ai = Shp ty she ponds tha ony pele.
ial octthon c Ruadonde
tt peste iY nyt to d ae he.
i et ony problem - Ciccats & domi Aa,
ate Dusenthe the fopte 4 ies ote ee +o templet the
the po aay
Beaute pe Me beth natavad preg
3 TRdkpen dunt 4 ry 55 ate Sent Independent -
' Surn 4 +ewo no-(s)-
4. Stout 1. Begin
a. Toxo No, od toput- a. Input My ne.
3B. Sums NTN. i
3, Add e no.
4 Oudpub sum cal
4, Dtspl
6. a. sig. end Chennelautien 4 “Alp:
a, Tnput '- O ov More
a. Oudpt i atteast
wm Detfrihenu 1 chon &
ae aus = ate shoes
i halt be bate snegh te pores usta
5 Chfeeto jens’ tops Show
available wouter
unambtg tous ote e
|
¢. Lang. Independence
{ oe
3 Pasthy — capable 4 my enuted — within ( 1) con tals.
‘ Anal ma ais is
9 Yrroeus, _- athe prfermonee 4 offs loremanee. my je
poate Itke space § ia ra
+ Deluimtne ay, a fer epee Wes
Spe nal sis
‘4 _Aapek 4 Abe LA _ Arnal ate
ee alle ee por 1, Jrone doleen to complete on &
input size.
. Space Cony lly 1— ame + Memory a wad ity Hotel.
5, Copalaiie te Alp prota coonst ofp fon sala /e
b dabbthl, :— hoo soit aes woth JP tm, Irena
6. Optienclt I- en ie ote provide but possible sol”
why?
To compote a oy algo.
© To ensue fofen!
oe pale 1 4
me
we adutng ete problem.
§ optirnal ee
thot seal. ort with Sea ye
”
reboUce ml Oh Notolton (0) —> Uppet Bound
{P= O(n) th JS co gteh 5 Some values 4 cdo ff fr all >No
——~ ) —
a fins o* qe a
1 i x“
cg Cn)
i?
i ees
crea eink
Rta Omega (st)
yo" age) if gine a f° some sg 070. Ah a See
ty gins Snty > gind= A
ot j § q : i conta)
: : 3 1"
: 1
a No i
n= 8 NG (« value. can cleo ” be {rocHonat )
Rta Theo (8)
— em eS ON sl ca 4 0,
aa roo hat
qo”) 4) jor ot a.
+
cag)
4
eae
sid
1
Ne ™ SECO
Companitson 4 Pn 3
| ole” 5 nage™
1 ney 2 rh
seh by tort) bg fo)
lan lyr A ln
we <
ug) 9 (088)
OP Bn ney (a ‘
Kn
OY Sey
Constant < 9 < polynorntal < enpeslta
i< tage vn < ai “nd ‘een <
Ferg eee an
atu”
q 4
npg oman Cag”)
& oa (
toa 4 tan)
“
Leh Oe q walt) 36
16 4
ona 64 4: tg (4) A.
tea
toa Soy 4 tegC tous) Jo © Smatt ob (0)
" gore og") % }
(nh < ce qn a
all volue 4 oo fi af volue i)
> No
(0
small ob aa Bh oh wll dew ated
di Sea nee
at oc 0 |
cue
Wy Srot_ Ora (wo)
feol= 09 qn) Ny yor? c q 4
(Fa
ath valued 4 6y0 44 9% M0.
Sim 400) 2 0
env ene 0 930 lain)
q q
Wi BK che n”
POM
(aioe Borel SL) ates
choy Bound (8)
—Bapote Nolatton Quetion
Ntoa
Check 9100 nlegn * (3
ur) @
2c. Sloan
\co
4 c= 10000 eats
z
Os Se ht > [oes]
Q
Gaps _Peyrpletie s Notation
| 1 qo) ol tn)
yrs ‘Se Fs
a) Synmedate 47 oun) then,
qe oly)
teo ole
ins 0 yo) 4
qo whe Then
yer o(ht)) Tre Comply bats en ee
K
a)
i Seuiea
ec (te 1p tens te ty) Fe at ke a
pri (Hello) 3 1
: rest © on)
“WA fo (tea pleen 3 ie)}
gag Ashi oad, (gb Seeger %
Phas fens te OL pep Geil ie a
‘ ; n
} pert (Hato) 5 3 ~ i
J OD uh ate
73 n
= T[tepede il
2 Noga
QRasut Al,
peaeea ?
BS tA 5.0L TO)st
yPvL T(n)= c+ at(2) i |
mid= t+} /a ratte -
ae TQ) = cay (0) eC)
iid ¥ Pe
4 (x ©
adie cedar GM joe \5
Tt): dt
T(n) = ct TIn-d)
Tine T (na) +e]
Thy-a)= T(n-n) + ¢
To) = T(n-a) +e
TCnea) = T(n-B) +0
rin) = Tlo-3)+ Be
Tne T(n-k)+ Ke
n-k= 1
o(n)
Tole wT (Q) + Sogn
Tae MQ) EUS
Thn}= wr (a)* leg ioe
“HG e Ts
In) ‘es ba
ies
Ta) = wT (S)+ a é
sen)= PT ee
(4)
TIA)s 9T(3)e
T(nl= PT (4 + 30
! (3
0ST (0
T{n) a Bee Kn.
