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                       Standard C++ Library
             Copyright 1998, Rogue Wave Software, Inc.


NAME
     accumulate

      - Accumulates all elements within a  range  into  a  single
     value.



SYNOPSIS
     #include <numeric>
     template <class InputIterator, class T>
     T accumulate (InputIterator first,
                  InputIterator last,
                  T init);

     template <class InputIterator,
              class T,
              class BinaryOperation>
     T accumulate (InputIterator first,
                  InputIterator last,
                  T init,
                  BinaryOperation binary_op);



DESCRIPTION
     accumulate applies a binary operation to init and each value
     in  the  range [first,last). The result of each operation is
     returned in init. This process aggregates the result of per-
     forming  the operation on every element of the sequence into
     a single value.

     Accumulation is done by  initializing  the  accumulator  acc
     with the initial value init and then modifying it with acc =
     acc + *i or acc = binary_op(acc, *i) for every iterator i in
     the  range [first, last) in order. If the sequence is empty,
     accumulate returns init.

     binary_op should not have side effects.



COMPLEXITY
     accumulate performs exactly last-first applications  of  the
     binary operation (operator+ by default).

EXAMPLE
     //
     // accum.cpp
     //
      #include <numeric>   //for accumulate
      #include <vector>    //for vector
      #include <functional> //for times
      #include <iostream>
     using namespace std;

     int main()
      {
        //
        //Typedef for vector iterators
        //
       typedef vector<int>::iterator iterator;
        //
        //Initialize a vector using an array of ints
        //
       int d1[10] = {1,2,3,4,5,6,7,8,9,10};
       vector<int> v1(d1, d1+10);
        //
        //Accumulate sums and products
        //
       int sum = accumulate(v1.begin(), v1.end(), 0);
       int prod = accumulate(v1.begin(), v1.end(),
                   1, times<int>());
        //
        //Output the results
        //
       cout << "For the series: ";
       for(iterator i = v1.begin(); i != v1.end(); i++)
           cout << *i << " ";

       cout << " where N = 10." << endl;
       cout << "The sum = (N*N + N)/2 = " << sum << endl;
       cout << "The product = N! = " << prod << 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



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