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

Let us briefly analyze the performance of a dictionary implemented with an un
ordered list. Beginning with the memory usage, we note that the space required
for a list-based dictionary with n entries is O(n), since the linked list data structure
has memory usage proportional to its size. In addition, with this implementation
of the dictionary ADT, we can realize operation insert(k, v) easily and efficiently,
just by a single call to the add Last method on S, which simply adds the new
entry to the end of the list. Thus, we achieve O(1) time for the insert(k, v)
operation on the dictionary D.
Unfortunately, this implementation does not allow for an efficient execution of
the find method. A find(k) operation requires, in the worst case, scanning
through the entire list S, examining each of its n entries. For example, we could
use an iterator on the positions in S, stopping as soon as we encounter an entry
with key equal to k (or reach the end of the list). The worst case for the running
time of this method clearly occurs when the search is unsuccessful, and we reach
the end of the list having examined all of its n entries. Thus, the find method runs
in O(n) time.
Similarly, time proportional to n is needed in the worst case to perform a
remove(e) operation on D, if we assume that entries do not keep track of their
positions in S. Thus the running time for performing operation remove(e) is
O(n). Alternatively, if we use location-aware entries that store their position in S,
then we can perform operation remove(e) in O(1) time. (See Section 9.5.1.)
The operation find All always requires scanning through the entire list S, and
therefore its running time is O(n). More precisely, using the big-Theta notation
(Section 4.2.3), we say that operation find All runs in Θ(n) time since it takes
time proportional to n in both the best and worst case.
In conclusion, implementing a dictionary with an unordered list provides for fast
insertions, but at the expense of slow searches and removals. Thus, we should
only use this implementation where we either expect the dictionary to always be
small or we expect the number of insertions to be large relative to the number of
searches and removals. Of course, archiving database and operating system
transactions are precisely situations such as this.
Nevertheless, there are many other scenarios where the number of insertions in a
dictionary will be roughly proportional to the number of searches and removals,
and in these cases the list implementation is clearly inappropriate. The unordered
dictionary implementation we discuss next can often be used, however, to achieve
fast insertions, removals, and searches in many such cases.
9.3.2 Hash Table Dictionary Implementation
We can use a hash table to implement the dictionary ADT, much in the same way as
we did for the map ADT. The main difference, of course, is that a dictionary allows
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