In a max-heap, what is the relationship between the height of the heap and the n
Practice Questions
Q1
In a max-heap, what is the relationship between the height of the heap and the number of elements?
Height is log(n)
Height is n
Height is n log(n)
Height is constant
Questions & Step-by-Step Solutions
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.
