In a complete binary tree, what is the relationship between the number of nodes
Practice Questions
Q1
In a complete binary tree, what is the relationship between the number of nodes and the height of the tree?
Nodes = 2^height
Nodes = 2^(height + 1) - 1
Nodes = height^2
Nodes = height!
Questions & Step-by-Step Solutions
In a complete binary tree, what is the relationship between the number of nodes and the height of the tree?
Step 1: Understand what a complete binary tree is. A complete binary tree is a type of binary tree where every level, except possibly the last, is fully filled, and all nodes are as far left as possible.
Step 2: Know what height means. The height of a tree is the number of edges on the longest path from the root to a leaf node.
Step 3: Recognize the relationship between nodes and height. In a complete binary tree, the number of nodes can be calculated using a specific formula.
Step 4: Learn the formula. The formula to find the number of nodes in a complete binary tree is Nodes = 2^(height + 1) - 1.
Step 5: Understand the formula components. 'height' is the height of the tree, and '2^(height + 1)' means you take 2 raised to the power of (height + 1). Then, you subtract 1 to get the total number of nodes.
