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<Title>upper_bound</Title>
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<H1>upper_bound</H1>
<Table CellPadding=0 CellSpacing=0 width=100%>
<TR>
<TD Align=left><Img src = "algorithms.gif" Alt="" WIDTH = "194" HEIGHT = "38" ></TD>
<TD Align=right><Img src = "function.gif" Alt="" WIDTH = "194" HEIGHT = "38" ></TD>
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<TR>
<TD Align=left VAlign=top><b>Category</b>: algorithms</TD>
<TD Align=right VAlign=top><b>Component type</b>: function</TD>
</TR>
</Table>
<h3>Prototype</h3>
<tt>Upper_bound</tt> is an overloaded name; there are actually two <tt>upper_bound</tt>
functions.
<pre>
template <class <A href="ForwardIterator.html">ForwardIterator</A>, class <A href="LessThanComparable.html">LessThanComparable</A>>
ForwardIterator upper_bound(ForwardIterator first, ForwardIterator last,
const LessThanComparable& value);
template <class <A href="ForwardIterator.html">ForwardIterator</A>, class T, class <A href="StrictWeakOrdering.html">StrictWeakOrdering</A>>
ForwardIterator upper_bound(ForwardIterator first, ForwardIterator last,
const T& value, StrictWeakOrdering comp);
</pre>
<h3>Description</h3>
<tt>Upper_bound</tt> is a version of binary search: it attempts to find the
element <tt>value</tt> in an ordered range <tt>[first, last)</tt> <A href="#1">[1]</A>. Specifically, it
returns the last position where <tt>value</tt> could be inserted without
violating the ordering. <A href="#2">[2]</A> The first version of <tt>upper_bound</tt>
uses <tt>operator<</tt> for comparison, and the second uses the
<A href="functors.html">function object</A> <tt>comp</tt>.
<P>
The first version of <tt>upper_bound</tt> returns the furthermost iterator
<tt>i</tt> in <tt>[first, last)</tt> such that, for every iterator <tt>j</tt> in <tt>[first, i)</tt>,
<tt>value < *j</tt> is <tt>false</tt>.
<P>
The second version of <tt>upper_bound</tt> returns the furthermost iterator
<tt>i</tt> in <tt>[first, last)</tt> such that, for every iterator <tt>j</tt> in <tt>[first, i)</tt>,
<tt>comp(value, *j)</tt> is <tt>false</tt>.
<h3>Definition</h3>
Defined in the standard header <A href="algorithm">algorithm</A>, and in the nonstandard
backward-compatibility header <A href="algo.h">algo.h</A>.
<h3>Requirements on types</h3>
For the first version:
<UL>
<LI>
<tt>ForwardIterator</tt> is a model of <A href="ForwardIterator.html">Forward Iterator</A>.
<LI>
<tt>LessThanComparable</tt> is a model of <A href="LessThanComparable.html">LessThan Comparable</A>.
<LI>
The ordering on objects of type <tt>LessThanComparable</tt> is a <i>strict
weak ordering</i>, as defined in the <A href="LessThanComparable.html">LessThan Comparable</A> requirements.
<LI>
<tt>ForwardIterator</tt>'s value type is the same type as <tt>LessThanComparable</tt>.
</UL>
For the second version:
<UL>
<LI>
<tt>ForwardIterator</tt> is a model of <A href="ForwardIterator.html">Forward Iterator</A>.
<LI>
<tt>StrictWeakOrdering</tt> is a model of <A href="StrictWeakOrdering.html">Strict Weak Ordering</A>.
<LI>
<tt>ForwardIterator</tt>'s value type is the same type as <tt>T</tt>.
<LI>
<tt>ForwardIterator</tt>'s value type is convertible to <tt>StrictWeakOrdering</tt>'s
argument type.
</UL>
<h3>Preconditions</h3>
For the first version:
<UL>
<LI>
<tt>[first, last)</tt> is a valid range.
<LI>
<tt>[first, last)</tt> is ordered in ascending order according to
<tt>operator<</tt>. That is, for every pair of iterators <tt>i</tt> and <tt>j</tt>
in <tt>[first, last)</tt> such that <tt>i</tt> precedes <tt>j</tt>,
<tt>*j < *i</tt> is <tt>false</tt>.
