An¢lise experimental de algoritmos de planaridade Alexandre

Transcrição

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RT P_WadPb XY hTR`R_WXRXY Y WbaY`aYb Ra fP ( Y gRh aSTP gP`a d R dRWP_ hR_aY XR `PaR OPU gP`gYWaPb Y XYi`W ( Yb SbRXPb RP TP` P XYbaR
XWbbY_aR OP d bY SWXRU `P gRh aSTP ZU bOP Rh_YbY`aRXPb RT S`b gP`gYWaPb Y _YbSTaRXPb bPe_Y
hTR`R_WXRXY SY bOP S`XRdY`aRWb hR_R R XYbg_W OP XP RT P_WadP XY Z U h_YbY`aY `P gRh %
aSTP \U Y hR_R R XYbg_W OP XR WdhTYdY`aR OP XYbbY RT P_WadP h_PhPbaR hP_ NfWf Y bS ' U `Pb
gRh aSTPb bY SW`aYb +, T P_WadP
SbTR`XY_U QR_aY_ Y PTXbaYW` dhTYdY`aR OP PdhTY WXRXY
P_W W`RT U g eWgP
Phg_P a Y R_( R` [ TW`YR_
YdhYTU cY` Y YXY_eRSd P_W W`RT Z SRX_ = aWgP
PPaf Y SY # Y_ Z TW`YR_
P Y_ Y V _cPTX \ TW`YR_
NfWf Y bS '
TW`YR_
> W S_R " ReYTR XPb h_W`gWhRWb RT P_WadPb XY hTR`R_WXRXY Y RT SdRb XY bSRb WdhTYdY`aR ( Yb 1 P gRh aSTP ! Rh_YbY`aRXR SdR R` = TWbY Y hY_WdY`aRT Y`a_Y Rb WdhTYdY`aR ( Yb XY PPaf
Y SY # Y_ Z U Phg_P a Y R_( R` [ U P Y_ Y V _cPTX \ Y XY NfWf Y bS
' > W`RTdY`aYU `P gRh aSTP U Y`gP`a_R % bY Sd _YbSdP XR `PbbR Y hY_W , `gWR XS_R`aY P
XYbY`cPTcWdY`aP XYbaY a_ReRTfP WdhTYdY`aR OP XY NfWf Y bS PW XYbY`cPTcWXR hYTPb RSaP_Yb XYbbR XWbbY_aR OP bPe_Y R
hTRaR P_dR ^ U cY_bOP U Y aYbaRXR `Sd gPdhSaRXP_ hYbbPRT gPd bWbaYdR 1 7 W`S QR_R gPdhWTR_ P g " XW P P`aY XR WdhTYdY`aR OPU `YgYbb = _WP hPbbSW_ P ^ W`baRTRXP `P
bYS bWbaYdRU RT d XY Sd gPdhWTRXP_ cY_bOP dRWb _YgY`aY XP ^ hR_R RcRTWR OP hPXY bY_ PeaWXR hYTR W`aY_`YaU `P Y` %
XY_Y P !" # ! Y P hRgPaY gPdhRgaRXP XP g " XW P P` %
aY XRb WdhTYdY`aR ( Yb XY Y XY hPXYd bY_ PeaWXPb hYTR W`aY_`YaU `P Y`XY_Y P
$ " ! % &# ! # ' ( QR_R XYbgPdhRgaR_ P R_ SWcP # ' ( `P XW_Ya " _WP $ ") U SaWTW Y
P gPdR`XP
$ "* + (,- . # ' ( $ ") h " b R XYbgPdhRgaR OPU P XW_Ya " _WP $ ") # ' g_WRXP g " XW P P`aY XR WdhTY %
dY`aR OP XY PW Y`aWTdY`aY gYXWXP hP_ / Pf` V P Y_U gS( R h = W`R hYbbPRT bY Y`gP`a_R `P
Y`XY_Y P . ! # $ & # # 0 % '$ QR_R gPdhWTR_ Pb h_P _RdRb 6 Y U eRbaR Y YgSaR_
$ "* + 1 $
+, - -, +
aYdhPbU Yd
+ baY h_P _RdR Wdh_WdYU `R bR XR hRX_OPU SdR aReYTR XY
