CS 146: Data Structures and Algorithms Slides

7/25/2019 CS 146: Data Structures and Algorithms Slides

http://slidepdf.com/reader/full/cs-146-data-structures-and-algorithms-slides 1/563

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–

7=*-51 '=1 next ;%-, '< -0;;

– h?.*'1 '=1 ;%-, '< '=1 last -<.1

7)89: 2*'* )'30+'031& *-. 4;5<3%'=>&( )?3%-5 @A8B( C 4-50& 610-5( D="2"

4 .<0G;L ;%-,1. -<.1

I*J* 7<;;1+P<-& 4DO• U*-L .*'* &'30+'031&( 1"5"( $%&' 42Q( *31

% ; . % I i 7 ;; P 4DO



%>?;1>1-'1. %- I*J*i& 7<;;1+P<-& 4DO

–

%- ?*+,*51 java.util"

• )*>?;1 >1'=<.& %- I*J* Collection O-'13M*+

– size] 31'03-& '=1 -0>G13 <M %'1>& %- '=1 +<;;1+P<-

–

isEmpty] 31'03-& ture %M *-. <-;L %M '=1 size %&j13<"

– contains] 31'03-& true %M x %& %- '=1 +<;;1+P<-

– addkremove] addkremove %'1> x '<kM3<> '=1

+<;;1+P<-7)89: 2*'* )'30+'031& *-. 4;5<3%'=>&( )?3%-5 @A8B( C 4-50& 610-5( D="2"

)0G&1' <M 7<;;1+P<- O-'13M*+1• Q=1 Collection %-'13M*+1 1N'1-.& '=1 Iterable %-'13M*

• 7;*&&1& '=*' %>?;1>1-' '=1 Iterable %-'13M*+1 +*- ?3<J%.1



• 7;*&&1& '=*' %>?;1>1-' '=1 Iterable %-'13M*+1 +*- ?3<J%.1K*L '< J%1K *;; '=1%3 %'1>&"

7)89: 2*'* )'30+'031& *-. 4;5<3%'=>&( )?3%-5 @A8B( C 4-50& 610-5( D="2"

7*?%'*;%j1. lOm

Q=%& l%m %& -<' +*?%'*;%j1."

O'13*'<3&• 7<;;1+P<-& '=*' %>?;1>1-' '=1 Iterable %-'13M*+1 >0&' ?3<J%.1 * >1'=<.

-*>1. iterator

= = . G



• Q=1 >1'=<. iterator 31'03-& *- <GS1+' 'L?1 Iterator"

•

Q=1 Iterator %& *- %-'13M*+1 .1`-1. %- ?*+,*51 S*J*"0P; *-. %& &=<K- G1;

7)89: 2*'* )'30+'031& *-. 4;5<3%'=>&( )?3%-5 @A8B( C 4-50& 610-5( D="2"

D3%-' 4;; '=1 O'1>&• X*+= +*;; '< next 5%J1& '=1 -1N' %'1> %- '=1 +<;;1+P<- *-. hasNext +*- G1

0&1. '< '1;; %M '=131 %& * -1N' %'1>"

H= = %; = . f ; G % . GS =



• H=1- '=1 +<>?%;13 &11& *- 1-=*-+1. for ;<<? G1%-5 0&1. <- *- <GS1+' '=*O'13*G;1( %' >1+=*-%+*;;L <G'*%-& *- Iterator *-. '=1- +*;;& '< next *-.

hasNext"

7)89: 2*'* )'30+'031& *-. 4;5<3%'=>&( )?3%-5 @A8B( C 4-50& 610-5( D="2"

Q=%& %& *- l1-=*-+1.for ;<<?m"

remove 0&%-5 Iterator• [<'= '=1 Collection *-. Iterator %-'13M*+1& +<-'*%- *

>1'=<. +*;;1. remove"



