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<b>Data Structures and Algorithms 
with Object-Oriented Design Patterns in C++</b><br>
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<H1><A NAME="SECTION0013100000000000000000">Basics</A></H1>
<P>
In this chapter we consider sets the elements of which are integers.
By using integers as the universe rather than arbitrary objects,
certain optimizations are possible.
For example, we can use a bit-vector of length <I>N</I>
to represent a set whose universe is  <IMG WIDTH=115 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline67264" SRC="img1601.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img1601.gif"  >.
Of course, using integers as the universe does not preclude the use of
more complex objects,
provided there is a one-to-one mapping between those objects
and the elements of the universal set.
<P>
A crucial requirement of any set representation scheme is that
it supports the common set operations including
<em>union</em><A NAME=28176>&#160;</A>,
<em>intersection</em><A NAME=28178>&#160;</A> and
set <em>difference</em><A NAME=28180>&#160;</A>.
We also need to compare sets and, specifically,
to determine whether a given set is a subset of another.
<P>
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