Lecture02-asymptotic

Lecture02-asymptotic - CS 312: Algorithm Analysis Lecture...

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Unformatted text preview: CS 312: Algorithm Analysis Lecture #2: Asymptotic Notation 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 Quiz Announcements § Your initial experiences with Visual Studio? § Currently scheduling TA office hours – announcement later today § Project #1 § Guidelines are linked from the online schedule § Help session with TA § Tuesday, 3pm, 5pm § In the Windows help lab (1066 TMCB) § Focus on intro. to C# and Visual Studio § Objectives § Revisit orders of growth § Formally introduce asymptotic notation: O, Ω, Θ § Classify functions in asymptotic orders of growth Orders of Growth § Efficiency : how cost grows with the difficulty n of a given problem instance. § C ( n ): the cost (number of steps) required by an algorithm on an input of size n. § Order of growth: the functional form of C ( n ) up to a constant multiple as n goes to infinity. Orders of Growth n log2 n n n log2 n n 2 n 3 10 3.3 10 3.3*10 102 103 102 6.6 102 6.6*102 104 106 103 10 103 1.0*104 106 109 104 13 104 1.3*105 108 1012 105 17 105 1.7*106 1010 1015 106 20 106 2.0*107 1012 1018 Orders of Growth n log2 n n n log2 n n 2 n 3 2 n n ! 10 3.3 10 3.3*10 102 103 103 3.6*106 102 6.6 102 6.6*102 104 106 1.3*103 9*1015 7 103 10 103 1.0*104 106 109 … … 104 13 104 1.3*105 108 1012 105 17 105 1.7*106 1010 1015 106 20 106 2.0*107 1012 1018 Efficient Kinds of Efficiency § Need to decide which instance of a given size to use as the representative for that class: Algorithm Domain Instance size 1 2 3 4 5 Instances • Average Case (over all possible instances) • Worst Case • Best Case Asymptotic Notation...
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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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Lecture02-asymptotic - CS 312: Algorithm Analysis Lecture...

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