• Collectioni& remove >1'=<. >0&' `3&' `-. '=1 %'1> '<

31><J1"•

Iteratori& remove >1'=<. 31><J1& '=1 ;*&' %'1> 31'03-1GL next" – Q=%& %& ><31 1_+%1-' %- &<>1 +*&1&( 1"5"( 31><J%-5 1J13L <'=13 %'1

%- '=1 +<;;1+P<-

•

[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'=<.( &<

'=131 %& -< * +<-+0331-+L ?3<G;1>"

7)89: 2*'* )'30+'031& *-. 4;5<3%'=>&( )?3%-5 @A8B( C 4-50& 610-5( D="2"

8

@

Q=1 List O-'13M*+1• Q=1 List %-'13M*+1 1N'1-.& Collection( &< %' +<-'*%-

4;; '=1 >1'=<.& %- '=1 Collection %-'13M*+1 ?;0&



–

4;; '=1 >1'=<.& %- '=1 Collection %-'13M*+1( ?;0&

–

4 M1K <'=13& Y&=<K- %- G1;<KZ

7)89: 2*'* )'30+'031& *-. 4;5<3%'=>&( )?3%-5 @A8B( C 4-50& 610-5( D="2"

4++1&& <3 +=*-51

*' %-.1Nn O-.1N 5

M3<> A '< size

^J13;<*.1. '< 31><J1

%'1> *' * &?1+%`1. ?<&

ArrayList *-. LinkedLi• Q=1 ArrayList ?3<J%.1& * 53<K*G;1 *33*L

%>?;1>1-'*P<-]



%>?;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

• Q=1 LinkedList ?3<J%.1& * .<0G;L ;%-,1. ;%&'%>?;1>1-'*P<- <M '=1 List 42Q"

–

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

7)89: 2*'* )'30+'031& *-. 4;5<3%'=>&( )?3%-5 @A8B( C 4-50& 610-5( D="2"

U*,%-5 * List• H=1'=13 *- ArrayList <3 LinkedList %& ?*&&1. *& *

?*3*>1'13( '=1 30--%-5 P>1 <M '=1 M<;;<K%-5 >1'=<. %& !"#$



– 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- –

ArrayList '*,1& !"#% $

– LinkedList %& !"#$ <?13*P<-

R131 K1 *31 *..%-5 * -1K %'1>

'< '=1 M3<-' <M '=1 ;%&'

)0> <M '=1 \0>G13& %- * Lis• XN*>?;1] +<>?0'1 '=1 &0> <M '=1 -0>G13& %- * Li

– F0--%-5 P>1 M<3 *- ArrayList] !"#$



F0--%-5 P>1 M<3 *- ArrayList] !"#$

–

F0--%-5 P>1 M<3 * LinkedList] !"#

%

$ G1+*0&1 +*;;& '51' *31 !"#$ <?13*P<-&"

– F0--%-5 P>1 0&%-5 *- 1-=*-+1. for ;<<? *-. Listi&iterator] !"#$

7)89: 2*'* )'30+'031& *-. 4;5<3%'=>&( )?3%-5 @A8B( C 4-50& 610-5( D="2"

)%>%;*3;L( K1 K*-' '< 0&1

contains *-. remove Collection G1+*0&1

ArrayList *-. LinkedL

*31 %-1_+%1-' M<3 &1*3+=1

451-.* M<3 $1+'031 f• $%&'&( )'*+,& *-. /0101& Y7=*?'13 !Z

– $%&'& %- '=1 I*J* 7<;;1+P<-& 4DO Y+<-i'ZWEEK #4



$%&'& %- '=1 I*J* 7<;;1+P<-& 4DO Y+<- 'Z

•

ListIterators

–

O>?;1>1-'*P<- <M 433*L$%&'

• Q=1 [*&%+ 7;*&&

•

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



•

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%'=



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 !"#$%



– 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<-'



– 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



– 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;*



7)89: 2*'* )'30+'031& *-. 4;5<3%'=>&( )?3%-5 @A8B( C 4-50& 610-5( D="2"

MyArrayList] Q=1 [*&%+ 7;*



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 +;*



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 +;*&&



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 +;*&&"



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



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 +;*&&



•

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



+;*&& & ?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"



– 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'=<."



