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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="SECTION004600000000000000000">Projects</A></H1>
<P>
<OL><LI>
Write a C++ function that takes a single integer argument <I>n</I>
and has a worst-case running time of <I>O</I>(<I>n</I>).<LI>
Write a C++ function that takes a single integer argument <I>n</I>
and has a worst-case running time of <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" >.<LI>
Write a C++ function that takes two integer arguments <I>n</I> and <I>k</I>
and has a worst-case running time of <IMG WIDTH=40 HEIGHT=27 ALIGN=MIDDLE ALT="tex2html_wrap_inline60893" SRC="img580.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img580.gif" >.<LI>
Write a C++ function that takes a single integer argument <I>n</I>
and has a worst-case running time of <IMG WIDTH=56 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline59891" SRC="img403.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img403.gif" >.<LI>
Write a C++ function that takes a single integer argument <I>n</I>
and has a worst-case running time of <IMG WIDTH=68 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline59897" SRC="img405.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img405.gif" >.<LI>
Write a C++ function that takes a single integer argument <I>n</I>
and has a worst-case running time of <IMG WIDTH=39 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline59907" SRC="img406.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img406.gif" >.<LI>
The generalized Fibonacci numbers of order <IMG WIDTH=36 HEIGHT=26 ALIGN=MIDDLE ALT="tex2html_wrap_inline60907" SRC="img581.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img581.gif" > are given by
<P> <IMG WIDTH=500 HEIGHT=67 ALIGN=BOTTOM ALT="equation2395" SRC="img582.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img582.gif" ><P>
Write both <em>recursive</em> and <em>non-recursive</em> functions
that compute <IMG WIDTH=28 HEIGHT=33 ALIGN=MIDDLE ALT="tex2html_wrap_inline60909" SRC="img583.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img583.gif" >.
Measure the running times of your algorithms
for various values of <I>k</I> and <I>n</I>.
</OL>
<P>
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