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What is the time complexity for deleting root key in a ternary heap of n elements?

(a) O (log n/ log 3)

(b) O (3log n/ log 3)

(c) O (n)

(d) O (1)

I need to ask this question from Ternary heap topic in portion Heap of Data Structures & Algorithms I

This question was posed to me in a job interview.

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The correct option is (b) O (3log n/ log 3)

The explanation is: In order to delete a root key in a ternary heap data structure having n elements, it performs downward swapping. So the time complexity for worst case is found to be O (3log n/ log 3).

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