Question

What is the behavior of insert for a binary heap, in the average case?

a) (1)
b) (log n)
c) (n)
d) (n log n)

Answer 1

option b.The behavior of insert for a binary heap in the average case is (log n). It takes approximately log n comparisons and swaps in the average case to insert an element into a binary heap.

Step-by-step explanation:

The behavior of insert for a binary heap in the average case is (log n).

When an element is inserted into a binary heap, it is placed at the next available position in the heap and then bubbled up until it satisfies the heap property. In the average case, this process takes on average log n comparisons and swaps, where n is the number of elements in the heap. This is because a binary heap is a complete binary tree, and the height of a complete binary tree is roughly log n.

For example, if we have a binary heap with 100 elements, the insert operation will take roughly log(100) = 7 comparisons and swaps in the average case.