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The document discusses various algorithms techniques including greedy algorithms, dynamic programming, and their application to problems like the activity selection problem and knapsack problem. It provides examples of optimal subproblems, overlapping subproblems, and how dynamic programming and greedy algorithms can be used to solve problems exhibiting these properties.

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CS 332: Algorithms Greedy Algorithms
Review: Dynamic Programming ,[object Object],[object Object]
Review: Optimal Substructure of LCS ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Review: Structure of Subproblems ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Memoization ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Review: Dynamic Programming ,[object Object],[object Object],[object Object],[object Object],[object Object]
Review: Dynamic Programming ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Greedy Algorithms ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Activity-Selection Problem ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Activity-Selection ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],1 2 3 4 5 6
Activity Selection: Optimal Substructure ,[object Object],[object Object],[object Object],[object Object],[object Object]
Activity Selection: Repeated Subproblems ,[object Object],S 1  A? S’ 2  A? S-{1} 2  A? S-{1,2} S’’ S’-{2} S’’ yes no no no yes yes
Greedy Choice Property ,[object Object],[object Object],[object Object],[object Object],[object Object]
Activity Selection: A Greedy Algorithm ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Minimum Spanning Tree Revisited ,[object Object],[object Object],[object Object],[object Object]
Review: The Knapsack Problem ,[object Object],[object Object]
Review: The Knapsack Problem ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Review: The Knapsack Problem And Optimal Substructure ,[object Object],[object Object],[object Object],[object Object]
Solving The Knapsack Problem ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The Knapsack Problem: Greedy Vs. Dynamic ,[object Object],[object Object],[object Object]

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