</UL>
For the second version:
<UL>
<LI>
<tt>[first, last)</tt> is a valid range.
<LI>
<tt>[first, last)</tt> is ordered in ascending order according to
the <A href="functors.html">function object</A> <tt>comp</tt>. That is, for every pair of iterators <tt>i</tt> and <tt>j</tt>
in <tt>[first, last)</tt> such that <tt>i</tt> precedes <tt>j</tt>,
<tt>comp(*j, *i)</tt> is <tt>false</tt>.
</UL>
<h3>Complexity</h3>
The number of comparisons is logarithmic: at most <tt>log(last - first) +
1</tt>. If <tt>ForwardIterator</tt> is a <A href="RandomAccessIterator.html">Random Access Iterator</A> then the
number of steps through the range is also logarithmic; otherwise,
the number of steps is proportional to <tt>last - first</tt>. <A href="#3">[3]</A>
<h3>Example</h3>
<pre>
int main()
{
int A[] = { 1, 2, 3, 3, 3, 5, 8 };
const int N = sizeof(A) / sizeof(int);
for (int i = 1; i <= 10; ++i) {
int* p = upper_bound(A, A + N, i);
cout << "Searching for " << i << ". ";
cout << "Result: index = " << p - A << ", ";
if (p != A + N)
cout << "A[" << p - A << "] == " << *p << endl;
else
cout << "which is off-the-end." << endl;
}
}
</pre>
The output is:
<pre>
Searching for 1. Result: index = 1, A[1] == 2
Searching for 2. Result: index = 2, A[2] == 3
Searching for 3. Result: index = 5, A[5] == 5
Searching for 4. Result: index = 5, A[5] == 5
Searching for 5. Result: index = 6, A[6] == 8
Searching for 6. Result: index = 6, A[6] == 8
Searching for 7. Result: index = 6, A[6] == 8
Searching for 8. Result: index = 7, which is off-the-end.
Searching for 9. Result: index = 7, which is off-the-end.
Searching for 10. Result: index = 7, which is off-the-end.
</pre>
<h3>Notes</h3>
<P><A name="1">[1]</A>
Note that you may use an ordering that is a strict weak ordering
but not a total ordering; that is, there might be values <tt>x</tt> and <tt>y</tt>
such that <tt>x < y</tt>, <tt>x > y</tt>, and <tt>x == y</tt> are all <tt>false</tt>. (See the
<A href="LessThanComparable.html">LessThan Comparable</A> requirements for a more complete discussion.)
Finding <tt>value</tt> in the range <tt>[first, last)</tt>, then, doesn't mean
finding an element that is equal to <tt>value</tt> but rather one that is
<i>equivalent to</i> <tt>value</tt>: one that is neither greater than nor less
than <tt>value</tt>. If you're using a total ordering, however (if you're
using <tt>strcmp</tt>, for example, or if you're using ordinary arithmetic
comparison on integers), then you can ignore this technical
distinction: for a total ordering, equality and equivalence are
the same.
<P><A name="2">[2]</A>
Note that even if an element that is equivalent to <A href="#1">[1]</A> <tt>value</tt> is
already present in the range <tt>[first, last)</tt>, the return value of
<tt>upper_bound</tt> will not point to that element. The return value is
either <tt>last</tt> or else an iterator <tt>i</tt> such that <tt>value < *i</tt>. If <tt>i</tt>
is not equal to <tt>first</tt>, however, then <tt>*(i - 1)</tt> is less than or
equivalent to <tt>value</tt>.
<P><A name="3">[3]</A>
This difference between <A href="RandomAccessIterator.html">Random Access Iterators</A> and
<A href="ForwardIterator.html">Forward Iterators</A> is simply because <tt><A href="advance.html">advance</A></tt> is constant
time for <A href="RandomAccessIterator.html">Random Access Iterators</A> and linear time for
<A href="ForwardIterator.html">Forward Iterators</A>.
<h3>See also</h3>
<tt><A href="lower_bound.html">lower_bound</A></tt>, <tt><A href="equal_range.html">equal_range</A></tt>, <tt><A href="binary_search.html">binary_search</A></tt>
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