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<Title>partial_sum</Title>
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<H1>partial_sum</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>Partial_sum</tt> is an overloaded name; there are actually two <tt>partial_sum</tt>
functions.
<pre>
template <class InputIterator, class OutputIterator>
OutputIterator partial_sum(InputIterator first, InputIterator last,
OutputIterator result);
template <class InputIterator, class OutputIterator, class BinaryOperation>
OutputIterator partial_sum(InputIterator first, InputIterator last,
OutputIterator result, BinaryOperation binary_op);
</pre>
<h3>Description</h3>
<tt>Partial_sum</tt> calculates a generalized partial sum: <tt>*first</tt> is assigned
to <tt>*result</tt>, the sum of <tt>*first</tt> and <tt>*(first + 1)</tt> is assigned to
<tt>*(result + 1)</tt>, and so on. <A href="#1">[1]</A>
<P>
More precisely, a running sum is first initialized to <tt>*first</tt> and
assigned to <tt>*result</tt>. For each iterator <tt>i</tt> in <tt>[first + 1, last)</tt>, in
order from beginning to end, the sum is updated by <tt>sum = sum + *i</tt>
(in the first version) or <tt>sum = binary_op(sum, *i)</tt> (in the second
version) and is assigned to <tt>*(result + (i - first))</tt>. <A href="#2">[2]</A>
<h3>Definition</h3>
Defined in the standard header <A href="numeric">numeric</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>InputIterator</tt> is a model of <A href="InputIterator.html">Input Iterator</A>.
<LI>
<tt>OutputIterator</tt> is a model of <A href="OutputIterator.html">Output Iterator</A>.
<LI>
If <tt>x</tt> and <tt>y</tt> are objects of <tt>InputIterator</tt>'s value type, then
<tt>x + y</tt> is defined.
<LI>
The return type of <tt>x + y</tt> is convertible to <tt>InputIterator</tt>'s
value type.
<LI>
<tt>InputIterator</tt>'s value type is convertible to a type in
<tt>OutputIterator</tt>'s set of value types.
</UL>
For the second version:
<UL>
<LI>
<tt>InputIterator</tt> is a model of <A href="InputIterator.html">Input Iterator</A>.
<LI>
<tt>OutputIterator</tt> is a model of <A href="OutputIterator.html">Output Iterator</A>.
<LI>
<tt>BinaryFunction</tt> is a model of <A href="BinaryFunction.html">BinaryFunction</A>.
<LI>
<tt>InputIterator</tt>'s value type is convertible to <tt>BinaryFunction</tt>'s
first argument type and second argument type.
<LI>
<tt>BinaryFunction</tt>'s result type is convertible to <tt>InputIterator</tt>'s
value type.
<LI>
<tt>InputIterator</tt>'s value type is convertible to a type in
<tt>OutputIterator</tt>'s set of value types.
</UL>
<h3>Preconditions</h3>
<UL>
<LI>
<tt>[first, last)</tt> is a valid range.
<LI>
<tt>[result, result + (last - first))</tt> is a valid range.
</UL>
<h3>Complexity</h3>
Linear. Zero applications of the binary operation if <tt>[first, last)</tt>
is a empty range, otherwise exactly <tt>(last - first) - 1</tt> applications.
<h3>Example</h3>
<pre>
int main()
{
const int N = 10;
int A[N];
fill(A, A+N, 1);
cout << "A: ";
<A href="copy.html">copy</A>(A, A+N, <A href="ostream_iterator.html">ostream_iterator</A><int>(cout, " "));
cout << endl;
cout << "Partial sums of A: ";
<A href="partial_sum.html">partial_sum</A>(A, A+N, <A href="ostream_iterator.html">ostream_iterator</A><int>(cout, " "));
cout << endl;
}
</pre>
<h3>Notes</h3>
<P><A name="1">[1]</A>
Note that <tt>result</tt> is permitted to be the same iterator as
<tt>first</tt>. This is useful for computing partial sums "in place".
<P><A name="2">[2]</A>
The binary operation is not required to be either associative or
commutative: the order of all operations is specified.
<h3>See also</h3>
<tt><A href="adjacent_difference.html">adjacent_difference</A></tt>, <tt><A href="accumulate.html">accumulate</A></tt>, <tt><A href="inner_product.html">inner_product</A></tt>,
<tt><A href="count.html">count</A></tt>
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