CSE 250 Spring 2011
Homework 3
Due Date: March 21, Monday, by 2:05pm
Total Points: 30
Due Time: 2:05’00” pm.
Print your Name, UB #, and Recitation section on the frst page.
IF these guidelines are not Followed, TA may deduct 10% oF points.
1. (10 pts) Order the following functions by growth rate. Indicate which functions grow at the same
rate. Use limit test to justify your answer.
N,
√
N, N
log
N, N
2
/
log
N, N
log(
N
3
)
,
2
N
,
2
N/
3
Note: The easiest way to solve this problem is: First, arrange the functions in the order of increasing
growth rate. Then, compare each pair of consecutive functions in the list.
Solution
:
(1)
√
N, N, N
log
N, N
log(
N
3
)
, N
2
/
log
N,
2
N/
3
,
2
N
where
N
log
N
and
N
log(
N
3
) grow at the same rate.
(2) lim
N
→∞
√
N
N
= lim
N
→∞
1
√
N
= 0
lim
N
→∞
N
N
log
N
= lim
N
→∞
1
log
N
= 0
lim
N
→∞
N
log
N
N
log(
N
3
)
= lim
N
→∞
log
N
3 log
N
=
1
3
lim
N
→∞
N
log(
N
3
)
N
2
/
log
N
= lim
N
→∞
3 log
N
log
N
N
= lim
N
→∞
3(log
N
)
2
N
= lim
N
→∞
6 log
N
1
N
1
= lim
N
→∞
6 log
N
N
= lim
N
→∞
6
N
= 0
Because
N
2
/
log
N
=
o
(
N
3
),
and lim
N
→∞
N
3
2
N/
3
= lim
N
→∞
3
N
2
2
N/
3
ln 2
/
3
= lim
N
→∞
6
N
2
N/
3
ln 2 ln 2
/
9
= lim
N
→∞
6
2
N/
3
ln 2 ln 2 ln 2
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 Spring '09
 Data Structures, Insertion Sort, #, Big O notation, 2 pts, Comparison sort

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