Question

For the given max heap, implemented with the array [9][7][6][5][3], what will be the content of the array after the removal of the root? Please remember to swap elements to maintain the max heap properties.

Select one of the following options:
a) [7][6][3][5]
b) [7][6][5][3]
c) [7][5][6][3]
d) [6][7][5][3]

Answer 1

b) [7][6][5][3] After removing the root from the max heap and performing the heapify process, the correct state of the array is [7][6][5][3], which maintains the max heap properties.

Step-by-step explanation:

When removing the root from a max heap, the last element in the heap is moved to the root position to keep the tree complete, and then the heap property is restored by repeatedly swapping this new root with its largest child until it is larger than both of its children.

In the given max heap represented by the array [9][7][6][5][3], after removing the root (9), we take the last element (3) and place it at the root. We end up with [3][7][6][5]. Then we perform the 'heapify' process, comparing the new root with its children (7 and 6).

The largest child (7) is swapped with the root, resulting in [7][3][6][5]. We once again compare the new root position with its children and this time it does not need to swap because 7 is larger than both 3 and 5. Thus, option (b), [7][6][5][3], is the correct state of the array after the heapify process.