# lec1 - 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 1 Introduction and Document Distance 6.006 Spring 2008 Lecture 1: Introduction and the Document Distance Problem Course Overview • Eﬃcient procedures for solving problems on large inputs (Ex: entire works of Shake- speare, human genome, U.S. Highway map) • Scalability • Classic data structures and elementary algorithms (CLRS text) Real implementations in Python Fun problem sets! • ⇔ β version of the class- feedback is welcome! • Pre-requisites • Familiarity with Python and Discrete Mathematics Contents The course is divided into 7 modules- each of which has a motivating problem and problem set (except for the last module). Modules and motivating problems are as described below: 1. Linked Data Structures: Document Distance (DD) 2. Hashing: DD, Genome Comparison 3. Sorting: Gas Simulation 4. Search: Rubik’s Cube 2 × 2 × 2 5. Shortest Paths: Caltech MIT → 6. Dynamic Programming: Stock Market 7. Numerics: √ 2 Document Distance Problem Motivation Given two documents, how similar are they? • Identical- easy? • Modified or related (Ex: DNA, Plagiarism, Authorship) 1 Lecture 1 Introduction and Document Distance 6.006 Spring 2008 • Did Francis Bacon write Shakespeare’s plays? To answer the above, we need to define practical metrics. Metrics are defined in terms of word frequencies. Definitions 1. Word : Sequence of alphanumeric characters. For example, the phrase “6.006 is fun” has 4 words. 2. Word Frequencies : Word frequency D ( w ) of a given word w is the number of times it occurs in a document D . For example, the words and word frequencies for the above phrase are as below: Count : 1 1 1 1 W ord : 6 the is 006 easy fun In practice, while counting, it is easy to choose some canonical ordering of words....
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lec1 - MIT OpenCourseWare http/ocw.mit.edu 6.006...

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