P_dRaP U Y`a_Y Rb WdhTYdY`aR ( Yb XY U U Y XY gPdhR_R OP XY
QR_R gPdhWTR_ R XWbbY_aR OPU `YgYbb = _WP hPbbSW_ P ^ U P Y P # $ % XYcWXRdY`aY
W`baRTRXPb `P bYS bWbaYdR # $ % SdR Y__RdY`aR hR_R h_P _RdR OP TWaY_ = _WR # $ % hPXY bY_
$$ ! -) $ )" &# # $ % 7
dR cY_bOP XP
PeaWXR hYTR W`aY_`YaU `P Y`XY_Y P
g " XW P P`aY XR XWbbY_aR OP hPXY bY_ PeaWXP hYTR W`aY_`YaU `P
$ " ! % &# ! ) !! $ ( QR_R XYbgPdhRgaR_ P R_ SWcP ) !! $ ( `P XW_Ya " _WP $ ") U SaWTW Y P
$ "* + (,- . ) !! $ ( $ ") h " b R XYbgPdhRgaR OPU P XW_Ya " _WP $ ") ) !! $ g_WRXP QR_R gPdhWTR_ R XWbbY_aR OPU Y YgSaY
$ "* + 1) !! $ R_ SWcP ) !! $ ! ( g_WRXP Y`XY_Y P
gPdR`XP
1 YbaY
gRh aSTP Rh_YbY`aRXR R dRWP_ hR_aY XR `PaR OP Y XYi`W ( Yb SbRXRb RP TP` P XYbaR
XWbbY_aR OP XR
baR bY OP W`a_PXS Pb gP`gYWaPb XY _R PbU gP`Y WXRXYU hTR`R_WXRXY Y PSa_Pb YTYdY`aPb e = bWgPb
aYP_WR XPb _R Pb d ,- , +- Sd Pe ( YaP XR P_dR U P`XY Sd gP`( S`aP i`WaP XY YTYdY`aPbU
gfRdRXPb ,+ . U Y Sd gP`( S`aP XY hR_Yb P_XY`RXPb XY YTYdY`aPb XWbaW`aPb XY U gfRdRXPb
-,. NY Y`aOP P _R P - NY Sd _R P P_WY`aRXPU P gP`( S`aP XPb c _aWgYb XY XY`PaRXP hP_ Y P gP`( S`aP XPb R_gPb XY hP_ 7 d R_gP XY`PaRXP hP_ ^W % bY SY
P , , XY NY Sd R_gPU Y`aOP
Y bOP Rb hP`aRb . - Y - XY U _YbhYgaWcRdY`aY ^W % bY aRde d SY Y bOP Y SY - XY Y +,- Yd NY Sd R_gPU Y`aOP XW % bY SY + , , ^W % bY SY ! Sd * ,- , +- XY bY ! Sd _R P P_WY`aRXP aRT SY " # Y " # NY ! gP`a d aPXPb Pb R_gPb XY gPd RdeRb Rb hP`aRb Yd " Y`aOP ! Sd
* ,- XY 1 YbaY gRbPU XY`PaR % bY ! hP_ $" % Y XW % bY SY ! P * ,- &'(
7
, " NY # Y`aOP ) P bSe _R P P_WY`aRXP XY _YbSTaR`aY XR _YdP OP XY aPXPb Pb c _aWgYb * XY Y XY aPXPb Pb R_gPb gPd hYTP dY`Pb SdR hP`aR Yd S bY( RU ) P _R P $ + % , - ,- NY( R ! Sd bSe _R P W`XS WXP XY Y Sd c _aWgY XY ^Y`PaR % bY hP_ ! P _R %
P $" % NWdWTR_dY`aYU XY`PaR % bY hP_ ! ) P _R P $" + % 7 d ,- bWd a_WgP Sd _R P P_WY`aRXP Yd SY aPXP R_gP aYd _YcY_bP 1 Sd _R PU Sd
gP`( S`aP gfRdRXP XY -,+- eSbR`XP XR `PaR OPU SdR R_YbaR XY`PaRXR
bWdhTYbdY`aY hP_ PS ^RXR SdR R_YbaR U XW % bY SY . + R Y R Y SY
Y bOP Rb +- XY T d XWbbPU Y bOP XWaPb - -. + NY Sd c _aWgYU Y`aOP P ,- XY P ` dY_P aPaRT XY R_YbaRb W`gWXY`aYb R NY Sd _R PU P gP`( S`aP XRb R_YbaRb XY Y Pb ` dY_Pb Y bOP XY`PaRXPbU
