In a max-heap, what is the relationship between the height of the heap and the n

₹0.0

Question: In a max-heap, what is the relationship between the height of the heap and the number of elements?

Options:

Correct Answer: Height is log(n)

Solution:

The height of a max-heap is log(n) because it is a complete binary tree, where n is the number of elements.

In a max-heap, what is the relationship between the height of the heap and the number of elements?

In a max-heap, what is the relationship between the height of the heap and the number of elements?

Step 1: Understand what a max-heap is. A max-heap is a special type of binary tree where the parent node is always greater than or equal to its child nodes.
Step 2: Know that a max-heap is a complete binary tree. This means that all levels of the tree are fully filled except possibly for the last level, which is filled from left to right.
Step 3: Learn about the height of a tree. The height of a tree is the number of edges on the longest path from the root to a leaf node.
Step 4: Realize that in a complete binary tree, the height (h) can be calculated using the formula h = log2(n), where n is the number of elements in the heap.
Step 5: Understand that log2(n) means you are finding the power to which 2 must be raised to get n. This shows how the height grows as you add more elements.

Max-Heap Properties – A max-heap is a complete binary tree where each parent node is greater than or equal to its child nodes, and the height of the heap is related to the number of elements.
Height of a Binary Tree – The height of a complete binary tree with n nodes is log(n), which is a key property in understanding the structure of heaps.