cs 146: data structures and algorithms slides
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7/25/2019 CS 146: Data Structures and Algorithms Slides
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– 4G&'3*+' 2*'* QL?1& Y42Q&Z
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'<51'=13 K%'= * &1' <M <?13*P<-&"
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*-. 31><J%-5 1;1>1-'& *-LK=131 %- '=1 ;%&'"
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7<-&]•
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• H<3&' +*&1] O-&13P-5 %-'< ?<&%P<- A 31c0%31& &=%d%-5 *;; '=11;1>1-'& %- '=1 ;%&' 0? <-1 &?<'"
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7/25/2019 CS 146: Data Structures and Algorithms Slides
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K1 +*- +31*'1 * .%b131-' *33*L K%'= .<0G;1 '=1
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– 4J<%. +<&' <M %-&13P<- *-. .1;1P<-"
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– 4J<%. +<&' <M %-&13P<- *-. .1;1P<-"
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21;1P<-
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– )1*3+= M<3 '=1 -<.1 K%'= next ;%-, '< '=1 ;*&' -<.1
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%>?;1>1-'1. %- I*J*i& 7<;;1+P<-& 4DO
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isEmpty] 31'03-& ture %M *-. <-;L %M '=1 size %&j13<"
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• 7;*&&1& '=*' %>?;1>1-' '=1 Iterable %-'13M*+1 +*- ?3<J%.1
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• 7;*&&1& '=*' %>?;1>1-' '=1 Iterable %-'13M*+1 +*- ?3<J%.1K*L '< J%1K *;; '=1%3 %'1>&"
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-*>1. iterator
= = . G
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• Q=1 >1'=<. iterator 31'03-& *- <GS1+' 'L?1 Iterator"
•
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• H=1- '=1 +<>?%;13 &11& *- 1-=*-+1. for ;<<? G1%-5 0&1. <- *- <GS1+' '=*O'13*G;1( %' >1+=*-%+*;;L <G'*%-& *- Iterator *-. '=1- +*;;& '< next *-.
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• Collectioni& remove >1'=<. >0&' `3&' `-. '=1 %'1> '<
31><J1"•
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[1 +*31M0; K%'= * ConcurrentModificationExceptioK=1- * &'30+'03*; +=*-51 Y1"5"( +*;; 0&%-5 Collectioni&removeZ '< '=1 +<;;1+P<- G1%-5 %'13*'1." – Q=*'i& *-<'=13 31*&<- '< ?31M13 '=1 %'13*'<3i& remove >1'=<.( &<
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–
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%>?;1>1-'*P<-]
–
4.J*-'*51] 7*;;& '< get *-. set '*,1 +<-&'*-' P>1 – 2%&*.J*-'*51] OM '=1 +=*-51& *31 -<' >*.1 *' '=1 1-.( 1$3*-'
*-. -*/"4&5 *31 1N?1-&%J1
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–
4.J*-'*51] OM '=1 ?<&%P<- <M '=1 +=*-51& %& ,-<K-( +$3*-'"$-1K %'1>& *-. -*/"4&5 <M 1N%&P-5 %'1>& %& +=1*?
