The height of a binary tree is the number of edges in the longest path from the root to a leaf. The

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GATE-CS is a competitive examination conducted in India. This question is from the 2026 GATE-CS Data Structures paper.

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Question

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

Accepted Answer

Answer: 11Concept -- Full Binary Tree Structure: A full binary tree has every node with either 0 or 2 children (no node with exactly 1 child). For such a tree, the relationship between internal nodes (I) and leaves (L) is L = I + 1. Total nodes N = I + L = 2I + 1 = 2L − 1. Given N = 23, we have 2I + 1 = 23 ⇒ I = 11, L = 12. To maximize height (number of edges on the longest root‑to‑leaf path), we want to make the tree as 'skinny' as possible while maintaining the full binary property. This is achieved by arranging the tree as a 'caterpillar': each internal node (except the deepest) has one leaf child and one internal child. The height then equals the number of internal nodes on the longest path. With I = 11 internal nodes, the maximum height is 11 (from root to deepest leaf, passing through all internal nodes). Any full binary tree with 23 nodes cannot have height greater than 11, and 11 is achievable.

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

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

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