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| <TITLE>partial_sum()</TITLE> |
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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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