–
2%&*.J*-'*51] )%-+1 LinkedList %& -<' 1*&%;L %-.1N*G;1( +'< get *31 1N?1-&%J1 Y0-;1&& '=1L *31 +;<&1 '< '=1 1-.Z
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– G1+*0&1 1*+= +*;; '< *.. Y'< '=1 1-. <M '=1 ;%&'Z( '*,1& +<-&'*-' P>
7)89: 2*'* )'30+'031& *-. 4;5<3%'=>&( )?3%-5 @A8B( C 4-50& 610-5( D="2"
• OM K1 *31 *..%-5 '< '=1 M3<-'( '=1- –
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$%&'& %- '=1 I*J* 7<;;1+P<-& 4DO Y+<- 'Z
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Q=1 O'13*'<3 *-. I*J* \1&'1. *-. O--13 7;*&&1&
•
I*J* F1J%1K] – )'*P+ 7;*&&
– O--13 7;*&&
–
$<+*; O--13 7;*&&
– 4-<-L><0& O--13 7;*&&
–
O>?;1>1-'*P<- <M $%-,1.$%&'
7)89: 2*'* )'30+'031& *-. 4;5<3%'=>&( )?3%-5 @A8B( C 4-50& 610-5( D="2"
LECTURE
XN*>?;1] remove XJ1- \0>G1• XN*>?;1] remove *;; 1J1-VJ*;01. %'1>& %- * List
– [1M<31] 6, 5, 1, 4, 2 " 4d13] 5, 1
• h&%-5 *- ArrayList %& * ;<&%-5 &'3*'15Lo
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•
h&%-5 *- ArrayList %& * ;<&%-5 &'3*'15Lo – Q=1 remove %& -<' 1_+%1-'( &< '=1 3<0P-1 '*,1& c0*.3*P+ P>1"
•
h&%-5 * LinkedList =*& ?3<G;1>& *& K1;;" – Q=1 +*;; '< get %& -<' 1_+%1-'( '*,%-5 c0*.3*P+ P>1"
– Q=1 +*;; '< remove %& 1c0*;;L %-1_+%1-'( G1+*0&1 %' %& 1N?1-&%J1 '< 51' '< ?<&%P<
7)89: 2*'* )'30+'031& *-. 4;5<3%'=>&( )?3%-5 @A8B( C 4-50& 610-5( D="2"
O>?3<J1>1-'] remove XJ1- \0>G1• O>?3<J1>1-' 8] h&1 iterator %-&'1*. <M get"
• D3<G;1>] ConcurrentModificationException K%'=
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Collectioni& remove
7)89: 2*'* )'30+'031& *-. 4;5<3%'=>&( )?3%-5 @A8B( C 4-50& 610-5( D="2"
•
O>?3<J1>1-' @] h&1 iteratori& remove '< *J<%. '=1ConcurrentModificationException ?3<G;1>"
[1M<31]
ArrayList Vp !"#% $
LinkedList Vp !"#% $
4d13]
ArrayList Vp !"#% $
'()*+,( *--*. /0(1, 1+,0 '( ,2/3(4
LinkedList Vp !"#$
F0--%-5 Q%>1& M<3 O>?3<J1>1-' q@• F0--%-5 P>1& M<3 <03 +<.1 %- O>?3<J1>1-' q@
– LinkedList: ;%-1*3 53<K'= 3*'1 !"#$%
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– ArrayList: c0*.3*P+ 53<K'= 3*'1 !"#% $
7)89: 2*'* )'30+'031& *-. 4;5<3%'=>&( )?3%-5 @A8B( C 4-50& 610-5( D="2"
6+30 789* :"; ", 10*/3 )#$$+$2 7+/* <3=
LinkedList<Integer> 800,000 0.039
LinkedList<Integer> 1,600,000 0.073
ArrayList<Integer> 800,000 300
ArrayList<Integer> 1,600,000 1,200
ListIterator& • 4 ListIterator 1N'1-.& '=1 M0-+P<-*;%'L <M *- Iterator M<3 List&]
– Previous *-. hasPrevious *;;<K '3*J13&*; <M '=1 list M3<> '=1 G*+, '< '=M3<-'
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– 4.. ?;*+1& * -1K %'1> %-'< '=1 list %- '=1 +0331-' ?<&%P<-
7)89: 2*'* )'30+'031& *-. 4;5<3%'=>&( )?3%-5 @A8B( C 4-50& 610-5( D="2"
\<3>*; &'*3P-5 ?<%-'] next
31'03-& B( previous %& %;;15*;(
add ?;*+1& %'1> G1M<31 B
next 31'03-& e( previous
31'03-& B( add ?;*+1& %'1>
G1'K11- B *-. e
next %& %;;15*;( previous
31'03-& r( add ?;*+1& %'1>
*d13 r
O>?;1>1-'*P<- <M ArrayLis• ^0';%-1& <M * 0&*G;1 ArrayList 51-13%+ +;*&&]MyArrayList
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– U*%-'*%- '=1 0-.13;L%-5 *33*L( '=1 *33*L +*?*+%'L( *-. '+0331-' -0>G13 <M %'1>& &'<31.
