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CS 573: Graduate Algorithms, Fall 2011
HW 0 (due Tuesday, August 30th in class)
This homework contains four problems.
Read the instructions for submitting homework on
the course webpage
. In particular,
make sure
that you write the solutions for the problems on
separate sheets of paper. Write your name and netid on each sheet.
Collaboration Policy:
For this home work, each student should work
independently
and write
up their own solutions and submit them.
0. Write the sentence
“I understand the course policies. I worked on this homework
on my own.”
Solutions that omit this sentence will not be graded.
1. (10 pts) Sort the following functions from asymptotically smallest to asymptotically largest.
Your answer should be a sorted list. Note that there may be ties.
lnln
n
(
√
3)
lg
n
n
1+1
/
lg
n
e
ln ln
n
√
n
H
n
4
H
n
n
1
.
2
lg
lg
n
n
n
n
n
!
(1 + 1
/n
)
3
n
ln
n
To jog your memory: lg
n
= log
2
n
and ln
n
= log
e
n
and
H
n
=
∑
n
i
=1
1
/i
’
ln
n
+0
.
577215
...
is the
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 Fall '08
 Chekuri,C
 Algorithms

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