dynamic programming - webpages.ursinus.eduwebpages.ursinus.edu/adhawan/algorithms/dynamic.pdf ·...
TRANSCRIPT
![Page 1: Dynamic Programming - webpages.ursinus.eduwebpages.ursinus.edu/adhawan/algorithms/Dynamic.pdf · Assembly line scheduling. ... Automobile factory with two assembly lines. Each line](https://reader033.vdocuments.site/reader033/viewer/2022051600/5aa164c37f8b9a80378b991f/html5/thumbnails/1.jpg)
Dynamic Programming
![Page 2: Dynamic Programming - webpages.ursinus.eduwebpages.ursinus.edu/adhawan/algorithms/Dynamic.pdf · Assembly line scheduling. ... Automobile factory with two assembly lines. Each line](https://reader033.vdocuments.site/reader033/viewer/2022051600/5aa164c37f8b9a80378b991f/html5/thumbnails/2.jpg)
Introduction
![Page 3: Dynamic Programming - webpages.ursinus.eduwebpages.ursinus.edu/adhawan/algorithms/Dynamic.pdf · Assembly line scheduling. ... Automobile factory with two assembly lines. Each line](https://reader033.vdocuments.site/reader033/viewer/2022051600/5aa164c37f8b9a80378b991f/html5/thumbnails/3.jpg)
Assembly line scheduling
![Page 4: Dynamic Programming - webpages.ursinus.eduwebpages.ursinus.edu/adhawan/algorithms/Dynamic.pdf · Assembly line scheduling. ... Automobile factory with two assembly lines. Each line](https://reader033.vdocuments.site/reader033/viewer/2022051600/5aa164c37f8b9a80378b991f/html5/thumbnails/4.jpg)
Assembly line scheduling
![Page 5: Dynamic Programming - webpages.ursinus.eduwebpages.ursinus.edu/adhawan/algorithms/Dynamic.pdf · Assembly line scheduling. ... Automobile factory with two assembly lines. Each line](https://reader033.vdocuments.site/reader033/viewer/2022051600/5aa164c37f8b9a80378b991f/html5/thumbnails/5.jpg)
Assembly line scheduling
![Page 6: Dynamic Programming - webpages.ursinus.eduwebpages.ursinus.edu/adhawan/algorithms/Dynamic.pdf · Assembly line scheduling. ... Automobile factory with two assembly lines. Each line](https://reader033.vdocuments.site/reader033/viewer/2022051600/5aa164c37f8b9a80378b991f/html5/thumbnails/6.jpg)
![Page 7: Dynamic Programming - webpages.ursinus.eduwebpages.ursinus.edu/adhawan/algorithms/Dynamic.pdf · Assembly line scheduling. ... Automobile factory with two assembly lines. Each line](https://reader033.vdocuments.site/reader033/viewer/2022051600/5aa164c37f8b9a80378b991f/html5/thumbnails/7.jpg)
Optimal Substructure
![Page 8: Dynamic Programming - webpages.ursinus.eduwebpages.ursinus.edu/adhawan/algorithms/Dynamic.pdf · Assembly line scheduling. ... Automobile factory with two assembly lines. Each line](https://reader033.vdocuments.site/reader033/viewer/2022051600/5aa164c37f8b9a80378b991f/html5/thumbnails/8.jpg)
Recursive solution
![Page 9: Dynamic Programming - webpages.ursinus.eduwebpages.ursinus.edu/adhawan/algorithms/Dynamic.pdf · Assembly line scheduling. ... Automobile factory with two assembly lines. Each line](https://reader033.vdocuments.site/reader033/viewer/2022051600/5aa164c37f8b9a80378b991f/html5/thumbnails/9.jpg)
Assembly line scheduling
![Page 10: Dynamic Programming - webpages.ursinus.eduwebpages.ursinus.edu/adhawan/algorithms/Dynamic.pdf · Assembly line scheduling. ... Automobile factory with two assembly lines. Each line](https://reader033.vdocuments.site/reader033/viewer/2022051600/5aa164c37f8b9a80378b991f/html5/thumbnails/10.jpg)
Computing the fastest time
![Page 11: Dynamic Programming - webpages.ursinus.eduwebpages.ursinus.edu/adhawan/algorithms/Dynamic.pdf · Assembly line scheduling. ... Automobile factory with two assembly lines. Each line](https://reader033.vdocuments.site/reader033/viewer/2022051600/5aa164c37f8b9a80378b991f/html5/thumbnails/11.jpg)
Computing the fastest time
![Page 12: Dynamic Programming - webpages.ursinus.eduwebpages.ursinus.edu/adhawan/algorithms/Dynamic.pdf · Assembly line scheduling. ... Automobile factory with two assembly lines. Each line](https://reader033.vdocuments.site/reader033/viewer/2022051600/5aa164c37f8b9a80378b991f/html5/thumbnails/12.jpg)
Constructing the fastest way
![Page 13: Dynamic Programming - webpages.ursinus.eduwebpages.ursinus.edu/adhawan/algorithms/Dynamic.pdf · Assembly line scheduling. ... Automobile factory with two assembly lines. Each line](https://reader033.vdocuments.site/reader033/viewer/2022051600/5aa164c37f8b9a80378b991f/html5/thumbnails/13.jpg)
Motivation
• We often want to compare the DNA of two or
more organisms.
• Expressed as a string over the set {A, C, G, T}
• S1=ACCGGTA………..• S1=ACCGGTA………..
• S2=ACCGCTA…………
• How similar are these two strands?
• How long is the longest-common-
subsequence?
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Longest common subsequence
![Page 15: Dynamic Programming - webpages.ursinus.eduwebpages.ursinus.edu/adhawan/algorithms/Dynamic.pdf · Assembly line scheduling. ... Automobile factory with two assembly lines. Each line](https://reader033.vdocuments.site/reader033/viewer/2022051600/5aa164c37f8b9a80378b991f/html5/thumbnails/15.jpg)
Optimal Substructure
Big Idea: The LCS of two sequences contains within it
an LCS of the prefixes of the two sequences.
![Page 16: Dynamic Programming - webpages.ursinus.eduwebpages.ursinus.edu/adhawan/algorithms/Dynamic.pdf · Assembly line scheduling. ... Automobile factory with two assembly lines. Each line](https://reader033.vdocuments.site/reader033/viewer/2022051600/5aa164c37f8b9a80378b991f/html5/thumbnails/16.jpg)
Recursive formulation
![Page 17: Dynamic Programming - webpages.ursinus.eduwebpages.ursinus.edu/adhawan/algorithms/Dynamic.pdf · Assembly line scheduling. ... Automobile factory with two assembly lines. Each line](https://reader033.vdocuments.site/reader033/viewer/2022051600/5aa164c37f8b9a80378b991f/html5/thumbnails/17.jpg)
Example
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Compute the length of the Optimal
solution
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Tables computed by LCS-Length
![Page 20: Dynamic Programming - webpages.ursinus.eduwebpages.ursinus.edu/adhawan/algorithms/Dynamic.pdf · Assembly line scheduling. ... Automobile factory with two assembly lines. Each line](https://reader033.vdocuments.site/reader033/viewer/2022051600/5aa164c37f8b9a80378b991f/html5/thumbnails/20.jpg)
Constructing the LCS