Question

I was reviewing for my data structures final exam, and I came across a question in past year’s final. Having worked on it for the past three hours, I still couldn’t figure out a way to solve it, except by trial and error. Here’s the question:

“Suppose that the size of your hash table is 31, the constant g is also 31, and that you use the following hash code

int hash = 0;
int n = s.length();
for (int i = 0; i < n; i++)
   hash = g * hash + s.charAt(i);

and that you use separate chaining to resolve collisions. List five different names that would hash to the same location in the table.”

I think there must be some kind of tricks, possibly involving the modulo operator, to solve this problem, considering the size of the hash table is 31, which is the same as the constant g. Sorry if I sound like it, but I’m not asking for code or anything, just some thoughts/hints on the question. Any comment is greatly appreciated. Thanks

Answer 1

According to the Wikipedia article on Java’s string hashing algorithm (which is the same as the algorithm you present):

As with any general hashing function, collisions are possible. For
example, the strings “FB” and “Ea” have the same hash value. The
hashCode() implementation of String uses the prime number 31 and the
difference between ‘a’ and ‘B’ is just 31, so the calculation is 70 ×
31 + 66 = 69 × 31 + 97.