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<TITLE>Tail, EnqueueHead,
    and DequeueTail Member Functions</TITLE>
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<b>Data Structures and Algorithms 
with Object-Oriented Design Patterns in C++</b><br>
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<H3><A NAME="SECTION007321000000000000000"><tt>Tail</tt>, <tt>EnqueueHead</tt>,
    and <tt>DequeueTail</tt> Member Functions</A></H3>
<P>
Program&nbsp;<A HREF="page160.html#progdeque3c" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page160.html#progdeque3c"><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> defines the <tt>Tail</tt>,
<tt>EnqueueHead</tt> and <tt>DequeueTail</tt> member functions
of the <tt>DequeAsArray</tt> class.
<P>
<P><A NAME="8664">&#160;</A><A NAME="progdeque5c">&#160;</A> <IMG WIDTH=575 HEIGHT=429 ALIGN=BOTTOM ALT="program8562" SRC="img759.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img759.gif"  ><BR>
<STRONG>Program:</STRONG> <tt>DequeAsLinkedList</tt> Class <tt>Tail</tt>, 	<tt>EnqueueTail</tt> and <tt>DequeueTail</tt> Member Function Definitions<BR>
<P>
<P>
The <tt>Tail</tt> member function 
returns a <tt>const</tt> reference to the object at the tail of the deque.
The tail of the deque is in the last element of the linked list.
In Chapter&nbsp;<A HREF="page79.html#chapfds" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page79.html#chapfds"><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> we saw that the running time of
<tt>LinkedList&lt;T&gt;::Last</tt> is a constant,
Therefore, the normal running time for the <tt>Tail</tt> function is <I>O</I>(1).
<P>
The <tt>EnqueueHead</tt> function takes a single argument--a reference to the object to be added to the head of the deque.
The function simply calls the <tt>LinkedList&lt;T&gt;::Prepend</tt> function.
Since the running time for <tt>Prepend</tt> is <I>O</I>(1),
the running time of <tt>EnqueueHead</tt> is also <I>O</I>(1).
<P>
The <tt>DequeueTail</tt> function removes an object from the tail
of the deque and returns a reference to that object.
First, it verifies that the deque is not empty
and throws an exception when it is.
If the deque is not empty,
<tt>DequeueTail</tt> saves a reference to the last item in the linked list
in the local variable <tt>result</tt>.
Then the item of the linked list is removed from the list.
When using the <tt>LinkedList&lt;T&gt;</tt> class from Chapter&nbsp;<A HREF="page79.html#chapfds" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/page79.html#chapfds"><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>,
the time required to delete the last item from a list is <I>O</I>(<I>n</I>),
where  <IMG WIDTH=72 HEIGHT=9 ALIGN=BOTTOM ALT="tex2html_wrap_inline61308" SRC="img709.gif" tppabs="http://dictator.uwaterloo.ca/Bruno.Preiss/books/opus4/html/img709.gif"  > is the number of items in the list.
As a result,
the running time of <tt>DequeueTail</tt> is <I>O</I>(<I>n</I>).
<P>
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