Data Structures and Algorithms in Java[1].pdf - Fulvio Frisone

of the word lists provided in two variants of Unix, we found that taking a to be
33, 37, 39, or 41 produced less than 7 collisions in each case! It should come as
no surprise, then, to learn that many Java implementations choose the polynomial
hash function, using one of these constants for a, as a default hash code for
strings. For the sake of speed, however, some Java implementations only apply
the polynomial hash function to a fraction of the characters in long strings.
Cyclic Shift Hash Codes
A variant of the polynomial hash code replaces multiplication by a with a cyclic
shift of a partial sum by a certain number of bits. Such a function, applied to
character strings in Java could, for example, look like the following:
static int hashCode(String s) {
int h=0;
for (int i=0; i> 27); // 5-bit cyclic shift of
the running sum
}
h + = (int) s.charAt(i); // add in next character
return h;
}
As with the traditional polynomial hash code, using the cyclic-shift hash code re
quires some fine-tuning. In this case, we must wisely choose the amount to shift
by for each new character. We show in Table 9.2 the results of some experiments
run on a list of just over 25,000 English words, which compare the number of col
lisions for various shift amounts. These and our previous experiments show that if
we choose our constant a or our shift value wisely, then either the polynomial
hash code or its cyclic-shift variant are suitable for any object that can be written
as a tuple (x 0 ,x 1 ,… ,x k 1), where the order in tuples matters.
Table 9.2: Comparison of collision behavior for the
cyclic shift variant of the poly nomial hash code as
applied to a list of just over 25,000 English words. The
"Total" column records the total number of collisions
and the "Max" column records the maximum number
527