CS161  Homework 1
Due: Thursday July 2, 5:00pm
1. (5 points) What sorting method does the function
sort
use from
java.util.Arrays?
Make sure to cite your source.
Why do you think
this is the case?
2. (10 points) The table below contains run times for 6 different algo
rithms.
The input sizes ranged from 1000 to 32000 seen at the top
of the table. For each of the algorithms, give the
θ
complexity of the
algorithms based on the running times and include a brief explaination
for your answer.
Algorithm
1000
2000
4000
8000
16000
32000
A
1
50
378
3,345
26,300
215,680
1,658,002
A
2
99
110
105
976
103
100
A
3
60
130
237
501
954
1999
A
4
1005
1095
1201
1289
1420
1540
A
5
5
21
84
311
1304
5280
A
6
10
22
50
108
245
533
3. (10 points) Arrange the functions below in ascending order of growth
rate. Specifically, if
f
(
n
) =
O
(
g
(
n
)) then
f
(
n
) should be before
g
(
n
) in
the list. If two functions are asympotically equal, i.e.
f
(
n
) = Θ(
g
(
n
))
then note this in the list by including all elements in a set. For exam
ple, given:
n,
log
n
,
n
+4, and
n
2
the list would be: log
n,
(
n, n
+4)
, n
2
.
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 Summer '09
 Algorithms, Sort, Big O notation

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