function template
<numeric>

# std::partial_sum

sum (1) ```template OutputIterator partial_sum (InputIterator first, InputIterator last, OutputIterator result); ``` ```template OutputIterator partial_sum (InputIterator first, InputIterator last, OutputIterator result, BinaryOperation binary_op); ```
Compute partial sums of range
Assigns to every element in the range starting at result the partial sum of the corresponding elements in the range `[first,last)`.

If x represents an element in `[first,last)` and y represents an element in result, the ys can be calculated as:

``` y0 = x0 y1 = x0 + x1 y2 = x0 + x1 + x2 y3 = x0 + x1 + x2 + x3 y4 = x0 + x1 + x2 + x3 + x4 ... ... ... ```
The default operation is to add the elements up, but a different operation can be specified as binary_op instead.

The behavior of this function template is equivalent to:
 ``123456789101112131415`` ``````template OutputIterator partial_sum (InputIterator first, InputIterator last, OutputIterator result) { if (first!=last) { typename iterator_traits::value_type val = *first; *result = val; while (++first!=last) { val = val + *first; // or: val = binary_op(val,*first) *++result = val; } ++result; } return result; }``````

### Parameters

first, last
Input iterators to the initial and final positions in a sequence. The range used is `[first,last)`, which contains all the elements between first and last, including the element pointed by first but not the element pointed by last.
result
Output iterator to the initial position in the destination sequence where the partial sums are stored. The range starts at result and shall have a size large enough to contain as many elements as the range above (`[first,last)`).
binary_op
Binary operation taking two elements of the type pointed by the InputIterator as arguments, and returning the result of the replacement for the sum operation.
This can either be a function pointer or a function object.

### Return value

An iterator pointing to past the last element of the destination sequence where resulting elements have been stored, or result if `[first,last)` is an empty range.

### Example

 ``123456789101112131415161718192021222324252627`` ``````// partial_sum example #include // std::cout #include // std::multiplies #include // std::partial_sum int myop (int x, int y) {return x+y+1;} int main () { int val[] = {1,2,3,4,5}; int result[5]; std::partial_sum (val, val+5, result); std::cout << "using default partial_sum: "; for (int i=0; i<5; i++) std::cout << result[i] << ' '; std::cout << '\n'; std::partial_sum (val, val+5, result, std::multiplies()); std::cout << "using functional operation multiplies: "; for (int i=0; i<5; i++) std::cout << result[i] << ' '; std::cout << '\n'; std::partial_sum (val, val+5, result, myop); std::cout << "using custom function: "; for (int i=0; i<5; i++) std::cout << result[i] << ' '; std::cout << '\n'; return 0; }``````

Output:
 ``` using default partial_sum: 1 3 6 10 15 using functional operation multiplies: 1 2 6 24 120 using custom function: 1 4 8 13 19 ```

### Complexity

Linear in the distance between first and last, minus one (in number of additions or applications of binary_op).

### Data races

The elements in the range `[first,last)` are accessed (each object is accessed exactly once).
The elements in the range beginning at result are modified.

### Exceptions

Throws if any of binary_op, the assignments or an operation on an iterator throws.
Note that invalid arguments cause undefined behavior.