GATE CS 2025 Set 1 Q.35: Binary Heaps and Priority Queues

The height of any rooted tree is defined as the maximum number of edges in the path from the root node to any leaf node.

Suppose a Min-Heap $T$ stores 32 keys. The height of $T$ is _____________. (Answer in integer)

Your answer

Official answer and solution

Official answer: 5
From: Official GATE 2025 answer key

Solution

Use the height formula $h = \lfloor \log_2 n \rfloor$ for a complete binary tree with $n$ nodes.

A binary Min-Heap with $n$ keys is stored as a complete binary tree of $n$ nodes. The height (maximum number of edges from the root to a leaf) of a complete binary tree with $n = 32$ nodes is:

h = \lfloor \log_2 32 \rfloor = 5

Final answer

Common trap

Counting the number of levels (6) instead of the number of edges (5).

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

Source

Paper: GATE 2025 Computer Science and Information Technology - Session 1 (CS1)
Question: 35 of 65
Section: Computer Science and Information Technology

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