GATE CS 2024 Set 1 — Question 43
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Programming & Data Structures → Heaps → Min-Heap & Max-Heap
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Question
Consider a binary min-heap containing 105 distinct elements. Let be the index (in the underlying array) of the maximum element stored in the heap. The number of possible values of is
Correct answer
(A) 53
Solution
In a min-heap, the property is that every parent node is smaller than or equal to its children. Consequently, the smallest element is at the root, and the largest element must be one of the leaf nodes. It cannot be an internal node because an internal node must be smaller than its children.In a binary heap with distinct elements, the structure is a complete binary tree. The number of leaf nodes in a complete binary tree with nodes is given by .Given :
Number of leaves = .The maximum element can be located at any of these leaf positions. Therefore, there are 53 possible values for the index .
Number of leaves = .The maximum element can be located at any of these leaf positions. Therefore, there are 53 possible values for the index .
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