– D3<J%.1 * >1+=*-%&> '< +=*-51 '=1 +*?*+%'L <M '=10-.13;L%-5 *33*L
– D3<J%.1 *- %>?;1>1-'*P<- <M get *-. set
–
D3<J%.1 G*&%+ 3<0-P-1&( &0+= *& size( isEmpty( *-.clear( *& K1;; *& remove( *-. 'K< J13&%<-& <M add 3<0P-1&
– D3<J%.1 * +;*&& '=*' %>?;1>1-'& '=1 Iterator %-'13M*X"5"( next( hasNext( *-. remove"
7)89: 2*'* )'30+'031& *-. 4;5<3%'=>&( )?3%-5 @A8B( C 4-50& 610-5( D="2"
MyArrayList] Q=1 [*&%+ 7;*
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7)89: 2*'* )'30+'031& *-. 4;5<3%'=>&( )?3%-5 @A8B( C 4-50& 610-5( D="2"
MyArrayList] Q=1 [*&%+ 7;*
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7)89: 2*'* )'30+'031& *-. 4;5<3%'=>&( )?3%-5 @A8B( C 4-50& 610-5( D="2"
O--13 7;*&& V 8• Q=%& %'13*'<3 J13&%<- .<1&-i' K<3, G1+*0&1 theItems *size() *31 -<' ?*3' <M '=1 ArrayListIterator +;*
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7)89: 2*'* )'30+'031& *-. 4;5<3%'=>&( )?3%-5 @A8B( C 4-50& 610-5( D="2"
D3<G;1> K%'= &+<?%-5
O--13 7;*&& V @• Q=1 %'13*'<3 %& * '<?V;1J1; +;*&& *-. &'<31& '=1 +0331-' ?<&%P<- *-. * ;%-, '< '
MyArrayList" O' .<1&-i' K<3, G1+*0&1 theItems %& ?3%J*'1 %- '=1MyArrayList +;*&&
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7)89: 2*'* )'30+'031& *-. 4;5<3%'=>&( )?3%-5 @A8B( C 4-50& 610-5( D="2"
O' %& .1`-1. *& * ?3%J*'1"
O' %& * lR4)V4m 31;*P<-&=
X33<3 R131o
O--13 7;*&& V !• Q=%& P>1 %' K<3,&] Q=1 iterator %& * -1&'1. +;*&& *-. &'<31& '=1 +0331-'
?<&%P<- *-. * ;%-, '< '=1 MyArrayList" O' K<3,& G1+*0&1 '=1 -1&'1. +;*&+<-&%.131. ?*3' <M '=1 MyArrayList +;*&&"
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7)89: 2*'* )'30+'031& *-. 4;5<3%'=>&( )?3%-5 @A8B( C 4-50& 610-5( D="2"
ArrayListIterator %& .1%-&%.1 <M MyArrayList
Static %-.%+*
* -1&'1. +;*&&
O--13 7;*&& V 9• Q=%& <-1 K<3,& *& K1;;] Q=1 %'13*'<3 %& *- %--13 +;*&& *-. &'<31
'=1 +0331-' ?<&%P<- *-. *- %>?;%+%' ;%-, '< '=1 MyArrayLis
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7)89: 2*'* )'30+'031& *-. 4;5<3%'=>&( )?3%-5 @A8B( C 4-50& 610-5( D="2"
H1 *31 0&%-5 '=1 %>?;%+%' ;%-,
'=1 MyArrayList =131"
O--13 +;*&& .<1&-i' =*J
'=1 static ,1LK<3.
\1&'1. 7;*&& %- I*J*• )'*P+ 7;*&&] .1+;*31. *& * &'*P+ >1>G13 <M
*-<'=13 +;*&&
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•
O--13 7;*&&] .1+;*31. *& *- %-&'*-+1 >1>G13 <M*-<'=13 +;*&&
•
$<+*; O--13 7;*&&] .1+;*31. %-&%.1 *- %-&'*-+1
>1'=<. <M *-<'=13 +;*&&• 4-<L><0& O--13 7;*&&] ;%,1 * ;<+*; %--13 +;*&&( G0
K3%E1- *& *- 1N?31&&%<- K=%+= 31'03-& * <-1V<b<GS1+'
7)89: 2*'* )'30+'031& *-. 4;5<3%'=>&( )?3%-5 @A8B( C 4-50& 610-5( D="2"
)'*P+ 7;*&&1&• Q=1 -1&'1. +;*&& =*& *++1&& '< %'& +<-'*%-%-5
+;*&&i& ?3%J*'1 &'*P+ >1>G13& Y%& %' 0&1M0; *' *;;s
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+;*&& & ?3%J*'1 &'*P+ >1>G13& Y%& %' 0&1M0; *' *;;s
package pizza;
public class Rhino {
...
public static class Goat {...
