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Consider the ...

Question

Consider the following operation along with Enqueue and Dequeue operations on queue where k is a global parameter.

Multi - Dequeue (Q)
{
m = k ;
while ((Q is not empty) and (m > 0))
{
Dequeue (Q);
m = m - 1 ;
}
}

What is the worst case time complexity of a sequence of n queue operations on an initially empty queue?

A

Θ (n)

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B

Θ (n + k)

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C

Θ (n^{2})

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D

Θ (n k)

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Solution

The correct option is A $Θ (n)$
Since there are 3 queue operation i.e., enqueue, dequeue and Multi - dequeue.

'n' enqueue operation will take $Θ (n)$ time, 'n' dequeue operation will $Θ (n)$ time, 'n' Multi- dequeue operation will take $Θ (n)$ time i.e., Min (n, k) but for worst case when n = k time complexity will be $Θ (n)$

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