How many nodes are there in a full binary tree of height h?
Practice Questions
Q1
How many nodes are there in a full binary tree of height h?
h
2^h
2^(h+1) - 1
2^h - 1
Questions & Step-by-Step Solutions
How many nodes are there in a full binary tree of height h?
Step 1: Understand what a full binary tree is. A full binary tree is a type of tree where every node has either 0 or 2 children.
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.
Step 3: Recognize that at height 0 (the root), there is 1 node.
Step 4: At height 1, the root has 2 children, so there are 1 (root) + 2 (children) = 3 nodes.
Step 5: At height 2, each of the 2 children from height 1 has 2 children of their own, resulting in 1 + 2 + 4 = 7 nodes.
Step 6: Notice the pattern: At each height h, the number of nodes is 2^(h+1) - 1. This is because each level doubles the number of nodes from the previous level.
Step 7: Conclude that for any height h, the formula 2^(h+1) - 1 gives the total number of nodes in a full binary tree.
Full Binary Tree – A tree in which every node other than the leaves has two children.
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 Count Formula – The formula for calculating the number of nodes in a full binary tree based on its height.
