4/14/20 1 Lecture 16 – Dynamic Programming Reading: KT Sections 6.1 and 6.2 Partial content of these slides have been obtained from the official lecture slides that accompany the textbook. A complete set of slides can be found at: http://www.cs.princeton.edu/~wayne/kleinberg-tardos/ Algorithm techniques Data structures • Use extra data structures • Exploit the structure to improve complexity Greedy algorithms • Build up a solution incrementally • Myopically optimizing some local criterion Divide and conquer • Break up a problem into independent subproblems • Solve each subproblem • Combine solutions to subproblems to form solution to original problem Dynamic Programming • Break up a problem into a series of overlapping subproblems • Build up solutions to larger and larger subproblems
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4/14/20
1
Lecture16– DynamicProgrammingReading:KTSections6.1and6.2
Partialcontentoftheseslideshavebeenobtainedfromtheofficiallectureslidesthataccompanythetextbook.Acompletesetofslidescanbefoundat:http://www.cs.princeton.edu/~wayne/kleinberg-tardos/
Algorithmtechniques
Datastructures•Useextradatastructures• Exploitthestructuretoimprovecomplexity
Greedyalgorithms•Buildupasolutionincrementally•Myopicallyoptimizingsomelocalcriterion
Divideandconquer•Breakupaproblemintoindependentsubproblems• Solveeachsubproblem•Combinesolutionstosubproblemstoformsolutiontooriginalproblem
DynamicProgramming•Breakupaproblemintoaseriesofoverlappingsubproblems
•Buildupsolutionstolargerandlargersubproblems
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Abitofhistory
WeightedIntervalSchedulingproblem
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WeightedIntervalSchedulingproblem
Let’strysolvingit
• Willgreedywork?
• Howaboutdivideandconquer?
• Istheresomestructureintheproblemthatwecanexploit?
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Let’sdefineafewnotions
Morenotations
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Abruteforcesolution
What’sthecomplexityofthisalgorithm?
Memoization
What’sthecomplexityofthisalgorithm?
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Bottom-updynamicprogramming
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