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

only the one entry. We leave the details of this final space optimization to an
exercise (C-9.5). In Figure 9.4, we give an illustration of a hash table with
separate chaining.
Assuming we use a good hash function to index the n entries of our map in a
bucket array of capacity N, we expect each bucket to be of size n/N. This value,
called the load factor of the hash table (and denoted with δ), should be bounded
by a small constant, preferably below 1. For, given a good hash function, the
expected running time of operations get, put, and remove in a map implemented
with a hash table that uses this function is O( n/N). Thus, we can implement
these operations to run in O(1) expected time, provided n is O(N).
Figure 9.4: A hash table of size 13, storing 10
entries with integer keys, with colli sions resolved by
separate chaining. The compression function is h(k) =
k mod 13. For simplicity, we do not show the values
associated with the keys.
Open Addressing
The separate chaining rule has many nice properties, such as allowing for simple
implementations of map operations, but it nevertheless has one slight disadvan
tage: it requires the use of an auxiliary data structure—a list—to hold entries with
colliding keys. We can handle collisions in other ways besides using the separate
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