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Consider the following operation along with Enqueue and Dequeue operations on queues,
where k is a global parameter
where k is a global parameter
MultiDequeue Q {
m k
while Q is not empty and m 0 {
Dequeue Q
m m 1
}
}
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?
empty queue?
- a)
- b)
- c)
- d)
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Consider the following operation along with Enqueue and Dequeue operat...
Initially the queue is empty and we have to perform n operations.
i) One option is to perform all Enqueue operations i.e. n Enqueue operations. Complexity
will be (n)
or
ii) We can perform a mix of Enqueue and Dequeue operations. It can be Enqueue for first
n/2 times and then Dequeue for next n/2, or Enqueue and Dequeue alternately, or any
permutation of Enqueues and Dequeues totaling ‘n’ times. Complexity will be (n)
or
iii) We can perform Enqueues and MultiDequeues. A general pattern could be as follows:
i) One option is to perform all Enqueue operations i.e. n Enqueue operations. Complexity
will be (n)
or
ii) We can perform a mix of Enqueue and Dequeue operations. It can be Enqueue for first
n/2 times and then Dequeue for next n/2, or Enqueue and Dequeue alternately, or any
permutation of Enqueues and Dequeues totaling ‘n’ times. Complexity will be (n)
or
iii) We can perform Enqueues and MultiDequeues. A general pattern could be as follows:
Enqueue Enqueue … (ktimes) MultiDequeue Enqueue Enqueue … (ktimes) MultiDequeue
… Up to total n
---- k items enqueued -----k items deleted----k items enqueued----k items deleted -- and
so on.
The number of times this k-Enqueues, MutiDequeue cycle is performed = n/k +1
So, Complexity will be k times Enqueue + 1 MultiDequeue) x n/k+1
… Up to total n
---- k items enqueued -----k items deleted----k items enqueued----k items deleted -- and
so on.
The number of times this k-Enqueues, MutiDequeue cycle is performed = n/k +1
So, Complexity will be k times Enqueue + 1 MultiDequeue) x n/k+1
or
iv) We can just perform n MultiDequeues (or n Dequeues for that matter):
Each time the while condition is false (empty queue), condition is checked just once for
each of the ‘n’ operations. So θ(n).
iv) We can just perform n MultiDequeues (or n Dequeues for that matter):
Each time the while condition is false (empty queue), condition is checked just once for
each of the ‘n’ operations. So θ(n).
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Consider the following operation along with Enqueue and Dequeue operations on queues,where k is a global parameterMultiDequeue Q {m kwhile Q is not empty and m 0 {Dequeue Qm m 1}}What is the worst case time complexity of a sequence of n queue operations on an initiallyempty queue?a)b)c)d)Correct answer is option 'A'. Can you explain this answer?
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Consider the following operation along with Enqueue and Dequeue operations on queues,where k is a global parameterMultiDequeue Q {m kwhile Q is not empty and m 0 {Dequeue Qm m 1}}What is the worst case time complexity of a sequence of n queue operations on an initiallyempty queue?a)b)c)d)Correct answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Consider the following operation along with Enqueue and Dequeue operations on queues,where k is a global parameterMultiDequeue Q {m kwhile Q is not empty and m 0 {Dequeue Qm m 1}}What is the worst case time complexity of a sequence of n queue operations on an initiallyempty queue?a)b)c)d)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following operation along with Enqueue and Dequeue operations on queues,where k is a global parameterMultiDequeue Q {m kwhile Q is not empty and m 0 {Dequeue Qm m 1}}What is the worst case time complexity of a sequence of n queue operations on an initiallyempty queue?a)b)c)d)Correct answer is option 'A'. Can you explain this answer?.
Consider the following operation along with Enqueue and Dequeue operations on queues,where k is a global parameterMultiDequeue Q {m kwhile Q is not empty and m 0 {Dequeue Qm m 1}}What is the worst case time complexity of a sequence of n queue operations on an initiallyempty queue?a)b)c)d)Correct answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Consider the following operation along with Enqueue and Dequeue operations on queues,where k is a global parameterMultiDequeue Q {m kwhile Q is not empty and m 0 {Dequeue Qm m 1}}What is the worst case time complexity of a sequence of n queue operations on an initiallyempty queue?a)b)c)d)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following operation along with Enqueue and Dequeue operations on queues,where k is a global parameterMultiDequeue Q {m kwhile Q is not empty and m 0 {Dequeue Qm m 1}}What is the worst case time complexity of a sequence of n queue operations on an initiallyempty queue?a)b)c)d)Correct answer is option 'A'. Can you explain this answer?.
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