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<HTML><HEAD><TITLE>getMin 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="tex2html4818" HREF="page315.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="../icons/next_motif.gif"></A> <A NAME="tex2html4816" HREF="page311.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="../icons/up_motif.gif"></A> <A NAME="tex2html4812" HREF="page313.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="../icons/previous_motif.gif"></A>  <A NAME="tex2html4820" HREF="page611.html"><IMG WIDTH=43 HEIGHT=24 ALIGN=BOTTOM ALT="index" SRC="../icons/index_motif.gif"></A> <BR><HR><H3><A NAME="SECTION0010413000000000000000"><tt>getMin</tt> Method</A></H3><P>Program&nbsp;<A HREF="page313.html#progbinarySearchTreeb"><IMG  ALIGN=BOTTOM ALT="gif" SRC="../icons/cross_ref_motif.gif"></A> also shows a recursive implementation ofthe <tt>getMin</tt> method of the <tt>BinarySearchTree</tt> class.It follows directly from the data ordering property of search treesthat to find the node containing the smallest key in the tree,we start at the root and follow the chain of left subtrees until weget to the node that has an empty left subtree.The key in that node is the smallest in the tree.Notice that no object comparisons are necessary to identify the smallestkey in the tree.<P>The running time analysis of the <tt>getMin</tt> methodfollows directly from that of the <tt>find</tt> method.The worst case running time of <tt>getMin</tt> is <I>O</I>(<I>n</I>)and the average running time is  <IMG WIDTH=56 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline59347" SRC="img400.gif"  >,where <I>n</I> is the number of internal nodes in the tree.<P><HR><A NAME="tex2html4818" HREF="page315.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="../icons/next_motif.gif"></A> <A NAME="tex2html4816" HREF="page311.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="../icons/up_motif.gif"></A> <A NAME="tex2html4812" HREF="page313.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="../icons/previous_motif.gif"></A>  <A NAME="tex2html4820" 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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