20
PR.AM LECTURE' .y A",.. MAH6SHWA RI . SAS/G T £CHNI'i tiE S . Po IN 7'"" JGJM PIN r; . OI~'O' AN]) CON~UER- . P. ",.,'+;'0",." , . Pil'e./,',,;,,! . Ace-e.'er.',' CQSC.qdJP'aJ . SYMMETRY 8REAkl~~. .~. f.', " " ... ".", t). , ., "I ~ ,

PR - Carleton Universitypeople.scs.carleton.ca/~maheshwa/courses/4009COMP/MyNotes/PRAM... · 8fjij..oin6, a ba 1-anc.~d bin .f()! tree on the i.npli t :£ j..e m&nt.j ~nd tr.a vel(

Embed Size (px)

Citation preview

PR.AM LECTURE'.y

A",.. MAH6SHWARI

. SAS/G T £CHNI'i tiE S

. Po IN 7'"" JGJM PIN r;

. OI~'O' AN]) CON~UER-

. P. ",.,'+;'0",.",. Pil'e./,',,;,,!

. Ace-e.'er.',' CQSC.qdJP'aJ

. SYMMETRY 8REAkl~~.

.~.f.',"

" ... ".", t)., ., "I ~,

MOO£L OF CDMPtJTATIDN

. .HHt re ~ 14 f, tf?V 'f'.J / 4 lobfA! M~ m_"~ PrDt-e ssor$ ,;ct

Sy "(,1,.,, (j~(;U.t.

SHAREb

"'TPI/r.. S= J:. A r l J.

f

~IN: ~-~. etL08AL. ~EAl>(AC"~ aJ;

1. ~L06AL.~A'TE (4) 8C,:1);

J.IDt'" h : = i IT I.'JI'I «0

';', (i ~ !!.)

. ~tr)\ ~'- !'- ..,

beJJf)~

t-9 k, .!-- '/' ~~ l .. -:': . #.q-t." I ., , ... '10 -0. \.

. ", . :A. 'v.'A'. , . ... ' 'f"~,' '\ :IJ'. ",..,..." ~.~ " ~., t... ." hi -!I .' /

' 'i:#,. , 1:, : -#~~ ;~ - -.-f

'~ } . .! .~.~,,~ . ' ':,': f',. :. r;"

1...

I. ~ 4

PRAMs

runorts algorH"W\ie,Je~tJAils ConCfrnit'\~ i

"rte~YO t) i2QJ,'OY'IM$ to It!..,m iUI"'o"

.:.'.

pc", ) pro ce.s.s0 \'""5 ~ n ~ Ten)

o ( TCn) PC"'V p) ~mt. ~QV"' t>,.,...y .

Y'~Mbt'" r ~ P!~J p'roc.e.ssot.t

(c(~.)

) t ' (\ oft

o -p T T( n ).: 4""~-t..r fA.Y\y no. ""r

al'm ,

,"~

.

e~ ch f$ ~.~ dJ h~. ( ") ~ (r;;t. nA 1-0"'01) $

-W. ~ r Wi'I'I) 7PP"rtA lit! .rl-,,? ~J' !-j..ii:. P- f11lft.W,r.

~~.

;,;::,

~. (~.,. .;:1

. r.I,.~.,~...!~:;~;o',e ~ l

.D \ ~-~"..~- \.

+0 1.),.:-.......

jt~..1

<:........ T

.' \,.4... ." ./ ,' ,~ . t .'.

,- ..,-.. q" "{) .1'1 ' .,'" .1I" J! . ... 10,1 it ~'- :

;L- ~':'.. i.. '..

* ~O~~IIAJh'~~ W~{I\~

~ a 11 OeQ!-ion ~ fQ.~k~,

ft) «,~!-"h ~..f.~ (A4.\ttV.

. .PT' MAL'TY NOTION.

8fJIJ..OIN6, A BA 1-ANC.~D BIN .f()! TReE ON

THE I.NPlI T :£ J..E M&NT.j ~ND TR.A VEl( SIN,

'-H E rP.E E' PO~H;r"J:J AN D J.5A,x./NM(J) 1~ itN'/;!

~ R'~J rH&' k.O!lT..1#

1rorn 01 ser-

,1~

$CAW\ S

.I!: ~~n.

