Fri March 12 Lecture Dynamic Programming Er
Transcript of Fri March 12 Lecture Dynamic Programming Er
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
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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