GATE CS 2026 Set 1 — Question 33
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Programming & Data Structures → Trees → Binary Tree Properties
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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 in the tree. The maximum possible height of a full binary tree with 23 nodes is _________. (answer in integer)
Correct answer
11 to 11
Solution
A full binary tree (also known as a strict or proper binary tree) is a binary tree where every node has either 0 or 2 children.
Let be the number of nodes and be the height (number of edges on the longest path).To maximize the height of a full binary tree with a fixed number of nodes, we should minimize the number of nodes at each level. This results in a skewed structure where each internal node has exactly one leaf child and one internal child (except for the deepest internal node which has two leaf children).For a full binary tree, the relationship between the number of nodes and the maximum height is given by:Given :Thus, the maximum possible height is 11.
Let be the number of nodes and be the height (number of edges on the longest path).To maximize the height of a full binary tree with a fixed number of nodes, we should minimize the number of nodes at each level. This results in a skewed structure where each internal node has exactly one leaf child and one internal child (except for the deepest internal node which has two leaf children).For a full binary tree, the relationship between the number of nodes and the maximum height is given by:Given :Thus, the maximum possible height is 11.
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