Asymptotic Notation Questions

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21.

O(n^2) means computing time is __________________

A

Constant

B

Quadratic

C

Linear

D

Cubic

Correct Answer: B

None.

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22.

O(n^3) means computing time is __________________

A

Exponential

B

Quadratic

C

Linear

D

Cubic

Correct Answer: D

None.

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23.

O(2^n) means computing time is __________________

A

Constant

B

Quadratic

C

Linear

D

Exponential

Correct Answer: D

None.

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24.

Time complexity of given algorithm 

 Algorithm Display (A)
 { 
 For I:=0 to n-1 
   { 
    For J:=0 to n-1 { Write A; }
    }
  }

A

2n^2+4n+4

B

2n^2+n

C

2n^2+4n+2

D

2n^2-1

Correct Answer: C

None.

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25.

Given two non-negative functions f(n)= 5n²+6n+1 and g(n)=n² . Calculate upper bound value ,C

A

C=5

B

C=12

C

C=6

D

C=11

Correct Answer: B

None.

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26.

Given two non-negative functions f(n)= 6n²+5n+1 and g(n)=n² . Calculate lower bound value ,C

A

C=5

B

C=12

C

C=6

D

C=11

Correct Answer: C

None.

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27.

The functions f & g are non-negative functions. The function f(n)=O(g(n)) if and only if there exist positive constants c & n0 such that __________ for all n, n≥ n0

A

f(n)≤C*g(n)

B

f(n) = C*g(n)

C

f(n) ≥ C*g(n)

D

f(n) != C*g(n)

Correct Answer: A

None.

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28.

The functions f & g are non-negative functions. The function f(n)=Ω(g(n)) if and only if there exist positive constants c & n0 such that ___________ for all n, n≥ n0

A

f(n) ≤ C*g(n)

B

f(n) = C*g(n)

C

f(n) ≥ C*g(n)

D

f(n) != C*g(n)

Correct Answer: C

None.

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29.

The functions f & g are non-negative functions. The function f(n)=θ(g(n)) if and only if there exist positive constants c1,c2 & n0 such that ________for all n, n≥ n0

A

C2*g(n)≤ f(n) ≤ C1*g(n)

B

C2*g(n)≥ f(n) = C1*g(n)

C

C2*g(n)!= f(n) = C1*g(n)

D

C2*g(n)≤ f(n) = C1*g(n)

Correct Answer: A

None.

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30.

Tight bound is denoted as _______

A

Ω

B

Θ

C

ω

D

O

Correct Answer: B

None.

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