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                       Standard C++ Library
             Copyright 1998, 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 pre-
     vious elements, or, in the second form of the algorithm,  by
     applying  the operation binary_op successively on every pre-
     vious element. That is, partial_sum assigns to every  itera-
     tor  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,)  yields
     (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>
     using namespace std;

     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;
      }

     Program 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!



WARNINGS
     If your compiler does not support default  template  parame-
     ters, then you always need to include the Allocator template
     argument. For instance, you need to write:

     vector<int, allocator<int> >

     instead of:

     vector<int>

     If your compiler does not support namespaces,  then  you  do
     not need the using declaration for std.

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