partial_sum

Generalized Numeric Operation

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Calculates successive partial sums of a range of values.

None

#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);

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, by 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,) 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.

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

//
// 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!

If your compiler does not support default template parameters, 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.