notes15 - overall sense of the nature of the algorithm what...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: overall sense of the nature of the algorithm, what counts is the N 2 part. If we double the size of the input to a program, how does that affect the running time? We use “big Theta” notation to express this sort of approximation. We say that the running time of the sort function is Θ( N 2 ) while the running time of the squares function is Θ( N ). The formal definition is f ( x ) = Θ( g ( x )) ⇔ ∃ k, N | ∀ x > N, | f ( x ) | ≤ k · | g ( x ) | What does all this mean? Basically that one function is always less than another function (e.g., the time for your program to run is less than x 2 ) except that we don’t care about constant factors (that’s what the k means) and we don’t care about small values of x (that’s what the N means). Why don’t we care about small values of x ? Because for small inputs, your program will be fast enough anyway. Let’s say one program is 1000 times faster than another, but one takes a millisecond and the other takes a second. Big deal.takes a second....
View Full Document

This note was uploaded on 02/17/2010 for the course COMPUTER S 26275 taught by Professor Harvey,b during the Spring '10 term at Berkeley.

Ask a homework question - tutors are online