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GATE CSE 2026 Session 1 Q33: Maximum height of a full binary tree with 23 nodes

Question

The height of a binary tree is the number of edges in the longest path from the root to a leaf in the tree. The maximum possible height of a full binary tree with 23 nodes is _________. (answer in integer)

Try it: numerical answer: type the value

Numerical answer. No negative marking.
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Answer: 11 (official GATE 2026 final answer key)

Concept used: A full binary tree with nn nodes has (n−1)/2(n-1)/2 internal nodes; height is maximised by a chain of internal nodes.

First step: There are (23−1)/2=11(23 - 1)/2 = 11 internal nodes; place them on a single root-to-leaf path.

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Source: official GATE 2026 Session 1 CS question paper and final answer key, organised by IIT Guwahati. Question paper · Answer key

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