•

)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-"



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'



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



7)89: 2*'* )'30+'031& *-. 4;5<3%'=>&( )?3%-5 @A8B( C 4-50& 610-5( D="2"

F1><J%-5 * \<.1



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



– 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 '=



;%&'( +*;;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 ;%&'



–

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"

•

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4'0 <,2:0 &0`.0)50 :F % <,07040,=()07 52)&4%

4'%4 (& 2<J=([07 42 4'0 .)70,8F()* 52=<.40,l&

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O'0 822;.< 52.87 :0 <%,%8808([07 42 &(=84%)02.&5'05; 4'0 :2.)707 &04 2G <2&&(:80 825%J2)&"

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•

O'0 '2<& 4088 E'(5' 2G 4'0 <2&(J2)& () 4'0 :825; %,0255.<(07 E(4' 5088& 52)4%()()* 4'(& '%&' C%8.0" O'.&$2<{i| g WW>W ()7(5%40& 4'%4 2)8F <2&(J2) >W5.,,0)48F 52)4%()& (40=& E'2&0 '%&' C%8.0 (& iV E'

<2&(J2)& iV }V %)7 >> 72 )24



$2<&5245' $%&'()*

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-60=<J)* 42 ()&0,4 @" M()0%, <,2:()* &.**0&4&

825%J2) >@V :.4 4'%4 (& 422 G%,V &2 E0 0C(54 A G,2

<2&(J2) >> 42 a)7 % 582&0, <2&(J2)



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-60=<J)* 42 ()&0,4 $" M()0%, <,2:()* &.**0&4& 825%J2) >KV :.4'%4 (& 422 G%,b 52)&.8J)* $2<{>>|V E0 &00 4'%4 A 5%) =2C072E)V 80%C()* <2&(J2) >@ 2<0)" 12)&.8J)* $2<{>W| *(C0& )2&.**0&J2)&" $2<{>>| 720& )24 '08< 0(4'0, ]E'F_^V &2 $2<{>?|&.**0&4& =2C()* B



$2<&5245' $%&'()*

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I)&0,J2) 2G $ 52)J).0&c m0H4 C (& 0C(5407V %)7

a)%88F E0 '%C0 % &<24 4'%4 (& 582&0 0)2.*' 42 4'

'%&' C%8.0 %)7 5%) ()&0,4 $



UH40)7(:80 $%&'()*

•

A'%4 (G 4'0 G.88 %=2.)4 2G 7%4% (& 422 8%,*0 42 a4 ()=0=2,F_

– e., =%() 52)50,) (& 4'0 ).=:0, 2G 7(&; %550&&0& 42 *04 *(C0) 7%4% (40=

–

m (40=& 42 &42,0V R (40=& a4 2) 0%5' 7(&; :825;

– 1288(&(2)& E(88 5%.&0 % ).=:0, 2G :825;& 42 :0 0H%=()07,0&.8J)* () &(*)(a5%)4 7(&; ,0%7 52&4



– A'0) '%&' :052=0& 422 G.88V ,0'%&'()* E(88 :0 )00707

•

O'0 52&4 E(88 :0 e]m^ 7(&; %550&&0&

– UH40)&(:80 '%&'()*c

• 30%,5'c 4E2 7(&; %550&&0&

• I)&0,J2)c G0E 7(&; %550&&0&

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•

e,(*()%8 +%4%



UH40)7(:80 $%&'()*

•

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-n0, ()&0,J2) 2G WWWWWW %)7 80%G &<8(4



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•

Y''<RZ,,>&01 – .'F08':7 'G M,H(;''< 4'+%5, 3'7,

• N:-=&01 [3=:>(,% W\ –

N:-= M:;8,- F&(= C'%-(R3:-, ][@\ /55,--

• N'>-5'(5= N:-=&01

– TH(,07&;8, N:-=&01

• $%&'%&() *+,+,- [N,:>-\ [3=:>(,% !\

WEEK #7

LECTURE #1



$%&'%&() *+,+,- [N,:>-\ [3=:>(,% !\

–

Q'7,8 – 4&?>8, I?>8,?,0(:J'0

– Y&0:%) N,:>

34@K! .:(: 4(%+5(+%,- :07 /81'%&(=?-U 4>%&01 AV@WU X /01+- 2,+01U $="."

