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<b>Data Structures and Algorithms
with Object-Oriented Design Patterns in C++</b><br>
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<H2><A NAME="SECTION009360000000000000000">Using <tt>Association</tt>s</A></H2>
<P>
Hashing provides a way to determine the position of a given object
directly from that object itself.
Given an object <I>x</I> we determine its position by
evaluating the appropriate hash function, <I>h</I>(<I>x</I>).
We find the location of object <I>x</I> in exactly the same way.
But of what use is this ability to find an object if,
in order to compute the hash function <I>h</I>(<I>x</I>),
we must be able to access the object <I>x</I> in the first place?
<P>
In practice, when using hashing
we are dealing with <em>keyed data</em><A NAME=11616> </A>.
Mathematically, keyed data consists of ordered pairs
<P> <IMG WIDTH=345 HEIGHT=16 ALIGN=BOTTOM ALT="displaymath62774" SRC="img962.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img962.gif" ><P>
where <I>K</I> is a set of keys,
and <I>V</I> is a set of values.
The idea is that we will access elements of the set <I>A</I> using the key.
I.e., the hash function for elements of the set <I>A</I> is given by
<P> <IMG WIDTH=315 HEIGHT=16 ALIGN=BOTTOM ALT="displaymath62775" SRC="img963.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img963.gif" ><P>
where <IMG WIDTH=18 HEIGHT=22 ALIGN=MIDDLE ALT="tex2html_wrap_inline62796" SRC="img964.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img964.gif" > is the hash function associated with the set <I>K</I>.
<P>
For example, suppose we wish to use hashing to implement
a database which contains driver's license records.
Each record contains information about a driver,
such as her name, address, and perhaps a summary of traffic violations.
Furthermore, each record has a unique driver's license number.
The driver's license number is the key
and the other information is the value associated with that key.
<P>
In Section <A HREF="page125.html#secadtsassociations" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page125.html#secadtsassociations"><IMG ALIGN=BOTTOM ALT="gif" SRC="cross_ref_motif.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/icons/cross_ref_motif.gif"></A> the class <tt>Association</tt>
was declared which comprises two objects, a key and a value:
<PRE>class Association : public Object, public Ownership
{
Object* key;
Object* value;
...
};</PRE>
Given this declaration,
the definition of the hash function for <tt>Association</tt>s is trivial.
As shown in Program <A HREF="page221.html#progassoc3c" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page221.html#progassoc3c"><IMG ALIGN=BOTTOM ALT="gif" SRC="cross_ref_motif.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/icons/cross_ref_motif.gif"></A>,
it simply calls the <tt>Hash</tt> member function
of the object to which the <tt>key</tt> member variable points.
<P>
<P><A NAME="11731"> </A><A NAME="progassoc3c"> </A> <IMG WIDTH=575 HEIGHT=50 ALIGN=BOTTOM ALT="program11623" SRC="img965.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img965.gif" ><BR>
<STRONG>Program:</STRONG> <tt>Association</tt> Class <tt>Hash</tt> Member Function Definition<BR>
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