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<H1>Front 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 Front Insertion Sequence is a <A href="Sequence.html">Sequence</A>
where it is possible to insert an element at the beginning, or to
access the first element, in amortized constant time.  Front 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 Front 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>
Front
</TD>
<TD VAlign=top>
<tt>a.front()</tt> <A href="#1">[1]</A>
</TD>
<TD VAlign=top>
&nbsp;
</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 front
</TD>
<TD VAlign=top>
<tt>a.push_front(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 front
</TD>
<TD VAlign=top>
<tt>a.pop_front()</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>
Front
</TD>
<TD VAlign=top>
<tt>a.front()</tt> <A href="#1">[1]</A>
</TD>
<TD VAlign=top>
<tt>!a.empty()</tt>
</TD>
<TD VAlign=top>
Equivalent to <tt>*(a.begin())</tt>.
</TD>
<TD VAlign=top>
&nbsp;
</TD>
</TR>
<TR>
<TD VAlign=top>
Push front
</TD>
<TD VAlign=top>
<tt>a.push_front(t)</tt>
</TD>
<TD VAlign=top>
&nbsp;
</TD>
<TD VAlign=top>
Equivalent to <tt>a.insert(a.begin(), t)</tt>
</TD>
<TD VAlign=top>
<tt>a.size</tt> is incremented by 1. <tt>a.front()</tt> is a copy of <tt>t</tt>.
</TD>
</TR>
<TR>
<TD VAlign=top>
Pop front
</TD>
<TD VAlign=top>
<tt>a.pop_front()</tt>
</TD>
<TD VAlign=top>
<tt>!a.empty()</tt>
</TD>
<TD VAlign=top>
Equivalent to <tt>a.erase(a.begin())</tt>
</TD>
<TD VAlign=top>
<tt>a.size()</tt> is decremented by 1.
</TD>
</tr>
</table>
<h3>Complexity guarantees</h3>
Front, push front, and pop front are amortized constant time.
<A href="#2">[2]</A>
<h3>Invariants</h3>
<Table border>
<TR>
<TD VAlign=top>
Symmetry of push and pop
</TD>
<TD VAlign=top>
<tt>push_front()</tt> followed by <tt>pop_front()</tt> is a null operation.
</TD>
</tr>
</table>
<h3>Models</h3>
<UL>
<LI>
 <A href="List.html">list</A>
<LI>
 <A href="Deque.html">deque</A>
</UL>
<h3>Notes</h3>
<P><A name="1">[1]</A>
Front is actually defined in <A href="Sequence.html">Sequence</A>,
since it is always possible to implement it in amortized constant
time.  Its definition is repeated here, along with push front and pop
front, in the interest of clarity.
<P><A name="2">[2]</A>
This complexity guarantee is the only reason that <tt>front()</tt>,
<tt>push_front()</tt>, and <tt>pop_front()</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="BackInsertionSequence.html">Back Insertion Sequence</A>,
<tt><A href="Deque.html">deque</A></tt>,
<tt><A href="List.html">list</A></tt>,
<tt><A href="Slist.html">slist</A></tt>

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