M,H(;''< 4'+%5, 3'7,

•

2'+ ?:) 7'F08':7 (=, (,H(;''<^- -'+%5, 5'7,=,%,_

• =6>_``+-,%-"5&-"a+",7+`bF,&--`7-::O:E:B`5'7,`



$%&?, c+?;,% 3=,5<&01

•

C, 7&-5+--,7 (=&- ?,(='7 ),-(,%7:)_

M=&- &- : -='%( 5+("



$%&?, c+?;,% 3=,5<&01

•

M=, 4&,E, 'G T%:('-(=,0,- – S&07&01 :88 >%&?, 0+?;,%- +> (' :0) 1&E,0 8&?&( ;)

&(,%:JE,8) ?:%<&01 :- (=, ?+8J>8,- 'G ,:5= >%&?,"

– / 0'0R>%&?, ?+-( ;, : 5'?>'-&(,_ prime x a_numb

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30



2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

2 3 5 7 11 13 17 19 23 29



3453167

N'>-5'(5= N:-=&01

•

3"89."0.: 3&9:+$2_ ;'+07 (=, ?:H&?:8 8,01(= (=, >%';, -,d+,05, ;) : >%,7,(,%?&0,7 5'0-(:

(=:( &- '>J?&e,7 (' (=, +07,%8)&01 5'?>+(,%^-

:%5=&(,5(+%," S'% ,H:?>8,_ !"#$%&'( * +"•

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5:-,"



•

M=, 8''<+> 5'+87 ;, >:%:88,8&e,7 (' -&?8(:0,'+-5=,5< (=, ;'+07,7 -,( 'G >'--&;8, 8'5:J'0-"

N'>-5'(5= N:-=&01

•

M=, ='>- (,88 F=&5= 'G (=, >'-&J'0- &0 (=, ;8'5< :%,'55+>&,7 F&(= 5,88- 5'0(:&0&01 (=&- =:-= E:8+," M=+-N'>ghi j VV@V &07&5:(,- (=:( '08) >'-&J'0 @V5+%%,0(8) 5'0(:&0- &(,?- F='-, =:-= E:8+, &- hU F=

>'-&J'0- hU kU :07 @@ 7' 0'(

V



V

@V

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•

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>'-&J'0 @@ (' a07 : 58'-,% >'-&J'0



N'>-5'(5= N:-=&01

•

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N'>-5'(5= N:-=&01

•

I0-,%J'0 'G & 5'0J0+,-_ c,H( / &- ,E&5(,7U :07a0:88) F, =:E, : ->'( (=:( &- 58'-, ,0'+1= (' (=

=:-= E:8+, :07 5:0 &0-,%( &



TH(,07&;8, N:-=&01

•

C=:( &G (=, G+88 :?'+0( 'G 7:(: &- ('' 8:%1, (' a( &0?,?'%)m

– ]+% ?:&0 5'05,%0 &- (=, 0+?;,% 'G 7&-< :55,--,- (' 1,( 1&E,0 7:(: &(,?

