GATE CS 2020 Set 1 — Question 57
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Programming & Data Structures → Heaps → Min-Heap & Max-Heap
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Question
Consider the array representation of a binary min-heap containing 1023 elements. The minimum number of comparisons required to find the maximum in the heap is ________.
Correct answer
511 to 511
Solution
In a min-heap, the minimum element is at the root. The maximum element must reside in one of the leaf nodes. For a binary heap with elements, the leaves are located at indices to (0-indexed).Given , the number of leaves is (since 1023 corresponds to a full binary tree of height 9, ).To find the maximum, we must compare all leaf nodes. Finding the maximum of elements requires comparisons.Number of comparisons = .
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