CSE 2320
Name
________________________________
Test 1
Fall 2004
Student ID #
___________________________
Multiple Choice.
Write your answer to the LEFT of each problem.
4 points each
1.
Counting sort is useful for implementing which other sort?
A.
I
NSERTION
S
ORT
B.
LSD radix sort
C.
M
ERGE
S
ORT
D.
Q
UICKSORT
2.
I
NSERTION
S
ORT
is the basis for which other sorting algorithm?
A.
LSD radix sort
B.
M
ERGE
S
ORT
C.
Q
UICKSORT
D.
S
HELL
S
ORT
3.
Which of the following sorting algorithms applies divideandconquer?
A.
H
EAP
S
ORT
B.
I
NSERTION
S
ORT
C.
LSD radix sort
D.
Q
UICKSORT
4.
Which of the following functions is not in
Ω
n
2
ae
è
ç
ö
ø
÷
?
A.
n
B.
n
2
C.
n
2
lg
n
D.
n
3
5.
Suppose that a binary search is to be performed on a table with 20 elements.
The maximum number of elements that could
be examined (probes) is:
A.
4
B.
5
C.
6
D.
7
6.
The function
n
+ log
n
is in which set?
A.
Ω
n
log
n
(
)
B.
Θ
log
n
(
)
C.
Θ
n
( )
D.
Θ
n
log
n
(
)
7.
4
lg7
evaluates to which of the following?
(Recall that
lg
x
= log
2
x
.)
A.
7
B.
7
C.
30
D.
49
8.
A sort is said to be stable when:
A.
Duplicate copies of a key will appear in the same order in the output as in the input.
B.
It removes duplicate copies of any key in the final output.
C.
It runs in
Ο
n
log
n
(
) time.
D.
The average time and the worstcase time are the same.
9.
Suppose
f x
( ) is a monotonically increasing function.
Which of the following approximates the summation?
A.
f
(
x
)
dx
m
n
ò
£
f
(
k
)
k
=
m
n
å
£
f
(
x
)
dx
m
n
ò
B.
f
(
x
)
dx
m
1
n
ò
£
f
(
k
)
k
=
m
n
å
£
f
(
x
)
dx
m
n
+1
ò
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f
(
x
)
dx
m
1
n
1
ò
£
f
(
k
)
k
=
m
n
å
£
f
(
x
)
dx
m
+1
n
+1
ò
D.
f
(
x
)
dx
m
n
+1
ò
£
f
(
k
)
k
=
m
n
å
£
f
(
x
)
dx
m
1
n
ò
10.
Which of the following will not be true regarding the decision tree for Q
UICKSORT
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
ae
è
ç
ö
ø
÷
decisions.
D.
There will be
n
! leaves.
Long Answer
1.
Prove that if
f
(
n
) Î O
g
(
n
)
(
) then
g n
( )
Î W
f n
( )
(
)
.
10 points
2.
List the four phases in a counting sort and the time for each.
5 points
3.
Use the substitution method to show that
T n
( )
= 2
T
n
2
(
)
+
n
2
is in
Θ
n
2
ae
è
ç
ö
ø
÷
.
15 points
4.
Use the recursiontree method to show that
T n
( )
= 2
T
n
2
(
)
+
n
2
is in
Θ
n
2
ae
è
ç
ö
ø
÷
.
15 points
5.
Demonstrate P
ARTITION
on the following array.
10 points
5
6
7
8
9
0
1
2
3
4
6.
Give two ways that heaps are relevant to mergesort with external devices.
5 points
CSE 2320
Name
________________________________
Test 2
Fall 2004
Student ID #
___________________________
Multiple Choice.
Write the letter of your answer to the LEFT of each problem.
4 points each
1.
The stack for ratinamaze stores
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 Spring '12
 BOBWEEMS
 Graph Theory, Sort, d., Flow network, Maximum flow problem, Graph algorithms

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