# std::transform_inclusive_scan

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< cpp‎ | algorithm

Defined in header `<numeric>` |  |
| (1) |
template< class InputIt, class OutputIt, class BinaryOperation, class UnaryOperation > OutputIt transform_inclusive_scan( InputIt first, InputIt last, OutputIt d_first, BinaryOperation binary_op, UnaryOperation unary_op ); |  | (since C++17) (until C++20)
template< class InputIt, class OutputIt, class BinaryOperation, class UnaryOperation > constexpr OutputIt transform_inclusive_scan( InputIt first, InputIt last, OutputIt d_first, BinaryOperation binary_op, UnaryOperation unary_op ); |  | (since C++20)
template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class BinaryOperation, class UnaryOperation > ForwardIt2 transform_inclusive_scan( ExecutionPolicy&& policy, ForwardIt1 first, ForwardIt1 last, ForwardIt2 d_first, BinaryOperation binary_op, UnaryOperation unary_op ); | (2) | (since C++17)
| (3) |
template< class InputIt, class OutputIt, class BinaryOperation, class UnaryOperation, class T > OutputIt transform_inclusive_scan( InputIt first, InputIt last, OutputIt d_first, BinaryOperation binary_op, UnaryOperation unary_op, T init ); |  | (since C++17) (until C++20)
template< class InputIt, class OutputIt, class BinaryOperation, class UnaryOperation, class T > constexpr OutputIt transform_inclusive_scan( InputIt first, InputIt last, OutputIt d_first, BinaryOperation binary_op, UnaryOperation unary_op, T init ); |  | (since C++20)
template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class BinaryOperation, class UnaryOperation, class T > ForwardIt2 transform_inclusive_scan( ExecutionPolicy&& policy, ForwardIt1 first, ForwardIt1 last, ForwardIt2 d_first, BinaryOperation binary_op, UnaryOperation unary_op, T init ); | (4) | (since C++17)

Transforms each element in the range `[`first`,` last`)` with unary_op, then computes an inclusive prefix sum operation using binary_op over the resulting range, optionally with init as the initial value, and writes the results to the range beginning at d_first. Inclusive means that the ith input element is included in the ith sum.

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

- for overloads (1-2), the generalized noncommutative sum of unary_op(*j)... for every `j` in `[`first`,` first + (i - d_first + 1)`)` over binary_op,
- for overloads (3-4), the generalized noncommutative sum of init, unary_op(*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) are executed according to policy. These overloads do not participate in overload resolution unless

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)

unary_op and 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
unary_op | - | unary FunctionObject that will be applied to each element of the input range. The return type must be acceptable as input to binary_op.
binary_op | - | binary FunctionObject that will be applied in to the result of unary_op, 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.
- `ForwardIt2` must meet the requirements of LegacyForwardIterator.
- If init is not provided, decltype(first)'s value type must be MoveConstructible and binary_op(unary_op(*first), unary_op(*first)) must be convertible to decltype(first)'s value type.
- `T (if init is provided)` must meet the requirements of MoveConstructible. All of binary_op(init, unary_op(*first)), binary_op(init, init), and binary_op(unary_op(*first), unary_op(*first)) must be convertible to T.

### Return value

Iterator to the element past the last element written.

### Complexity

O(last - first) applications of each of binary_op and unary_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.

### Notes

unary_op is not applied to init.

The parameter init appears last, differing from std::transform_exclusive_scan, because it is optional for this function.

### 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};

      auto times_10 = [](int x) { return x * 10; };

      std::cout << "10 times exclusive sum: ";
      std::transform_exclusive_scan(data.begin(), data.end(),
    				std::ostream_iterator<int>(std::cout, " "),
    				0, std::plus<int>{}, times_10);
      std::cout << "\n10 times inclusive sum: ";
      std::transform_inclusive_scan(data.begin(), data.end(),
    				std::ostream_iterator<int>(std::cout, " "),
    				std::plus<int>{}, times_10);
    }

Output:

    10 times exclusive sum: 0 30 40 80 90 140 230 250
    10 times inclusive sum: 30 40 80 90 140 230 250 310

### See also

partial_sum | computes the partial sum of a range of elements (function template)
transform | applies a function to a range of elements, storing results in a destination range (function template)
inclusive_scan (C++17) | similar to std::partial_sum, includes the ith input element in the ith sum (function template)
transform_exclusive_scan (C++17) | applies an invocable, then calculates exclusive scan (function template)

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