CSE310 HW01 Grading Keys
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1. (10 pts) Let
f
(
n
) =
n
3
and
g
(
n
) = 100
×
n
×
log
2
n
. Find the smallest integer
N
≥
1 such
that
f
(
N
)
≤
g
(
N
) but
f
(
N
+ 1)
> g
(
N
+ 1). Show the values of
N
,
f
(
N
),
g
(
N
),
f
(
N
+ 1)
and
g
(
N
+ 1).
Solution:
N
= 20,
f
(
N
) = 8000,
g
(
N
) = 8643
.
86,
f
(
N
+ 1) = 9261,
g
(
N
+ 1) = 9223
.
87.
Grading Keys:
6 pts for
N
;
1 pt for each of the other values.
2. (10 pts) For each function
f
(
n
) (the row index in the following table) and time
t
(the column
index in the following table),
determine the largest size
n
of a problem that can be solved in
time
t
, assuming that the algorithm takes
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 Spring '08
 Davulcu,H
 Algorithms, Data Structures, pts, Existence, LHS, positive constants c1

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