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<HTML><HEAD><TITLE>Basics</TITLE></HEAD><BODY bgcolor="#FFFFFF"> <a href="../index.html" target="_top"><img src="../icons/usins.gif" alt="Logo" align=right></a><b>Data Structures and Algorithms with Object-Oriented Design Patterns in Python</b><br><A NAME="tex2html5646" HREF="page388.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="../icons/next_motif.gif"></A> <A NAME="tex2html5644" HREF="page386.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="../icons/up_motif.gif"></A> <A NAME="tex2html5638" HREF="page386.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="../icons/previous_motif.gif"></A>  <A NAME="tex2html5648" HREF="page611.html"><IMG WIDTH=43 HEIGHT=24 ALIGN=BOTTOM ALT="index" SRC="../icons/index_motif.gif"></A> <BR><HR><H1><A NAME="SECTION0012100000000000000000">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_inline66639" SRC="img1549.gif"  >.Of course, using integers as the universe does not preclude the use ofmore complex objects,provided there is a one-to-one mapping between those objectsand the elements of the universal set.<P>A crucial requirement of any set representation scheme is thatit supports the common set operations including<em>union</em><A NAME=27615>&#160;</A>,<em>intersection</em><A NAME=27617>&#160;</A>, andset <em>difference</em><A NAME=27619>&#160;</A>.We also need to compare sets and, specifically,to determine whether a given set is a subset of another.<P><BR> <HR><UL> <LI> <A NAME="tex2html5649" HREF="page388.html#SECTION0012110000000000000000">Implementing Sets</A></UL><HR><A NAME="tex2html5646" HREF="page388.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="../icons/next_motif.gif"></A> <A NAME="tex2html5644" HREF="page386.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="../icons/up_motif.gif"></A> <A NAME="tex2html5638" HREF="page386.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="../icons/previous_motif.gif"></A>  <A NAME="tex2html5648" HREF="page611.html"><IMG WIDTH=43 HEIGHT=24 ALIGN=BOTTOM ALT="index" SRC="../icons/index_motif.gif"></A> <P><ADDRESS><img src="../icons/bruno.gif" alt="Bruno" align=right><a href="../copyright.html">Copyright &#169; 2003</a> by <a href="../signature.html">Bruno R. Preiss, P.Eng.</a>  All rights reserved.</ADDRESS></BODY></HTML>

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