What are the differences between O(1) and O(2) in algorithm-analysis?

There is no difference between O(1) and O(2) . Algorithms classifying as O(1) are O(2) and vice versa. In fact O(c1) is O(c2) for any positive constants c1 and c2 .

O(1) and O(2) are the same, as is any O(constant value).

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