In a complete binary tree, how many nodes are there at height 'h'?
Practice Questions
Q1
In a complete binary tree, how many nodes are there at height 'h'?
h + 1
2^h
2^(h+1) - 1
h^2
Questions & Step-by-Step Solutions
In a complete binary tree, how many nodes are there at height 'h'?
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.
Step 2: Know what height 'h' means. The height of a tree is the number of edges on the longest path from the root to a leaf. For example, if the root is at height 0, then its children are at height 1, and so on.
Step 3: Realize that at height 'h', the nodes are the leaves of the tree. Each level of a complete binary tree doubles the number of nodes from the previous level.
Step 4: Calculate the number of nodes at height 'h'. The formula for the number of nodes at height 'h' is 2^h. However, this counts only the nodes at that specific height.
Step 5: To find the total number of nodes from height 0 to height 'h', you need to sum the nodes at each height. This gives you 1 + 2 + 4 + ... + 2^h.
Step 6: Use the formula for the sum of a geometric series. The total number of nodes from height 0 to height 'h' is 2^(h+1) - 1.