O(n)

'. Tt n= 1.. I-hc.,., s1:::' %.1 j STOP;.

. ,/-0ye 1 S A, ~!2 el ()2-

fj-i : =- 'Xl.~:--j,.* ')(2 i ;

, Re CIAr.s" ve,ly CDrn reA I-e." fN-, P'(!f i'J(

SlAmS of {91.1 !ll-~ -.. 8.J ~PlI.J,.5 ~

. fDr i = 1. -1-0 tr) Dl 0.{

'. eve,n", 0:: 1-

l ()~ ,A~i.

: 3(,:::. Z<e:/2.;. S 0_"".,.r 1 8- ~ ~. IV .S . . - ~ ... ".8

. . 0 - C.-I) "V-.a..

-

£R.£/N- PRAM I." n..,. I AAA. I ~ .'- ..- "",.n

rf caIlotAS fhc 1-asJ- p,.occs.si",.!J tp oI-reJI .31-0red.

in f""-L ~ rlfn .fJ. CA .se-I- er; ,.ool-c 0( - «.J.rc c I-c «frt£J".

'11." A rrlJ\Y pC'.. 9'1] .$14cA J.Ju/Jt1-

Pl4:] =J ~ CiJ j) i6 ~n

f* f.' A r r lAY s r. ,- - '"] ~fA e,1t f h elf I- S Lj J uIht 'rOD r cS) 1-#1~ fT~e. C,.on"~;"j".J J .

",t;t.2,rif/tJ.. A i90 ri """m :

reA lIe.' A'3 0 rl rh r(")

Oen) elf s.

s [,0] =t= S [.s C(.3J olo

se,. J: :. .s l s C(- J ] ;

or-un: ~i ytn 01 'fo~sl- DJ rook-cl dirtc.l-eJ."'I~L. J, ~ klA. nf Inn ~") ~i WIt. 'tA.~i" l\

OIHEM: po/{ £'ACH 'J C.OWlflA~ f-N.- .$£tm .p..

N ""JJ..J-.> .sI-, rt, rJ. ,,, -fN ", 0 tJl ~~ 0'" +-h f!.,

pO r~ ~ rfJrn rt\t.. n{) lilt., t fo rN. ro D J-

~ i, '.s hUe

FD~ se ,:1 ::. Pt.". 1;

JJh ,.'L .s l f:J :F S I se.".]] IJl0

{WCi]:: W[c.}+ Wc.st.".]];s t..:J: = S (.s [iJJ

'/ DE AND CONafJ£~

"

7k 'f..ir.sl- .srcp I's fo por/-l,..,°ern ~

il'\p~" ;1'\ fo ..5evl rA I }>eAr}-,/-,.oY1S elf "/""ASr

VJ lAf)t I si 2.e..6.11w. ~I'\o( .s}c~ l~ 10 ~o/"e ~UAK&;ve!y"

~ JlAbpY't:J bIt M. ,(e-,/,.~J lP, f2At..~

ptJA.Y"!-.' H,,, ., . fNo - j", r",j-.

rh.L f:kire( sl-u= t6 .ItJ 'W7erJ~ ~

$olu "'cm 'I- ""' H,Yl nl- S".., prohkm s. #,

.

..

,. *.. -, -,. -, ,, ,.,(,

"'....

,~~

~I

I

L.oWefl HULL-

I&\,tmpl-,on: " t\",W'~r5 ~~ b~ SOT'~,e~ f""

OC.\O<jV\) ~iW' e. CAS'~3 O(n~h) Work. .

6ty\

ns~U H <-S1V 1,2..) .

.

\ (

.r/-i f-'.onin9I,b~ laki ""J ""P IN. .!I"~" I'r"hJ~ Ir\ ;,..1-0

;,., .I.~l>e"'Afll)l- $tA.~rrDblems 'almosl-~fAt'AI SlZu, fAn tJ rh" n .so/v i"!,J ""'" t:'

'A 'I rfJblf.WI.$ C,t:JI'Ic. lA rrc1)Hy ~ """'~~... ". IN.. 11t-c M hI Y 0) prfJ U SStJ rs 1,.

"

J(aW)I'I~: Mer9';,.9 -IIND Sf:)rJ-~~A ~"..c 8.