–

c &(,?- (' -('%,U Q &(,?- a( '0 ,:5= 7&-< ;8'5<

– 3'88&-&'0- F&88 5:+-, : 0+?;,% 'G ;8'5<- (' ;, ,H:?&0,7%,-+8J01 &0 -&10&a5:0( 7&-< %,:7 5'-(

C=,0 =:-= ;,5'?,- ('' G+88 %,=:-=&01 F&88 ;, 0,,7,7



– C=,0 =:-= ;,5'?,- ('' G+88U %,=:-=&01 F&88 ;, 0,,7,7

•

M=, 5'-( F&88 ;, ][c\ 7&-< :55,--,-

– TH(,0-&;8, =:-=&01_

• 4,:%5=_ (F' 7&-< :55,--,-

• I0-,%J'0_ G,F 7&-< :55,--,-

TH(,07&;8, N:-=&01

•

]%&1&0:8 .:(:



TH(,07&;8, N:-=&01

•

/n,% &0-,%J'0 'G @VV@VV :07 7&%,5('%) ->8&(



TH(,07&;8, N:-=&01

•

/n,% &0-,%J'0 'G VVVVVV :07 8,:G ->8&(





;)1<)1=> ?@A@A5

3=:>(,% ]E,%E&,F

•

$%&'%&() d+,+, :%, +-,7 &0 ?:0) :>>8&5:J'0-_ –

*+,+, G'% (=, >%&0( O';- -,0( (' : >%&0(,%

• @R>:1, O';- -='+87 ;, >%&'%&Je,7 'E,% @VVR>:1, O';

– ]>,%:J01 -)-(,? -5=,7+8,% G'% ?+8J+-,% ,0E&%'0?

• 4='%( O';- -='+87 a0&-= :- G:-( :- >'--&;8,U (:<&01>%,5,7,05, 'E,% O';- (=:( =:E, :8%,:7) ;,,0 %+00&01

• I0 (=&- 5=:>(,%U F, F&88 7&-5+--_



–

To5&,0( &?>8,?,0(:J'0 'G (=, >%&'%&() d+,+, /.M –

p-,%- 'G >%&'%&() d+,+,-

– /7E:05,7 &?>8,?,0(:J'0- 'G >%&'%&() d+,+,-

Q'7,8

•

MF' ?:&0 '>,%:J'0- G'% : >%&'%&() d+,+,_ – insert q (=, ,d+&E:8,0( 'G ,0d+,+, '>,%:J'0

– deleteMin q ,d+&E:8,0( 'G 7,d+,+, '>,%:J'0

•

Y:-&5 ?'7,8 'G : >%&'%&() d+,+,_



4&?>8, I?>8,?,0(:J'0-

•

M=,%, :%, -,E,%:8 ';E&'+- F:)- (' &?>8,?,0( :>%&'%&() d+,+,_ – L&0<,7 L&-(

• 0123 G'% &0-,%J'0- :( (=, G%'0(

• 0143 G'% (%:E,%-&01 (=, 8&-( (' 7,8,(, (=, ?&0&?+?

–

4'%(,7 L&0<,7 L&-(• 0143 G'% &0-,%J'0-

• 0123 G'% 7,8,J01 (=, ?&0&?+?

– Y&0:%) 4,:%5= M%,, [Y4M\



Y&0:%) 4,:%5= M%,, [Y4M\•

01567 43 G'% &0-,%J'0-• 01567 43 G'% 7,8,J01 (=, ?&0&?+?

• 9,>,:J01 7,8,J01 (=, ?&0&?+? F&88 =+%( (=, ;:8:05, 'G (=, (

Y&0:%) N,:>

•

/ ;&0:%) =,:> ['% O+-( =,:>\ &- : ;&0:%) (%,, (=:( &- 5'?>8,(,"•

/88 8,E,8- 'G (=, (%,, :%, G+88 ,H5,>( >'--&;8) G'% (=, ;'6'? 8,E,

F=&5= &- a88,7 G%'? 8,n (' %&1=("



Y&0:%) N,:>

•

3'05,>(+:88)U : =,:> &- : ;&0:%) (%,,"•

Y+( F, 5:0 &?>8,?,0( &( :- :0 :%%:)"

•

S'% :0) ,8,?,0( &0 :%%:) >'-&J'0 i_

–

L,n 5=&87 &- :( >'-&J'0 2i

–

9&1=( 5=&87 &- :( >'-&J'0 2i + 1 – $:%,0( &- :( >'-&J'0 ! "2/i



N,:>R]%7,% $%&'%&()

