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<b>Data Structures and Algorithms
with Object-Oriented Design Patterns in C++</b><br>
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<H3><A NAME="SECTION0016431000000000000000">Worst-Case Running Time</A></H3>
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In the worst case the <I>i</I> in Equation <A HREF="page496.html#eqnsortingii" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page496.html#eqnsortingii"><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 always zero.<A NAME="tex2html968" HREF="footnode.html#37868" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/footnode.html#37868"><IMG ALIGN=BOTTOM ALT="gif" SRC="foot_motif.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/icons/foot_motif.gif"></A>
In this case,
we solve the recurrence using repeated substitution like this:
<P> <IMG WIDTH=500 HEIGHT=281 ALIGN=BOTTOM ALT="eqnarray37869" SRC="img2163.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img2163.gif" ><P>
The worst case occurs when the two subsequences
are as unbalanced as they can be--one sequence has all the remaining elements
and the other has none.
<P>
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