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<H2>accumulate()</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">Standards Conformance</A></LI>
</UL>
<A NAME="sec1"><H3>Local Index</H3></A>
No Entries
<A NAME="sec2"><H3>Summary</H3></A>
<P>A generalized numeric operation that accumulates all elements within a range into a single value</P>
<A NAME="sec3"><H3>Synopsis</H3></A>

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

namespace std {
  template &lt;class InputIterator, class T&gt;
  T accumulate(InputIterator start,
               InputIterator finish,
               T init);

  template &lt;class InputIterator,
            class T,
            class BinaryOperation&gt;
  T accumulate(InputIterator start,
               InputIterator finish,
               T init,
               BinaryOperation binary_op);
}
</PRE>
<A NAME="sec4"><H3>Description</H3></A>
<P><SAMP>accumulate()</SAMP> applies a binary operation to <SAMP>init</SAMP> and each value in the range <SAMP>[start,finish)</SAMP>. The result of each operation is returned in <SAMP>init</SAMP>. This process aggregates the result of performing the operation on every element of the sequence into a single value.</P>
<P>The accumulator <SAMP>acc</SAMP> is initialized with the value <SAMP>init </SAMP>and modified with <SAMP>acc = acc + *i</SAMP> or <SAMP>acc = binary_op(acc, *i)</SAMP> for each interator <SAMP>i</SAMP>, in order, in the range <SAMP>[start, finish)</SAMP>.</P>
<A NAME="sec5"><H3>Complexity</H3></A>
<P><SAMP>accumulate()</SAMP> performs exactly <SAMP>finish-start</SAMP> applications of the binary operation, <SAMP>operator+ </SAMP>by default.</P>
<A NAME="sec6"><H3>Example</H3></A>

<UL><PRE>//
// accum.cpp
//

#include &lt;numeric&gt;    // for accumulate
#include &lt;vector&gt;     // for vector
#include &lt;functional&gt; // for multiplies
#include &lt;iostream&gt;   // for cout


int main ()
{
    // Typedef for convenience.
    typedef std::vector&lt;int, std::allocator&lt;int&gt; &gt; vector;

    // Initialize a vector using an array of integers.
    const vector::value_type arr[] = 
      { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 };
    vector v1 (arr, arr + sizeof arr / sizeof *arr);

    // Accumulate sums and products.
    vector::value_type sum =
        std::accumulate (v1.begin (), v1.end (), 0);

    vector::value_type prod =
        std::accumulate (v1.begin (), v1.end (), 1,
                         std::multiplies&lt;vector::value_type&gt;());

    // Output the results.
    std::cout &lt;&lt; "For the series: ";
    for (vector::iterator i = v1.begin (); i != v1.end (); ++i)
        std::cout &lt;&lt; *i &lt;&lt; " ";

    std::cout &lt;&lt; "where N = " &lt;&lt; v1.size ()
              &lt;&lt; "\nThe sum = (N * N + N) / 2 = " &lt;&lt; sum
              &lt;&lt; "\nThe product = N! = " &lt;&lt; prod &lt;&lt; std::endl;

    return 0;
}


Program Output:

For the series: 1 2 3 4 5 6 7 8 9 10 where N = 10
The sum = (N * N + N) / 2 = 55
The product = N! = 3628800
</PRE></UL>
<UL><PRE></PRE></UL>
<A NAME="sec7"><H3>Standards Conformance</H3></A>
<P><I>ISO/IEC 14882:1998 -- International Standard for Information Systems -- Programming Language C++, Section 26.4.1</I></P>

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