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5VI Semester B.Tech. (Information Technology) IT-352, Analysis & Design of Algorithms

Sessional

Theory

LT 4T

Duration

10c

Unit-l: Introduction: 4lggtitlon,

&ay4ry

alggrith{rr-peslgrlgf algorithm, Concept

effrciency, Run time ananysis of slgorithmj' Asymptgtrc

of

algorithmic

ltollttglu

quick Divide and' conquerl structure of divide and conquer algorithms: examples; Binary searoh, relatlons. strasscn lvtultiplicatiorrl Analysis of divide and coirquer run time recunence

^sort.

. . 1.,., - nl:

r' I ' t

JJ?'':t itro' r-igl: '{lhstl/"" tt;'|$rn' gtJrufl

unit-2:

solution Greedy Methodl Overview of the greedy pararfigfi\ _ examples of exact ôptimization shortest (minimum cost spanning tree), Approiimate iolutign (Knapsack problem), single-source paths.

and divide and Dynamic programming: Overview, difference between dynamic programming in3le|esman Problem' conquer, Appiicatioris: Slio;iest path in graph, Matrix multiplication, Travel longest

Co1ry

sequence.

Unit-3:

Bnck trocking: Overview, 8-queen problem, and Knap-sack problem Brach and bound: LC t"*"ttini no*iing, FIFb branch and bound' application: 0/l Knapsack problem, Traveling Salesman Problem

LC branch and bcund

Unit-4:

breadth fi'st search) Graph seercbing and Traversal: overview, Traversal methods (depth first anrj Search Ttee, in Binary I'rees: Review of tres, Binary search tree, T.raversal, lnsertion & Deletion 6]Trees, B+Trees, Basic operations on B trees

time complexity; computational comptexify: complexity nreasures, Polynomial Vs non-pol;rnomial NP-hard and NP-complete classes, examples'

&,v

%frr

f*",

7 \

\

t'\

\--

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gfu*' .,

(r)

-qt

Text Book:

F;llltJHF

S. Sahni, and S. Rajsekan, ..Funadnrental

of Compurer Alsorirhms,.,calsotia

Reference Boola:

l. 2

T. H. Cormen, t eiserson . Rivest and stein, ,,lntoduction ofCompurer dlgorithm,_ pHI Sara Baf,se, A. V. Gelder, ', Computer Algorithms,,,AJai.on

wlf.y

Note: Eisir queslions wilt be ser il_alllrl€€xani,,.., ot ing qu"rrionffilri".t srudenb will be required to anempt . unir. five questions in all, />el7i:f * A;i*,;; _-r_T ^ _ a . 14\h.u e'* tftrv\ Qâ,.^ t+.v':t.

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fuu,itftizift g,e'l'

-tl

Ii,4J -''-"42 ur"fa.uo & .toi*1, oT I

t) -= 1t duua! . ,, )n r- uhlt't ",,1""1i-l' a,)a-z<, - n 4,at lo AL teilu^ld &, "4 fu Q- t' , at) r- -' qn-, , n) , it tul'ttr-tt 9) n) qt - H,t ztAfii+ fu AQ- rtal&ld Lt (fuVrtt

Qj

tqj+t

Q1

klAri/et lt ( "t' I' t aTtt - - - -', at,n) V -' | (nt) lz1

,ketd ,2-4P'- oP &h attg ---------7 J t t,)

Bi,ottT ,fuor,/)

*[flLw)'lhn

ht

Auuivt s) 1twrtw

ls/.,rJu;w

&"orl

&ar,Lh

r,' Atauthn &ntqrh ( o, i,.{1:r)

2'll Giwn o^ ,"*f afi,lJ of
4,/

3'

q,

iC ( a --atLJNt', *tfuuln dle knla,rrr O r'

"t;

tb' 4

,,.

h"

s'hlkelknno!* r / ^tl#t')o ry ! rt PtfutL ,s." = Lci+Dlz) ^jd: ,tt . ;f ( n Yofutx, nu'cl i r. ttn fn;d1 ) ]s eh< .if= (t- L.a yruaJ) b,'an H. tafulao 8'}^9A ( q, t' , nid - t 1 r); tt. elte- wtutn $ingtc1, ( a, ,rrtd+t , ! t{,, tg,t n'J a

/.tetu^-t-

.