_YbhYgaWcRdY`aYU hP_ Y +- - P ` dY_P 7 d _R P hPXY bY_ `RaS_RTdY`aY _Yh_YbY`aRXP Ra_Rc b XY Sd XWR _RdR gPdP P XR i S_R R U
P`XY Pb c _aWgYb bOP hY SY`Pb g _gSTPbU Pb R_gPb bOP bYaRb TW R`XP Pb XPWb g _gSTPb SY gP__Yb%
hP`XYd Rb bSRb hP`aRb Y_RTdY`aY YbbY XWR _RdR bWdhTWigRXP hR_R R SYTY _Yh_YbY`aRXP `R
i S_R e U P`XY gRXR R_gPU ( S`aP gPd bYS _YcY_bPU bSebaWaS XP hP_ SdR TW`fR bWdhTYb W S_R R ^WR _RdR XY Sd _R P e Y_bOP bWdhTWigRXR XP XWR _RdR >
7
d - `Sd _R P P_WY`aRXP SdR bY , `gWR
* P`XY bOP c _aWgYb YU hR_R gRXR U P R_gP * ^W % bY SY P hRbbYWP Y`a_Y Y U PS SY gPdY R Yd Y aY_dW`R Yd Y SY Y bOP Rb +- XP hRbbYWP RT
hRbbYWP dSWaRb cY Yb XY`PaRXP hP_ * gPdh_WdY`aP XY Sd hRbbYWP P
` dY_P Y Pb c _aWgYb * bOP Pb c _aWgYb +, XP hRbbYWP 7 d . . `Sd
_R P Sd bSe _R P P_WY`aRXP XY P_dRXP hYTPb c _aWgYb Y R_gPb XY Sd hRbbYWP SY gPdY R Y
aY_dW`R `Sd dYbdP c _aWgY 7 d gWgTP XYaY_dW`RXP hYTP hRbbYWP * XY`PaRXP
hP_ * 7 d .- Sd hRbbYWP bYd _YhYaW OP XY c _aWgYb 7 d . ,. +
Sd hRbbYWP * XY gPdh_WdY`aP hYTP dY`Pb a_ , b Yd SY * bOP
c _aWgYb XWbaW`aPb Y , -,
b cY Yb gP` S`XWdPb Sd _R P PS Sd hRbbYWP gPd bYS gP`( S`aP XY R_YbaRb NY( R Sd
gRdW`fP aRT SY cR WP `aOP XWaP +, - 7 . 7 . +
d _R P
bYU hR_R aPXP hR_ XY c _aWgYb Y XP _R PU Y WbaY Sd gRdW`fP Y`a_Y
Y d
XY Sd _R P Sd bSe _R P gP`Y P dR WdRT _R P cR WP gP`Y P 7 d ,+ . .,+ XY Sd _R P Sd c _aWgY aRT SY ) aYd dRWb gPdhP`Y`aYb
SY 7 d _R P * . bY gP`Y P Y `OP hPbbSW c _aWgYb XY gP_aY 7 d bSe _R P eWgP`Y P
dR WdRT gfRdRXP XY * . 7 d _R P * -,+ bY hPXY bY_ hR_aWgWP`RXP Yd XPWb gP`( S`aPb Y aRWb SYU hR_R
gRXR R_YbaR XY U bY Sd c _aWgY XY Y`aOP Yba = Yd U Y bY Sd c _aWgY XY Y`aOP
Yba = Yd dR , , Sd _R P gP`Y P bYd gW_gSWaPb 1 SdR = _cP_YU Y WbaY Sd `WgP gRdW`fP Y`a_Y
XY SRT SY_ c _aWgY R SRT SY_ PSa_P 7 dR = _cP_Y gPd Sd c _aWgY YbhYgWRT XWaR ,- - - c _aWgY gfRdRXP XY ,- NY( R Sd c _aWgY XY SdR = _cP_Y gPd _RW SRT SY_ c _aWgY `P gRdW`fP XY R
Yd gfRdRXP XY - .+,- XY Yd 7 d R`gYba_RT XY , , bY NY Sd