•

C, F:0( (' a07 (=, ?&0&?+? E:8+, [=&1=,-(>%&'%&()\ E,%) d+&5<8)"

• Q:<, (=, ?&0&?+? E:8+, :8F:)- :( (=, %''("

•

/>>8) (=&- %+8, :8-' (' %''(- 'G -+;(%,,-"

•

C,:<,% %+8, (=:0 G'% : ;&0:%) -,:%5= (%,,"

– c'( 0,5,--:%) (=:( E:8+,- &0 (=, 8,n -+;(%,, ;, 8,--



(=:0 (=, %''( E:8+, :07 E:8+,- &0 (=, %&1=( -+;(%,, ;1%,:(,% (=:0 (=, %''( E:8+,"

N,:>R]%7,% $%&'%&()

•

MF' 5'?>8,(, (%,,- ['08) (=, 8,n (%,, &- : =,:>



N,:> I0-,%J'0

•

I0-,%J'0 4(%:(,1) q $,%5'8:(, +>_ – 9,>,:(,78) 7' : =,:> &0-,%J'0 '0 (=, 8&-( 'G E:8+,-

– $,%5'8:(, +> (=, ='8, ,:5= J?, G%'? (=, ;'6'? 'G (=, =,:



I0-,%J01 @K

N,:> I0-,%J'0

•

$%'5,7+%, (' &0-,%( &0(' : ;&0:%) =,:>_



.,8,(, (=, Q&0&?+?

•

deleteMin 4(%:(,1) q $,%5'8:(, 7'F0_ – S&07&01 (=, ?&0&?+? &- ,:-)l (=, =:%7 >:%7 &- %,?'E&01 &("

– / ='8, &- 5%,:(,7 :( %''( F=,0 (=, ?&0&?+? &- %,?'E,7"

– 48&7, (=, -?:88,% 'G (=, ='8,^- 5=&87%,0 &0(' (=, ='8,"



.,8,(, (=, Q&0&?+?

•

Q,(='7 (' >,%G'%? deleteMin &0 : ;&0:%) =,:>



buildHeap

•

T:5= 7:-=,7 8&0, &0 (=, a1+%,- 5'%%,->'07- (' (F' 5'?>:%&-'0-7+%&01 : 5:88 (' percolateDown()_

– ]0, (' a07 (=, -?:88,% 5=&87"

– ]0, (' 5'?>:%, (=, -?:88,% 5=&87 (' (=, 0'7,"

•

S'% (=, ;'+07 'G (=, %+00&01 J?, 'G buildHeap()U F, ?+-(

;'+07 (=, 0+?;,% 'G 7:-=,7 8&0,-" –

T:5= 5:88 (' >,%5'8:(, 7'F0 : 0'7, 5:0 >'--&;8) 1' :88 (=, F:) 7'F0 (' (;'6'? 'G (=, =,:>"

• M=,%, 5'+87 ;, :- ?:0) 7:-=,7 8&0,- G%'? : 0'7, :- (=, =,&1=( 'G (=, 0'7,"

–

M=, ?:H&?+? 0+?;,% 'G 7:-=,7 8&0,- &- (=, -+? 'G (=, =,&1=(- 'G :88 (=,



0'7,- &0 (=, =,:>" – $%'E, (=:( (=&- -+? &- 014 ).

Y+&87&01 N,:>

•

4<,(5= 'G buildHeap



Y+&87&01 N,:>

•

I0&J:8 N,:> :07 :n,% percolateDown(7)



Y+&87&01 N,:>

•

percolateDown(6) :07 percolateDown(5)



Y+&87&01 N,:>

•




Y+&87&01 N,:>

•




9+00&01 M&?, G'% buildHea

•

;-"B*C S'% : >,%G,5( ;&0:%) (%,, 'G =,&1=( h 5'0(:&0&01 2h+1

– 1 0'7,-U (=, -+? 'G (=, =,&1=(- 'G (=, 0'7,- &-

2h+1 – 1 – (h+1)

–

M=,%, &- '0, 0'7, [(=, %''(\ :( =,&1=( hU A 0'7,- :( =,&1=( h-1U K 0'7,- :

=,&1=( h-2U :07 &0 1,0,%:8U 2i 0'7,- :( =,&1=( h-i"

)(20

ihS

h

i

i !="=

)1(2...)3(8)2(4)1(2 1!++!+!+!+=

hhhhh

h

[:\

Q+8J>8) ;'(= -&7,- ;) A_



)1(2...)3(16)2(8)1(422 h

hhhhS ++!

