lecture 38 cse 331 dec 3, 2010. a new grading proposal towards your final score in the course max (...
Post on 15-Jan-2016
212 views
TRANSCRIPT
![Page 1: Lecture 38 CSE 331 Dec 3, 2010. A new grading proposal Towards your final score in the course MAX ( mid-term as 25%+ finals as 40%, finals as 65%) Email](https://reader035.vdocument.in/reader035/viewer/2022070412/56649d4e5503460f94a2e69d/html5/thumbnails/1.jpg)
Lecture 38
CSE 331Dec 3, 2010
![Page 2: Lecture 38 CSE 331 Dec 3, 2010. A new grading proposal Towards your final score in the course MAX ( mid-term as 25%+ finals as 40%, finals as 65%) Email](https://reader035.vdocument.in/reader035/viewer/2022070412/56649d4e5503460f94a2e69d/html5/thumbnails/2.jpg)
A new grading proposal
Towards your final score in the course
MAX ( mid-term as 25%+ finals as 40%, finals as 65%)
Email me any objections (or support) by Monday, Dec 6, noon
Individual choice for
every student
Individual choice for
every student
![Page 3: Lecture 38 CSE 331 Dec 3, 2010. A new grading proposal Towards your final score in the course MAX ( mid-term as 25%+ finals as 40%, finals as 65%) Email](https://reader035.vdocument.in/reader035/viewer/2022070412/56649d4e5503460f94a2e69d/html5/thumbnails/3.jpg)
Homework stuff
http://xkcd.com/336/
HW 10 posted
Graded HW 9 pickups: my office hours today
Jeff/Alex next week
![Page 4: Lecture 38 CSE 331 Dec 3, 2010. A new grading proposal Towards your final score in the course MAX ( mid-term as 25%+ finals as 40%, finals as 65%) Email](https://reader035.vdocument.in/reader035/viewer/2022070412/56649d4e5503460f94a2e69d/html5/thumbnails/4.jpg)
Weighted Interval Scheduling
Input: n jobs (si,ti,vi)
Output: A schedule S s.t. no two jobs in S have a conflict
Goal: max Σj in S vj
Assume: jobs are sorted by their finish time
![Page 5: Lecture 38 CSE 331 Dec 3, 2010. A new grading proposal Towards your final score in the course MAX ( mid-term as 25%+ finals as 40%, finals as 65%) Email](https://reader035.vdocument.in/reader035/viewer/2022070412/56649d4e5503460f94a2e69d/html5/thumbnails/5.jpg)
Property of OPT
OPT(j) = max { vj + OPT( p(j) ), OPT(j-1) }
![Page 6: Lecture 38 CSE 331 Dec 3, 2010. A new grading proposal Towards your final score in the course MAX ( mid-term as 25%+ finals as 40%, finals as 65%) Email](https://reader035.vdocument.in/reader035/viewer/2022070412/56649d4e5503460f94a2e69d/html5/thumbnails/6.jpg)
A recursive algorithm
M-Compute-Opt(j)
If j = 0 then return 0
M[j] = max { vj + M-Compute-Opt( p(j) ), M-Compute-Opt( j-1 ) }
If M[j] is not null then return M[j]
return M[j]
M-Compute-Opt(j) = OPT(j)
M-Compute-Opt(j) = OPT(j)
Run time = O(# recursive calls)Run time = O(# recursive calls)
![Page 7: Lecture 38 CSE 331 Dec 3, 2010. A new grading proposal Towards your final score in the course MAX ( mid-term as 25%+ finals as 40%, finals as 65%) Email](https://reader035.vdocument.in/reader035/viewer/2022070412/56649d4e5503460f94a2e69d/html5/thumbnails/7.jpg)
Bounding # recursionsM-Compute-Opt(j)
If j = 0 then return 0
M[j] = max { vj + M-Compute-Opt( p(j) ), M-Compute-Opt( j-1 ) }
If M[j] is not null then return M[j]
return M[j]
Whenever a recursive call is made an M value of assigned
Whenever a recursive call is made an M value of assigned
At most n values of M can be assignedAt most n values of M can be assigned
