I read a post today saying that hash search performance is O(1), which is wrong.

I am posting this short meditation to correct the expectation. (I don't know how many times this false analysis have appeared in the past)

O(1) means that the worst case performance is not a function of the number of elements in the hash (n). Or the performance is a constant regardless how many elements you store in the hash.

That's not true.

The worst case hash search performance is O(n). This happens when all the hash elements happen to resolve the same hash key. In this case, a hash is no difference than a list.

If the number of valid hash keys is m, and you have n elements in a hash, the average search performance is o(n/2m), as the average queue length under a valid hash key in this case is n/m. I assume the search algorithm for the queue is simply go from the beginning to the end, so in average you have to go thru half length of the queue.