Basic Question

Question

Can any algorithms exist which take less than O(1) time????

Answer 1

Big-Oh notation is a mathematical abstraction to characterize the runtime of algorithms. O(1) is one such mathematical abstraction to describe an algorithm or a computer program that takes the same amount of time to run irrespective of the input that is provided to it. That is, if we provide 50 items as input to the algorithm, it will take the same amount of time when we provide 50000 items as input. Thus, from an abstraction point of view, there can not be an algorithm which takes less than O(1) time. However, empirically, when you measure the runtime, you may get a different empirical value.

Comments

1/100 and 10 are both O(1)

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So U mean

1 /100 < 1  < Logn

and 1 < 1/100 < Logn  both are same right??????

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You can only mathematically compare 1/100 and 1. You cannot compare the two using Big-Oh. They are both O(1). Mathematically the above inequality stands.