I have been browsing through the book "Introduction to Algorithms", and I was reading the chapter on Hash Tables/Hash Functions. (Ch.12). There are three hash function algorithms described: Division method, Multiplication method, and Universal Hashing.

Division method is simple, it is just: h(k) = k % m, where m is the maximum elements in the table. It is assumed that the key k is an integer (and if it is string there are methods given for converting string to int). So far, so good: For an implementation that at core uses something like "vector< list<T> > vec", we can always be sure that the value for key will be within bounds of the vector (because of k % vec.size()).

Now for multiplication method, it gives the function: h(k) = floor( M * ( (k * A) - floor(k * A))), where 0 < A < 1. The book suggests A = (sqrt(5) - 1)/2 as a good choice. M is an integer, and the books says the choice of M is not critical. In it's example it gives M as being 10000.

Now my question is, this function will return some value for h(k), and that will be my index into my vector<list<T>>. But how do I know that it will be within bounds of the array? Am I supposed to apply the division method after I have applied the multiplication method, to ensure that I have a value that is in the proper range? If so, this is not explained in the text.

Thanks.