1
GATE CSE 2007
MCQ (Single Correct Answer)
+2
-0.6
Consider the process of inserting an element into a Max Heap, where the Max Heap is represented by an array. Suppose we perform a binary search on the path from the new leaf to the root to find the position for the newly inserted element, the number of comparisons performed is:
A
$$\Theta(\log_2n)$$
B
$$\Theta(\log_2\log_2n)$$
C
$$\Theta(n)$$
D
$$\Theta(n\log_2n)$$
2
GATE CSE 2007
MCQ (Single Correct Answer)
+2
-0.6
In the following C function, let n $$ \ge $$ m.
int gcd(n,m)
{
if (n % m == 0) return m;
n = n % m;
return gcd(m,n);
}
How many recursive calls are made by this function?
A
$$\Theta(\log_2n)$$
B
$$\Omega(n)$$
C
$$\Theta(\log_2\log_2n)$$
D
$$\Theta(\sqrt{n})$$
3
GATE CSE 2007
MCQ (Single Correct Answer)
+2
-0.6
An array of n numbers is given, where n is an even number. The maximum as well as the minimum of these n numbers needs to be determined. Which of the following is TRUE about the number of comparisons needed?
A
At least 2n – c comparisons, for some constant c, are needed.
B
At most 1.5n – 2 comparisons are needed.
C
At least n log2 n comparisons are needed.
D
None of the above.
4
GATE CSE 2007
MCQ (Single Correct Answer)
+2
-0.6
Suppose the letters a, b, c, d, e, f have probabilities 1/2, 1/4, 1/8, 1/16, 1/32, 1/32 respectively. Which of the following is the Huffman code for the letter a, b, c, d, e, f?
A
0, 10, 110, 1110, 11110, 11111
B
11, 10, 011, 010, 001, 000
C
11, 10, 01, 001, 0001, 0000
D
110, 100, 010, 000, 001, 111
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