Fri March 12 Lecture 20

Dynamic ProgrammingSuppose we have requests R Er rnwith start si finish fi value vi Assumethese are sorted by finish t.me

f E f E n E faGiven any set of requests 5 define OGto bethe score of the optimal solutionusing the requests in S we want OCR

Rk rich Me

Question If we know 042 0422 0423OCRe i can we use this to

compute OCRe

If so OCR is easyUse OCR to compute OCRUseOCR and 01122 0423iy

Use OCR 01km to compute042in

TR

r 1 1 Z

re 5B 1 1 Iri 1 1 I

rs 1 1 4ro

0426 he is either in an optimal solutionor it's not

If not Otra O RsIf it is 0 Rg 7 01K

7 0 Ry

OCRa max Oleg 7 t Ryor i

don't take ra do lake ra

Fanctrarcalltree.ORGMax O Rs 7 044

0Rs xCofy B 0441 1 4 23

1 I

Otra ok der

0k 19 0041

04122Okc

Iam been dead

ftp.y A lot of repeat work

MareprecisLet pls be the intervals in s thatdon't conflict with the last elementof S

EI p Rg Er rz.rs no

p Ry Er

Tien 042km ftp.RKIEvktOCplRxD

otherwise

Repeat works just store a value thefirst time you compute it

Memoization

Pseudocodei.memo empty dictionary global variable

function wits list of requests sortedby end time

if S is a key in memoreturn memo6T

if 5 93memo 3 0return O

r last request in Svalue of r

score max w S Er ut wi plsmemoIs Scorereturn scare

Linear t.me OG

This returns the score because

recursively keeping track of the setswould take exponential time

More

To get the solution itself trace backthrough and build it upAt the end of our example thememo diet is

3 O Ry 5Ri 2 Rs 9Rz 5 126 12Rs 5

wi Ra Max Wilks It WilRy12 Max 9 7 52

ra V took ro and called on Ryrs XwitRy Max wilks I t wiCR5 max 5 It 2

wRy X not taking Rywi Rs don't take B xwi Rz do take rz V

rz.ro optimal