---',Q7,_t

l, ;l

&atuA,

t&xnl)rc-

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---->t

-

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I

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5.

I

g.

I

6. bu t =l; ilXh :=n; r. uttib (b, e qh) #

1. n'4 :'= L' (,ttu) + ffi)/21,, ' iF (r'z qtna) i"t- &#l: =rwd- 1; ,.,-' Ut!, (t> alîa1) V*n' JeD= rid + | re

t2, ebe x.tharn *,d;

'

tr.

I tlIê

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t1.

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B

(x,i)

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o

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>g s + + bu$ulin1Tr'rv-

v-

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-r/ t | (")=

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=

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ol

| ^*f"*,; a.r4_ _

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^tilJdPj

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w

cl,u/r'nz

n€to 7 aahjx

= 1 A,, v Arr) ( l5n * B,' Ar:= (4r,+ Ar) 0,,

)

M, :

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:,

tt turt h exlewz fra Cii u4- e.Lininah av' ushix *"Lai"l;"

wilct

M ol r"t* ' a;t4 no' b He wdtt^tt 'V

in ;Ltltn't

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Mr

I

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* M4

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M,

+ M\AWPL^^@h P

/t |

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*

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4

ttt *
1/,,. '4- tb" co"dt-/

}torAr K 2 ur-hq -itq p.,..lt cfu&b"J Yr\rln ^\.xlf .I it^'to{h. ,r.r^r.4- q,' i 1l-# ,r-'-+o| rlo.Bboat'd q ffi^ util^ itour ua- roMo t! Flare tlexi rAh

*;'ffi *'m ll -n

:"^,,1" qrtqrJ4 *.:; $,or'I ^T:,I"# ac$n ,.l. r."- ic- f-lgtt a dtrrtruru b}' Joirrur.lt-i- n T{rrad '-Pt-, trilr^ ii^^^ r.n h*r.r-. ^

! ql r , tffli

**:Hfr,ru -,ffi ffi. Effi

,s.ryr

z

Eiperience (From dale to date)

Oesillnation

Organisation with address

=

List of Publicatlons (Attacfi separafe steet

Mode ofobtaining lhe

Form

il required)

Dq{'/nloaded

From Bank Bank Draft No.

n

I

Date:

Orawnon:

Have you ever studied and discontinued your studies at llT Delhi

?

lf YES, give Entry number

and the particulars of lhe programme earlier

YES

!

NO

n

attended and the reason for discontinuation.

(Signature of the Candidate)

Date FOR DEPA RT M

EN

T/CEIVIRE'S USE

FOR P.G. SECTION USE ONLY (Recommendations/observations of the office) The candidate may be provisionally admitted.lnot admitted subiect to the following : 1)

Submrssion of attested copies of the qualitying degree certificab and marks sheet showing the rcquircd y" of marks/CGPA by 22.7.20101 31.10.2010. Submission of proof from the u nlverstty/Head ol the lnstitution of having appeared/passed ;n the quatifying Degree Examination by 22.7.2010. Submission of GATE Score Cad/CSINNEr awad letter (in origina,) by 22.7.2010.

4)

Submission of relieving cettificate ftom Employer by 22,7,2010,

DR|AR (P6S&R)

Signature of OS (PGSER)

Tev,d*byy flr.yucfi'y 7' en

.

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oTl' ,t- ,Qb@-94* ri

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fr ,"oa t7 l?,y::- a: o

rea/o'aw f JA^r Trez "T-

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e/ ,to^txi*lr Itu! uL Q W A t, trAhul Ju'trAnj eel'tt rt; It bkt Pl -6al . u"lt i'ffi* -I

va'1"2t

al*' ttl' hn non -ttre "'o"I *'! ^+ au 3l t ot );'t- d, o '^

t! hAfu' t'n il" e/ pl'phttu''^t-aoJ /tu.p)n + tul^s * ' ir Dhtuitu 'ry la'] tt'ifuionn toathn ,f^"' f' :eg. ila )4r11fu' 'h) oil)^ ofl@l &ur+ tt" fl^l )n Uhtil ni

ii

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t"")'--

a

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t<'a|x'"u

i

$ar*hM*uAt Esilahaul&'^4

tyu*

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& q M!*hodrca-l alolilonl .q,rid u/a ?t'd i*' u'011

'A bl-

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I

ole"lQ-J

:

-> ? ,...-..*l =?

