GATE CS 2023 Set 1 — Question 46
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Programming & Data Structures → Heaps → Heap Insert & Extract
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Question
Let be a priority queue for maintaining a set of elements. Suppose is implemented using a max-heap data structure. The operation EXTRACT-MAX() extracts and deletes the maximum element from . The operation INSERT() inserts a new element in . The properties of a max-heap are preserved at the end of each of these operations.When contains elements, which one of the following statements about the worst case running time of these two operations is TRUE?
Correct answer
(B) Both EXTRACT-MAX (A) and INSERT (A, key) run in O(log(n)).
Solution
In a max-heap of size :
1.EXTRACT-MAX(): This operation involves removing the root element (the maximum), replacing it with the last leaf, and then performing a 'heapify-down' (or sink) operation to restore the heap property. The height of the heap is , so the worst-case time complexity is .
2.INSERT(): This operation involves adding the new element as a leaf at the end of the heap and then performing a 'heapify-up' (or swim) operation to restore the heap property. Similarly, the worst-case time complexity is .
Therefore, both operations run in .Continue learning with Success Tracker
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