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

Of course, if there are two or more keys with the same hash value, then two
different entries will be mapped to the same bucket in A. In this case, we say that a
collision has occurred. Clearly, if each bucket of A can store only a single entry,
then we cannot associate more than one entry with a single bucket, which is a
problem in the case of collisions. To be sure, there are ways of dealing with
collisions, which we will discuss later, but the best strategy is to try to avoid them
in the first place. We say that a hash function is "good" if it maps the keys in our
map so as to minimize collisions as much as possible. For practical reasons, we also
would like a hash function to be fast and easy to compute.
Following the convention in Java, we view the evaluation of a hash function, h(k),
as consisting of two actions—mapping the key k to an integer, called the hash code,
and mapping the hash code to an integer within the range of indices ([0,N − 1]) of a
bucket array, called the compression function. (See Figure 9.3.)
Figure 9.3: The two parts of a hash function: a hash
code and a compression func tion.
9.2.3 Hash Codes
The first action that a hash function performs is to take an arbitrary key k in our
map and assign it an integer value. The integer assigned to a key k is called the
hash code for k. This integer value need not be in the range [0,N − 1], and may even
be negative, but we desire that the set of hash codes assigned to our keys should
avoid collisions as much as possible. For if the hash codes of our keys cause
collisions, then there is no hope for our compression function to avoid them. In
addition, to be consistent with all of our keys, the hash code we use for a key k
should be the same as the hash code for any key that is equal to k.
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