1
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.

Suppose the elements 7, 2, 10 and 4 are inserted, in that order, into the valid 3- ary max heap found in the previous question. Which one of the following is the sequence of items in the array representing the resultant heap?

A
10, 7, 9, 8, 3, 1, 5, 2, 6, 4
B
10, 9, 8, 7, 6, 5, 4, 3, 2, 1
C
10, 9, 4, 5, 7, 6, 8, 2, 1, 3
D
10, 8, 6, 9, 7, 2, 3, 4, 1, 5
2
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
3
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
4
GATE CSE 2005
MCQ (Single Correct Answer)
+2
-0.6
Let G(V, E) an undirected graph with positive edge weights. Dijkstra's single-source shortest path algorithm can be implemented using the binary heap data structure with time complexity:
A
$$O\left( {{{\left| V \right|}^2}} \right)$$
B
$$O\left(|E|+|V|\log |V|\right)$$
C
$$O\left(|V|\log|V|\right)$$
D
$$O\left(\left(|E|+|V|\right)\log|V|\right)$$
GATE CSE Subjects
Software Engineering
Web Technologies
EXAM MAP