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l

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t) 9P N .ir a

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.

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d. uq.e

q'

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t{rl

u

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w\DuF

hr-lrt,t

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uoi'th

cov"Lbqttn.h

e--ggg.' pagtlq ,ylavrnQl rylavrnQr ov\ ov\ ov\ serh celaJ{

N-lp'oan

ro$.r4-

4{'t Sddllt-l

a 4a

'

.{."rliln; 34 *dthin a Cor^t'f"{+ A} o|

;y&*\ 'i4,L i'l 1'l* 'b h'*ti"*

-0" rr,xvr #fu.,:r on rr'Xvr h*,"ryLffi t@ 1,.

T^

io.l-uu"'',n

"ttqfia"a0

hffi*,':"^,^"^ _#ry.^ @'^# ,Da,nt ^ry * TTi 0r 'n"-;*ffi" o+

trt ""si fi"r*K'*,Î| tr

*,*rrr"rl

.{+,* o**

fro^ "r4pxt0+

."J*:* #o1JT***l ?11{:*Y tu'- !arvr.- *tl-drT" ugT ;T,!:,:jl::

f,

to

ffi ru, ffi';:1vut""

[nfrr,o.re^{ dt6ttt ovr sq tluâ dEo"q{ -tt^4d W Attt" {n.upp* 9,ln^t to*l .n^,tl tsf+ 'f0' {+o Jart{u J{orD + LoL.;"., vqJur- oy i" t"., Utf"- .r 1paru n lctr^d ql I i, i ) L (r, t) . n^{' xq o}'t Dv\ l*r -eqma- .h{b*o{ i I ,i-'i 9 r'- t o{ o'r i+i = +*1 ' r<,-.i

rrtett

,',{oo

? j-r: i-1--t

lr on 7,g-t

Jqryu-

5= Ia; = -- [ i-r'\

dlrd'"!'{ rd

(-tl

prui i,., Eurourt u _bj-llr^ *^ s) lpuRonnn Urq l+lx' rl'l u ,) Eilo,.r{1'n

i{

q

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;lffi

6> l,

+)

s> q)

h^ i:=11att-l i4

ir'$= o^r ( *u,'),:1,\l'ri= {{-L$ 1.6 rcb'a^ <t;

r+

'u') 1e)

dD

'pdbun $

thl.

J4rrn4'

tn-!rrt"''^ ' ,

b"(J-8)) /lot'"

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trtra-}

), -,

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n fa*,Uw

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nuwAttt

h

A.o-w

ilj

z*

7.i

l+r'1n

4

tn

2

lej

Pi d'; 1n

tl

P'*h

âka& ,ttU, tttt nO,t',-io
3 /r/"rt7 P"'

-

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nb Pin d b|lt L>

PoAlh-

toAia&' klb t-{|4'att n&.t /i"u-' tN

e.* b1/'bn- oJ&i n"hlt +Pt oF Aa -93r

bt-/ /l7hlurnu d'\ 'l+^ *l- Z at ls''!

-"7 "nW'J *

ilqtn+n M $,t-A (.p,*rA) ,. tttf u uttu4sl-f fu4.;f hbî , ArD, u *4 1- lt A a uaoi rcn-,^d ;fuA ' Ir

{,

lf ,n

t-

L

6.

a=

+Q. q' t! ' n. t2-

l9' l||.

uL

:1,/

b bt J8'

n

4 ,, t_=ctDl

lo' )=-P-tt $ nolo

t

c-'

c-+ u

[lJ

b" P/il; ,, d)e t1eb.,t1^ bt I t - (c-^) / ,l';])* I tl (c z^)

-ta,hto. / J'

b

i

't'i,-tn bt--

Pl'J

i

c-'4t--i -'/'

rofs!

