lec2 - MIT OpenCourseWare http://ocw.mit.edu 6.006...

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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 6.006 Introduction to Algorithms Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . Lecture 2 Ver 2.0 More on Document Distance 6.006 Spring 2008 Lecture 2: More on the Document Distance Problem Lecture Overview Today we will continue improving the algorithm for solving the document distance problem. Asymptotic Notation: Define notation precisely as we will use it to compare the complexity and eciency of the various algorithms for approaching a given problem (here Document Distance). Document Distance Summary- place everything we did last time in perspective. Translate to speed up the Get Words from String routine. Merge Sort instead of Insertion Sort routine Divide and Conquer Analysis of Recurrences Get rid of sorting altogether? Readings CLRS Chapter 4 Asymptotic Notation General Idea For any problem (or input), parametrize problem (or input) size as n Now consider many different problems (or inputs) of size n . Then, T ( n ) = worst case running time for input size n = max running time on X X : Input of Size n How to make this more precise? Dont care about T ( n ) for small n Dont care about constant factors (these may come about differently with different computers, languages, . . . ) For example, the time (or the number of...
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lec2 - MIT OpenCourseWare http://ocw.mit.edu 6.006...

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