page494.html

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<HTML><HEAD><TITLE>Best-Case Running Time</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="tex2html6854" HREF="page495.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="../icons/next_motif.gif"></A> <A NAME="tex2html6852" HREF="page492.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="../icons/up_motif.gif"></A> <A NAME="tex2html6848" HREF="page493.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="../icons/previous_motif.gif"></A>  <A NAME="tex2html6856" HREF="page611.html"><IMG WIDTH=43 HEIGHT=24 ALIGN=BOTTOM ALT="index" SRC="../icons/index_motif.gif"></A> <BR><HR><H3><A NAME="SECTION0015432000000000000000">Best-Case Running Time</A></H3><P>In the best case,the partitioning step divides the remaining elementsinto two sequences with exactly the same number of elements.For example,suppose that  <IMG WIDTH=78 HEIGHT=20 ALIGN=MIDDLE ALT="tex2html_wrap_inline69407" SRC="img2049.gif"  > for some integer <I>m</I><I>&gt;</I>0.After removing the pivot  <IMG WIDTH=45 HEIGHT=20 ALIGN=MIDDLE ALT="tex2html_wrap_inline69411" SRC="img2050.gif"  > elements remain.If these are divided evenly, each sequence will have  <IMG WIDTH=62 HEIGHT=26 ALIGN=MIDDLE ALT="tex2html_wrap_inline69413" SRC="img2051.gif"  > elements.In this case Equation&nbsp;<A HREF="page492.html#eqnsortingii"><IMG  ALIGN=BOTTOM ALT="gif" SRC="../icons/cross_ref_motif.gif"></A> gives<P> <IMG WIDTH=536 HEIGHT=285 ALIGN=BOTTOM ALT="eqnarray37683" SRC="img2052.gif"  ><P><HR><A NAME="tex2html6854" HREF="page495.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="../icons/next_motif.gif"></A> <A NAME="tex2html6852" HREF="page492.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="../icons/up_motif.gif"></A> <A NAME="tex2html6848" HREF="page493.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="../icons/previous_motif.gif"></A>  <A NAME="tex2html6856" 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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