OUTPUT Enter the no. of processes but less than 10

t

Enter the size of each process Enter 1th process size 24 Enter 2th process size 56 Enter 3th process size . 14 Enter 4th process size 76 Enter sth process size 38 Enter the no. of memory blocks but less than 20 7 enter the size of each memorv.block Enter 1th memory block size 10 Enter 2th memory block size 30 Enter 3th memory block size 40 Enter 4th memory block size 60 Enter sth memory block size 80 Enter 6th memory block 50 Enter 7th memory 20

\f Process 2 Process 3 Process 4 Process 5

of size 56 assigned of size 14 assigned of size 76 assigned of size 38 assigned

to to to to

memory memory memory memory

4 of size 60 3 of size 40 5 of size 80 8 of size 50

fV-t/

\|/

we fu${g

d;

4'L',

2

\o

tttlay r"=l I L- lti , b=th i,2=9, b=lo'

dl,ttl

-r'=2,L=dtD/9J

:, L= Itt

5

30

5o \D

ir[+4t6)*n

Lo

5 lt 1tt,

=].b=6+PltJ = lot go =7o '

)--?, Ln e+ a/s) = ltlo 1? ;{

[+t

tr)

i* /t - (r- d/u/'Dv E , 7>+(t' (e-tl/rc) + ro .,. ?o+(t_+)*.fo

hottun

?o+ i ,?{ la

t, 4lilatuttw Unnlo 1 v, r"p,

=16+vf=-/)!

tL)

{dh

bz<, aP 1tt *ufiaA, n d r/a- ,a' ol 4P 3' n pl1 l a[/ at<"- p"Prt 4 ,-'4t^fu . 't' )t il,Jlol;J | fl)'l/a/;rtl , ra )t tu e'""! *"'/U aF A-t/r"^rA ' t' tt W .t At' A^"-l' t^tu-u-r,t ftoW' u[rJ. p ;1 -/rJ
2'

)"t

mA

1

hl+ dilU' j, ?;C (q, +,'rLx) z a)

tl

"'/ s,

g?^4tefu

lo, / rt

.

t2. ,3,

gfrf,= t iP [t,z^) ilu1 BR*ib tL L( cp+plttJ , (f)'

ttt'.= cp + p[,.J .,

t{.

t5.

tt' t?'

)t' t1

,

Lt, t-2 .

2\'

5

'

(*rt , 4+ Pf,*J t'n' d (t '- n)) ttu-' Pu : - ! I

ful i=trox ti ^Lil t:

i q,** ,iN tt"il

r,', frJ

s/i''l)

I

e

2s'

L3'

t+v"

;F ( Bo,,.A' 7 ctt Ld,t {>. fP) t*-' t ^r(F.^ )t *tu \K"^h (r+r, zhc-)) ir Jf*J'D,' i[ tf rr'rPp) a,d @= n)) vt^t-

t

+

aLdL'

?+tP+v

EXPERIMENTNO.2 Program for best

lit allocation

method.

€

#include #include void mainQ

tfot5o

t

int temp,processI I 0],memoryt20l,ii,n,m,min,minimum=500; clrscr0; print("Enter the no. of processes but less than 10\n"); scanf("%od",&n); print("Enter the size of each process\n");

|{

otsot

+Y:tF

q

'- 1?

fo(i=0;i
Qo\e4Yrtr2 9".

fo(i=0;i
print("enter Todth memory block size\n"'i+l ); scan("70d",&memory [i]); )

fo(i--0;i
for(=0j
if(memorylil !:0) {

if(memory[i]<=ninimum&&memory[j ]>=processIi]) { temFmemoryLil; minimum=menoryli]; min=j;

t ) )

memory[min]=0;

print('\nproiess

%od

of

size %d is assigned to memory %od

",i+ l,process[i],min+ l,temP);

) gerchO;

)

of sizeVod

3.

b' "lP--Lil; faD=rN; 26. fov i= t to p )o tf jJ= Vtjl'' { 27-

%'t

\

qd; w

t

,__!9 4"

,X,J

(- |

ct ) '- Z,i',' ut;Jfu t tt 4 tP = E,^- t tL-

|

rrfl

(us'

^

bE

flJ ![iJ

'

.:r 1

15'

5=

Ea lp, lo.j, 5r .,L.

