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1

### GATE CSE 2012

MCQ (Single Correct Answer)
Let W(n) and A(n) denote respectively, the worst case and average case running time of an algorithm executed on an input of size n. Which of the following is ALWAYS TRUE?
A
$$A(n) = \Omega (W(n))$$
B
$$A(n) = \Theta (W(n))$$
C
$$A(n) = O (W(n))$$
D
$$A(n) = 0 (W(n))$$
2

### GATE CSE 2012

MCQ (Single Correct Answer)
The worst case running time to search for an element in a balanced binary search tree with n2n elements is
A
$$\Theta (n\,\log \,n)$$
B
$$\Theta (n{2^n})$$
C
$$\Theta (n)$$
D
$$\Theta (\log \,n)$$
3

### GATE CSE 2010

MCQ (Single Correct Answer)
Two alternate packages A and B are available for processing a database having 10k records. Package A requires 0.0001n2 time units and package B requires $$10n.\log _{10}^n$$ time units to process n records. What is the smallest value of k for which package B will be preferred over A?
A
12
B
10
C
6
D
5
4

### GATE CSE 2007

MCQ (Single Correct Answer)
Consider the following segment of C-code:
int j, n;
j=1;
while(j <= n)
j = j * 2;
The number of comparisons made in the execution of the loop for any n > 0 is:
A
$$\left\lceil {{{\log }_2}n} \right\rceil + 1$$
B
n
C
$$\left\lceil {{{\log }_2}n} \right\rceil$$
D
$$\left\lfloor {{{\log }_2}n} \right\rfloor + 1$$
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