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<Head>
<Title>Sorted Associative Container</Title>
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<BR Clear>
<H1>Sorted Associative Container</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 Sorted Associative Container is a type of <A href="AssociativeContainer.html">Associative Container</A>.
Sorted Associative Containers use an ordering relation on their keys;
two keys are considered to be equivalent if neither one is less than
the other. (If the ordering relation is case-insensitive string
comparison, for example, then the keys "abcde" and "aBcDe" are
equivalent.)
<P>
Sorted Associative Containers guarantee that the complexity for most
operations is never worse than logarithmic <A href="#1">[1]</A>, and they also
guarantee that their elements are always sorted in ascending order by
key.
<h3>Refinement of</h3>
<A href="ReversibleContainer.html">Reversible Container</A>, <A href="AssociativeContainer.html">Associative Container</A>
<h3>Associated types</h3>
Two new types are introduced, in addition to the types defined in the
<A href="AssociativeContainer.html">Associative Container</A> and <A href="ReversibleContainer.html">Reversible Container</A> requirements.
<Table border>
<TR>
<TD VAlign=top>
<tt>X::key_compare</tt>
</TD>
<TD VAlign=top>
The type of a <A href="StrictWeakOrdering.html">Strict Weak Ordering</A> used to compare keys.
Its argument type must be <tt>X::key_type</tt>.
</TD>
</TR>
<TR>
<TD VAlign=top>
<tt>X::value_compare</tt>
</TD>
<TD VAlign=top>
The type of a <A href="StrictWeakOrdering.html">Strict Weak Ordering</A> used to compare values.
Its argument type must be <tt>X::value_type</tt>, and it compares two
objects of <tt>value_type</tt> by passing the keys associated with those
objects to a function object of type <tt>key_compare</tt>.
</TD>
</tr>
</table>
<h3>Notation</h3>
<Table>
<TR>
<TD VAlign=top>
<tt>X</tt>
</TD>
<TD VAlign=top>
A type that is a model of Sorted Associative Container
</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>
Object of type <tt>X::value_type</tt>
</TD>
</TR>
<TR>
<TD VAlign=top>
<tt>k</tt>
</TD>
<TD VAlign=top>
Object of type <tt>X::key_type</tt>
</TD>
</TR>
<TR>
<TD VAlign=top>
<tt>p</tt>, <tt>q</tt>
</TD>
<TD VAlign=top>
Object of type <tt>X::iterator</tt>
</TD>
</TR>
<TR>
<TD VAlign=top>
<tt>c</tt>
</TD>
<TD VAlign=top>
Object of type <tt>X::key_compare</tt>
</TD>
</tr>
</table>
<h3>Definitions</h3>
<h3>Valid expressions</h3>
In addition to the expressions defined in <A href="AssociativeContainer.html">Associative Container</A>
and <A href="ReversibleContainer.html">Reversible Container</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>
Default constructor
</TD>
<TD VAlign=top>
<pre>
X()
X a;
</pre>
</TD>
<TD VAlign=top>
</TD>
<TD VAlign=top>
</TD>
</TR>
<TR>
<TD VAlign=top>
Constructor with compare
</TD>
<TD VAlign=top>
<pre>
X(c)
X a(c);
</pre>
</TD>
<TD VAlign=top>
</TD>
<TD VAlign=top>
</TD>
</TR>
<TR>
<TD VAlign=top>
Key comparison
</TD>
<TD VAlign=top>
<tt>a.key_comp()</tt>
</TD>
<TD VAlign=top>
</TD>
<TD VAlign=top>
<tt>X::key_compare</tt>
</TD>
</TR>
<TR>
<TD VAlign=top>
Value comparison
</TD>
<TD VAlign=top>
<tt>a::value_compare()</tt>
</TD>
<TD VAlign=top>
</TD>
<TD VAlign=top>
<tt>X::value_compare</tt>
</TD>
</TR>
<TR>
<TD VAlign=top>
Lower bound
</TD>
<TD VAlign=top>
<tt>a.lower_bound(k)</tt>
</TD>
<TD VAlign=top>
</TD>
<TD VAlign=top>
<tt>iterator</tt> if <tt>a</tt> is mutable, otherwise <tt>const_iterator</tt>.
</TD>
</TR>
<TR>
<TD VAlign=top>
Upper bound
</TD>
<TD VAlign=top>
<tt>a.upper_bound(k)</tt>
</TD>
<TD VAlign=top>
</TD>
<TD VAlign=top>
<tt>iterator</tt> if <tt>a</tt> is mutable, otherwise <tt>const_iterator</tt>.
</TD>
</TR>
<TR>
<TD VAlign=top>
Equal range
</TD>
<TD VAlign=top>
<tt>a.equal_range(k)</tt>
</TD>
<TD VAlign=top>
</TD>
<TD VAlign=top>
<tt>pair<iterator, iterator></tt> if <tt>a</tt> is mutable, otherwise
<tt>pair<const_iterator, const_iterator></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>
Default constructor
</TD>
<TD VAlign=top>
<pre>
X()
X a;
</pre>
</TD>
<TD VAlign=top>
</TD>
<TD VAlign=top>
Creates an empty container, using <tt>key_compare()</tt> as the comparison
object.
</TD>
<TD VAlign=top>
The size of the container is <tt>0</tt>.
</TD>
</TR>
<TR>
<TD VAlign=top>
Constructor with compare
</TD>
<TD VAlign=top>
<pre>
X(c)
X a(c);
</pre>
</TD>
<TD VAlign=top>
</TD>
<TD VAlign=top>
Creates an empty container, using <tt>c</tt> as the comparison
object.
</TD>
<TD VAlign=top>
The size of the container is <tt>0</tt>. <tt>key_comp()</tt> returns a function
object that is equivalent to <tt>c</tt>.
