CSE 2320
Name
____________________________________
Test 1
Fall 2011
Last 4 Digits of Mav ID # _____________________
Multiple Choice.
Write your answer to the LEFT of each problem.
4 points each
1.
The time to compute the sum 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.
Suppose there is a large table with
n
integers, possibly with repeated values, in ascending order.
How much time is
needed to determine the number of occurences of a particular value?
A.
Θ
1
( )
B.
Θ
log
n
(
)
C.
Θ
n
( )
D.
Θ
n
log
n
(
)
3.
Suppose you have correctly determined some
c
and
n
o
to prove
g n
( )
Î W
f n
( )
(
)
.
Which of the following is not
necessarily true?
A.
c
may be increased
B.
c
may be decreased
C.
n
o
may be increased
D.
f n
( )
Î O
g n
( )
(
)
4.
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 Wlog
n
(
) and
T n
( )
Î O
n
3
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
÷
5.
The function
n
log
n
+ log
n
is in which set?
A.
Ω
n
2
ae
è
ç
ö
ø
÷
B.
Θ
log
n
(
)
C.
Θ
n
( )
D.
Θ
n
log
n
(
)
6.
Which of the following is not true?
A.
n
2
Î O
n
3
ae
è
ç
ö
ø
÷
B.
n
log
n
Î O
n
2
ae
è
ç
ö
ø
÷
C.
g n
( )
Î O
f n
( )
(
)
Û
f n
( )
Î W
g n
( )
(
)
D.
log
n
Î O loglog
n
(
)
7.
Suppose a binary search is to be performed on a table with 28 elements.
The maximum number of elements that could be
examined (probes) is:
A.
4
B.
5
C.
6
D.
7
8.
Which of the following functions is not in
Ω
n
log
n
(
)?
A.
n
B.
n
lg
n
C.
n
2
D.
n
3
9.
4
lg7
evaluates to which of the following?
(Recall that
lg
x
= log
2
x
.)
A.
7
B.
7
C.
30
D.
49
10. What is required when calling
union(i,j)
for maintaining disjoint subsets?
A.
i
and
j
are in the same subset
B.
i
and
j
are leaders for different subsets
C.
i
and
j
are leaders for the same subset
D.
i
is the ancestor of
j
in one of the trees
Short Answer.
5 points each
1.
Explain what it means for a sort to be stable.
2.
Suppose
f n
( )
Î O
g n
( )
(
)
,
g n
( )
Î O
h n
( )
(
)
, and
h n
( )
Î O
f n
( )
(
)
.
What conclusion may be drawn about the three
functions in terms of
Θ
sets?
3.
Perform an asymptotic analysis for the following code segment to determine an appropriate
Θ
set for the time used.
sum=0;
for (i=0; i<n; i=i+2)
for (j=1; j<n; j=j+j)
sum=sum + a[i]/a[j];
Long Answer
1.
Two
int
arrays,
A
and
B
, contain
m
and
n
int
s each, respectively with
m<=n
.
The elements within both of these arrays
appear in
ascending order
without duplicates (i.e. each table represents a set).
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C
code for a
Θ
m
+
n
(
) algorithm to test
set containment
(
A
⊆
B
) by checking that every
value in
A
appears as a
value in
B
.
If set containment holds, your code should
return 1
.
If an element of
A
does not appear in
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 Spring '12
 BOBWEEMS
 Dynamic Programming, d., A., B., c.

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