R`gYba_RT XY U Y`aOP Sd . + XY 7 d XYbgY`XY`aY XY , , bY NY Y R TaWdR R_YbaR XP gRdW`fP XY R U Y`aOP P - XY Y Sd XY
Yd ^PWb c _aWgYb gPd P dYbdP hRW bOP gfRdRXPb XY , 7 dR , , ,- ,- XY Sd _R P gP`Y P Sd bSe _R P XY SY SdR = _cP_Y Y gP`a d
aPXPb Pb c _aWgYb XY bSe = _cP_Y XY gPd _RW gS( Pb c _aWgYb bOP aPXPb Pb XYbgY`XY`aYb XY Yd XY`PaRXR
hP_ 7 dR ,+- Sd _R P aRT SY gRXR Sd XY bYSb gPdhP`Y`aYb SdR = _cP_Y 7 dR * , , PS SdR , , *.- , - XY Sd _R P gP`Y P SdR = _cP_Y Y_RXP_R Y`_RW RXR XY aRT SYU hR_R gRXR R_YbaR Yd U PS XYbgY`XY`aY XY
`R = _cP_Y PS XYbgY`XY`aY XY i S_R Z e NY( R SdR eh % = _cP_Y XY 7 dR P_XY`R OP XPb c _aWgYb XY aRT SY
bY R`gYba_RT XY Yd Y`aOP 7
, - ,- XWaR SdR * , - XY Yd _YTR OP R Y( R R i S_R Z * , XY Sd
c _aWgY Yd _YTR OP R SdR eh % P_XY`R OP U XY`PaRXP hP_ eh U P `XWgY aRT SY 1 PaY
SY bY R _RW XY Y`aOP eh R e W S_R Z R 7 d _R P gPd c _aWgYb `SdY_RXPb XY RgP_XP gPd SdR eh % P_XY`R OP e 7 dR
eh % = _cP_Y XY U W`XWgRXR hP_ TW`fRb b " TWXRbU Y`_RW RXR `P c _aWgY b bYaRb RhP`aRd hR_R
P hRW XY gRXR ` " Yd >
d _R P hPXY bY_ _Yh_YbY`aRXP Yd Sd gPdhSaRXP_ hYTRb bSRb +- - -. . - TWbaR XY RX( Rg , `gWR XY Sd c _aWgY U XY`PaRXR hP_ U gP`bWbaY XY SdR TWbaR SY gP`a d
aPXPb Pb R_gPb gPd hP`aR W`WgWRT i S_R \ R YbhR P gP`bSdWXP hP_ YbaR _Yh_YbY`aR OP
7
1 PaY SY Rb TWbaRb XY RX( Rg , `gWRb XY Sd _R P hPXYd bY_ _Yh_YbY`aRXRb hP_ SdR TWbaR `WgR XY
R_gPb i S_R \ e Y hPXY % bY gP`cY_aY_ XY SdR _Yh_YbY`aR OP hR_R R PSa_R Yd aYdhP , -,
WbaRb XY
RX( Rg , `gWRb R & Yh_YbY`aR OP hP_ SdR TWbaR e W S_R \ R 7 d _R P Y SdR _Yh_YbY`aR OP XYbaY hP_ TWbaRb XY RX( Rg , `gWRb e & Yh_YbY`aR OP
XRb TWbaRb XY RX( Rg , `gWRb hP_ SdR `WgR TWbaR XY hR_Yb XY c _aWgYb >
6 3 SdR hTRaR P_dR hR_R RT P_Wa %
dPb gPdeW`Ra " _WPb XYbY`cPTcWXRU W`WgWRTdY`aYU hP_ 1 fY_ Y VYfTfP_` TR PW SaWTW RXR hR_R R
WdhTYdY`aR OP XY NfWf Y bS XYbg_WaR `YbaY a_ReRTfP eRW P Y`gP`a_R % bY SdR e_YcY Rh_YbY`aR OP XY gPdP _Yh_YbY`aR_ _R Pb P_WY`aRXPbU c _aWgYb
Y R_gPb `P ^ Y Pb gPdR`XPb SbRXPb hR_R g_WR_ Y hY_gP__Y_ c _aWgYb Y Pb R_gPb XY Sd XRXP
_R P NOP Rh_YbY`aRXRb aRde d RT SdRb Yba_SaS_Rb XY XRXPb XP ^ SY bOP SaWTW RXRb `YbaY
a_ReRTfP ^ 1 )6
.
