Lecture11-quicksortavg

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CS 312: Algorithm Analysis Lecture #11: Average Case Analysis of Quicksort This work is licensed under a Creative Commons Attribution-Share Alike 3.0 Unported License. Slides by: Eric Ringger, with contributions from Mike Jones, Eric Mercer, Sean Warnick
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Announcements § Project #2 § Due: today § Questions? § Code Reviews are good § Project #3 § Help session: Tuesday at 3pm § Help session: Thursday at 5pm § Both in 1066 TMCB
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Starting a Career § Career Fair Preview § Wednesday, Feb. 1 § 5:00 p.m. § in 1170 TMCB § BYU Technical Career Fair § Thursday, Feb. 2 § 9 a.m. to 3 p.m. § Wilkinson Center Ballroom
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Objectives § Learn important ideas from probability theory § Begin the proof of the average case analysis of Quicksort
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Average Case Analysis
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Average Case Analysis § How would you approach an average case analysis?
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Basic Probability Theory We need the following ideas: § Samples / Outcomes § Events § Probability Measures § Random Variables § Values of Random Variables § Expected value of random variable
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Samples
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Samples
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Events
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Sigma Field
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Probability Measure
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Probability Space
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Example: One Fair Die
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Probability in 3-D
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Random Variables
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Random Variables
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Example: Two Rolls of a Die
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Values of Random Variables § We speak of values of x (in the range) as “events”, just as we did for subsets of the domain.
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Expected Value of RV
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Expected Value of RV
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Questions? § Samples / Outcomes § Events § Probability Measures § Random Variables § Values of Random Variables § Expected value of random variable
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Recall Elementary Probability § Usually we think of an experiment as a procedure that yields the same outcome each time it is repeated.
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This note was uploaded on 03/02/2012 for the course C S 312 taught by Professor Jones,m during the Winter '08 term at BYU.

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