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

In other words (recalling that we omit a logarithm's base when it is 2), m > logn.
Thus, we have
m = logn + 1,
which implies that binary search runs in O(logn) time.
There is a simple variation of binary search that performs findAll(k) in time
O(logn + s), where s is the number of entries in the iterator returned. The details
are left as an exercise (C-9.4).
Thus, we can use an ordered search table to perform fast dictionary searches, but
using such a table for lots of dictionary updates would take a considerable amount
of time. For this reason, the primary applications for search tables are in situations
where we expect few updates to the dictionary but many searches. Such a
situation could arise, for example, in an ordered list of English words we use to
order entries in an encyclopedia or help file.
Comparing Dictionary Implementations
Table 9.3 compares the running times of the methods of a dictionary realized by
either an unordered list, a hash table, or an ordered search table. Note that an
unordered list allows for fast insertions but slow searches and removals, whereas
a search table allows for fast searches but slow insertions and removals.
Incidentally, although we don't explicitly discuss it, we note that a sorted list
implemented with a doubly linked list would be slow in performing almost all the
dictionary operations. (See Exercise R-9.3.)
Table 9.3: Comparison of the running times of the
methods of a dictionary realized by means of an
unordered list, a hash table, or an ordered search
table. We let n denote the number of entries in the
dictionary, N denote the capacity of the bucket array
in the hash table implementations, and s denote the
size of collection returned by operation findAll. The
space requirement of all the implementations is O(n),
assuming that the arrays supporting the hash table
and search table implementations are maintained such
that their capacity is proportional to the number of
entries in the dictionary.
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