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Asymptotic Notation&
eview of Functions
Review of Functions
8 October 2008
CS 570
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notation
For function
g
(
n
), we define
Θ
(
g
(
n
)),
bigTheta of
n
, as the set:
Θ
(
g
(
n
)) =
{
f
(
n
) :
∃
positive constants
c
1
,
c
2
, and
n
0,
such that
∀
n
≥
n
0
,
we have
0
≤
c
1
g
(
n
)
≤
f
(
n
)
≤
c
2
g
(
n
)
}
Intuitively
: Set of all functions that
isan
symptotically tight bound
r
have the same
rate of growth
as
g
(
n
).
asymp  1
Comp 122
g
(
n
) is an
asymptotically tight bound
for
f
(
n
).
notation
For function
g
(
n
), we define
O
(
g
(
n
)),
bigO of
n
, as the set:
O
(
g
(
n
)) =
{
f
(
n
) :
∃
positive constants
c
and
n
0,
such that
∀
n
≥
n
0
,
we have
0
≤
f
(
n
)
≤
c
g
(
n
)
}
Intuitively
: Set of all functions
whose
rate of growth
is the same as
r lower than that of
g
(
n
) is an
asymptotic upper bound
for
f
(
n
).
or lower than that of
g
(
n
).
=
=
asymp  2
Comp 122
f
(
n
) =
Θ
(
g
(
n
))
⇒
f
(
n
) =
O
(
g
(
n
)).
Θ
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This note was uploaded on 01/24/2011 for the course CS 570 at USC.
 '08
 SHAHRIARSHAMSIAN

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