Algorithm en& �1� ahenstruletunes

Woche 13

tents 2 2016

KKY 3 Kant Jalen Zid : Fuss

Is *.MMM 3 Mrstionae

KauiJalesFlusJ1elee.2us2anelehinsehrerfenk@oYs-Dmnese2idiEei9n.oIkjEphasmLozIusaaeeKurushWyeinGrapLesauderesBespiel.5chiekpnrrleMsIEs.y

.IT#Nani : ¥1 ,

non s naeht ( Somee → target)s - t

4 hie is 2 dv Graph explnitgeffen

SBB : mitral nod AsfalhszsthKoupleeer ah in weseitbelen day

glade Pullen

Einfaelv Fall : kabukooten = I

Lssny : Butter suite as S

s.¥F..¥)tI9II'sIII.FinneyAnpassuy auf Cup hers wf Gewclt .

cyesen : C - CYE , c),

c : E→R+,

s.de V

Cesudt ; Large elms keirusteu Ages von s naeht

Wy : ( Saro, Y ,

... ,vn=t ),

Cui, vi. ,

) c- E ieo. .

K - I

k - 1

Kosten = [ CC vi. vie , ) ( slight as use of nedehun )is 0

Ph > miles Berspml : Silele Cmephn wrt fhuuhen

dre are Loyen hates .Zile s and t Sy staff

gist kinesics Wy . COCD ! )Phish Kahn nanehuel Protein Schneller teen

.

Sv5 •

0/77

s • ⇒ u •£¥w~vk.se osnsirahe

Roseman ( niy )→ ist min

osene fclraihe

S = They uo man min way EV

alleandeen@Daa.m.Bnertensucheumhenaws2ufinelenofeyUygAt.ExrshuzuonUegenAnnalur.esgmhlyvensnadti-Cdamntgptesehenknhesten.l

Dnpuef ; es Kann uuenelbel well hlge fefh-7 • →

atsoopje•← .

ah da c per Liv Kam men 2 > then

ausschliessen,

d. 4 .

,ein kisneotr Uy

is L Zyklyfnei ( also her thotu ebppeld ) .

Daunt DL are gross Le Lange n - 1.

And iron dryer gist es nweeeloel well.

Arnall Uefe

lvlau,

IEI = in es Kann eepouesiell well gfes

�1�

spat -

abt

Zune , de Zan Dljowthny ;

ludulhnn oh 151 :

alle andean

s.IQ#Dt8susmiKu

.

30 • 50

n•

-4 • 16 ← ✓ ! bilhyskn Oy roms had HS

Welle Known e V\S not klenstw other fehnalleand Age a S him

.

S - { s },

des )=O

while IS I < u do

a Ihle ( u,

v ) e E,

ues,

v ¢ S

unit dcu ) + ccyv ) minimal

S= Su { v3,

dcu ) = dcw ) + ccu,

u )

Kemelthoteskawsscndessvurelhsnnmfs.s@I.Ew.aLsiFauTaummYr.bieehranelaetI-s.IP.t

Wy naeh Der Algorithms is L one . to - all

v is 2 layer ( Kinnan Cly ven s nah ellen

audios )

1s2 gewssv masses ein vuellgeuwuehe Tfotsswhe( known under nah Britain asgeasoht )"

ein Welle flour Dntanres wind inter Gapsges chosen

"

Pnewsieny des Algorithms"

wave.

. .

"

; shame alle Pferle en ,u ) duneh,

( tnineh push utsjv ¢ S,

mere MinimumVanek ) von diesen

Lanfrof : 0cm ),

also Ocnu ) for gauun Ago"

uoihle .. .

"

:

'

2•i

( Dijksaag n•¥±•vwjbrde : 17+1,12+5 ,

...

noFf Deosaeltuys Lene

is • Vetrndnyen winders

niehels gchaneltAlso ldee : take In je Kuhn

die valente ofeefelrenke

inspiziwe alle Kueter v e V\Sand nimm Wu elcv )

g-geradlanfgenomheh

, , c-jetzt 4in Wyuaqw

wpdehe oh

in;!YtjsF→ah'¥£→•¥ Dinan

7- wfwudy

also ; ninh v in S ayf urs ellv )for each Cv

,w ) c- E

if w ¢ S : if dw )tc( yw ) < dcw ) :

d ( w ) = dcv ) + ccyw )

kihialrsienuy : des ) =O

dcu ) = no fir alle u c- V\{ s ]S= of

Laifnrf : men , update of Drsttanres art den

Kaiser are non v ausgesenCinsgesawt 0cm ) dnjeele Kate einuel )

Also insgesaus OCu2+m ) = Ocr )

Celt es Lesser ? es frauds well wins → tleepwellerltOdell Openehrohen Snowden an ?

