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<Head>
<Title>Back Insertion Sequence</Title>
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<H1>Back Insertion Sequence</H1>
<Table CellPadding=0 CellSpacing=0 width=100%>
<TR>
<TD Align=left><Img src = "containers.gif" Alt="" WIDTH = "194" HEIGHT = "38" ></TD>
<TD Align=right><Img src = "concept.gif" Alt="" WIDTH = "194" HEIGHT = "38" ></TD>
</TR>
<TR>
<TD Align=left VAlign=top><b>Category</b>: containers</TD>
<TD Align=right VAlign=top><b>Component type</b>: concept</TD>
</TR>
</Table>
<h3>Description</h3>
A Back Insertion Sequence is a <A href="Sequence.html">Sequence</A> where it is possible
to append an element to the end, or to access the last element,
in amortized constant time. Back Insertion Sequences have special
member functions as a shorthand for those operations.
<h3>Refinement of</h3>
<A href="Sequence.html">Sequence</A>
<h3>Associated types</h3>
None, except for those of <A href="Sequence.html">Sequence</A>.
<h3>Notation</h3>
<Table>
<TR>
<TD VAlign=top>
<tt>X</tt>
</TD>
<TD VAlign=top>
A type that is a model of Back Insertion Sequence
</TD>
</TR>
<TR>
<TD VAlign=top>
<tt>a</tt>
</TD>
<TD VAlign=top>
Object of type <tt>X</tt>
</TD>
</TR>
<TR>
<TD VAlign=top>
<tt>T</tt>
</TD>
<TD VAlign=top>
The value type of <tt>X</tt>
</TD>
</TR>
<TR>
<TD VAlign=top>
<tt>t</tt>
</TD>
<TD VAlign=top>
Object of type <tt>T</tt>
</TD>
</tr>
</table>
<h3>Definitions</h3>
<h3>Valid expressions</h3>
In addition to the expressions defined in <A href="Sequence.html">Sequence</A>, the following
expressions must be valid.
<Table border>
<TR>
<TH>
Name
</TH>
<TH>
Expression
</TH>
<TH>
Type requirements
</TH>
<TH>
Return type
</TH>
</TR>
<TR>
<TD VAlign=top>
Back
</TD>
<TD VAlign=top>
<tt>a.back()</tt>
</TD>
<TD VAlign=top>
</TD>
<TD VAlign=top>
<tt>reference</tt> if <tt>a</tt> is mutable, otherwise <tt>const_reference</tt>.
</TD>
</TR>
<TR>
<TD VAlign=top>
Push back
</TD>
<TD VAlign=top>
<tt>a.push_back(t)</tt>
</TD>
<TD VAlign=top>
<tt>a</tt> is mutable.
</TD>
<TD VAlign=top>
<tt>void</tt>
</TD>
</TR>
<TR>
<TD VAlign=top>
Pop back
</TD>
<TD VAlign=top>
<tt>a.pop_back()</tt>
</TD>
<TD VAlign=top>
<tt>a</tt> is mutable.
</TD>
<TD VAlign=top>
<tt>void</tt>
</TD>
</tr>
</table>
<h3>Expression semantics</h3>
<Table border>
<TR>
<TH>
Name
</TH>
<TH>
Expression
</TH>
<TH>
Precondition
</TH>
<TH>
Semantics
</TH>
<TH>
Postcondition
</TH>
</TR>
<TR>
<TD VAlign=top>
Back
</TD>
<TD VAlign=top>
<tt>a.back()</tt>
</TD>
<TD VAlign=top>
<tt>!a.empty()</tt>
</TD>
<TD VAlign=top>
Equivalent to <tt>*(--a.end())</tt>.
</TD>
<TD VAlign=top>
</TD>
</TR>
<TR>
<TD VAlign=top>
Push back
</TD>
<TD VAlign=top>
<tt>a.push_back(t)</tt>
</TD>
<TD VAlign=top>
</TD>
<TD VAlign=top>
Equivalent to <tt>a.insert(a.end(), t)</tt>
</TD>
<TD VAlign=top>
<tt>a.size</tt> is incremented by 1. <tt>a.back()</tt> is a copy of <tt>t</tt>.
</TD>
</TR>
<TR>
<TD VAlign=top>
Pop back
</TD>
<TD VAlign=top>
<tt>a.pop_back()</tt>
</TD>
<TD VAlign=top>
<tt>!a.empty()</tt>
</TD>
<TD VAlign=top>
Equivalent to <tt>a.erase(--a.end())</tt>
</TD>
<TD VAlign=top>
<tt>a.size()</tt> is decremented by 1.
</TD>
</tr>
</table>
<h3>Complexity guarantees</h3>
Back, push back, and pop back are amortized constant time. <A href="#1">[1]</A>
<h3>Invariants</h3>
<Table border>
<TR>
<TD VAlign=top>
Symmetry of push and pop
</TD>
<TD VAlign=top>
<tt>push_back()</tt> followed by <tt>pop_back()</tt> is a null operation.
</TD>
</tr>
</table>
<h3>Models</h3>
<UL>
<LI>
<A href="Vector.html">vector</A>
<LI>
<A href="List.html">list</A>
<LI>
<A href="Deque.html">deque</A>
</UL>
<h3>Notes</h3>
<P><A name="1">[1]</A>
This complexity guarantee is the only reason that <tt>back()</tt>,
<tt>push_back()</tt>, and <tt>pop_back()</tt> are defined: they provide
no additional functionality. Not every sequence must define these
operations, but it is guaranteed that they are efficient if they
exist at all.
<h3>See also</h3>
<A href="Container.html">Container</A>, <A href="Sequence.html">Sequence</A>, <A href="FrontInsertionSequence.html">Front Insertion Sequence</A>,
<tt><A href="Vector.html">vector</A></tt>, <tt><A href="Deque.html">deque</A></tt>, <tt><A href="List.html">list</A></tt>
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