' ! d _R P P_WY`aRXP _Yh_YbY`aRXP `P ^ hYTP aWhP ,- U Sd c _aWgY hYTP aWhP Y
Sd R_gP hYTP aWhP i S_R " b S` ( Yb . Y XYcPTcYd U _YbhYgaWcRdY`aYU Rb hP`aRb W`WgWRT Y i`RT XY Sd
R_gP deRb RbaRd aYdhP gP`baR`aY ` dY_P XY c _aWgYb Y XY R_gPb XY Sd _R P bOP PeaWXPbU _YbhYgaWcRdY`aYU hYTRb S` ( Yb
) Y ) deRb gP`bPdYd aYdhP gP`baR`aY 7
)
W S_R " cR_W =cYT _Yh_YbY`aR Sd _R P P_WY`aRXP cR WP b cR_W =cYWb bOP RhP`aRXP_Yb
hR_R c _aWgYb Y Sd RhP`aRXP_ hR_R Sd R_gP `WgWRTdY`aYU Y YbaOP gPd cRTP_Yb
W`XYi`WXPb >
QR_R RXWgWP`R_ Sd c _aWgY Y Sd R_gP R Sd _R P U SbR % bYU _YbhYgaWcRdY`aYU Rb S` ( Yb
Y i S_R ' QR_R _YdPcY_ Sd c _aWgY Y Sd R_gP XY U SbR % bYU _YbhYgaWcR %
dY`aYU Rb S` ( Yb Y baRb SRa_P S` ( Yb gP`bPdYd aYdhP gP`baR`aY !"#$ #% &' ( )*+,- *./+01
( )*+,-*./+01
( )*+,- +/2+0 1
)*+,- +/2+0)*+,- *./+01 1
W S_R ' P`ba_S OP XY Sd _R P `P ^
>
QR_R hY_gP__Y_ aPXPb Pb c _aWgYb Y R_gPb XY U SbR % bYU _YbhYgaWcRdY`aYU Rb dRg_Pb Y i S_R TRb RbaRd aYdhP h_PhP_gWP`RT R Y R U _YbhYgaWcRdY`aY 3 QR_R _Yh_YbY`aR_ SdR TWbaR XY YTYdY`aPb XY Sd dYbdP aWhPU SbR % bY P aWhP + Y hR_R _Yh_Y %
bY`aR_ Sd cYaP_ XY YTYdY`aPbU SbR % bY P aWhP -,,- QP_ Y YdhTPU + 4 5 SbRXP hR_R
XYgTR_R_ SdR TWbaR XY R_YbaRb QR_R W`bY_W_ Sd YTYdY`aP `P W` gWP XY SdR TWbaRU SbR % bY R S` OP Y hR_R W`bY_W_ Sd
YTYdY`aP `P id XY SdR TWbaRU SbR % bY R S` OP 7 d RhP`aRXP_ hR_R Sd YTYdY`aP XY SdR
TWbaR XP aWhP + + ^RXP Sd RhP`aRXP_ hR_R Sd YTYdY`aP XY SdR TWbaRU SbR % bY R S` OP
hR_R _YdPcY_ P YTYdY`aP W`XWgRXP hYTP RhP`aRXP_ QR_R hY_gP__Y_ aPXPb Pb YTYdY`aPb XY SdR TWbaRU SbR % bY R dRg_P , -,
aWhP * + U h_PhPbaP hP_ P Y_ Y V _cPTX \ U gP`bWbaY XY SdR TWbaR SY hPXY bY_ W`cY_aWXR
Yd aYdhP gP`baR`aY 1 YTRU gRXR g TSTR hPbbSW XPWb RhP`aRXP_Yb gRdhPb Y YU hR_R
hRbbR_ hR_R P h_ " WdP YTYdY`aP `R TWbaRU PTfR % bY Pb XPWb RhP`aRXP_Yb Y YbgPTfY % bY P RhP`aRXP_
SY `OP TYcR RP YTYdY`aP R`aY_WP_dY`aY hY_gP__WXP bbWd U hR_R W`cY_aY_ YbbR TWbaRU eRbaR a_PgR_
Rb g TSTRb SY bOP Pb Y a_YdPb XR TWbaR QR_R hY_gP__Y_ aPXPb Pb YTYdY`aPb XY SdR * + U PW g_WRXP R dRg_P 6 QR_R Ra_WeSW_ W` P_dR ( Yb R aPXPb Pb c _aWgYb Y R_gPb XY Sd _R P U SbR % bY cYaP_Yb W`XY RXPb
hP_ c _aWgYb Y R_gPbU _YbhYgaWcRdY`aY i S_R b cYaP_Yb W`XY RXPb hP_ c _aWgYb bOP Pb aWhPb
-,,- Y - XW Y_Y` R Y`a_Y YbaYb SY P h_WdYW_P SbRXP hR_R _R Pb
Yba = aWgPb Y P bY S`XP hR_R _R Pb XW` dWgPb `RTP RdY`aYU Pb cYaP_Yb W`XY RXPb hP_ R_gPb bOP
Pb aWhPb -,,- Y - b aWhPb - 4 5 Y - 4 5 hPXYd bY_ SbRXPb `Pb TS R_Yb XY - Y - U _YbhYgaWcRdY`aY aWhP - aWT SR`XP XYbY( R % bY RbbPgWR_ W` P_dR ( Yb R Sd
hY SY`P ` dY_P XY c _aWgYb PS R_gPb XP _R P aYdhP RbaP hR_R RgYbbR_ gRXR YTYdY`aP XY Sd cYaP_ -,,- PS -,,- gP`baR`aYU Y` SR`aP SY P aYdhP RbaP YbhY_RXP hR_R Pb aWhPb - U - Y - gP`baR`aY !#%$ " *./+* + 01
+/2+* + 01
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0, 1 *./+* + , ( ( +