</TD>
</TR>
<TR>
<TD VAlign=top>
Key comparison
</TD>
<TD VAlign=top>
<tt>a.key_comp()</tt>
</TD>
<TD VAlign=top>
</TD>
<TD VAlign=top>
Returns the key comparison object used by <tt>a</tt>.
</TD>
<TD VAlign=top>
</TD>
</TR>
<TR>
<TD VAlign=top>
Value comparison
</TD>
<TD VAlign=top>
<tt>a::value_compare()</tt>
</TD>
<TD VAlign=top>
</TD>
<TD VAlign=top>
Returns the value comparison object used by <tt>a</tt>.
</TD>
<TD VAlign=top>
If <tt>t1</tt> and <tt>t2</tt> are objects of type <tt>value_type</tt>, and <tt>k1</tt> and
<tt>k2</tt> are the keys associated with them, then <tt>a.value_comp()(t1, t2)</tt>
is equivalent to <tt>a.key_comp()(k1, k2)</tt>.
</TD>
</TR>
<TR>
<TD VAlign=top>
Lower bound
</TD>
<TD VAlign=top>
<tt>a.lower_bound(k)</tt>
</TD>
<TD VAlign=top>
</TD>
<TD VAlign=top>
Returns an iterator pointing to the first element whose key
is not less than <tt>k</tt>. Returns <tt>a.end()</tt> if no such element exists.
</TD>
<TD VAlign=top>
If <tt>a</tt> contains any elements that have the same key as <tt>k</tt>, then
the return value of <tt>lower_bound</tt> points to the first such element.
</TD>
</TR>
<TR>
<TD VAlign=top>
Upper bound
</TD>
<TD VAlign=top>
<tt>a.upper_bound(k)</tt>
</TD>
<TD VAlign=top>
</TD>
<TD VAlign=top>
Returns an iterator pointing to the first element whose key
is greater than <tt>k</tt>. Returns <tt>a.end()</tt> if no such element exists.
</TD>
<TD VAlign=top>
If <tt>a</tt> contains any elements that have the same key as <tt>k</tt>, then
the return value of <tt>upper_bound</tt> points to one past the last such
element.
</TD>
</TR>
<TR>
<TD VAlign=top>
Equal range
</TD>
<TD VAlign=top>
<tt>a.equal_range(k)</tt>
</TD>
<TD VAlign=top>
</TD>
<TD VAlign=top>
Returns a pair whose first element is <tt>a.lower_bound(k)</tt> and whose
second element is <tt>a.upper_bound(k)</tt>.
</TD>
<TD VAlign=top>
</TD>
</tr>
</table>
<h3>Complexity guarantees</h3>
<tt>key_comp()</tt> and <tt>value_comp()</tt> are constant time.
<P>
Erase element is constant time.
<P>
Erase key is <tt>O(log(size()) + count(k))</tt>. <A href="#1">[1]</A>
<P>
Erase range is <tt>O(log(size()) + N)</tt>, where <tt>N</tt> is the length of the
range. <A href="#1">[1]</A>
<P>
Find is logarithmic. <A href="#1">[1]</A>
<P>
Count is <tt>O(log(size()) + count(k))</tt>. <A href="#1">[1]</A>
<P>
Lower bound, upper bound, and equal range are logarithmic. <A href="#1">[1]</A>
<h3>Invariants</h3>
<Table border>
<TR>
<TD VAlign=top>
Definition of <tt>value_comp</tt>
</TD>
<TD VAlign=top>
If <tt>t1</tt> and <tt>t2</tt> are objects of type <tt>X::value_type</tt> and
<tt>k1</tt> and <tt>k2</tt> are the keys associated with those objects, then
<tt>a.value_comp()</tt> returns a <A href="functors.html">function object</A> such that
<tt>a.value_comp()(t1, t2)</tt> is equivalent to <tt>a.key_comp()(k1, k2)</tt>.
</TD>
</TR>
<TR>
<TD VAlign=top>
Ascending order
</TD>
<TD VAlign=top>
The elements in a Sorted Associative Container are always arranged
in ascending order by key. That is, if <tt>a</tt> is a Sorted Associative
Container, then <tt><A href="is_sorted.html">is_sorted</A>(a.begin(), a.end(), a.value_comp())</tt>
is always <tt>true</tt>.
</TD>
</tr>
</table>
<h3>Models</h3>
<UL>
<LI>
<tt><A href="set.html">set</A></tt>
<LI>
<tt><A href="multiset.html">multiset</A></tt>
<LI>
<tt><A href="Map.html">map</A></tt>
<LI>
<tt><A href="Multimap.html">multimap</A></tt>
</UL>
<h3>Notes</h3>
<P><A name="1">[1]</A>
This is a much stronger guarantee than the one provided
by <A href="AssociativeContainer.html">Associative Container</A>. The guarantees in <A href="AssociativeContainer.html">Associative Container</A>
only apply to average complexity; worst case complexity is allowed to
be greater. Sorted Associative Container, however, provides an upper
limit on worst case complexity.
<P><A name="2">[2]</A>
This definition is consistent with the semantics described in
<A href="AssociativeContainer.html">Associative Container</A>. It is a stronger condition, though: if
<tt>a</tt> contains no elements with the key <tt>k</tt>, then <tt>a.equal_range(k)</tt>
returns an empty range that indicates the position where those elements
would be if they did exist. The <A href="AssociativeContainer.html">Associative Container</A> requirements,
however, merely state that the return value is an arbitrary empty range.
<h3>See also</h3>
<A href="AssociativeContainer.html">Associative Container</A>, <A href="HashedAssociativeContainer.html">Hashed Associative Container</A>
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