This preview shows pages 1–9. Sign up to view the full content.
CSCI 2670
Introduction to Theory of
Computing
November 10, 2005
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document November 10, 2005
Agenda
•Today
– Continue Section 7.1
•Next
week
– Finish Section 7.1
November 10, 2005
Announcement
• Quiz next Tuesday (11/15)
– BigO and smallo notation
– Identify BitO and smallo relationships
– Importance of proper encoding (today’s
material)
• This is simplified material from Section 6.4
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document November 10, 2005
n, logn, log(log n), and n*log n
50
0
50
100
150
200
250
0
50
100
150
n
f(n
)
n
log n
log log n
n log n
November 10, 2005
log n and log log n
1
0.5
0
0.5
1
1.5
2
2.5
0
50
100
150
n
f(n
)
log n
log log n
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document November 10, 2005
n, n log n, n^2, n^2 log n
0
5000
10000
15000
20000
25000
1
12
23
34
45
56
67
78
89
n
f(n
)
n
n log n
n^2
n^2 log n
November 10, 2005
Smallo vs. bigO
• Smallo is strictly less than
• BigO is less than or equal to
• For any function f, is f(n) = o(f(n))?
– No … never!
• For any function f, is f(n) = O(f(n))?
–Yes
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document November 10, 2005
Some identities
•n
i
= o(n
k
) for every i < k
• log n = o(n)
• log log n = o(log n)
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 02/07/2011 for the course CS 501 taught by Professor Sm during the Spring '11 term at Indiana.
 Spring '11
 sm

Click to edit the document details