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Perform and Internet search on the Big O of hash functions and discuss your findings. We...

Perform and Internet search on the Big O of hash functions and discuss your findings. We have said that the Big O is (1) if there are no collisions, and to account for searching due to collisions, we take an average value for the amount of searches necessary to find a spot to place the item. Given that the number of searches increases (dramatically) as the table fills up, what can we say about the Big O (1), is is really constant? if not, what is it?.

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Answer #1

Hashng Time Complexities

Operation Worst Amortized Comments
Access/Search O(n) O(1) O(n) is an extreme case when there are too many collisions
Insert/Edit O(n) O(1) O(n) only happens with rehash when the Hash is 0.75 full
Delete O(n) O(1) O(n) is an extreme case when there are too many collisions

The Big-O Asymptotic Notation gives us the Upper Bound Idea, mathematically described below:

f(n) = O(g(n)) if there exists a positive integer n0 and a positive constant c, such that f(n) <= c.g(n) ∀ n >= n0

So, if you observe carefully, if the number of searches increases as the table fills up, this means that the time complexity of search becomes O(n) which is not a constant.

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