What is the height of a complete binary tree with n nodes?
Practice Questions
Q1
What is the height of a complete binary tree with n nodes?
log(n)
n
log(n + 1)
n/2
Questions & Step-by-Step Solutions
What is the height of a complete binary tree with n nodes?
Step 1: Understand what a complete binary tree is. A complete binary tree is a type of binary tree where all levels are fully filled except possibly for the last level, which is filled from left to right.
Step 2: Know that the height of a tree is the number of edges on the longest path from the root to a leaf. In a complete binary tree, the height can be calculated based on the number of nodes.
Step 3: Recognize that the number of nodes (n) in a complete binary tree is related to its height (h) by the formula: n = 2^(h+1) - 1. This means that if you know the height, you can find the number of nodes.
Step 4: Rearranging the formula gives us h = log2(n + 1) - 1. However, we often express height in terms of log base 2, which is simply log(n + 1) when considering the complete tree structure.
Step 5: Therefore, the height of a complete binary tree with n nodes is log(n + 1).
