Question

“All O(1) functions take exactly the same amount of time to run.” True or false? Can anybody explain the answer to me?

Answer 1

False. O(1) means constant time. This means that no matter what the size of the input is, the function will run in more or less the same amount of time – the runtime does not scale with the input.

This means that two O(1) functions will each run in constant time, though their constants may be different. So if you have two O(1) functions f and g, each of which compute the same result, expecting similar inputs (lets say they expect lists, for the sake of discussion), the runtime of f does not depend on the size of the list; nor does the runtime of g.

However, if f makes more complicated (or otherwise time-consuming) steps to compute the answer than does g, then f‘s runtime will be more than g‘s – the number of seconds required for f to terminate (let’s call this value fsec) will be more than the number of seconds required for g to terminate (let’s call this value gsec). Still, neither fsec nor gsec depend on the size of the input list – they’ll be the same no matter how big or small the input list – but gsec will always be smaller than fsec.

It is because the runtime does not depend on the size of the input list that they are classified as O(1) algorithms – NOT because they perform a particular number of operations.