+!

+!

+=

hhhS 22...842

1++++++!=

!

)1()12( 1+!!=

+

hh

[;\

4+;(%:5( [;\ q [:\" c'(, (=:( 2h – 2(h-1) = 2U 4(h-1)-4(h-2) = 4U ,(5"

9+00&01 M&?, G'% buildHea

•

/ 5'?>8,(, (%,, &- 0'( 0,5,--:%&8) : >,%G,5( ;&0:%) (%,,U ;+( &(

5'0(:&0- ;,(F,,0 N = 2h :07 2h+1 0'7,-" M=,%,G'%,U S = O( N )"

•

/07 -' buildHeap() %+0- &0 0[4\ J?,"

)1()12( 1+!!=

+

hS h



/1,07: G'% L,5(+%, @W

•

Y''<RZ,,>&01 – /--&10?,0( rB :E:&8:;8, '0 3:0E:-

• $%&'%&() *+,+,- [N,:>-\ [3=:>(,% !\

–

L,n&-( =,:>-

–

4<,F N,:>-

– Y&0'?&:8 *+,+,-

WEEK #8LECTURE #1



34@K! .:(: 4(%+5(+%,- :07 /81'%&(=?-U 4>%&01 AV@WU X /01+- 2,+01U $="."

L,n&-( N,:>-

•

/ 8,n&-( =,:> &- : =,:> (=:( -+>>'%(- ,o5&,0(?,%1&01"

– / 0'7, &0-,%J'0 &0(' : 8,n&-( =,:> &- : ?,%1,% F&(=

'0,R0'7, (%,," –

/ 0'7, 7,8,J'0 'G (=, %''( ->8&(- : 8,n&-( (%,, &0(' (

(%,,- F=&5= :%, (=,0 ?,%1,7 ;:5< ('1,(=,%"

•

/ 8,n&-( =,:> (,07- (' ;, +0;:8:05,7"



c+88 $:(= L,01(=

•

c+88 >:(= 8,01(= npl ( X ) 'G :0) 0'7, X &- (=,8,01(= 'G (=, -='%(,-( >:(= G%'? X (' :0'7, (=:( =:- '08) V '% @ 5=&87"

– M=, npl 'G : 0'7, F&(= V '% @ 5=&87 &- V"

–

M=, npl (null) = -1"

• M=, 8,n&-( =,:> >%'>,%()_

– S'% ,E,%) 0'7, X U (=, npl (left child) ! npl (right child



c+88 $:(= L,01(=

•

c+88 >:(= 8,01(=- G'% (F' (%,,-l '08) (=, 8,n (%,&- 8,n&-("



L,n&-( N,:> Q,%1,%

•

M' ?,%1, (F' 8,n&-( =,:>- H 1 :07 H 2_ –

IG ,&(=,% =,:> &- ,?>()U %,(+%0 (=, '(=,% '0,"

–

](=,%F&-,U 5'?>:%, (=,&% %''(- :07 %,5+%-&E,

?,%1, (=, =,:> F&(= (=, 8:%1,% %''( F&(= (=,%&1=( -+;=,:> 'G (=, =,:> F&(= (=, -?:88,% %'

– Q:<, (=, 0,F =,:> (=, %&1=( 5=&87 'G (=,



'%&1&0:8 =,:> F&(= (=, -?:88,% %''("

–

4F:> (=, 8,n :07 %&1=( 5=&87%,0 &G 0,5,--:%)