• exdraitwin ( n' fv dens )• deweesehey (

yCgeltuw in line Rnlswy : asserted

doin → drew• Same Dnfaysstvultwr

Heaps•

eehhitwn in Ochgu ) ( Heep wedvhentellef• decrease key

niclt kler wo doin stelt ! Csonst Occgn ) )

LOJY : make Powhvs in Adjaunlrte

Dufay : ocu )not Heap

Lafneft ; n x eeknaetwh Of nlyn )

-in x deeeesehey

ofmGyn )

1 × i - it Of n )dajeete

=Kah drunk 0cm lyn )einmd

oix , - . - sex

get we - m with a press

Es gets nod Lesser wem men den ADT fenanfar den Dlgowdh my elegy - J ( extnaetwin

,deereeseke > )

�1� as geld : Fibonacci . sleeps → 0 Cut ucgu )( one Erhleinwy )

Ues passret news c : E → IR ?v

•

µ 7 w

• - •

S u in

dcw ) £ dcu ) + CCY w ) nelaeieneh

gilt inner uoeh

Zyhln males brhh and Pwfle he ? see hives

Uye whiners,

d. L.

,es uuss jrhhhei=name Wyeth -

• me# •

o C- •

melee Pfeelcu ,w )

"

if dcw ) > deutcchw ) :

dcw ) = debt ccyw ) by gel Welty wet ahebt

Ford 's Dtgohfhmug : f€reach ( v. w ) c- E : mlaxlyw )

Problem : mrt Zyhlh Kann des niemely enelen

an dem girt es and nine Losnuy

negative Zyhly (⇒ es gist kinenkineskn Wey

Own es Gun tinny Len Wy got dem At

diesv einfad Chiu ebppeltes the hen )

kdultnu oh Pknlzahl i :

did = Kines h Wyleiyr s -7W

mid is i Pferlen

di = men ( di' '

, egg

,n⇐Cdr+ can ) ) )

lnitialrsienay : ds°=odie = W

,v & S

i

Tetleau ; a I .. . . - . ut

soensty DP

. a von Bellman: • 7 \ , ✓

; a 5 ,•

.

,/

v ' 5 s • t' §• w

ein Eivhg ; ocu )~

•

042 ) Eiwhaye Manners in Tableau uw

Latus Ocn ' )

drelehtefpeltenitfihesBellmn-Rnels@reeehCyw1eE.mlexCv.w) }oH

Sis welts pasfferfooh n evneielt ( weun Wd dem

wd etnas aheht

Lafwf :

Ocmn) ⇒ Zychs )

Between ness Centrally

auf wiewelen luhsten Oyen at eh Knoth

in Gneph ? ( so ein known At Welty ,2. B

,

,in

Facebook graph )

D as fnauclt : All - to - KCL sherbet path

c= E→lR+ : u Mal Dijksha ocn . m . lgu )0 7

c = E → R :• µ

•

→ •

ldu : snstralrue÷ Klassen city6 felt weht der

u Mel Bellmen - fuel ; Ocmi ) # Susaalhones

= ¥ Kath

Flo > d- Wardell

dnl = Kiuush htglayl u → v not

Zwseheskutes - Nummeu I i;

kdultnn risen i : ±jP\'s it

diznincdii'

,dime on

'

)" •

'• v

rlgewthny ;

init

for i= 1. .

n

for u= I - . 4

for v =L . - 4

Kann man - dui = win ( dii'

,di's + duij

'

)in place healers

Johnson new :

t.tt#g.g@hteueinsk.m

ro Ecu ,v)= ccu ,v ) +4 ( u ) - ha )NEU • - -

-

-7Ziel : E : E → Rt

0

• Kiner Pfed Sleet Kiinest

g•

t ↳ P -7• e-

ICs→ d) = ecsnit ) + hcs ) - KD( dre Hiler uihraegs heben

der were Term in E Weh auf )heft uw von s and t of

and AL dahv glaiel fir elle Wye s → t

• Zyklenkeslen Sletten : da ICs → s )= ecs → s )

Oie defining air h ( so def c : E.) Rt what ) ?

Definition : hlu ) = Leye clues kcivuth Pfeely

,

→•

4 non NEU nad u

/>

• ✓

Neu • - -- hcu ) 3- hcu )t ccu ,u )

⇒ Ipass W~

Lanfurl ; NEU,

Pforle : Ocw )h - were CBIF ) ; 0 Cmu )

in Mal Drjhsha : Ocnmhejn )

lusgesawf : ocum hey n )

Anwueluyen : Tnausalhiesen art hasten