1
GATE CSE 2008
MCQ (Single Correct Answer)
+2
-0.6
We have a binary heap on n elements and wish to insert n more elements (not necessarily one after another) into this heap. The total time required for this is
A
$$\Theta(\log n)$$
B
$$\Theta(n)$$
C
$$\Theta(n\log n)$$
D
$$\Theta(n^2)$$
2
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
$$\Theta(n\log_2n)$$
3
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6
Given two arrays of numbers a1,......,an and b1,......, bn where each number is 0 or 1, the fastest algorithm to find the largest span (i, j) such that ai+ai+1......aj = bi+bi+1......bj or report that there is not such span,
A
Takes O(3n) and $$\Omega(2^{n})$$ time if hashing is permitted
B
Takes O(n3) and $$\Omega(n^{2.5})$$ time in the key comparison model
C
Takes θ(n) time and space
D
Takes $$O(\sqrt n)$$ time only if the sum of the 2n elements is an even number
4
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6

A 3-ary max heap is like a binary max heap, but instead of 2 children, nodes have 3 children. A 3-ary heap can be represented by an array as follows: The root is stored in the first location, a[0], nodes in the next level, from left to right, is stored from a[1] to a[3]. The nodes from the second level of the tree from left to right are stored from a[4] location onward. An item x can be inserted into a 3-ary heap containing n items by placing x in the location a[n] and pushing it up the tree to satisfy the heap property.

Which one of the following is a valid sequence of elements in an array representing 3-ary max heap?

A
1, 3, 5, 6, 8, 9
B
9, 6, 3, 1, 8, 5
C
9, 3, 6, 8, 5, 1
D
9, 5, 6, 8, 3, 1
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