# 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 eﬃciency 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? • Don’t care about T ( n ) for small n • Don’t 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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