Nie ne W'
v K= to
tn) = ATUL) + 9 tg
Tne H+ Nbegn
Ttn)= O( Nlogn)
T(N= aT ( rar oar 4g o+ oe
9
+ bee y+ to 9]
Ne nL lt dt St. + ee ¢ 0
nen [eye (eger hy)
orn [ Vane a fe
Nef tea de tay on
Ryser. ny yh
“Oger” "Wha
= blood
Ta ee) Tb
O( nlodn) q + y Qasutie Tere Method
Tals at (ay oo
1
f+ . Henan. a
A SLivaaaeer 3. | aN a DR} cos emechs eh = en ( 8
GR aes 8) PR PG
(
! A NPE Are) Seay We
pinto of 04 j
ae ak A
ene ent ene... ten eee carer (hp 4 +e)
ae es. eo en, wm |
K Hrs.
Ken 5 cal ton)
= pe o< sd
Tn}= AT (Wa) Fe (6) aa
stn) aT (0/4) Fe T(He
a(ni)= aT (alt) + Cade
TON = at (ns) +e
T(n¥) = AT (07) #erder atc:
Tlo)= BT (0%) KC.
1
Tine wT (vst) +4 we cay ee See
¢ yk = ha | ty o's) = legal
= Acorn a
SOE a
Dot = wk
Big: dx hue eae + a] o( =
aod re[ 20%) |
i Ba eph Moston’ Theorem
——— tal M0.
p K ay jb5l, R20 oes
T(n)= on (hh + O(n! taf)
() orbs [rents 0 (o'te®)
(a) ar 8 42 OC nH ant)
yp to ole a ieee
) pe-2 A Ten) = 6 (page tegten)
c) pe-t hen Tn) = 6( 9%")
ae EE eg
%) ach
a) pyo hen Tins O (ok tog?)
b) 90. Then Thal = 6(0K)
Ti
ea” ate
Le aT(a}+e(at tan)
Y ade — Tay= O(N)
i) a=b*
a) pr-1 Tin)= 8 Coie ty" 0)
b) pet T(n)= 6 (too ugg)
9 p<-t TOO) = (ntyer)
di) ach
a) p20 TLn)= B( nk tog?n)
b) p TM)
Ne
5. LUT= alpet-s] watt (pie) 978
& Jon ( jx 4 to mu) ee or _
site ta catyey] rose Apaya) — fn)
8, Lindi] = co :
9, RI nett] = 0 T(aj= 97 (4) +
for tel, je a
Mh doo (Ke p to)
» yor « RljT)
=i) y Seamp|
le a § % 3 8
vsloloT elves Tss] a
P att w Belk Sock (Tory Home)
1, partition (A: PD)
Re eate) Sr
zw tp
4 (pe pare }cg 5 ft)
5 CAT)
6 te ted
43
swoop (Ast, |)
portttion (Arp. 9)
x= ALpI
tz p
for (fr pts i<93 p+]
CALE x)
seoap (At, ])
Swap (8,4, p)
qutekSort (arpa) {
Creat
ine pasrtlton (A: pit) —— o(n)
qutekSorct ( Axpy md):
qutek Sent (Ap MHL 9)
}
j
Tinle Tn) + T(M2)+ O(N)
| Qu corct- inde AT (M/)+ 060)
8. Swap (Ast, p)
Rondontiaed Quick Sart
i
Cea e git eens ke
> Pondorn, pivot thet
]
Tin)= o(alegn)
pe Se
cit udowst Coe !— -TENV= To) + T(n-1) + O(n)
(alenady ane) T(n)= oto’)
ite as
| onl ndee
gas (apt
¥p chtld
Letilent Pro: Nee
Rete sate Heap
PUR) = | Rant < child
YS
SeueraY My, Ne ight x a tiag %
mantiaplty (At) | c Of endo RET |
ih
ge tye) ut
ds
a
uO waned a th : P
ay (ug Arheapatee gh AOD att) ) 3
5 lasigut = ) 7
cde ft. t ®) 6 ®@
4. 4 (w¢ A: heapstee ah ale] > Allauga!l) @ » J
&.
5
‘0.
losiget = L
' are ie
onchange (ACI, ALtaupat)
Ne Moh pity (a, tavgut)
OO GS @S/\
Busia Mov Heap (4)
i heapstee = A length
+ for te |B dan fo Sure
Max Bey HU)
a) Lele
aoe.
A
Node. EO eae ee eee
Heep Cabeeade max (0) |
4 (A. heap ita < 1)
"Heap undue”
det
max: ALL] :
ALI = Alhap sai]
+ heapstze = A-heap Stee J
Mox Heap! yen)
y rebon max
{
AS oC alain)
Seta
HeapSort(A) {
1. Gutld Mar heap (9)
ae ore te Aten fou
> emthong ALT § ATT
4 Av heapstee “Arheap size “1
§ May Baek (A, 1)
|
bsp.
afl maxHeap (A) {
1. A, heap Size = A, length
v Ww t- | Alaa oe WE
3 Mav Heeey CAPO
}
m%
pes reerlty YU 1
de LOM at
a me Reht(t) > ates
BHC LE Arhapite Hf atay> att)
4
&.
Les dl;
dhe wat =
a ' (or Arheapstn, 44 ALI > A Clow)
4 tonygat =
& ‘ Capa v|
4 \ Moan (at, tasput)
. rete (A, tage)
o