Answer :
To solve this question, we need to understand the basics of a min heap data structure. A min heap is a complete binary tree where each parent node is less than or equal to its child nodes. The root of the heap, which is the smallest element, is at the top.
Given the initial array representation of the min heap:
[tex]\text{86, 96, 106, 116, 122, 113}[/tex]
We are instructed to remove the value 96 from this heap. When removing an element from a min heap, especially if it's not the root, we typically replace the last element of the heap with the element to be removed and then rearrange the heap to maintain the heap property.
Here's a step-by-step process of what happens:
Remove the element 96. The last element, 113, takes its position.
New array: [tex]\text{86, 113, 106, 116, 122}[/tex]
Now, 113 does not satisfy the min heap property because it is greater than its child, 106. To fix this, we need to 'sift down' the element 113.
Compare 113 with its children (106 and 116) and swap it with the smallest child, which is 106.
New array: [tex]\text{86, 106, 113, 116, 122}[/tex]
Now, 113 is correctly placed as all child nodes are greater than the parent node.
Thus, the array representation of the heap after deleting 96 is:
[tex]\text{86, 106, 113, 116, 122}[/tex]
Therefore, the correct multiple choice option is B. 86, 113, 106, 116, 122.
