Question

For the following max heap implemented with arrays [9][7][6][5][3], what would be the content of the array after the removal of the root?

A) [7][6][3][5]
B) [7][6][5][3]
C) [7][5][6][3]
D) [6][7][5][3]

Answer 1

The correct content of the max heap array after removing the root is [7][5][6][3]. The heap is restructured to maintain max heap properties by replacing the root with the last element, removing the last element, and then heapifying from the new root.

Step-by-step explanation:

Upon the removal of the root from a max heap, the heap must be restructured to maintain its max heap properties. These properties dictate that each parent node should be greater than its children, and the heap should be a complete binary tree.

The process for removing the root is as follows: Replace the root with the last element in the heap. Remove the last element. Heapify the heap starting from the new root to ensure the max heap property is restored. In your case, with the max heap [9][7][6][5][3], after removing the root (9), we replace it with the last element (3). Now the array is [3][7][6][5]. Next, we need to heapify at the root.

Since 7 is the largest of 3's children, we swap 3 and 7, resulting in [7][3][6][5]. We then continue to heapify, but since 3 is in its correct place (no children), no more swaps are needed. Thus, the content of the max heap array after removing the root is [7][5][6][3]. The correct answer is B) [7][5][6][3].