Standard C++	Library
 		 Copyright 1996, Rogue Wave Software, Inc.

 NAME

   partial_sum  - Calculates successive partial sums of a range of values.

 SYNOPSIS

   #include <numeric>

   template <class InputIterator, class OutputIterator>
   OutputIterator partial_sum (InputIterator first,
 			     InputIterator last,
 			     OutputIterator result);

   template <class InputIterator,
 	   class OutputIterator,
 	   class BinaryOperation>
   OutputIterator partial_sum (InputIterator first,
 			     InputIterator last,
 			     OutputIterator result,
 			     BinaryOperation binary_op);

 DESCRIPTION

   The partial_sum 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, applying the operation
   binary_op successively on every	previous element.  That	is,
   partial_sum	assigns	to every iterator i in the range [result,
   result	 +  (last - first)) a value equal to:

   ((...(*first + *(first + 1)) + ... ) + *(first + (i -	result)))

    or, in the second version of	the algorithm:

   binary_op(binary_op(..., binary_op (*first, *(first +
   1)),...),*(first + (i - result)))

   For instance,	applying partial_sum to	(1,2,3,4,) will	yield
   (1,3,6,10).

   The partial_sum algorithm returns result + (last - first).

   If result is equal to	first, the elements of the new sequence
   successively replace the elements in the original sequence,
   effectively turning partial_sum into an inplace transformation.

 COMPLEXITY

   Exactly (last	- first) - 1 applications of the default + operator or
   binary_op are	performed.

 EXAMPLE

   //
   // partsum.cpp
   //
    #include <numeric>	//for accumulate
    #include <vector>	//for vector
    #include <functional> //for times
    #include <iostream.h>

   int main()
    {
      //Initialize a vector using an array of ints
     int	d1[10] = {1,2,3,4,5,6,7,8,9,10};
     vector<int>	v(d1, d1+10);

      //Create an empty vectors to store	results
     vector<int>	sums((size_t)10), prods((size_t)10);

      //Compute partial_sums and	partial_products
      partial_sum(v.begin(), v.end(), sums.begin());
      partial_sum(v.begin(), v.end(), prods.begin(), times<int>());

      //Output the results
     cout << "For the series: " << endl << "	";
     copy(v.begin(),v.end(),ostream_iterator<int,char>(cout," "));
     cout << endl << endl;

     cout << "The partial sums: " << endl << "	  " ;
     copy(sums.begin(),sums.end(),
 	 ostream_iterator<int,char>(cout," "));
     cout <<" should each equal (N*N + N)/2" << endl << endl;

     cout << "The partial products: " <<	endl <<	"     ";
     copy(prods.begin(),prods.end(),
 	 ostream_iterator<int,char>(cout," "));
     cout << " should each equal	N!" << endl;

     return 0;
    }

   Output :
   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!

 WARNING

   If your compiler does	not support default template parameters, then
   you need to always provide the Allocator template	argument.  For
   instance, you will need to write :

   vector<int, allocator<int> >

   instead of :

   vector<int>

 STANDARDS CONFORMANCE
   ANSI X3J16/ISO WG21 Joint C++	Committee