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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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	<A HREF="partial-sort-copy.html"><IMG SRC="images/bprev.gif" WIDTH=20 HEIGHT=21 ALT="Previous file" BORDER=O></A><A HREF="noframes.html"><IMG SRC="images/btop.gif" WIDTH=56 HEIGHT=21 ALT="Top of Document" BORDER=O></A><A HREF="booktoc.html"><IMG SRC="images/btoc.gif" WIDTH=56 HEIGHT=21 ALT="Contents" BORDER=O></A><A HREF="tindex.html"><IMG SRC="images/bindex.gif" WIDTH=56 HEIGHT=21 ALT="Index page" BORDER=O></A><A HREF="partition.html"><IMG SRC="images/bnext.gif" WIDTH=25 HEIGHT=21 ALT="Next file" BORDER=O></A><DIV CLASS="DOCUMENTNAME"><B>Apache C++ Standard Library Reference Guide</B></DIV>
	<H2>partial_sum()</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">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 <numeric>

	namespace std {
	template <class InputIterator, class OutputIterator>
	OutputIterator partial_sum(InputIterator start,
	InputIterator finish,
	OutputIterator result);

	template <class InputIterator,
	class OutputIterator,
	class BinaryOperation>
	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 <algorithm> // for copy
	#include <functional> // for multiplies
	#include <iostream> // for cout, endl
	#include <iterator> // for ostream_iterator
	#include <numeric> // for partial_sum
	#include <vector> // for vector



	int main ()
	{
	typedef std::vector<int, std::allocator<int> > Vector;
	typedef std::ostream_iterator<int, char,
	std::char_traits<char> >
	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<Vector::value_type>());

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

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

	std::cout << "The partial products: \n ";
	std::copy (prods.begin (), prods.end (), Iter (std::cout,
	" "));
	std::cout << " should each equal N!" << 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"><algorithm></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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