0+ 1 +/2+* + + ( W S_R `SdY_R OP XPb c _aWgYb Y R_gPb XP _R P gP`ba_S XP `R i S_R ' >
7
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lmnop
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q vt wstxop yv nz p xp{ v|p wsz py z vrlr py rs vy} p s wst ynz lrs } so wpr p lz }|v z vtxp us } pop mop sy rs xl} s "% #$ q vyxv wpys ~ s{ yvosn yv n v s{xvv s }lso rvyvz } vt€ s q
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- mnop
q y} p s wst ynz lrs } pop mop sy }|pt povy p|vpx olsy "% #$ wsz &  oxlwvy q
pop wpr p
q } pop mop sy p|vpx olsy }|pt povy yus l|n yxoprsy t p
q q sy rsly moŽ - wsy ~ s{ yvop yv n v py lz }|vz vtxp  vy rv v rv s{xlvopz sy
z v|€ sovy rvyvz } vt€ sy q
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10
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HT
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50000"& $
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BL
HT
BM
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20
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10000
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q + vz } sy m pyxsy } v|py lz }|vz vtxp  vy wsz mop sy }|pt povy p|vpx olsy "% #$ q  }olz vlos
moŽ - ws l|n yxop s xvz } s } pop p} vt py xvyxpo }|pt polr prv q vyxv ~ p} vt py v vwnxp s wŽ|wn|s
rs wvoxl - wprs q  yvmnt rs l|n yxop s xvz } s m pyxs } pop xvyxpo ~ , n yxl - wpo v vol - wpo s wvoxl - wprs
wst yxon rs q
 y mopsy t us }|pt povy rs xl} s "% & $ sopz mvoprsy wstsoz v z syxoprs t p - mnop q q
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'( *+,-. +-./01 .2,.34-501 62.7 .-,1 '( 89
C g @V
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LKKL^ YR ; =Z [ IT V
b;K I<RS g ! V Y V "" T d e g Pf#H BBjaD @ BAaIT V
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Z=JZ aV
b;KL WW ]Z=JZX IaQ PT
<b IIjB%>#aIaT & d e ' ( ?>G a ( IaT & d` e T ) I ( ?>G a ( IaT & d e ' jB%>#aIaT & d`e TT
$ @ P g SKh Z V
<b Ic $ @ PT Pf@ a*D aAG aI d e Q d`e TV
k
lmnop
p - mnop
q +ovw€ s rv w+ rlms "rs * $ } pop mvopo mopsy t us }|pt povy rs xl} s "% & $ q
q # , vt wstxop yv nz p xp{ v|p wsz py z vrlr py rs vy} p-s wst ynz lrs } so wpr p lz }|vz vtxp-us } pop mopsy rs xl} s "% & $ q vyxv wpys ~ s{ yvosn yv .n v / v 0 wst ynz lopz z ply
vy} p-s q
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q # , y} p-s wst ynz lrs } pop mopsy rs xl} s "% & $ wsz & oxlwvy q
pop wpr p p|so rv &
sl z vrlrs s vy} p-s m pyxs } so wpr p p|msolxz s ~ vz 5 {Œxvy q
 y moŽ - wsy wsz sy r prsy r p xp{ v|p q } pop mopsy rs xl} s "% & $ yus l|n yxoprsy t p - mnop q ## q
s }olz vlos ~ p} vypo rv 0 xvo p}ovyvtxprs s z v|€ so rvyvz } vt€ s ~ , ntxpz vtxv wsz ~ 0
p}ovyvtxsn s }lso rvyvz } vt€ s t s yvmnt rs ~ , ntxpz vtxv wsz q . sz s p lz }|vz vtxp-us rv /
t us wp|wn|p s wvoxl - wprs } pop mopsy t us }|pt povy ~ vyxp sl sz lxlr p rs yvmnt rs moŽ - ws q
"% & $ + + 12
