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presented in this chapter are tabulated below
in Table&nbsp;<A HREF="page53.html#tblgeometricsummary" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page53.html#tblgeometricsummary"><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>
and are plotted for  <IMG WIDTH=82 HEIGHT=25 ALIGN=MIDDLE ALT="tex2html_wrap_inline58895" SRC="img207.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img207.gif"  > in Figure&nbsp;<A HREF="page53.html#figgeometric" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page53.html#figgeometric"><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>.
Figure&nbsp;<A HREF="page53.html#figgeometric" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page53.html#figgeometric"><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> shows that,
according to our simplified model of the computer,
for <I>n</I><I>&lt;</I>4, Program&nbsp;<A HREF="page50.html#proggeometric2c" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page50.html#proggeometric2c"><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> has the best running time.
However as <I>n</I> increases,
Program&nbsp;<A HREF="page53.html#proggeometric3c" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page53.html#proggeometric3c"><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> is clearly the fastest of the three
and Program&nbsp;<A HREF="page48.html#proggeometricc" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page48.html#proggeometricc"><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> is the slowest for all values of <I>n</I>.
<P>
<P><A NAME="1160">&#160;</A>
<P>
    <A NAME="tblgeometricsummary">&#160;</A>
    <DIV ALIGN=CENTER><P ALIGN=CENTER><TABLE COLS=2 BORDER FRAME=HSIDES RULES=GROUPS>
<COL ALIGN=CENTER><COL ALIGN=CENTER>
<TBODY>
<TR><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>
	    program </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> T(n) </TD></TR>
</TBODY><TBODY>
<TR><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>Program&nbsp;<A HREF="page48.html#proggeometricc" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page48.html#proggeometricc"><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> </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>  <IMG WIDTH=124 HEIGHT=29 ALIGN=MIDDLE ALT="tex2html_wrap_inline58903" SRC="img208.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img208.gif"  > </TD></TR>
<TR><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 
	    Program&nbsp;<A HREF="page50.html#proggeometric2c" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page50.html#proggeometric2c"><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> </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 13<I>n</I>+22 </TD></TR>
<TR><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP> 
	    Program&nbsp;<A HREF="page53.html#proggeometric3c" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page53.html#proggeometric3c"><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> </TD><TD VALIGN=BASELINE ALIGN=CENTER NOWRAP>  <IMG WIDTH=181 HEIGHT=26 ALIGN=MIDDLE ALT="tex2html_wrap_inline58907" SRC="img209.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img209.gif"  > </TD></TR>
</TBODY>
<CAPTION ALIGN=BOTTOM><STRONG>Table:</STRONG> Running Times of
	Programs&nbsp;<A HREF="page48.html#proggeometricc" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page48.html#proggeometricc"><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>, <A HREF="page50.html#proggeometric2c" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page50.html#proggeometric2c"><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> and&nbsp;<A HREF="page53.html#proggeometric3c" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page53.html#proggeometric3c"><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></CAPTION></TABLE>
</P></DIV><P>
<P>
<P><A NAME="1301">&#160;</A><A NAME="figgeometric">&#160;</A> <IMG WIDTH=575 HEIGHT=322 ALIGN=BOTTOM ALT="figure1123" SRC="img210.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img210.gif"  ><BR>
<STRONG>Figure:</STRONG> Plot of Running Time vs. <I>n</I> for 	Programs&nbsp;<A HREF="page48.html#proggeometricc" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page48.html#proggeometricc"><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>, <A HREF="page50.html#proggeometric2c" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page50.html#proggeometric2c"><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> and&nbsp;<A HREF="page53.html#proggeometric3c" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page53.html#proggeometric3c"><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><BR>
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