Category: algorithms Component type: function


Partial_sum is an overloaded name; there are actually two partial_sum functions.
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);


Partial_sum calculates a generalized partial sum: *first is assigned to *result, the sum of *first and *(first + 1) is assigned to *(result + 1), and so on. [1]

More precisely, a running sum is first initialized to *first and assigned to *result. For each iterator i in [first + 1, last), in order from beginning to end, the sum is updated by sum = sum + *i (in the first version) or sum = binary_op(sum, *i) (in the second version) and is assigned to *(result + (i - first)). [2]


Defined in the standard header numeric, and in the nonstandard backward-compatibility header algo.h.

Requirements on types

For the first version: For the second version:



Linear. Zero applications of the binary operation if [first, last) is a empty range, otherwise exactly (last - first) - 1 applications.


int main()
  const int N = 10;
  int A[N];

  fill(A, A+N, 1);
  cout << "A:                 ";
  copy(A, A+N, ostream_iterator<int>(cout, " "));
  cout << endl;

  cout << "Partial sums of A: ";
  partial_sum(A, A+N, ostream_iterator<int>(cout, " "));
  cout << endl;


[1] Note that result is permitted to be the same iterator as first. This is useful for computing partial sums "in place".

[2] The binary operation is not required to be either associative or commutative: the order of all operations is specified.

See also

adjacent_difference, accumulate, inner_product, count
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