Direction: 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.
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Suppose the elements 7, 2, 10 and 4 are inserted in that order, into the valid 3 – ary max heap found in the above question 60. Which one of the following is the sequence of items in the array representing the resultant heap?
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- 10, 7, 9, 8, 3, 1, 5, 2, 6, 4
- 10, 9, 8, 7, 6, 5, 4, 3, 2, 1
- 10, 9, 4, 5, 7, 6, 8, 2, 1, 3
- 10, 8, 6, 9, 7, 2, 3, 4, 1, 5
- 10, 7, 9, 8, 3, 1, 5, 2, 6, 4
Correct Option: A
Given heap is as follows
To add 7, 2, 10, 4 we add the node at the end of array
We keep if at right place in the heap tree. Compare elements with its parent node.
Since 10 > 6 and 7 > 5, we interchange.
Since 10 > 9, we interchange and we get
n/ 2 = 10/2 = 5
3 is at right position
4 is at right position
Order
10 7 9 8 3 1 5 2 6 4
Hence (a) is correct option.
