Question

The Big O notation for an algorithm with exactly 50 constant time operations is a. O ( 50 ) b. 0(1) C. 0, 50 N ) d. 50.0(1)

Answer 1

Dear student,

In asymptotic analysis of an algorithm, Big O notation or O notation is used to define the worst case complexity of the algorithm.

So, if the algorithm takes n time in processing an input of n, then the complexity is O(n).

But, if the algorithm takes constant time, irrespective of the input size, then the complexity is said to be O(1).

So, as we see in the given question, it is said that the whole algorithm has 50 operations of constant time, let us say 1 unit of time. Then, the complexity will be O(50) but it is not written so. As 50 is constant, it is written as O(1) as it takes 50 units irrespective of the size of input. This means that even if the input size is 1 or 10000000, the time taken is same.

So, the Big O notation for this algorithm is O(1).

Therefore, Option b is correct.

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