(' ?:&0(:&0 (=, 8,n&-( >%'>,%()"

L,n&-( N,:> Q,%1,%

•

MF' 8,n&-( =,:>- N@ :07 NA"



L,n&-( N,:> Q,%1,%

•

9,-+8( 'G ?,%1&01 NA F&(= N@^- %&1=( -+;=,:>"



L,n&-( N,:> Q,%1,%

•

9,-+8( 'G ?,%1&01 NA F&(= N@^- %&1=( -+;=,:>"



L,n&-( N,:> Q,%1,%

•

9,-+8( 'G :6:5=&01 8,n&-( =,:> 'G >%,E&'+- a1+%:- N@^- %&1=( 5=&87"



L,n&-( N,:> Q,%1,%

•

9,-+8( 'G -F:>>&01 5=&87%,0 'G N@^- %''("



L,n&-( N,:> Q,%1,%

•

9,-+8( 'G ?,%1&01 %&1=( >:(=- 'G N@ :07 NA"



I?>8,?,0(:J'0 'G L,n&-( N,:

•

/0 &0-,%J'0 'G : 0,F E:8+, &- : ?,%1,% F&(= :-&018, 0'7,"



I?>8,?,0(:J'0 'G L,n&-( N,:

•

/ 7,8,J'0 ['G (=, %''(\ ->8&(- (=, =,:> &0(' (F'>:%(- F=&5= :%, (=,0 ?,%1,7 ;:5< ('1,(=,%"



I?>8,?,0(:J'0 'G L,n&-( N,:

•

.%&E&01 %'+J0,- G'% ?,%1&01 8,n&-( =,:>-



I?>8,?,0(:J'0 'G L,n&-( N,:

•

/5(+:8 %'+J0, (' ?,%1, 8,n&-( =,:>-



4<,F N,:>-

•

4<,F N,:>-_ – 4,8GR:7O+-J01 E,%-&'0 'G : 8,n&-( =,:>

– 4&?>8, (' &?>8,?,0(

–

/%, ;&0:%) (%,,- F&(= =,:> '%7,% ;+( F&(='+( -(%+5(+%:8

5'0-(%:&0( '0 (=,-, (%,,-

– p08&<, L,n&-( N,:>-U 4<,F N,:>- :8F:)-

• 3'0(:&0 0' c$L &0G'%?:J'0 'G :0) 0'7,

•

$,%G'%? +05'07&J'0:8 -F:>

– L,n&-( =,:>-_ F&88 5=,5< (' -,, F=,(=,% (=, 8,n :07 %&1=( 5=&87%,0 -:J-G



L,n&-( =,:>-_ F&88 5=,5< (' -,, F=,(=,% (=, 8,n :07 %&1=( 5=&87%,0 -:J-G8,n&-( =,:> -(%+5(+%, >%'>,%() :07 -F:> (=,? &G (=,) 7' 0'("

– 4<,F N,:>-_ '0, ,H5,>J'0 q (=, 8:%1,-( 'G :88 (=, 0'7,- '0 (=, %&1=( >:

7',- 0'( =:-E, &(- 5=&87%,0 -F:>>,7"

4<,F N,:>-

•

MF' -<,F =,:>- N@ :07 NA_



4<,F N,:>-

•

9,-+8( 'G ?,%1&01 NA F&(= N@^- %&1=( -+;=,:>



4<,F N,:>-

•

9,-+8( 'G ?,%1&01 -<,F =,:>- N@ :07 NA



Y&0'?&:8 *+,+,-

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WEEK #10LECTURE #2



0$>JK *717 $1&,21,&/- 7(4 +5)%&<1:=-V $;&<() ?W>XV Y +(),- ./,()V D:"*"

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WEEK #11

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0$>JK *717 $1&,21,&/- 7(4 +5)%&<1:=-V $;&<() ?W>XV Y +(),- ./,()V D:"*"

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WEEK #11

LECTURE #2



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WEEK #12

LECTURE #2



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Documents

CS 146: Data Structures and Algorithms Slides