O(n) overallO(n) overall
![Page 8: Lecture 38 CSE 331 Dec 3, 2010. A new grading proposal Towards your final score in the course MAX ( mid-term as 25%+ finals as 40%, finals as 65%) Email](https://reader035.vdocument.in/reader035/viewer/2022070412/56649d4e5503460f94a2e69d/html5/thumbnails/8.jpg)
![Page 9: Lecture 38 CSE 331 Dec 3, 2010. A new grading proposal Towards your final score in the course MAX ( mid-term as 25%+ finals as 40%, finals as 65%) Email](https://reader035.vdocument.in/reader035/viewer/2022070412/56649d4e5503460f94a2e69d/html5/thumbnails/9.jpg)
Property of OPT
OPT(j) = max { vj + OPT( p(j) ), OPT(j-1) }
Given OPT(1), …, OPT(j-1), one can compute OPT(j)
Given OPT(1), …, OPT(j-1), one can compute OPT(j)
![Page 10: Lecture 38 CSE 331 Dec 3, 2010. A new grading proposal Towards your final score in the course MAX ( mid-term as 25%+ finals as 40%, finals as 65%) Email](https://reader035.vdocument.in/reader035/viewer/2022070412/56649d4e5503460f94a2e69d/html5/thumbnails/10.jpg)
Recursion+ memory = IterationIteratively compute the OPT(j) valuesIteratively compute the OPT(j) values
M[0] = 0
M[j] = max { vj + M[p(j)], M[j-1] }
For j=1,…,n
Iterative-Compute-Opt
M[j] = OPT(j)M[j] = OPT(j) O(n) run timeO(n) run time
![Page 11: Lecture 38 CSE 331 Dec 3, 2010. A new grading proposal Towards your final score in the course MAX ( mid-term as 25%+ finals as 40%, finals as 65%) Email](https://reader035.vdocument.in/reader035/viewer/2022070412/56649d4e5503460f94a2e69d/html5/thumbnails/11.jpg)
Reading AssignmentSec 6.1, 6.2 of [KT]
![Page 12: Lecture 38 CSE 331 Dec 3, 2010. A new grading proposal Towards your final score in the course MAX ( mid-term as 25%+ finals as 40%, finals as 65%) Email](https://reader035.vdocument.in/reader035/viewer/2022070412/56649d4e5503460f94a2e69d/html5/thumbnails/12.jpg)
When to use Dynamic Programming
There are polynomially many sub-problems
Optimal solution can be computed from solutions to sub-problems
There is an ordering among sub-problem that allows for iterative solution
Richard Bellman
![Page 13: Lecture 38 CSE 331 Dec 3, 2010. A new grading proposal Towards your final score in the course MAX ( mid-term as 25%+ finals as 40%, finals as 65%) Email](https://reader035.vdocument.in/reader035/viewer/2022070412/56649d4e5503460f94a2e69d/html5/thumbnails/13.jpg)
Shortest Path Problem
Input: (Directed) Graph G=(V,E) and for every edge e has a cost ce (can be <0)
t in V
Output: Shortest path from every s to t
1 1
100
-1000
899
s t
Shortest path has cost negative
infinity
Shortest path has cost negative
infinity
Assume that G has no negative
cycle
Assume that G has no negative
cycle
![Page 14: Lecture 38 CSE 331 Dec 3, 2010. A new grading proposal Towards your final score in the course MAX ( mid-term as 25%+ finals as 40%, finals as 65%) Email](https://reader035.vdocument.in/reader035/viewer/2022070412/56649d4e5503460f94a2e69d/html5/thumbnails/14.jpg)
Today’s agenda
Dynamic Program for shortest path
![Page 15: Lecture 38 CSE 331 Dec 3, 2010. A new grading proposal Towards your final score in the course MAX ( mid-term as 25%+ finals as 40%, finals as 65%) Email](https://reader035.vdocument.in/reader035/viewer/2022070412/56649d4e5503460f94a2e69d/html5/thumbnails/15.jpg)
May the Bellman force be with you