQG
SURFHGXUH/HIW[GRXEOH

EHJLQ

DQJOH DQJOH[

HQG

background image

-HU]\3HMD $OJRU\WP\LVWUXNWXU\GDQ\FK

$/*25<70<5(.85(1&<-1(

SURFHGXUH)RUZDUGGLVWDQFHGRXEOH

EHJLQ

/LQH5HO5RXQGFRVDQJOH0B3,GLVWDQFH

5RXQGVLQDQJOH0B3,GLVWDQFH

HQG
SURFHGXUH'UDZ)RXU/LQHVGLVWDQFHGRXEOHOHYHOLQWHJHU

EHJLQ

LIOHYHO WKHQ

)RUZDUGGLVWDQFH

HOVH

EHJLQ

'UDZ)RXU/LQHVGLVWDQFHOHYHO

/HIW

'UDZ)RXU/LQHVGLVWDQFHOHYHO

5LJKW

'UDZ)RXU/LQHVGLVWDQFHOHYHO

/HIW

'UDZ)RXU/LQHVGLVWDQFHOHYHO

HQG

HQG
SURFHGXUH6QRZ)ODNHVL]HGRXEOHOHYHOLQWHJHU

YDULLQWHJHU

EHJLQ

IRUL WRGR

EHJLQ

'UDZ)RXU/LQHVVL]HOHYHO

5LJKW

HQG

HQG
EHJLQ

JUERDUG '(7(&7

GHWHFWJUDSKJUERDUGJUPRGH

FDVHJUERDUGRI

(*$JUPRGH (*$+,

(*$JUPRGH (*$/2

9*$JUPRGH 9*$+,

HOVH

EHJLQ

:ULWH/Q3URJUDPZ\PDJDSU]\QDMPQLHMNDUW\(*$([LW

HQG

HQG
LQLWJUDSKJUERDUGJUPRGH%*,

JUUHVXOW JUDSKUHVXOW

LIJUUHVXOWWKHQ

:ULWH/QJUDSKHUURUPVJJUUHVXOW

VHWFRORU:+,7(

VHWENFRORU%/8(

PRYHWR

DQJOH

6QRZ)ODNH

HQG

background image

-HU]\3HMD $OJRU\WP\LVWUXNWXU\GDQ\FK

$/*25<70<5(.85(1&<-1(

3U]\NáDG\SURFHGXUUHNXUHQF\MQ\FKFG

5\V3U]\NáDGRZ\Z\QLNHNVSHU\PHQWyZ]SURFHGXU 59RQ.RFK

3U]\NáDG :LH H +DQRL .ROHMQ\ SU]\NáDG GRW\F]\ ]QDQHJR MX

QDP SUREOHPX :LH +DQRL 3U]\SX üP\ H PDP\ WU]\ ZLH H OXE

VNURPQLHMWU]\NRáNL$%L&1DSLHUZV]\PNRáNX$]QDMGXM VL WU]\

NU NL QDáR RQH MHGHQ QD GUXJL Z SRU] GNX PDOHM F\FK UR]PLDUyZ

OLF] FRGGRáXSRGF]DVJG\SR]RVWDáHNRáNLV SXVWHSDWU]U\V

5\V:LH H+DQRL]WU]HPDNU NDPL

=DGDQLHMDNZLHP\SROHJDQDSU]HQLHVLHQLXNU NyZ]NRáND$QD

%E\üPR HSRGURG]HX \ZDM FNRáND&ZJ FL OHRNUH ORQ\FKUHJXá

background image

-HU]\3HMD $OJRU\WP\LVWUXNWXU\GDQ\FK

$/*25<70<5(.85(1&<-1(

3U]\NáDG\SURFHGXUUHNXUHQF\MQ\FKFG

àDPLJáyZNDWDGODWU]HFKNU NyZPDQDVW SXM FHUR]ZL ]DQLH;Ž<

R]QDF]DSU]HQLHVLHQLHJyUQHJRNU ND]NRáND;QDNRáHN<

$Ž%$Ž&%Ž&$Ž%&Ž$&Ž%$Ž%

” -H OLMHGQDN]DáR \ü HSU]HVWU]HJDP\UHJXá\SU]\SU]HQRV]HQLXQ

NU NyZ WR Z\QLND H FDá\ SURFHV F]\OL SU]HQRV]HQLH Q

NU NyZRGE\ZDVL WDN H]JRGQLH]UHJXáDPLJU\

3U]HQLHVQ;<=

^3U]HQLH QNU NyZ]NRáND;QD<NRU]\VWDM F]=`

LIQ WKHQ
Z\SLV]³;Ž

HOVH

3U]HQLHVQ;=<
Z\SLV]³;Ž

3U]HQLHVQ=<;

