# std::inclusive_scan

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Defined in header `<numeric>` |  |
template< class InputIt, class OutputIt > OutputIt inclusive_scan( InputIt first, InputIt last, OutputIt d_first ); | (1) | (since C++17) (constexpr since C++20)
template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2 > ForwardIt2 inclusive_scan( ExecutionPolicy&& policy, ForwardIt1 first, ForwardIt1 last, ForwardIt2 d_first ); | (2) | (since C++17)
template< class InputIt, class OutputIt, class BinaryOp > OutputIt inclusive_scan( InputIt first, InputIt last, OutputIt d_first, BinaryOp op ); | (3) | (since C++17) (constexpr since C++20)
template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class BinaryOp > ForwardIt2 inclusive_scan( ExecutionPolicy&& policy, ForwardIt1 first, ForwardIt1 last, ForwardIt2 d_first, BinaryOp op ); | (4) | (since C++17)
template< class InputIt, class OutputIt, class BinaryOp, class T > OutputIt inclusive_scan( InputIt first, InputIt last, OutputIt d_first, BinaryOp op, T init ); | (5) | (since C++17) (constexpr since C++20)
template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class BinaryOp, class T > ForwardIt2 inclusive_scan( ExecutionPolicy&& policy, ForwardIt1 first, ForwardIt1 last, ForwardIt2 d_first, BinaryOp op, T init ); | (6) | (since C++17)

1) Equivalent to inclusive_scan(first, last, d_first, std::plus <>().
3) Computes the inclusive prefix sum using op.
For each integer i in `[`​0​`,` std::distance (first, last)`)`, performs the following operations in order:

1. Creates a sequence which is formed by the elements of `[`first`,` iter`]` in order, where iter is the next ith iterator of first.
2. Computes the generalized noncommutative sum of the sequence over op.
3. Assigns the result to *dest, where dest is the next ith iterator of d_first.

5) Same as (3), but each sequence created is formed by init followed by the elements of `[`first`,` iter`]` in order.
2,4,6) Same as (1,3,5), but executed according to policy.
These overloads participate in overload resolution only if all following conditions are satisfied:

std::is_execution_policy_v < std::decay_t <ExecutionPolicy>> is true. | (until C++20)
std::is_execution_policy_v < std::remove_cvref_t <ExecutionPolicy>> is true. | (since C++20)

The generalized, noncommutative sum of a sequence of elements over a binary operation binary_op is defined as follows:

- If the sequence only has one element, the sum is the value of the element.
- Otherwise, performs the following operations in order:

1. Selects any two adjacent elements elem1 and elem2 from the sequence.
2. Calculates binary_op(elem1, elem2) and replaces the two elements in the sequence with the result.
3. Repeats steps 1 and 2 until there is only one element in the sequence.

Given binary_op as the actual binary operation:

- The result is non-deterministic if the binary_op is not associative (such as floating-point addition).

- For overloads (1-4), if binary_op(*first, *first) is not convertible to the value type of decltype(first), the program is ill-formed.

- For overloads (5,6), if any of the following values is not convertible to `T`, the program is ill-formed:

  - binary_op(init, *first)
  - binary_op(init, init)
  - binary_op(*first, *first)

- If any of the following conditions is satisfied, the behavior is undefined:

  - For overloads (1-4), the value type of decltype(first) is not MoveConstructible.
  - For overloads (5,6), `T` is not MoveConstructible.
  - binary_op modifies any element of `[`first`,` last`)`.
  - binary_op invalidates any iterator or subrange of `[`first`,` last`]`.

### 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
init | - | the initial value
op | - | binary FunctionObject that will be applied in to the result of dereferencing the input iterators, the results of other op, and init (if provided)
Type requirements
- `InputIt` must meet the requirements of LegacyInputIterator.
- `OutputIt` must meet the requirements of LegacyOutputIterator.
- `ForwardIt1, ForwardIt2` must meet the requirements of LegacyForwardIterator.

### Return value

Iterator to the element past the last element written.

### Complexity

Given \(\scriptsize N\)N as std::distance (first, last):

1,2) \(\scriptsize O(N)\)O(N) applications of std::plus <>().
3-6) \(\scriptsize O(N)\)O(N) applications of op.

### 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 or folds 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 an invocable, 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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