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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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	<H2>accumulate()</H2>
	<P><B>Library:</B>  <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 <numeric>

	namespace std {
	template <class InputIterator, class T>
	T accumulate(InputIterator start,
	InputIterator finish,
	T init);

	template <class InputIterator,
	class T,
	class BinaryOperation>
	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 <numeric> // for accumulate
	#include <vector> // for vector
	#include <functional> // for multiplies
	#include <iostream> // for cout


	int main ()
	{
	// Typedef for convenience.
	typedef std::vector<int, std::allocator<int> > 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<vector::value_type>());

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

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