# partial_sum

 Category: algorithms Component type: function

### Prototype

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);
```

### Description

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]

### Definition

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

### Requirements on types

For the first version:
• InputIterator is a model of Input Iterator.
• OutputIterator is a model of Output Iterator.
• If x and y are objects of InputIterator's value type, then x + y is defined.
• The return type of x + y is convertible to InputIterator's value type.
• InputIterator's value type is convertible to a type in OutputIterator's set of value types.
For the second version:
• InputIterator is a model of Input Iterator.
• OutputIterator is a model of Output Iterator.
• BinaryFunction is a model of BinaryFunction.
• InputIterator's value type is convertible to BinaryFunction's first argument type and second argument type.
• BinaryFunction's result type is convertible to InputIterator's value type.
• InputIterator's value type is convertible to a type in OutputIterator's set of value types.

### Preconditions

• [first, last) is a valid range.
• [result, result + (last - first)) is a valid range.

### Complexity

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

### Example

```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;
}
```

### Notes

[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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