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<TITLE>partial_sum()</TITLE>
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<H2>partial_sum()</H2>
<P><B>Library:</B>&nbsp;&nbsp;<A HREF="2-10.html">Numerics</A></P>

<PRE><HR><B><I>Function</I></B><HR></PRE>

<UL>
<LI><A HREF="#sec1">Local Index</A></LI>
<LI><A HREF="#sec2">Summary</A></LI>
<LI><A HREF="#sec3">Synopsis</A></LI>
<LI><A HREF="#sec4">Description</A></LI>
<LI><A HREF="#sec5">Complexity</A></LI>
<LI><A HREF="#sec6">Example</A></LI>
<LI><A HREF="#sec7">See Also</A></LI>
<LI><A HREF="#sec8">Standards Conformance</A></LI>
</UL>
<A NAME="sec1"><H3>Local Index</H3></A>
No Entries
<A NAME="sec2"><H3>Summary</H3></A>
<P>Generalized numeric operation that calculates successive partial sums of a range of values</P>
<A NAME="sec3"><H3>Synopsis</H3></A>

<PRE>#include &lt;numeric&gt;

namespace std {
  template &lt;class InputIterator, class OutputIterator&gt;
  OutputIterator partial_sum(InputIterator start,
                             InputIterator finish,
                             OutputIterator result);

  template &lt;class InputIterator,
            class OutputIterator,
            class BinaryOperation&gt;
  OutputIterator partial_sum(InputIterator start,
                             InputIterator finish,
                             OutputIterator result,
                             BinaryOperation binary_op);
}
</PRE>
<A NAME="sec4"><H3>Description</H3></A>
<P>The <SAMP>partial_sum()</SAMP> algorithm creates a new sequence in which every element is formed by adding all the values of the previous elements, or, in the second form of the algorithm, by applying the operation <SAMP>binary_op</SAMP> successively on every previous element. That is, <SAMP>partial_sum()</SAMP> assigns to every iterator <SAMP>i</SAMP> in the range <SAMP>[result,  result  +  (finish - start))</SAMP> a value equal to:</P>

<UL><PRE>((...(*start + *(start + 1)) + ... ) + 
      *(start + (i - result)))
</PRE></UL>
<P> or, in the second version of the algorithm:</P>

<UL><PRE>binary_op(binary_op(..., binary_op (*start, 
          *(start + 1)),...),*(start + (i - result)))
</PRE></UL>
<P>For instance, applying <SAMP>partial_sum()</SAMP> to (1,2,3,4,) yields (1,3,6,10).</P>
<P>The <SAMP>partial_sum()</SAMP> algorithm returns <SAMP>result</SAMP> <SAMP>+ (finish - start)</SAMP>.</P>
<P>If <SAMP>result</SAMP> is equal to <SAMP>start</SAMP>, the elements of the new sequence successively replace the elements in the original sequence, effectively turning <SAMP>partial_sum()</SAMP> into an inplace transformation. </P>
<A NAME="sec5"><H3>Complexity</H3></A>
<P>Exactly <SAMP>(finish - start) - 1</SAMP> applications of the default <SAMP>+</SAMP> operator or <SAMP>binary_op</SAMP> are performed.</P>
<A NAME="sec6"><H3>Example</H3></A>

<UL><PRE>//
//  partsum.cpp
//

#include &lt;algorithm&gt;  // for copy
#include &lt;functional&gt; // for multiplies
#include &lt;iostream&gt;   // for cout, endl
#include &lt;iterator&gt;   // for ostream_iterator
#include &lt;numeric&gt;    // for partial_sum
#include &lt;vector&gt;     // for vector


int main ()
{
    typedef std::vector&lt;int, std::allocator&lt;int&gt; &gt; Vector;
    typedef std::ostream_iterator&lt;int, char,
                                  std::char_traits&lt;char&gt; &gt;
            Iter;

    // Initialize a vector using an array of integers.
    const Vector::value_type a[] = { 1, 2, 3, 4, 5, 
                                     6, 7, 8, 9, 10 };
    Vector v (a + 0, a + sizeof a / sizeof *a);

    // Create an empty vectors to store results.
    Vector sums  (Vector::size_type (10));
    Vector prods (Vector::size_type (10));

    // Compute partial_sums and partial_products.
    std::partial_sum (v.begin (), v.end (), sums.begin ());
    std::partial_sum (v.begin (), v.end (), prods.begin (),
                      std::multiplies&lt;Vector::value_type&gt;());

    // Output the results.
    std::cout &lt;&lt; "For the series: \n     ";
    std::copy (v.begin (), v.end (), Iter (std::cout, " "));

    std::cout &lt;&lt; "\n\nThe partial sums: \n     ";
    std::copy (sums.begin (), sums.end (), Iter (std::cout,
                                                 " "));
    std::cout &lt;&lt; " should each equal (N*N + N)/2\n\n";

    std::cout &lt;&lt; "The partial products: \n     ";
    std::copy (prods.begin (), prods.end (), Iter (std::cout,
                                                   " "));
    std::cout &lt;&lt; " should each equal N!" &lt;&lt; std::endl;

    return 0;
}


Program Output:
</PRE></UL>
<UL><PRE>For the series: 
     1 2 3 4 5 6 7 8 9 10 

The partial sums: 
     1 3 6 10 15 21 28 36 45 55  should each equal (N*N + N)/2

The partial products: 
     1 2 6 24 120 720 5040 40320 362880 3628800  should each
equal N!
</PRE></UL>
<A NAME="sec7"><H3>See Also</H3></A>
<P><A HREF="algorithms.html">Algorithms</A>, <A HREF="algorithm-h.html">&lt;algorithm&gt;</A></P>
<A NAME="sec8"><H3>Standards Conformance</H3></A>
<P><I>ISO/IEC 14882:1998 -- International Standard for Information Systems -- Programming Language C++, Section 26.4.3</I></P>

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