GATE CS 2025 Set 1 — Question 35
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Programming & Data Structures → Heaps → Binary Tree Properties
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Question
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 stores 32 keys. The height of is _____________ . (Answer in integer)
Correct answer
5 to 5
Solution
A Min-Heap is a complete binary tree. The height of a rooted tree is defined here as the maximum number of edges from the root to any leaf node. In a complete binary tree with nodes, the number of nodes at each level (where the root is at level 0) is .
Since the Min-Heap stores 32 keys, the key must be placed at level 5. The path from the root (level 0) to a node at level 5 consists of 5 edges. Therefore, the maximum number of edges in a path from the root to any leaf is 5. Height = 5.
- Level 0: node (root)
- Level 1: nodes
- Level 2: nodes
- Level 3: nodes
- Level 4: nodes
Since the Min-Heap stores 32 keys, the key must be placed at level 5. The path from the root (level 0) to a node at level 5 consists of 5 edges. Therefore, the maximum number of edges in a path from the root to any leaf is 5. Height = 5.
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