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<TITLE>Implementation</TITLE>
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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="SECTION0016311000000000000000">Implementation</A></H3>
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Program <A HREF="page489.html#progsorter1c" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page489.html#progsorter1c"><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> defines the class template
<tt>StraightInsertionSorter<T></tt>.
This class simply provides an implementation for the <tt>DoSort</tt> routine.
<tt>DoSort</tt> takes one argument--a reference to an <tt>Array<T></tt> instance.
The array initially contains the data to be sorted.
When the function returns,
the contents of the array are sorted.
<P>
<P><A NAME="35502"> </A><A NAME="progsorter1c"> </A> <IMG WIDTH=575 HEIGHT=294 ALIGN=BOTTOM ALT="program35297" SRC="img2117.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img2117.gif" ><BR>
<STRONG>Program:</STRONG> <tt>StraightInsertionSorter<T></tt> Class <tt>DoSort</tt> Member Function Definition<BR>
<P>
<P>
In order to determine the running time
of the <tt>DoSort</tt> routine given in Program <A HREF="page489.html#progsorter1c" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page489.html#progsorter1c"><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>,
we need to determine the number of iterations of the inner loop (lines 12-14).
The number of iterations of the inner loop
in the <IMG WIDTH=17 HEIGHT=13 ALIGN=BOTTOM ALT="tex2html_wrap_inline58387" SRC="img77.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img77.gif" > iteration of the outer loop
depends on the positions of the values in the array.
In the best case, the value in position <I>i</I> of the array
is larger than that in position <I>i</I>-1
and zero iterations of the inner loop are done.
In this case, the running time for insertion sort is <I>O</I>(<I>n</I>).
Notice that the best case performance occurs
when we sort an array that is already sorted!
<P>
In the worst case, <I>i</I> iterations of the inner loop are required
in the <IMG WIDTH=17 HEIGHT=13 ALIGN=BOTTOM ALT="tex2html_wrap_inline58387" SRC="img77.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img77.gif" > iteration of the outer loop.
This occurs when the value in position <I>i</I> of the array is smaller
than the values at positions 0 through <I>i</I>-1.
Therefore, the worst case arises when we sort an array in which the elements
are initially sorted in reverse.
In this case the running time for insertion sort is <IMG WIDTH=40 HEIGHT=25 ALIGN=MIDDLE ALT="tex2html_wrap_inline59179" SRC="img261.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img261.gif" >.
<P>
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