10
8
6
BL
HT
BM(TJ)
SH
4
2
0
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20
15
10
10000
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50000"& $
30000
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60000
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BM
SH
5
0
0
lmnop
10000
20000
40000
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30000
z vos rv
oxlwvy
60000
q ## +vz } sy m pyxsy } v|py lz }|vz vtxp- vy wsz mopsy t us }|pt povy rs xl} s "% & $ q 
}olz vlos moŽ - ws l|n yxop s xvz } s m pyxs } pop p} vt py xvyxpo }|pt polr prv q vyxv ~ p} vt py v vwnxp
s wŽ|wn|s rs wvoxl - wprs q  yvmnt rs l|n yxop s xvz } s m pyxs } pop xvyxpo ~ , n yxl - wpo v vol - wpo s
wvoxl - wprs wst yxon rs q
 y mopsy t us }|pt povy rs xl} s "% ' $ sopz mvoprsy wstsoz v z syxoprs t p - mnop q #& q
olz vl opz vtxv nz mops }|pt po # wsz & oxlwvy v ( ) & povyxpy mvoprs p|vpxsolpz vtxv q z yvmnlr p ~
wlt ws oxlwvy rv # yus vyws|€lrsy } pop p ! vo } poxv rv nz vz # ~ wst yxon rs prlwlst pt rs yv
povyxpy p # q
'( *+,-. +-./01 .2,.34-501 62.7 .-,1 '( 89
C g @V
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LKKL^ YR ; =Z [ I T V
b;K I<RS g ! V Y V "" T
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Z=JZ aV
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<b IIjB%>#aIaT & d e ' ( ?>G a ( IaT & d` e T) I ( ?>G a ( IaT & d e ' jB%>#aIaT & d`e TT
$ @ P g SKh Z V
<b Ic $ @ PT Pf@ a*D aAG aI d e Q d`e TV
k
lmnop
q #& +ovw€ s rv w+ rlms "rs * $ } pop mvopo mopsy t us }|pt povy rs xl} s "% ' $ q
p - mnop
q #' vt wstxop yv nz p xp{ v|p wsz py z vrlr py rs vy} p-s wst ynz lrs } pop mopsy rs
xl} s "% ' $ q vyxv wpys ~ s{ yvosn yv t spz vtxv .n v / v 0 wst ynz lopz z ply vy} p-s q

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1
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(‹ '4()
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4
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q #' y} p-s wst ynz lrs } pop mopsy rs xl} s "% ' $ wsz & oxlwvy q
pop wpr p p|so rv &
sl z vrlrs s vy} p-s m pyxs } so wpr p p|msolxz s ~ vz 5 {Œxvy q
 y moŽ - wsy wsz sy r prsy r p xp{ v|p q } pop mopsy rs xl} s "% ' $ yus l|n yxoprsy t p - mnop q # q
. sz s s{ yvoprs t p yv-us ptxvolso ~ 0 v p}ovyvtxpopz nz { sz rvyvz } vt€ s t s }olz vlos
moŽ - ws q Ž t s yvmnt rs ~ 0 v p}ovyvtxpopz sy }lsovy rvyvz } vt€ sy q
"% ' $ + + 12
10
8
6
BL
HT
BM(TJ)
SH
4
2
0
0
20
15
10
10000
20000
"% ' $ + + 40000
50000"& $
30000
z vos rv
oxlwvy
60000
. + . * 
BL
BM(TJC)
SH
5
0
0
lmnop
10000
20000
40000
50000"& $
30000
z vos rv
oxlwvy
60000
q # +vz } sy m pyxsy } v|py lz }|vz vtxp- vy wsz mopsy t us }|pt povy rs xl} s "% ' $ q 
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s wŽ|wn|s rs wvoxl - wprs q  yvmnt rs l|n yxop s xvz } s m pyxs } pop xvyxpo ~ , n yxl - wpo v vol - wpo s
wvoxl - wprs wst yxon rs q