}
}
7)89: 2*'* )'30+'031& *-. 4;5<3%'=>&( )?3%-5 @A8B( C 4-50& 610-5( D="2"
O--13 7;*&&1&• 4- %--13 +;*&& %& * +;*&& .1+;*31. *& * -<-V&'*P+ >1>G13 <M *-<'=13 +
• Q=1 %--13 +;*&& %-&'*-+1 =*& *++1&& '< '=1 %-&'*-+1 >1>G13& <M '=1+<-'*%-%-5 +;*&& %-&'*-+1"
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– Q=1&1 1-+;<&%-5 %-&'*-+1 >1>G13& *31 31M1331. '< %-&%.1 '=1 %--13 +;*&& S0&' '=1%3 &%>?;1 -*>1&( -<' 5/* 02/, Ythis %- '=1 %--13 +;*&& 31M13& '< '=1%--13 +;*&& %-&'*-+1( -<' '=1 *&&<+%*'1. +<-'*%-%-5 +;*&& %-&'*-+1Z"
package pizza;
public class Rhino {
public class Goat {...}
private void jerry() {Goat g = new Goat();
}}
7)89: 2*'* )'30+'031& *-. 4;5<3%'=>&( )?3%-5 @A8B( C 4-50& 610-5( D="2"
$<+*; O--13 7;*&&1&• 4 ;<+*; %--13 +;*&& %& * +;*&& .1+;*31. %- '=1 G<.L <M
>1'=<."
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•
)0+= * +;*&& %& <-;L ,-<K- K%'=%- %'& +<-'*%-%-5>1'=<.( &< %' +*- <-;L G1 %-&'*-P*'1. *-. =*J1 %'&>1>G13& *++1&&1. K%'=%- %'& +<-'*%-%-5 >1'=<."
• [1+*0&1 * ;<+*; %--13 +;*&& %& -1%'=13 '=1 >1>G13 <
+;*&& <3 ?*+,*51( %' %& -<' .1+;*31. K%'= *- *++1&&;1J1;"
• 4++1&& '< '=1 +<-'*%-%-5 +;*&&i& %-&'*-+1 >1>G13& ;%,1 %- *- %-&'*-+1 %--13 +;*&&"
7)89: 2*'* )'30+'031& *-. 4;5<3%'=>&( )?3%-5 @A8B( C 4-50& 610-5( D="2"
4-<-L><0& O--13 7;*&&1&• 4 ;<+*; %--13 +;*&& %& %-&'*-P*'1. *' ><&' S0&' <-
1*+= P>1 %'& +<-'*%-%-5 >1'=<. %& 30-"
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5
•
h&1 ;%,1 '=%&]new *ParentClassName*(*constructorArgs*) {*members*
• 7*--<' &0??;L L<03 <K- +<-&'30+'<3
•
)1'0? 0&%-5 *- %-%P*;%j13 G;<+,] * {} G;<+, ?;*+1<0'&%.1 *-L >1'=<.
7)89: 2*'* )'30+'031& *-. 4;5<3%'=>&( )?3%-5 @A8B( C 4-50& 610-5( D="2"
O>?;1>1-'*P<- <M $%-,1.$%&• MyLinkedList ] +<-'*%-& ;%-,& '< G<'= 1-.&( '=1 &%j1 <
'=1 ;%&'( *-. * =<&' <M >1'=<.&"
• Node ] +<-'*%-& .*'* *-. ;%-,& '< '=1 ?31J%<0& *-. -1N'
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Node ] +<-'*%-& .*'* *-. ;%-,& '< '=1 ?31J%<0& *-. -1N'
-<.1&( *;<-5 K%'= *??3<?3%*'1 +<-&'30+'<3&"• LinkedListIterator ] %>?;1>1-'& Iterator K%'next, hasNext *-. remove >1'=<.&"
7)89: 2*'* )'30+'031& *-. 4;5<3%'=>&( )?3%-5 @A8B( C 4-50& 610-5( D="2"
4..%-5 * \<.1
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7)89: 2*'* )'30+'031& *-. 4;5<3%'=>&( )?3%-5 @A8B( C 4-50& 610-5( D="2"
F1><J%-5 * \<.1
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7)89: 2*'* )'30+'031& *-. 4;5<3%'=>&( )?3%-5 @A8B( C 4-50& 610-5( D="2"
451-.* M<3 $1+'031 e• [<<, t11?%-5
–
)<;0P<-& M<3 4&&%5->1-' q8
– 4&&%5->1-' q@
WEEK #4
LECTURE
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– 4&&%5->1-' q@
•
$%&'&( )'*+,& *-. /0101& Y7=*?'13 !Z – Q=1 )'*+, 42Q
• )'*+, U<.1;
• O>?;1>1-'*P<- <M )'*+,&
•
4??;%+*P<-&
–
Q=1 /0101 42Q• /0101 U<.1;
• 433*L O>?;1>1-'*P<- <M /0101&
• )=<3' F1J%1K /01&P<-&
7)89: 2*'* )'30+'031& *-. 4;5<3%'=>&( )?3%-5 @A8B( C 4-50& 610-5( D="2"
Q=1 )'*+, 42Q• 4 &'*+, %& * ;%&' K%'= '=1 31&'3%+P<- '=*' %-&13P<-
*-. .1;1P<-& +*- G1 ?13M<3>1. *' '=1 1-. <M '=
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;%&'( +*;;1. '=1 '<?"
