Recurrence Recap Dorr-351-Oct-02-2007

Recurrence Recap Dorr-351-Oct-02-2007 - Recurrence trees...

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You should review material going back to the first week. For example: Rules for logs, calculus, sums, expected values, … Constructive induction, the Fibonacci examples and proofs… Algorithms that you’ve seen and now analyzed in more detail such as transitive closure, several sorts… Techniques to go from code or pseudocode to either summations or recurrences… The five asymptotic relationships, their quantified definitions, how to construct c and then n 0 for the ones that start with existential quantifiers, the limit-based definitions, how we can use these relationships to answer specific questions…
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Unformatted text preview: Recurrence trees and how they can be used to get nice Big-O and Big-Omega bounds Exam #1 is Thursday 6-7:30pm We are given some recurrence relation that doesnt fit into the Master Theorem well such as: T(1)=1 T(n)=T(n/4)+T(3n/4)+1 Things we want to observe. Structure of the tree Symmetrical? Density? Number of levels? Work done At full interior levels? At leaves? Asymptotic relationships Big-Omega Big-O What if we make a change to only the f(n) in the previous recurrence: T(1)=1 T(n)=T(n/4)+T(3n/4)+ n What is the impact of the f( n )?...
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Recurrence Recap Dorr-351-Oct-02-2007 - Recurrence trees...

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