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<HTML><HEAD><TITLE>Running Time Analysis</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="tex2html7730" HREF="page573.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="../icons/next_motif.gif"></A> <A NAME="tex2html7728" HREF="page569.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="../icons/up_motif.gif"></A> <A NAME="tex2html7724" HREF="page571.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="../icons/previous_motif.gif"></A>  <A NAME="tex2html7732" HREF="page611.html"><IMG WIDTH=43 HEIGHT=24 ALIGN=BOTTOM ALT="index" SRC="../icons/index_motif.gif"></A> <BR><HR><H3><A NAME="SECTION0016423000000000000000">Running Time Analysis</A></H3><P>The worst-case running time for Floyd's algorithm is easily determined.Creating and initializing the <tt>distance</tt> matrix is  <IMG WIDTH=50 HEIGHT=28 ALIGN=MIDDLE ALT="tex2html_wrap_inline70923" SRC="img2242.gif"  >(lines&nbsp;5-8).Transferring the weights from the input graph to the <tt>distance</tt> matrixrequires  <IMG WIDTH=81 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline71119" SRC="img2282.gif"  > time if adjacency lists are used,and  <IMG WIDTH=50 HEIGHT=28 ALIGN=MIDDLE ALT="tex2html_wrap_inline70923" SRC="img2242.gif"  > time when an adjacency matrix is used to representthe input graph (lines&nbsp;9-10).<P>The running time for the three nested loopsis  <IMG WIDTH=50 HEIGHT=28 ALIGN=MIDDLE ALT="tex2html_wrap_inline71371" SRC="img2325.gif"  > in the worst case.Finally, constructing the result graphand transferring the entries from the <tt>distance</tt> matrixto the result requires  <IMG WIDTH=50 HEIGHT=28 ALIGN=MIDDLE ALT="tex2html_wrap_inline70923" SRC="img2242.gif"  > time.As a result, the worst-case running time of Floyd's algorithmis  <IMG WIDTH=50 HEIGHT=28 ALIGN=MIDDLE ALT="tex2html_wrap_inline71371" SRC="img2325.gif"  >.<P><HR><A NAME="tex2html7730" HREF="page573.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="../icons/next_motif.gif"></A> <A NAME="tex2html7728" HREF="page569.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="../icons/up_motif.gif"></A> <A NAME="tex2html7724" HREF="page571.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="../icons/previous_motif.gif"></A>  <A NAME="tex2html7732" 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 &#169; 2003</a> by <a href="../signature.html">Bruno R. Preiss, P.Eng.</a>  All rights reserved.</ADDRESS></BODY></HTML>

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