GATE | GATE-CS-2005 | Question 34

A Priority-Queue is implemented as a Max-Heap. Initially, it has 5 elements. The level-order traversal of the heap is given below: 10, 8, 5, 3, 2 Two new elements ”1‘ and ”7‘ are inserted in the heap in that order. The level-order traversal of the heap after the insertion of the elements is:

(A)

10, 8, 7, 5, 3, 2, 1

(B)

10, 8, 7, 2, 3, 1, 5

(C)

10, 8, 7, 1, 2, 3, 5

(D)

10, 8, 7, 3, 2, 1, 5

Answer: (D)

Explanation:

The correct answer is (D), 10, 8, 7, 3, 2, 1, 5.

The level-order traversal of a max-heap is a traversal of the heap where the elements are visited in level order, from left to right. In a max-heap, the parent node must always be greater than or equal to its children.

The initial level-order traversal of the heap is 10, 8, 5, 3, 2. When the elements 1 and 7 are inserted, they are placed at the bottom of the heap, in the rightmost positions. The heap is then re-heapified, which means that the elements are swapped with their parents if necessary to maintain the max-heap property.

After the heap is re-heapified, the level-order traversal of the heap is 10, 8, 7, 3, 2, 1, 5.

Here is a diagram of the heap after the elements are inserted:

10

/ \

8 7

/ \ / \

5 3 2 1

https://www.geeksforgeeks.org/data-structures-and-algorithms-set-22/

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