CSE 2320
Name
____________________________________
Test 1
Summer 2005
Last 4 Digits of Student ID #
__________________
Multiple Choice.
Write your answer to the LEFT of each problem.
4 points each
1.
Suppose you are sorting millions of keys that consist of three decimal digits each.
Which of the following sorts uses time
beyond O(n lg n) in the worst case?
A.
counting
B.
heapsort
C.
merge
D.
quick
2.
Which sort never compares two inputs (to each other) twice?
A.
heap
B.
merge
C.
quick
D.
shell
3.
Suppose that a binary search is to be performed on a table with 30 elements.
The maximum number of elements that could
be examined (probes) is:
A.
4
B.
5
C.
6
D.
7
4.
Which function is in neither
Ω
(2
n
) nor O(3
n
)?
A.
2
n
+ n
2
B.
3
n
 n
2
C.
2.5
n
D.
ln n
5.
Which recurrence describes the worstcase time used by Q
UICKSORT
?
A.
T n
( )
=
T
n
2
(
)
+
n
B.
T n
( )
= 2
T
n
2
(
)
+
n
C.
T n
( )
=
T n
 1
(
)
+
n
D.
T n
( )
=
T
n
2
(
)
+1
6.
Which of the following sorts is not stable?
A.
insertion
B.
mergesort
C.
radix
D.
quick
7.
What is the value of
H
4

H
3
?
A.
lg 4
B.
1
4
C.
11
6
D.
3
8.
Which of the following will not be true regarding the decision tree for M
ERGE
S
ORT
for sorting
n
input values?
A.
Every path from the root to a leaf will have
Ο
n
log
n
(
)
decisions.
B.
The height of the tree is
Ω
n
log
n
(
)
.
C.
There will be a path from the root to a leaf with
Ω
n
2
æ
è
ç
ö
ø
÷
decisions.
D.
There will be
n
! leaves.
9.
What is the value of
1
3
k
k
=0
¥
å
?
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A.
1
3
B.
2
3
C.
3
2
D.
3
10.
Suppose the input to H
EAPSORT
is always a table of identical integers.
The worstcase time will be
A.
Θ
(1)
B.
Θ
(n)
C.
Θ
(n lg n)
D.
Θ
(n
2
)
Long Answer
1.
Prove that if
g n
( )
Î W
f n
( )
(
)
then
f
(
n
) Î O
g
(
n
)
(
)
.
10 points
2.
Suppose that a maxheap is used for the subfile production phase of external mergesort.
If the available memory size is
m
,
what is the best case, worst case, and expected case for the size of the subfiles produced?
10 points
3.
Use the substitution method to show that
T n
( )
= 8
T
n
2
(
)
+
n
3
is in
Θ
n
3
lg
n
æ
è
ç
ö
ø
÷
.
10 points
4.
Use the recursiontree method to show that
T n
( )
= 8
T
n
2
(
)
+
n
3
is in
Θ
n
3
lg
n
æ
è
ç
ö
ø
÷
.
10 points
5.
Demonstrate how several executions of P
ARTITION
may be used to determine the median of the following array.
10 points
9
3
1
8
5
6
2
7
4
6.
Perform B
UILD
M
AX
H
EAP
and then E
XTRACT
M
AX
(once).
10 points
11
6
1
10
8
4
3
2
5
1
2
3
4
5
6
7
8
9
9
10
7
11
1
2
3
4
5
6
7
8
9
10
11
1
2
3
4
5
6
7
8
9
10
11
CSE 2320
Name
________________________________
Test 2
Summer 2005
Last 4 Digits of Student ID #
___________________________
Multiple Choice.
Write the letter of your answer to the LEFT of each problem.
4 points each
1.
Why is it common for a circular queue implementation to waste one table element?
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 Spring '12
 BOBWEEMS
 Graph Theory, Sort, d., B., c.

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