(\or2

,'f"hf) lb*"

(3 ,

&,,i

$ALtr ,!hb '&hett^ *rcJut ?fu,A*h 8 '^'l' 4/'t'b'1'^ ol { "on/e' a*- i""tt*/d o €-"tal"' Jt/t^"( A!'/, An e-far- ry o{A'o''t ôd; b (u) "x/e' ssr *?i *.,tsr e (') fa' o*â.-,? ft /"^'nn n .* E @X!rr,rj, ,rarpr tlê boli! t1tudrJ ,!,ve ''li' t''/o'' t'aot^ €-'ado^''''[]l'1n/

,il-G'l

@---''o*

q *i' * 'fu,6 *q

";'

-^,

*t?t lF ,re t{ 'Ntl /r nX i'n l^0^

t'otlu 3o

'a !'emt *a"t"

Zo 'z;'Q bt^L '/J'4 Wfu ""t/t tt&, AA "ab'l)/ '/'t'o U""a noJ-e't u:Ll! ntz'ztr u'zlt^t"''{ et' ffa p - noc'h- /ol&a êl: 9o ltutlb * *" a/a'^+'"on oL lue^le-

OUTPUT processes 10 than but less Enter the no. of 5

Enter the size of each Process Enter 1th process size 18 Enter 2th process size 23 Enter 3th process size

.

31

Enter 4th process size 45 Enter Sth process size 59 Enter the no. of memory blocks but less than 20 7

Enter the size of each memory block enter 1th memory block size 10 enter 2th memory block size 20 enter 3th memory block size 30 enter 4th memory block size 40 enter sth memory block size 7o enter 6th memory block size 50 enter 7th memory block size tru 2 ot size 2Q process 1 of size 18 is assigned to memory 3 of size 30 process 2 of size 23 is process 3 of size 31 is to memory 4 of size 40 process 4 of size 45 ned to memory 6 of size 50 process 5 of size 59 is assigned to memory 7 of size 60

I

lcl,oa.( .//

,uoq h ttt*'"

cat"fu

arat// b

.o

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EXPERIMENT NO.3 Program for first fit allocation method. #include #include void main0

i

int temp,processI I 0].memory[20],i j,h,m; clrscr0; printf("Enter the no. of processes but less than l0\n"): scanf("%d",&n); printf("Enter the size of each process\n");

for(i:0;i
printf("Enter %dth process size\n".i+ 1 ); scanf( "%d",&process Ii] ); J

printf("Enter the no. of memory blocks but less than 20\n"); scanf("%d",&m); printf("enter the size of each memory block\n")l for(i=0;i
for(i=0;i
for(:0j
if(memory[jl !=0) {

if(processIi] <:memory [ ] ) {

tenp=memory[i]; memory[j]:0; break; ) ) )

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OUTPUT:

Enter the no. of process for first come first serve Enter the processes A R

Enter the burst time of processes Process lAl6 Process IB]4 Process [C]7

Start and finish time of process A is 0 and 8 Start and finish time of process B is 8 and

1.2

Start and finish time of process C is 12 and 19

Turn around time of process A is 8 Turn around time of process B is 12 Turn around time of orocess C is i.9 The average turn around

13.000000

Waiting time of process A is 0 Waiting time of process B is 8 Waiting time of process C is 12 The average waiting time is 6.000000 The average response time is 5.000000

v J/.

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printf("\nWaiting time of process %c is %d ",processlil,startlil); )

avg=count/n

printf("\nThe average waiting tirre is %f",avg); printf("\nThe average response time is %f",avg); getch0; )

// \

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fo(i=1;i<=n;i++) {

printf("Start and finish time of process %c is %d and %d\n",processlil,startlil,finishlil)j )

for(i=1;i<=n;i++) {

count:count+finish Ii];

printf("\nTurn around time

rocess %c is 96,d",processIi],finish Ii]);

avg=(flcatlcount/n; printf("\nThe average turn around time is %fln",avg); count=0;

for(i=1;i<=n;i++) {

count=count+startIi];

dt44

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I lProgram for first-come first-serve scheduling.//

#include

fincludecconio.h> void main()

{ int burst[10],i,n,m=0,start[10],finish[10],count=0; float avg=Q; char proCess[10];

printf("Enter the no, of process for first come first serve\t"); scanf("%d",&n); printf("Enter the processes\t"); for(i=1;i<=n;i++) {

fflush(stdin); sca

nf("%c",&processIi]);

)

a

printf("Enter the burst time of processes\n"); for(i=1;i<=n;i++) {

printf("Process [/oc]",processIil); scanf("96d",&burstIi] ];

for(i=1;i<=n;i++)

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DAA Notes

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