Let A be a priority queue for maintaining a set of elements. Suppose A is…

GATE · 2023 · CS · Computer Science & IT

Let A be a priority queue for maintaining a set of elements. Suppose A is implemented using a max-heap data structure. The operation Extract-Max(A) extracts and deletes the maximum element from A. The operation Insert(A,key) inserts a new element key in A. The properties of a max-heap are preserved at the end of each of these operations.

When A contains n elements, which one of the following statements about the worst case running time of these two operations is TRUE?

  1. A.

    Both Extract-Max(A) and Insert(A,key) run in O(1).

  2. B.

    Both Extract-Max(A) and Insert(A,key) run in O(log(n)).

  3. C.

    Extract-Max(A) runs in O(1) whereas Insert(A,key) runs in O(n).

  4. D.

    Extract-Max(A) runs in O(1) whereas Insert(A,key) runs in O(log(n)).

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Correct answer: B

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