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Name
____________________________________
Test 1
Spring 2010
Last 4 Digits of Mav ID # _____________________
Multiple Choice.
Write your answer to the LEFT of each problem.
3 points each
1.
The time to find the minimum of the
n
elements of an integer array is in:
A.
Θ
n
( )
B.
Θ
n
log
n
(
)
C.
Θ
n
2
ae
è
ç
ö
ø
÷
D.
Θ
n
3
ae
è
ç
ö
ø
÷
2. The goal of the Huffman coding method is:
A.
Construct a maxheap for the symbols in an alphabet
B.
Find the symbols with high probability of occuring.
C.
Maximize the compression for every string.
D.
Minimize the expected bits per symbol.
3.
Which of the following is true?
A.
n
3
Î W
n
2
ae
è
ç
ö
ø
÷
B.
n
log
n
Î W
n
2
ae
è
ç
ö
ø
÷
C.
g n
( )
Î O
f n
( )
(
)
Û
f n
( )
Î O
g n
( )
(
)
D.
3
n
Î O 2
n
ae
è
ç
ö
ø
÷
4.
Which of the following facts cannot be proven using one of the limit theorems?
A.
n
2
Î O
n
3
ae
è
ç
ö
ø
÷
B.
n
2
Î W
n
log
n
(
)
C.
g n
( )
Î Q
f n
( )
(
)
Û
f n
( )
Î Q
g n
( )
(
)
D.
3
n
Î W 2
n
ae
è
ç
ö
ø
÷
5.
The function
2log
n
+ log
n
is in which set?
A.
Ω
n
log
n
(
)
B.
Θ
log
n
(
)
C.
Θ
n
( )
D.
Θ
n
log
n
(
)
6.
f n
( )
=
n
lg
n
is in all of the following sets, except
A.
Ο
log
n
(
)
B.
Θ
log
n
!
(
)
(
)
C.
Ω
n
( )
D.
Ο
n
2
ae
è
ç
ö
ø
÷
7.
The number of calls to
mergeAB
while performing
mergesort
on
n
items is in:
A.
Θ
log
n
(
)
B.
Θ
m
+
n
(
)
C.
Θ
n
( )
D.
Θ
n
log
n
(
)
8.
What is required when calling
union(i,j)
for maintaining disjoint subsets?
A.
i
is the ancestor of
j
in one of the trees
B.
i
and
j
are in the same subset
C.
i
and
j
are leaders for different subsets
D.
i
and
j
are leaders for the same subset
9.
Suppose that you have correctly determined some
c
and
n
o
to prove that
g n
( )
Î W
f n
( )
(
)
.
Which of the following is not
necessarily true?
A.
c
may be decreased
B.
n
o
may be decreased
C.
n
o
may be increased
D.
f n
( )
Î O
g n
( )
(
)
10. Suppose you are using the substitution method to establish a
Θ
bound on a recurrence
T n
( ) and you already know that
T n
( )
Î W1
( ) and
T n
( )
Î O
n
2
ae
è
ç
ö
ø
÷
.
Which of the following cannot be shown as an improvement?
A.
T n
( )
Î O 1
( )
B.
T n
( )
Î O log
n
(
)
C.
T n
( )
Î W
n
2
ae
è
ç
ö
ø
÷
D.
T n
( )
Î W
n
3
ae
è
ç
ö
ø
÷
11. What is
n
, the number of elements, for the largest table that can be processed by binary search using no more than 6
probes?
A.
31
B.
63
C.
64
D.
127
12. The time to determine whether an integer array, in ascending order, has any duplicate values is in which set?
A.
Θ
log
n
(
)
B.
Θ
n
( )
C.
Θ
n
log
n
(
)
D.
Θ
n
2
ae
è
ç
ö
ø
÷
13. Which of the following functions is not in
Ω
n
2
ae
è
ç
ö
ø
÷
?
A.
n
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 Spring '12
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