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<HTML><HEAD><TITLE>find Method</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="tex2html4809" HREF="page314.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="../icons/next_motif.gif"></A> <A NAME="tex2html4807" HREF="page311.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="../icons/up_motif.gif"></A> <A NAME="tex2html4801" HREF="page312.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="../icons/previous_motif.gif"></A>  <A NAME="tex2html4811" HREF="page611.html"><IMG WIDTH=43 HEIGHT=24 ALIGN=BOTTOM ALT="index" SRC="../icons/index_motif.gif"></A> <BR><HR><H3><A NAME="SECTION0010412000000000000000"><tt>find</tt> Method</A></H3><P>Program&nbsp;<A HREF="page313.html#progbinarySearchTreeb"><IMG  ALIGN=BOTTOM ALT="gif" SRC="../icons/cross_ref_motif.gif"></A> gives the code for the <tt>find</tt> methodof the <tt>BinarySearchTree</tt> class.In addition to <tt>self</tt>,the <tt>find</tt> method takes as its argument an object.The purpose of the method is to search the tree for an object in the treethat matches the argument.If a match is found, <tt>find</tt> returns the matching object.Otherwise, <tt>find</tt> returns <tt>None</tt>.<P><P><A NAME="18796">&#160;</A><A NAME="progbinarySearchTreeb">&#160;</A> <IMG WIDTH=575 HEIGHT=428 ALIGN=BOTTOM ALT="program18679" SRC="img1235.gif"  ><BR><STRONG>Program:</STRONG> <tt>BinarySearchTree</tt> class <tt>find</tt> and <tt>getMin</tt> methods.<BR><P><P>The recursive <tt>find</tt> method starts its search at the rootand descends one level in the tree for each recursive call.At each level at most one object comparison is made (line&nbsp;6).The worst case running time for a search is<P> <IMG WIDTH=305 HEIGHT=16 ALIGN=BOTTOM ALT="displaymath64133" SRC="img1236.gif"  ><P>where  <IMG WIDTH=42 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline63515" SRC="img1154.gif"  > is the time to compare two objectsand <I>n</I> is the number of internal nodes in the tree.The same asymptotic running time applies for both successfuland unsuccessful searches.<P>The average running time for a successful search is <IMG WIDTH=142 HEIGHT=30 ALIGN=MIDDLE ALT="tex2html_wrap_inline64139" SRC="img1237.gif"  >,where  <IMG WIDTH=154 HEIGHT=30 ALIGN=MIDDLE ALT="tex2html_wrap_inline64141" SRC="img1238.gif"  > is the average depthof an internal node in a binary search tree.If  <IMG WIDTH=96 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline64143" SRC="img1239.gif"  >, the average time of a successful search is  <IMG WIDTH=56 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline59347" SRC="img400.gif"  >.<P>The average running time for an unsuccessful search is <IMG WIDTH=101 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline64147" SRC="img1240.gif"  >,where  <IMG WIDTH=151 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline64149" SRC="img1241.gif"  > is the average depthof an external node in a binary search tree.If  <IMG WIDTH=96 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline64143" SRC="img1239.gif"  >, the average time of an unsuccessful search is  <IMG WIDTH=56 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline59347" SRC="img400.gif"  >.<P><HR><A NAME="tex2html4809" HREF="page314.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="../icons/next_motif.gif"></A> <A NAME="tex2html4807" HREF="page311.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="../icons/up_motif.gif"></A> <A NAME="tex2html4801" HREF="page312.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="../icons/previous_motif.gif"></A>  <A NAME="tex2html4811" 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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