GATE CSE 2007 | GATE CSE Year Wise Previous Years Questions

GATE CSE 2007

MCQ (Single Correct Answer)

-0.3

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:

$$\left\lceil {{{\log }_2}n} \right\rceil + 1$$

$$\left\lceil {{{\log }_2}n} \right\rceil $$

$$\left\lfloor {{{\log }_2}n} \right\rfloor + 1$$

GATE CSE 2007

MCQ (Single Correct Answer)

-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:

$$\Theta(\log_2n)$$

$$\Theta(\log_2\log_2n)$$

$$\Theta(n)$$

$$\Theta(n\log_2n)$$

GATE CSE 2007

MCQ (Single Correct Answer)

-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?

There is a minimum spanning tree containing e.

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.

Every minimum spanning tree has an edge of weight w .

e is present in every minimum spanning tree.

GATE CSE 2007

MCQ (Single Correct Answer)

-0.6

In an unweighted, undirected connected graph, the shortest path from a node S to every other node is computed most efficiently, in terms of time complexity by

Dijkstra’s algorithm starting from S.

Warshall’s algorithm

Performing a DFS starting from S.

Performing a BFS starting from S.

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