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<TITLE>Putting Items into a Leftist Heap</TITLE>
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<b>Data Structures and Algorithms 
with Object-Oriented Design Patterns in C++</b><br>
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<H2><A NAME="SECTION0012340000000000000000">Putting Items into a Leftist Heap</A></H2>
<P>
The <tt>Enqueue</tt> member function of the <tt>LeftistHeap</tt> class
is used to put items into the heap.
<tt>Enqueue</tt> is easily implemented using the <tt>Merge</tt> operation.
I.e., to enqueue an item in a given heap,
we simply create a new heap containing the one item to be enqueued
and merge it with the given heap.
The algorithm to do this is shown in Program&nbsp;<A HREF="page368.html#progleftist2c" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page368.html#progleftist2c"><IMG  ALIGN=BOTTOM ALT="gif" SRC="cross_ref_motif.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/icons/cross_ref_motif.gif"></A>.
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<P><A NAME="26663">&#160;</A><A NAME="progleftist2c">&#160;</A> <IMG WIDTH=575 HEIGHT=105 ALIGN=BOTTOM ALT="program26551" SRC="img1491.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img1491.gif"  ><BR>
<STRONG>Program:</STRONG> <tt>LeftistHeap</tt> Class 	<tt>Enqueue</tt> Member Function Definition<BR>
<P>
<P>
The expression for the running time for the <tt>Insert</tt> operation
follows directly from that of the <tt>Merge</tt> operation.
I.e., the time required for the <tt>Insert</tt> operation in the worst case is
<P> <IMG WIDTH=364 HEIGHT=17 ALIGN=BOTTOM ALT="displaymath66532" SRC="img1492.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img1492.gif"  ><P>
where <I>d</I> is the null path length of the heap into which the item is inserted.
If we assume that two keys can be compared in constant time,
the running time for <tt>Insert</tt> becomes simply  <IMG WIDTH=56 HEIGHT=24 ALIGN=MIDDLE ALT="tex2html_wrap_inline59891" SRC="img403.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img403.gif"  >,
where <I>n</I> is the number of nodes in the tree into which the item is inserted.
<P>
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