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<TITLE>Putting Items into a Binomial Queue</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="SECTION0012450000000000000000">Putting Items into a Binomial Queue</A></H2>
<P>
With the <tt>Merge</tt> routine at our disposal,
the <tt>Enqueue</tt> operation is easy to implement.
To enqueue an item in a given binomial queue,
we create another binomial queue that contains just the one item to be enqueued
and merge that queue with the original one.
<P>
Program <A HREF="page380.html#progbinom6c" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page380.html#progbinom6c"><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> shows how easily this can be done.
Creating the empty queue (line 3) takes a constant amount of time.
Creating the binomial tree <IMG WIDTH=18 HEIGHT=23 ALIGN=MIDDLE ALT="tex2html_wrap_inline66594" SRC="img1501.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img1501.gif" > with the one object at its root (line 4)
can also be done in constant time.
Finally, the time required to merge the two queues is
<P> <IMG WIDTH=397 HEIGHT=17 ALIGN=BOTTOM ALT="displaymath67048" SRC="img1568.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img1568.gif" ><P>
where <I>n</I> is the number of items originally in the queue.
<P>
<P><A NAME="27728"> </A><A NAME="progbinom6c"> </A> <IMG WIDTH=575 HEIGHT=124 ALIGN=BOTTOM ALT="program27626" SRC="img1569.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img1569.gif" ><BR>
<STRONG>Program:</STRONG> <tt>BinomialQueue</tt> Class <tt>Enqueue</tt> Member Function Definition<BR>
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