1
GATE CSE 2006
+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, nodes in the next level, from left to right, is stored from a to a. The nodes from the second level of the tree from left to right are stored from a 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
2
GATE CSE 2006
+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
+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, nodes in the next level, from left to right, is stored from a to a. The nodes from the second level of the tree from left to right are stored from a 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
4
GATE CSE 2005
+2
-0.6
Suppose there are $$\lceil \log n \rceil$$ sorted lists of $$\left\lfloor {{n \over {\log n}}} \right\rfloor$$ elements each. The time complexity of producing a sorted list of all these elements is :
(Hint : Use a heap data structure)
A
$$O(n \log \log n)$$
B
$$\Theta(n \log n)$$
C
$$\Omega(n \log n)$$
D
$$\Omega\left(n^{3/2}\right)$$
GATE CSE Subjects
Discrete Mathematics
Programming Languages
Theory of Computation
Operating Systems
Digital Logic
Computer Organization
Database Management System
Data Structures
Computer Networks
Algorithms
Compiler Design
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