7)89: 2*'* )'30+'031& *-. 4;5<3%'=>&( )?3%-5 @A8B( C 4-50& 610-5( D="2"
)'*+, ><.1;]
^-;L '=1 '<? 1;1>1-' %& *++1&&%G;1"
D0&= *-. ?<? <?13*P<-& *31 G*&1. <-
$OW^ Y;*&' %-( `3&' <0'Z
O>?;1>1-'*P<- <M )'*+,&• $%-,1. $%&' O>?;1>1-'*P<- <M )'*+,&
– D0&=] %-&13' *' '=1 M3<-' <M '=1 ;%&'
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–
Q<?kD<?] 31'03- '=1 J*;01 <M '=1 1;1>1-' *' '=1 M3<<M '=1 ;%&' *-. .1;1'1 %'"
•
433*L O>?;1>1-'*P<- <M )'*+,&
–
D0&=] %-+31>1-' topOfStack *-. &1' '=1 1;1>1-topOfStack"
– Q<?kD<?] 31'03- '=1 J*;01 <M '=1 1;1>1-' *'
topOfStack *-. .1+31>1-' topOfStack"
7)89: 2*'* )'30+'031& *-. 4;5<3%'=>&( )?3%-5 @A8B( C 4-50& 610-5( D="2"
4??;%+*P<-] [*;*-+%-5 )L>G<• 7<>?%;13& -11. '< +=1+, %M *;; &L>G<;& *31 G*;*-+1.( 1"5"
uYZv %& ;15*;( G0' uYv %& K3<-5"
•
^-1 +*- 0&1 &'*+, '< G*;*-+1 &L>G<;&]
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L –
U*,1 *- 1>?'L &'*+," – F1*. +=*3*+'13& 0-P; 1-. <M `;1"
–
OM '=1 +=*3*+'13 %& *- <?1-%-5 &L>G<;( ?0&= %' <-'< '=1 &'*+,"
– OM %' %& * +;<&%-5 &L>G<;( '=1- %M '=1 &'*+, %& 1>?'L 31?<3' *-133<3n
–
^'=13K%&1( ?<? '=1 &'*+,"
–
OM '=1 &L>G<; ?<??1. %& -<' '=1 +<331&?<-.%-5 <?1-%-5 &L>G'=1- 31?<3' *- 133<3"
– 4' 1-. <M `;1( %M '=1 &'*+, %& -<' 1>?'L 31?<3' *- 133<3"
7)89: 2*'* )'30+'031& *-. 4;5<3%'=>&( )?3%-5 @A8B( C 4-50& 610-5( D="2"
4??;%+*P<-] D<&w%N XN?31&&%<• D<&w%N <3 31J13&1 D<;%&= -<'*P<- 1N?31&& *- 1N?31&&%<-]
4.99 * 1.06 + 5.99 + 6.99 * 1.06 =( %-'<
4.99 1.06 * 5.99 + 6.99 1.06 * +
• Q=1 1*&%1&' K*L '< .< ?<&w%N %& '< 0&1 * &'*+,"
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Q=1 1*&%1&' K*L '< .< ?<&w%N %& '< 0&1 * &'*+,"
•
W<3 1N*>?;1( 6 5 2 3 + 8 * + 3 + *
7)89: 2*'* )'30+'031& *-. 4;5<3%'=>&( )?3%-5 @A8B( C 4-50& 610-5( D="2"
4 xyi %& 31*.( &< ! *-. @
*31 ?<?1. M3<> '=1 &'*+,"
Q=1 &0> B %& ?0&=1." \1N' e %& ?0&=1. H%'= * xzi( e *-. B *31
?<?1. *-. 9A %& ?0&=1."
