GATE CS 2026 Set 1 Q.33: Binary Trees, Binary Search Trees and Balanced Trees

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)

Your answer

Official answer and solution

Official answer: 11
From: Official GATE 2026 answer key

Solution

Minimize the number of nodes at each level of a full (strict) binary tree, where every internal node has exactly 2 children.

In a full (strict) binary tree, every node has either $0$ or $2$ children. To maximize the height $h$ for a given number of nodes $n = 23$ , each level from $1$ to $h$ should contain the minimum possible number of nodes, which is $2$ nodes per level (one internal node and one leaf at levels $1, \dots, h-1$ , and two leaves at level $h$ ). Thus:

n = 2h + 1 \implies 23 = 2h + 1 \implies h = 11

Final answer

Common trap

Confusing a full binary tree with a general binary tree (which would have max height $22$ ).

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2026 Computer Science and Information Technology - Session 1 (CS1)
Question: 33 of 65
Section: Computer Science and Information Technology

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