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<HTML><HEAD><TITLE>Projects</TITLE></HEAD><BODY bgcolor="#FFFFFF"> <a href="../index.html" target="_top"><img src="../icons/usins.gif" alt="Logo" align=right></a><b>Data Structures and Algorithms with Object-Oriented Design Patterns in Python</b><br><A NAME="tex2html2123" HREF="page81.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="../icons/next_motif.gif"></A> <A NAME="tex2html2121" HREF="page58.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="../icons/up_motif.gif"></A> <A NAME="tex2html2117" HREF="page79.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="../icons/previous_motif.gif"></A> <A NAME="tex2html2125" HREF="page611.html"><IMG WIDTH=43 HEIGHT=24 ALIGN=BOTTOM ALT="index" SRC="../icons/index_motif.gif"></A> <BR><HR><H1><A NAME="SECTION003600000000000000000">Projects</A></H1><P><OL><LI> Write a Python method 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 Python method that takes a single integer argument <I>n</I> and has a worst-case running time of <IMG WIDTH=39 HEIGHT=28 ALIGN=MIDDLE ALT="tex2html_wrap_inline58629" SRC="img258.gif" >.<LI> Write a Python method that takes two integer arguments <I>n</I> and <I>k</I> and has a worst-case running time of <IMG WIDTH=41 HEIGHT=28 ALIGN=MIDDLE ALT="tex2html_wrap_inline60361" SRC="img575.gif" >.<LI> Write a Python method 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_inline59347" SRC="img400.gif" >.<LI> Write a Python method 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_inline59353" SRC="img402.gif" >.<LI> Write a Python method that takes a single integer argument <I>n</I> and has a worst-case running time of <IMG WIDTH=40 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline59363" SRC="img403.gif" >.<LI> The generalized Fibonacci numbers of order <IMG WIDTH=36 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline60375" SRC="img576.gif" > are given by <P> <IMG WIDTH=500 HEIGHT=67 ALIGN=BOTTOM ALT="equation2483" SRC="img577.gif" ><P> Write both <em>recursive</em> and <em>non-recursive</em> methods that compute <IMG WIDTH=28 HEIGHT=35 ALIGN=MIDDLE ALT="tex2html_wrap_inline60377" SRC="img578.gif" >. Measure the running times of your algorithms for various values of <I>k</I> and <I>n</I>.</OL><P><HR><A NAME="tex2html2123" HREF="page81.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="../icons/next_motif.gif"></A> <A NAME="tex2html2121" HREF="page58.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="../icons/up_motif.gif"></A> <A NAME="tex2html2117" HREF="page79.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="../icons/previous_motif.gif"></A> <A NAME="tex2html2125" HREF="page611.html"><IMG WIDTH=43 HEIGHT=24 ALIGN=BOTTOM ALT="index" SRC="../icons/index_motif.gif"></A> <P><ADDRESS><img src="../icons/bruno.gif" alt="Bruno" align=right><a href="../copyright.html">Copyright © 2003</a> by <a href="../signature.html">Bruno R. Preiss, P.Eng.</a> All rights reserved.</ADDRESS></BODY></HTML>
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