需要有关大O符号的信息

Question

Bit of a random question for you. If you have a method that has to check every single individual place inside an array, would it be okay to say that this method has notation of O(n)?

The reason i'm not sure if my answer is correct is due to the fact that as far as i'm aware O(n) relates to the number of items held in the array, while my assumption is based on the actual size of the array?

Answer 1

If your algorithm has to look at every item in the array, that algorithm is O(n). If doesn't really matter if the array is full or not, since you can be flexible in how you define n. It can be either the size of the array or the number of non-null elements in the array. If your algorithm has to look in empty array slots to see if they're empty or not, use the size. (If that's a real performance issue, probably a different data structure is called for.)

For a really contrived example, if it takes one hour to process each non-null array element, but one nanosecond to check for null, then you should define n to be the number of elements that actually exist, because that's what's going to dictate how the algorithm scales.