CSE 2320
Name
____________________________________
Test 1
Spring 2006
Last 4 Digits of Student ID #
__________________
Multiple Choice.
Write your answer to the LEFT of each problem.
3 points each
1.
Suppose
f x
( ) is a monotonically increasing function.
Which of the following approximates the
summation?
A.
f
(
x
)
dx
m
n
+1
ò
£
f
(
k
)
k
=
m
n
å
£
f
(
x
)
dx
m
1
n
ò
B.
f
(
x
)
dx
m
1
n
1
ò
£
f
(
k
)
k
=
m
n
å
£
f
(
x
)
dx
m
+1
n
+1
ò
C.
f
(
x
)
dx
m
1
n
ò
£
f
(
k
)
k
=
m
n
å
£
f
(
x
)
dx
m
n
+1
ò
D.
f
(
x
)
dx
m
n
ò
£
f
(
k
)
k
=
m
n
å
£
f
(
x
)
dx
m
n
ò
2.
For which of the following sorts does the decision tree model not apply?
A. Insertion
B.
LSD Radix Sort
C.
M
ERGE
S
ORT
D.
Q
UICKSORT
3.
Which of the following sorts is not stable?
A. Insertion
B.
LSD Radix Sort
C.
M
ERGE
S
ORT
D.
Q
UICKSORT
4.
What is the definition of
H
n
?
A.
Θ
n
(
)
B.
k
k
=1
n
å
C.
ln
n
D.
1
k
k
=1
n
å
5.
Which of the following functions is not in
Ω
n
( )?
A.
lg
n
B.
n
lg
n
C.
n
2
lg
n
D.
n
3
6.
B
UILD
M
AX
H
EAP
is based on applying M
AX
H
EAPIFY
in the following fashion:
A. In ascending slot number order, for each slot that is a parent.
B. In descending slot number order, for each slot that is a parent.
C.
n
2
times, each time from the root of the heap.
D.
n
 1 times, each time from the root of the heap.
7.
Suppose that a binary search is to be performed on a table with 100 elements.
The maximum number
of elements that could be examined (probes) is:
A.
4
B.
5
C.
6
D.
7
8.
f n
( )
=
n
lg
n
is in all of the following sets, except
A.
Ο
log
n
(
)
B.
Θ
log
n
!
(
)
(
)
C.
Ω
1
n
(
)
D.
Ο
n
2
ae
è
ç
ö
ø
÷
9.
The expected time for insertion sort for
n
keys is in which set?
(All
n
! input permutations are equally
likely.)
A.
Θ
log
n
(
)
B.
Θ
n
( )
C.
Θ
n
log
n
(
)
D.
Θ
n
2
ae
è
ç
ö
ø
÷
10. What is the value of
1
2
(
)
k
=0
¥
å
k
?
A.
1
2
B.
2
3
C.
3
2
D.
2
11. Suppose that you have correctly determined some
c
and
n
o
to prove that
f n
( )
Î W
g n
( )
(
)
.
Which of
the following is not necessarily true?
A.
c
may be decreased
B.
c
may be increased
C.
n
o
may be increased
D.
g n
( )
Î O
f n
( )
(
)
12. Suppose you are using the substitution method to establish a
Θ
bound on a recurrence
T n
( ) and that
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View Full Documentyou already know that
T n
( )
Î Wlg
n
(
) 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 lg
n
(
)
B.
T n
( )
Î O
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
÷
13. Which of the following is not true regarding a minheap with 1000 elements?
A. Subscript 1 will store the maximum priority.
B. The parent for the node with subscript 500 is stored at subscript 250.
C. The left child for the node with subscript 200 is stored at subscript 400.
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 Spring '12
 BOBWEEMS
 Graph Theory, d., LG, B., c.

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