O -Notation. April 23, 2003 Prepared by Doug Hogan CSE 260. O -notation: The Idea. Big-O notation is a way of ranking about how much time it takes for an algorithm to execute How many operations will be done when the program is executed?
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
April 23, 2003
Prepared by Doug Hogan
After x0, |f(x)| ≤ M ∙ |g(x)|
Before x0, nothing claimed about f’s growth
such that for all x in the domain of f and g, |f(x)| ≤ M ∙ |g(x)| when x > x0
17x6 – 3x3 + 2x + 8 is O(x6); M = 30; x0 = 1
17x6 – 3x3 + 2x + 8
M = 45; x0 = 6
f(x) = 7x3 - 2x + 3
M = 12, x0 = 1 7x3 - 2x + 3 is O(x3)
xr is O(xs)
anxn+an-1xn-1 +… + a1x + a0is O(xm) for all m ≥ n
such that |x2| ≤ M ∙ |x| for all x > x0 (1)
anxn+an-1xn-1 +… + a1x + a0is NOTO(xm) for all m<n
Let f and g be functions and k be a constant.
Let f and g be functions and a,b,m,n be constants.
Epp, Susanna. Discrete Mathematics with Applications. 2nd Ed. Belmont, CA: Brooks, 1995.
Headington, Mark A., and David Riley. Data Abstraction and Structures using C++. Lexington, MA: Heath, 1994.