1
GATE CSE 2007
MCQ (Single Correct Answer)
+2
-0.6
Let w be the minimum weight among all edge weights in an undirected connected graph. Let e be a specific edge of weight w . Which of the following is FALSE?
A
There is a minimum spanning tree containing e.
B
If e is not in a minimum spanning tree T, then in the cycle formed by adding e to T, all edges have the same weight.
C
Every minimum spanning tree has an edge of weight w .
D
e is present in every minimum spanning tree.
2
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
3
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
$$\Theta(n\log_2n)$$
4
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
$$\Theta(\sqrt{n})$$
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