lecture17 - 4/12/2009 Today's topics COMPUTER SCIENCE 51...

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1 COMPUTER SCIENCE 51 Spring 2009 cs51.seas.harvard.edu Prof. Greg Morrisett Prof. Ramin Zabih Today’s topics Streams and impossible programs Fitting 2D points with line of best fit Interpolating images A different impossible program Impossible streams Simple questions about streams are actually impossible for a computer Example: count how often a number appears in a stream This is easy in a list! ; Gap between successive stream elements ( define (gap s) (lcons (- (lcar (lcdr s)) (lcar s)) (gap (lcdr s))) ( define prime-gap (gap primes)) ; Fields medal for implementing counts function ( define twin-primes-false-proof ( counts 2 prime-gap)) Computation and data For the next few lectures we are going to look at the CS of “real-world” data Anything actually measured Physics, economics, chemistry, government… How can we use computers to make sense of data? Especially for large data sets Real data always has errors in it So we need error-tolerant algorithms! Example data 0 10 20 30 40 50 60 70 80 55 65 75 85 95 105 115 MPT Speed Understanding data What is the relationship between two quantities? (Model) fitting For 2D data, we’ll look at lines Later: find structure in the data Fitting often used for interpolation What happened between data points? Extrapolation: before/after data points
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lecture17 - 4/12/2009 Today's topics COMPUTER SCIENCE 51...

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