Question
1
Consider the ArrayFind algorithm.
input : an element x, n, an array A
of n integers
Output : The index i such that
A[i]=x or -1 if no element in A is equal to x
i ← 0
while i <n do
if x = A[i] then
return i
else
i ←i+1
return -1
The number of primitive
operations for the best case is
Select one:
a.
5n+3
b.
5n-2
c.
None of the above
d.
5n
e.
5n+1
Feedback
The correct answer is: 5n+1
Question
2
T(n) = b if n=1
2T(n-1) +b otherwise
Then T(n) is
Select one:
a.
O(2^n)
b.
O(n)
c.
O(n^b)
d.
None of the above
e.
O(n2)
Feedback
The correct answer is: O(2^n)
Question
3
1+3+9+27+... +3^n
Select one:
a.
O(n^3)
b.
O(2^n)
c.
O(n)
d.
O(4^n)
e.
None of the above
Feedback
The
correct answer is: O(4^n)
Question
4
Algorithm Loop(n)
p ← 1
for i← 1 to n do
p ← p.i
return p
What is the value of Loop(6)?
Select one:
a.
720
b.
5
c.
1
d.
None of the above
e.
120
Feedback
The correct answer is: 720
Question
5
Which of these is the correct big-O
expression for 1+4+9+...+(n+2)²?
Select one:
a.
O(log n)
b.
O(n log n)
c.
O(n²)
d.
None of the above
e.
O(n³)
Feedback
The correct answer is: O(n³)
Question
6
Consider the ArrayFind algorithm.
input : an element x, n, an array A
of n integers
Output : The index i such that
A[i]=x or -1 if no element in A is equal to x
i ← 0
while i <n do
if x = A[i] then
return i
else
i ←i+1
return -1
The number of primitive operations
for the best case is
Select one:
a.
5
b.
n/2
c.
None of the above
d.
4
e.
n
Feedback
The correct answer is: 5
Question
7
Consider the following recurrence
relation.
T(n) = 5 if n <= 2
T(n-1)+ n otherwise
Closed form solution for T(n) is
Select one:
a.
n(n+1)/2 +2
b.
n(n+1)/2 +7
c.
n(n-1)/2
d.
n(n+1)/2
e.
None of the above
Feedback
The
correct answer is: n(n+1)/2 +2
Question
8
Which of the following statements
are true?
i. If f(n) is O(n^3), then f(n)+10n^3 is
O(n^3)
ii. If f(n) is O(n^3), then f(n) is Θ(n^3)
iii. If f(n)+10n^3 is O(n^3), then f(n) is O(n^3)
Select one:
a.
None of the above
b.
All of them are true
c.
iii only
d.
i only
e.
i and iii only
Feedback
The correct answer is: i and iii
only
Question
9
If C =1, what would be the
appropriate value of n0 to show that 2n² +9 is O( n²)?
Select one:
a.
4
b.
None of the above
c.
100
d.
5
e.
10
Feedback
The correct answer is: None of the
above
Question
10
Consider the array implementation of
Stack ADT with array size N.
Which of the following statements
are true?
- We can store at max N-1 elements in the stack
- Stack ADT supports inserting elements anywhere
Select one:
a.
Both of them are true
b.
i only
c.
ii only
d.
None of them are true
Feedback
The correct answer is: None of them
are true
Question
11
Which of the following statements
are true?
i) n! is O(n)
ii) n! is O(n^n)
iii) n! is O(2^n)
Select one:
a.
i only
b.
None of the above
c.
ii and iii only
d.
i and iii only
e.
ii only
Feedback
The correct answer is: ii only
Question
12
Algorithm Loop(n)
p ← 1
for i← 1 to n do
p ← p.i
return p
Give a big-Oh characterization for
the above algorithm.
Select one:
a.
O(1)
b.
O(√n)
c.
O(log n)
d.
O(n)
e.
None of the above
Feedback
The correct answer is: O(n)
Question
13
Which of the following statements
are true.
i) (2^(n+1)) is
O(2^(n/2))
ii) (2^(2n)) is
O(2^n)
Select one:
a.
i only
b.
None of them true
c.
Both of them are true
d.
None of the above
e.
ii only
Feedback
The correct answer is: None of them
true
Question
14
Consider the array implementation of
Stack ADT S and we modify the Pop operation as follows.
Algorithm pop()
if isEmpty() then
return Error
dummy ← ???
t ← t-1
return dummy
What should ??? be replaced with?
Select one:
a.
S[t+1]
b.
S[t]
c.
None of the above
d.
S[t-1]
e.
S[0]
Feedback
The correct answer is: S[t]
Question
15
Algorithm A uses 5nlog n operations
and algorithm B uses n√
operations. Determine the value n0 such that A is better than B for n > n0
Select one:
a.
2048
b.
1024
c.
None of the above
d.
512
e.
4096
Feedback
The correct answer is: 512
Question
16
Consider the following stack
operations. new(), push(a), push(b), pop(), push (c), pop(), push(5). what is
the index of top element in the array implementation?
Select one:
a.
0
b.
-1
c.
2
d.
1
e.
None of the above
Feedback
The correct answer is: 1
Question
17
Which of the following formulas in
big-O notation best represent the expression 10n²+5nlogn?
Select one:
a.
None of the above
b.
O(n)
c.
O(n³)
d.
O(42)
e.
O(n²)
Feedback
The correct answer is: O(n²)
Question
18
Which of the following expressions
is not sublinear?
Select one:
a.
O(logn)
b.
O(n)
c.
None of the above
d.
O(n√)
e.
O(log log n)
Feedback
The correct answer is: O(n)
Question
19
Log^2 (n/2) is
Select one:
a.
log^2 (n)−2logn+1
b. log^2 (n) -1
c. None of the above
d.
log log (n/2)
e.
log(n2)
Feedback
The correct answer is: log^2 (n)−2logn+1
Question
20
Consider the Array implementation
for Stack ADT. Stack is empty when
Select one:
a.
t=1
b.
t=0
c.
None of the above
d.
t= -1
Feedback
The correct answer is: t= -1
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