TCI)
not TEH
for exceed
every the
I
of bar
size n c- f- Cn ) .
,
plot does
example ,
Extranotesonasgmptoticanalysisconsi.de
Let
Def if
an TCI ) =
We say
exist
> O I
on input I time Ocfcn ) )
.
there constant c
number
energy input
In other words,
n, f-(n)
.
c-) fan
irked .
n
( Note :
x-axis
enumerates
all I
of size
n )
.
of
size
.. of size
n
algorithm steps
A
has run natural
of TCI )
S
t .
size E c-
A.
A takes
no and
for every n > no and
for any n > no,
if we TCI )
For c-fln)
ITI )
)
E
#
xtranotesonasgmptoticanalysc.SI
We
A
np
ut
rlfcn
))
has
time
co
nst
the
re
say
ru
n
if
natura
l
number
and
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ant
or
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t
e
e
>
O
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ry
n
o
,
n
e
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c
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>
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ts
i
for
n
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e
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n
,
f
(
)
CI
)
s
I
n
w
or
ds
c-
n
.
ot
her
if
we
plot
any
>
T
,
,
CI)
every
I
of
TCI )
for
size
n
e
xceeds
SOME
,
For
the
bar
I
exam
ple
at
TEH
_
,
or
ITI )
Eit
her
.
of
.
of
size
.
n
size
n
hr
T
z
Extranotesonasgmptoticanalysc.SI
)# We say A has run time Ocfln ))
if there exist natural number no and
.
constants c d>O S- t for every n > no there
exists S#lE AID for
input I of size
n ,
of
In other words,
TCI ) s d- f-Cn) for any n > no,
TCI)
exceeds never
I of size
catch ) for the bar
ITI ) d. fin )
if we plot n , TCI )
for every
the bar exceeds
or
SOME I and d. fan ).
TEH dftn )
,,
s c- f-(n) ERL input I
TCI )
size
n
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