\1N' * xyi %& &11-( &< 9A
*-. B *31 ?<??1. *-. B y9A { 9B %& ?0&=1."
\<K ! %& ?0&=1." H%'= * xyi( ! *-. 9B *31
?<??1. *-. 9e %&?0&=1."
W%-*;;L( * xzi %& &11- *-.
9e *-. : *31 ?<??1." Q=131&0;' : z 9e { @ee %&
?0&=1."
O-`N '< D<&w%N 7<-J13&%<-• )'*+, +*- G1 0&1. '< +<-J13' *- 1N?31&&%<- %- &'*-.*3. M<3> Y,-<K-
%-`NZ %-'< ?<&w%N"
• T%J1- '=1 %-`N 1N?31&&%<-]a + b * c + (d * e + f) * g
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a + b c + (d e + f) g (
'=1 ?<&w%N %&]a b c * + d e * f + g * +
• Q=1 &'*+, 31?31&1-'& ?1-.%-5 <?13*'<3&" )<>1 <M '=1 <?13*'<3& <- '=&'*+, '=*' =*J1 =%5= ?31+1.1-+1 *31 ,-<K- '< G1 +<>?;1'1. *-. &=<G1 ?<??1."
7)89: 2*'* )'30+'031& *-. 4;5<3%'=>&( )?3%-5 @A8B( C 4-50& 610-5( D="2"
O-`N '< D<&w%N 4;5<3%'=>• O-`N '< D<&w%N +<-J13&%<- 0&%-5 &'*+,]a + b * c + (d * e + f) * g
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7)89: 2*'* )'30+'031& *-. 4;5<3%'=>&( )?3%-5 @A8B( C 4-50& 610-5( D="2"
8" )L>G<; * Vp <0'?0'( ^?13*'<3 y Vp )'*+,(
)L>G<; G Vp <0'?0'"
@" ^?13*'<3 z Vp )'*+,( '=1 '<? 1-'3L <M <?13*'<3
&'*+, =*& * ;<K13 ?31+1.1-+1 Vp -<'=%-5 %& <0'?0'"
!" ^?13*'<3 y Vp &'*+,( ?<? z *-. y"
9" ^?13*'<3 Y Vp )'*+,( )L>G<; . Vp <0'?0'"
B" ^?13*'<3 z Vp )'*+,( '=131 %& -< <0'?0'
G1+*0&1 <M Y( )L>G<; 1 Vp <0'?0'"
:" ^?13*'<3 y Vp &'*+,( ?<? *-. <0'?0' z"
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–
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9+00&01 M&?, G'% buildHea
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•
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– M=, npl 'G : 0'7, F&(= V '% @ 5=&87 &- V"
–
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–
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Y&0'?&:8 *+,+, deleteMin
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•
UH :/ 6 @ +,/1 @ A :7 6 @ <1: :1 A @ 6 1 -50+ <&0( =/ ?)/0/1+ *1pw %1: +,*0 *0 2;bM
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UH : 6 @P +,/1 @ : 6 @ <1: : @ 6 1 -50+ <&0( =/ ?)/0/1+ *1pw %1: +,*0 *0 2;bM#
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• UH : / 6 >P +,/1 : / A : ; 6 > <1: : 1 A : / 6 > pw %1: +,*0 *0UJEc88U\WM#
• 8( F/ ,<D/ +( =<3>+)<3> <1: :/+/)-*1/ +,<+ : ? F(1f+ F()
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• 8( F/ ,<D/ +( =<3>+)<3> <1: :/+/)-*1/ +,<+ : > 6 ? F(1f+ F()
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2,/ 25)1?*>/ ;/3(10+)53V(1 E)(=&/
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2,/ 25)1?*>/ ;/3(10+)53V(1 E)(=&/
• 25)1?*>/ )/3(10+)53V(1 <&'()*+,-e :)*D/) )(5V1/ l?0/5:(3(:
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