;, WoR.~ 1.5 ~E42(J/~£/) rHjJ

'/HE CHPIJT.

'AATI TIONIN4j

J LNPtJT

FUNCTION: RANK(Z: A).

'141<..(x.: A us) = Rank. (x:A)+ ~nl((x.: 8).p

fit: ~ CoMUT£ RANK. (B: lA). AnrJ.A n

\lAIty SEA~CHII' OCtQ)"] f/mt" 1A'i"J a{i1/"9n)HIJRJc.

,

TIHA.L MeA6IN' A.-Lfi,fJR.I TH~

~ -

~ ,- ".

T~P j = Ronk b, ""1") ;Y'\ A by tA$i"9

a'NARY .sEA RC",

rE P 2 '. O&TA)N PA~T'TIDNS (Ai.. Si ).

,CDLE .$

REPLIC~ TIN~

""T: AN A~R"Y DF SiZE O(/ognJ.

.

.

,,,,, EItErl,.

5 B

)U

PI) T: )( = {X, ~"~ ~ .. .. - .~ X" ~ groWl -- /lnt! fA ~/'1

o r~ se,'" $. (~c: E S)

1PV1: MAXI MVM X.

~!)~, THM i: oc 1) -4-'Me. CA5;'':9 O(,,~.> wo rk: .CReW.

~OI(I THCVt ~: O('09nJ +imt. \A"Y'\j 0(") WO~.SASw.

: 0 C I. ~ I.jY't) HW( '-'"''3 0 <.."\'.s\~,,) w~

DOU B LY L C7t4A R.. T'" M'C.'-T I M If' A LIt.,UT"I1

I(~

"'Co.2 ..;!("'9

;2.&~....

~10

-, ~~

i ~I"T 3:,

:'~

t: 2. Q.;.

,

1\

\\

. ,1\.\.

, .10~ ~..: ~. .- ",",..".~ ',-'.-r r.. '.; t - l( . ~.., , .. ..

. . .......2.-2-

L"" \c ~c, I :: 2-

le.'I( ... ,c .,cA :. 2. 2. ::: ~

.3-

'( h) -:: QC '0.9)"9 n)

.J(n) = ?

.,

S71 L L

r -..... ~.-- ~~--"""J ;

L f) j,.J

brA1-

IfL ff:)A1rH~

0/='6(/ MAL.

FA,ST AI-- GJoA /TH~'lA 1- NDN- OPTJ~A 1.

e>(/ogID9,,) l-iW\L(;(,.,.,'"It)~o~t -

I-ar" wil-h I-A.c, 01' J-;w.Ai c.(j l)r;""~ "'-,/

J.hc sfU-'. H..c. pro hI~,... id.

re JM CM:1 -Fo fA Gt* Y"'J.()u.Y' f~ ~~D It{

flv.. ItA' 1 110 n or J-,;.,.~I.

A~, N ~".,." .

J£ I: Bi".,y Ir4A., AIJori~M

rl_~/.J/.,"7It",,/s.

N, , 'J eltM,,,1i r'MAiAi"1 =

SE D..: A P~'Y fkt

\ . ~(

+C(S f-

t)ot1-opH

.. , .fIt ..

5Jow

oP k~)

/ \\\ \ \

,"1\l .

, i j",

. r; ,. ''''1 I .~~.~ ." ..: .'

.. \, ""

.\. \".. '.

/ j. !'~. .i." '"

\\ /\ \, \

\

\ .",

T ('I\)-=.D( ("j f"11.'1~...-

~ r~.' =- ,C:( ~V..,

:...., oe

CRe ~ P~AM OCn) ,.".()'~.

CRE t\J .PII.~ - "OU.,~) .I-.'~.'1 ,~,~ Of,,, ",.,f'!..r. ( - -' ~ 'lit' -.-:1*'-,.0,J', . I[ ~,-

~

~ CiA I C'lSe :

"

FA~TA Lt)O i' T"''1

,,-I '\

. / ,

->~ I~ -1'.9,.,., 1.,1.9~

I

)~~,~~~ Alg,l) r ~ ~~ .

"

- - .. -

. . ''/,. ,4" n~ VQ\~t~.

'.,10'"

/