# std::inclusive_scan

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< cpp‎ | algorithm

Defined in header `<numeric>` |  |
template< class InputIt, class OutputIt > OutputIt inclusive_scan( InputIt first, InputIt last, OutputIt d_first ); | (1) | (since C++17)
template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2 > ForwardtIt2 inclusive_scan( ExecutionPolicy&& policy, ForwardIt1 first, ForwardIt1 last, ForwardIt2 d_first ); | (2) | (since C++17)
template< class InputIt, class OutputIt, class BinaryOperation > OutputIt inclusive_scan( InputIt first, InputIt last, OutputIt d_first, BinaryOperation binary_op ); | (3) | (since C++17)
template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class BinaryOperation > ForwardIt2 inclusive_scan( ExecutionPolicy&& policy, ForwardIt1 first, ForwardIt1 last, ForwardIt2 d_first, BinaryOperation binary_op ); | (4) | (since C++17)
template< class InputIt, class OutputIt, class BinaryOperation, class T > OutputIt inclusive_scan( InputIt first, InputIt last, OutputIt d_first, BinaryOperation binary_op, T init ); | (5) | (since C++17)
template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class BinaryOperation, class T > ForwardIt2 inclusive_scan( ExecutionPolicy&& policy, ForwardIt1 first, ForwardIt1 last, ForwardIt2 d_first, BinaryOperation binary_op, T init ); | (6) | (since C++17)

Computes an inclusive prefix sum operation using `binary_op` (or std::plus<>() for overloads (1-2)) for the range `[first, last)`, using `init` as the initial value (if provided), and writes the results to the range beginning at `d_first`. "inclusive" means that the i-th input element is included in the i-th sum.

Formally, assigns through each iterator `i` in [d_first, d_first + (last - first)) the value of:

- for overloads (1-4), the generalized noncommutative sum of `*j...` for every `j` in [first, first + (i - d_first + 1)) over `binary_op`
- for overloads (5-6), the generalized noncommutative sum of `init, *j...` for every `j` in [first, first + (i - d_first + 1)) over `binary_op`

where generalized noncommutative sum GNSUM(op, a
1, ..., a
N) is defined as follows:

- if N=1, a
  1
- if N > 1, op(GNSUM(op, a
  1, ..., a
  K), GNSUM(op, a
  M, ..., a
  N)) for any K where 1 < K+1 = M ≤ N

In other words, the summation operations may be performed in arbitrary order, and the behavior is nondeterministic if `binary_op` is not associative.

Overloads (2,4,6) are executed according to `policy`. This overload only participates in overload resolution if std::is_execution_policy_v<std::decay_t<ExecutionPolicy>> is true.

`binary_op` shall not invalidate iterators (including the end iterators) or subranges, nor modify elements in the ranges [first, last) or [d_first, d_first + (last - first)). Otherwise, the behavior is undefined.

### Parameters

first, last | - | the range of elements to sum
d_first | - | the beginning of the destination range; may be equal to `first`
policy | - | the execution policy to use. See execution policy for details.
init | - | the initial value (optional)
binary_op | - | binary FunctionObject that will be applied in to the result of dereferencing the input iterators, the results of other `binary_op`, and `init` (if provided).
Type requirements
- `InputIt` must meet the requirements of LegacyInputIterator.
- `OutputIt` must meet the requirements of LegacyOutputIterator.
- `ForwardIt1` must meet the requirements of LegacyForwardIterator. and, if `init` is not provided, ForwardIt1's value_type must be MoveConstructible and `binary_op(*first, *first)` must be convertible to ForwardIt1's value type
- `ForwardIt2` must meet the requirements of LegacyForwardIterator.
- `T (if init is provided)` must meet the requirements of MoveConstructible. All of `binary_op(init, *first)`, `binary_op(init, init)`, and `binary_op(*first, *first)` must be convertible to T

### Return value

Iterator to the element past the last element written.

### Complexity

O(last - first) applications of the binary operation

### Exceptions

The overloads with a template parameter named `ExecutionPolicy` report errors as follows:

- If execution of a function invoked as part of the algorithm throws an exception and `ExecutionPolicy` is one of the standard policies, std::terminate is called. For any other `ExecutionPolicy`, the behavior is implementation-defined.
- If the algorithm fails to allocate memory, std::bad_alloc is thrown.

### Example

Run this code

    #include <functional>
    #include <iostream>
    #include <iterator>
    #include <numeric>
    #include <vector>

    int main()
    {
      std::vector data {3, 1, 4, 1, 5, 9, 2, 6};

      std::cout << "exclusive sum: ";
      std::exclusive_scan(data.begin(), data.end(),
    		      std::ostream_iterator<int>(std::cout, " "),
    		      0);
      std::cout << "\ninclusive sum: ";
      std::inclusive_scan(data.begin(), data.end(),
    		      std::ostream_iterator<int>(std::cout, " "));

      std::cout << "\n\nexclusive product: ";
      std::exclusive_scan(data.begin(), data.end(),
    		      std::ostream_iterator<int>(std::cout, " "),
    		      1, std::multiplies<>{});
      std::cout << "\ninclusive product: ";
      std::inclusive_scan(data.begin(), data.end(),
    		      std::ostream_iterator<int>(std::cout, " "),
    		      std::multiplies<>{});
    }

Output:

    exclusive sum: 0 3 4 8 9 14 23 25
    inclusive sum: 3 4 8 9 14 23 25 31

    exclusive product: 1 3 3 12 12 60 540 1080
    inclusive product: 3 3 12 12 60 540 1080 6480

### See also

adjacent_difference | computes the differences between adjacent elements in a range (function template)
accumulate | sums up a range of elements (function template)
partial_sum | computes the partial sum of a range of elements (function template)
transform_inclusive_scan (C++17) | applies a functor, then calculates inclusive scan (function template)
exclusive_scan (C++17) | similar to std::partial_sum, excludes the ith input element from the ith sum (function template)

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