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<b>Data Structures and Algorithms
with Object-Oriented Design Patterns in C++</b><br>
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<H1><A NAME="SECTION0014600000000000000000">Exercises</A></H1>
<P>
<OL><LI>
Consider the memory map shown in Figure <A HREF="page417.html#figpool1" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page417.html#figpool1"><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>.
The figure suggests that smaller areas (both free and reserved)
are more likely to be found at lower address than
at higher addresses.
<OL><LI>
Explain why this phenomenon occurs
and why it is undesirable.<LI>
Propose a modification to the acquire algorithm
that alleviates this effect.
</OL><LI> <A NAME="exerciseheapi"> </A>
Consider a singly-linked storage pool.
Several strategies are possible when searching a free list
for an area of a given size:
<DL ><DT><STRONG>first fit</STRONG>
<DD><A NAME=32135> </A>
Select the first area encountered that is large enough
to satisfy the request.
<DT><STRONG>next fit</STRONG>
<DD><A NAME=32136> </A>
This is similar to first fit,
except that the free list is treated as a circular list.
Each subsequent search begins from
the position where the previous search ended.
<DT><STRONG>best fit</STRONG>
<DD><A NAME=32137> </A>
Select the smallest area that is large enough
to satisfy the request.
<DT><STRONG>worst fit</STRONG>
<DD><A NAME=32138> </A>
Select the largest area as long as it is large enough
to satisfy the request.
<P>
</DL>
<OL><LI>
Devise a scenario which illustrates that <em>next fit</em>
can be better than <em>first fit</em>.<LI>
Devise a scenario which illustrates that <em>best fit</em>
can be better than <em>first fit</em>.<LI>
Devise a scenario which illustrates that <em>first fit</em>
can be better than <em>best fit</em>.<LI>
Under what conditions (if any) does the <em>worst fit</em>
scenario make sense.
</OL><LI>
Show how Program <A HREF="page424.html#progpool2c" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page424.html#progpool2c"><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> can be modified
to implement the <em>next fit</em> storage allocation
strategy described in Exercise <A HREF="page438.html#exerciseheapi" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page438.html#exerciseheapi"><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>.
What is the running time of your algorithm?<LI>
Show how Program <A HREF="page424.html#progpool2c" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page424.html#progpool2c"><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> can be modified
to implement the <em>best fit</em> storage allocation.
What is the running time of your algorithm?<LI>
Devise optimal algorithms for <tt>acquire</tt> and <tt>release</tt>
given we know <em>a priori</em> that all the areas
acquired from a storage pool will have the same size.
What are the running times of your algorithms?<LI>
Consider the memory maps shown in Figure <A HREF="page417.html#figpool1" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page417.html#figpool1"><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 Figure <A HREF="page426.html#figpool2" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page426.html#figpool2"><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>.
When using the <tt>SinglyLinkedPool</tt> a large block
of unused memory is located at one end the pool
whereas when using the <tt>DoublyLinkedPool</tt>
the large free area is located at the other end.
Explain why this is so.<LI>
Show how Program <A HREF="page430.html#progpool5c" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page430.html#progpool5c"><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> can be modified
to implement the <em>best fit</em> storage allocation.
<OL><LI>
What effect does using the best-fit strategy have
on the length of the free list in this case?<LI>
What is the running time of your algorithm?
</OL><LI>
Consider the implementations of the <tt>SinglyLinkedPool</tt>
and <tt>DoublyLinkedPool</tt> classes.
In both cases,
the sentinel is located immediately following the last
block of the storage pool.
Explain how the implementations depend on this.<LI>
Devise an algorithm that uses bit manipulation operations to compute
<P> <IMG WIDTH=277 HEIGHT=17 ALIGN=BOTTOM ALT="displaymath68387" SRC="img1803.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img1803.gif" ><P>
where <I>n</I> is an integer such that <IMG WIDTH=38 HEIGHT=25 ALIGN=MIDDLE ALT="tex2html_wrap_inline59533" SRC="img344.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img344.gif" >.<LI>
It is possible to implement a buddy pool
in which the size of the pool is not a power of two.
What modifications to the algorithms
are necessary in order to do this?
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