pop mvopo mopsy z p lz ply }|pt povy ~ n ysn yv p nt -us rs *
"- mnop
q # $ ~ .n v ovwv{ v wsz s } po"z vxosy nz p polŽv| # rs xl} s $ % v nz ltxvlos & ov}ov yvtxpt rs s t z vos rv oxlwvy rs mops p yvo mvoprs q
'Šˆ
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:;<= C ? $ C ?FDE F?@ ?>D G >?E H IJKLM N O PQ <RS @T
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k
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lmnop
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q # . + rlms r p osxlt p rs * q
q # ! z syxop py z vrlr py rs vy} p-s wst ynz lrs } pop mopsy }|pt povy z p l z ply q vyxv wpys ~ s{ yvosn yv .n v / sl p lz }|vz vtxp-us .n v wst ynz ln z ply vy} p-s q
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lmnop
1
2
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ˆˆ‰ 4
q # ! y} p-s wst ynz lrs } pop mopsy }|pt povy z p lz ply "% $ wsz & oxlwvy q
 y moŽ - wsy wsz sy r prsy r p xp{ v|p
- mnop
3
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Š) )Š 4ˆŠ
‹) ') 4ˆ‹
q } pop mopsy }|pt povy z p lz ply yus l|n yxoprsy t p
q # q sy rsly moŽ - wsy ~ 0 v p}ovyvtxpopz sy z v|€ sovy rvyvz } vt€ sy v sl s }lso q
$ + + "
20
15
10
BL
HT
BM(TJ)
SH
5
0
0
10000
20000
$ + + "
40000
50000"& $
30000
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oxlwvy
60000
. + . * 
120
BL
HT
BM
SH
100
80
60
40
20
0
0
lmnop
10000
20000
40000
50000"& $ 60000
30000
z vos rv
oxlwvy
q # + vz } sy m pyxsy } v|py lz }|vz vtxp- vy wsz mopsy }|pt povy z p lz ply "% $ q  }ol z vlos moŽ - ws l|n yxop s xvz } s m pyxs } pop p} vt py xvyxpo }|pt polr prv q vyxv ~ p} vt py v vwnxp
s wŽ|wn|s rs wvoxl - wprs q  yvmnt rs l|n yxop s xvz } s m pyxs } pop xvyxpo ~ , n yxl - wpo v vol - wpo s
wvoxl - wprs wst yxon rs q
 y mopsy t us }|pt povy rs xl} s "% $ n yprsy t sy xvyxvy sopz mvoprsy wstsoz v z syxop p
- mnop
q# q
olz vlopz vtxv sl mvoprs nz mops }|pt po z p lz p| # wsz & oxlwvy v vz yvmnlr p
prlwlst sn yv nz p t sp povyxp p # vtxov rsly oxlwvy t us pr, pwvtxvy q
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*+,-. +-./01 .5 .51 62.7.-,1 .51 . .-,13. 'Š(89
C ? $ C ?FDE F?@ ?>D G >?E H I PQ@T V
R; = Z i g Pf#H BBjaD @ BAaITV
R; = Z * V _ ; ; W D B` V Z=JZ aV
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b;KL WW ]L= ]Z= JZX IaQiT
<b I Pf ( ?>G a ( IaT & * T D B` g bL W XZ V
k N< W Z I D B` & bL W XZ T V
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lmnop
q #  +ovw€ s rv w+ rlms } pop mvopo mopsy t us }|pt povy rs xl} s "% $ q
* xp{ v|p r p - mnop
q # z syxop py z vrlr py rs vy} p-s wst ynz lrs } pop mopsy rs xl} s "% $ q
vyxv wpys ~ s{ yvosn yv .n v 0 sl p lz }|vz vtxp-us .n v wst ynz ln z ply vy} p-s q
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1
2
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p Žosov
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