The interpretation of expected time bound for searches in a hash table-CodePudding

As CLRS book,page 260 stated,

I wouldn't have any problem if the author says the bound is eventually
or even

What kind of theories shall we apply to simplify the original result, i.e, cancelling the factor 1/n of a. Since n is one of inputs of the function, is it necessary to cancel it by treating it as a constant? What i've missed? is anyone got the same confusion T_T?

CodePudding user response：

alpha/n is asimptotically smaller (has lower order) being compared with alpha, so it might be ignored. When n (hashtable size, AFAIU) becomes larger, 1/n value tends to zero.
Note - wiki table does not contain 1/n function because it is evaluated as having zero impact

Alike situation - if time is Theta(n^2 100*n 10000), dominating summand is quadratic, and

Theta(n^2   100*n   10000)` = Theta(n^2)