Question
Download Solution PDFMaximum number of nodes in a binary tree with height k, where root is height 0, is :
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe correct answer is option 2: 2k+1 − 1
Key Points
- In a binary tree, each level can contain at most twice the number of nodes as the previous level.
- If height k means the root is at level 0 and the last level is k, then total levels = k + 1.
- The maximum number of nodes in such a binary tree is given by the sum of the geometric progression:
- Nodes =
- This is the formula for the number of nodes in a perfect binary tree of height k.
Additional Information
- 2k − 1: This would be valid if height was defined as number of levels minus one.
- 2k−1 + 1 and 2k + 1: Incorrect and do not follow from the geometric progression formula.
- Therefore, for height k starting from root at 0, maximum nodes =
Hence, the correct answer is: option 2: 2k+1 − 1
Last updated on Jul 3, 2025
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