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<HTML><HEAD><TITLE>Union</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="tex2html5801" HREF="page402.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="../icons/next_motif.gif"></A> <A NAME="tex2html5799" HREF="page400.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="../icons/up_motif.gif"></A> <A NAME="tex2html5793" HREF="page400.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="../icons/previous_motif.gif"></A>  <A NAME="tex2html5803" HREF="page611.html"><IMG WIDTH=43 HEIGHT=24 ALIGN=BOTTOM ALT="index" SRC="../icons/index_motif.gif"></A> <BR><HR><H3><A NAME="SECTION0012321000000000000000">Union</A></H3><P>The union operation for <tt>MultisetAsLinkedList</tt> classrequires the merging of two ordered, linked listsas shown in Program&nbsp;<A HREF="page401.html#progmultisetAsLinkedListb"><IMG  ALIGN=BOTTOM ALT="gif" SRC="../icons/cross_ref_motif.gif"></A>.We have assumed that the smallest element contained in a multisetis found at the head of the linked list and the largest is at the tail.<P><P><A NAME="28252">&#160;</A><A NAME="progmultisetAsLinkedListb">&#160;</A> <IMG WIDTH=575 HEIGHT=466 ALIGN=BOTTOM ALT="program28071" SRC="img1595.gif"  ><BR><STRONG>Program:</STRONG> <tt>MultisetAsLinkedList</tt> class <tt>__or__</tt> method.<BR><P><P>The <tt>__or__</tt> method computes its result as follows:The main loop of the program (lines&nbsp;9-15) traverses the linked listsof the two operands,in each iteration appending the smallest remaining element to the result.Once one of the lists has been exhausted,the remaining elements in the other list are simply appended to the result(lines&nbsp;16-21).The total running time for the <tt>__or__</tt> method is <I>O</I>(<I>m</I>+<I>n</I>),where  <IMG WIDTH=76 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline66943" SRC="img1596.gif"  > and  <IMG WIDTH=64 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline66945" SRC="img1597.gif"  >.<P><HR><A NAME="tex2html5801" HREF="page402.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="../icons/next_motif.gif"></A> <A NAME="tex2html5799" HREF="page400.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="../icons/up_motif.gif"></A> <A NAME="tex2html5793" HREF="page400.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="../icons/previous_motif.gif"></A>  <A NAME="tex2html5803" 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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