HQGLI

HQG

” 2GSRZLDGDM F\ WHPX RSLVRZL DOJRU\WP 3U]HQLHV Z SRVWDFL

RSLVXM FHM SU]HGVWDZLRQ\ MHVW SRZ\ HM $E\ ]LOXVWURZDü MHJR

G]LDáDQLHXUXFKRPP\JRGODQ W]Q]DF]QLMP\RGZ\ZRáDQLD

SURFHGXU\3U]HQLHVZQDVW SXM F\VSRVyE

3U]HQLHV$%&

” 3LHUZV]HZ\ZRáDQLHSURFHGXU\LQLFMXMHUHNXUHQF\MQLHZ\ZRá\ZDQLH

VDPHM VLHELH 3HáQH GU]HZR Z\ZRáD GOD WU]HFK NU NyZ

SU]HGVWDZLD U\VXQHN QD QDVW SQHM VWURQLH 5\VXQHN WHQ

RG]ZLHUFLHGOD ]QDQ\ QDP MX SR]LRP ]DJá ELHQLD UHNXUHQFML RUD]

VSRVyEZMDNLSDUDPHWU\]PLHQLDM ZDUWR FL6WU]DáNLSU]HGVWDZLDM

Z GUyZNL SURFHVRUD VWU]DáNL Z Gyá RGSRZLDGDM Z\ZRáDQLRP

VWU]DáNL Z JyU ] SRZURWHP D VWU]DáNL SR]LRPH SURVWHPX

QDVW SVWZX

background image

-HU]\3HMD $OJRU\WP\LVWUXNWXU\GDQ\FK

$/*25<70<5(.85(1&<-1(

'U]HZRZ\ZRáD UHNXUHQF\MQHMSURFHGXU\:LH +DQRL

8ZDJLNR FRZH
” 5HNXUHQFMDMDNND GDPHWRGDSRZLQQDE\üVWRVRZDQD]UR]ZDJ
” 5HNXUHQFMD MHVW ]Z\NOH PQLHM HIHNW\ZQD QL MHM LWHUDF\MQ\

RGSRZLHGQLN

,VWQLHM GZLH V\WXDFMH NLHG\ OHSLHM MHVW X \ü QLHUHNXUHQF\MQHM ZHUVML

DOJRU\WPXQDZHWMH OLUHNXUHQFMDMHVWEDUG]LHMQDWXUDOQ\PRSLVHP
” 3R SLHUZV]H LWHUDFML QDOH \ X \ZDü ]DZV]H ZWHG\ JG\ V]\ENR ü

G]LDáDQLD DOJRU\WPX MHVW NOXF]RZD GOD SRSUDZQHJR G]LDáDQLD

SURJUDPX

” 3R GUXJLH UHNXUHQFML SRZLQQR VL XQLNDü Z SURFHGXUDFK NWyUH V

Z\ZRá\ZDQH ZLHORNURWQLH 1DMOHSV]\P SU]\NáDGHP SURFHGXU WHJR

W\SXMHVWNRPSLODWRU


Wyszukiwarka

Podobne podstrony:
Metody układania algorytmów rekurencja, metoda dziel i zwyciężaj, programowanie dynamiczne, metoda
Algorytmy Rekurencja
Cykl Hamiltona algorytm rekurencyjny
Metody układania algorytmów rekurencja, metoda dziel i zwyciężaj, programowanie dynamiczne, metoda
Algorytmy Rekurencja
Algorytmy i struktury danych 02 Rekurencja i złożoność obliczeniowa
Układy Napędowe oraz algorytmy sterowania w bioprotezach
5 Algorytmy
5 Algorytmy wyznaczania dyskretnej transformaty Fouriera (CPS)
Tętniak aorty brzusznej algorytm
Algorytmy rastrowe
Algorytmy genetyczne

więcej podobnych podstron