# 27 Algorithms library [algorithms]

## 27.10 Generalized numeric operations [numeric.ops]

### 27.10.11 Transform inclusive scan [transform.inclusive.scan]

```template<class InputIterator, class OutputIterator, class BinaryOperation, class UnaryOperation> constexpr OutputIterator transform_inclusive_scan(InputIterator first, InputIterator last, OutputIterator result, BinaryOperation binary_op, UnaryOperation unary_op); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class BinaryOperation, class UnaryOperation> ForwardIterator2 transform_inclusive_scan(ExecutionPolicy&& exec, ForwardIterator1 first, ForwardIterator1 last, ForwardIterator2 result, BinaryOperation binary_op, UnaryOperation unary_op); template<class InputIterator, class OutputIterator, class BinaryOperation, class UnaryOperation, class T> constexpr OutputIterator transform_inclusive_scan(InputIterator first, InputIterator last, OutputIterator result, BinaryOperation binary_op, UnaryOperation unary_op, T init); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class BinaryOperation, class UnaryOperation, class T> ForwardIterator2 transform_inclusive_scan(ExecutionPolicy&& exec, ForwardIterator1 first, ForwardIterator1 last, ForwardIterator2 result, BinaryOperation binary_op, UnaryOperation unary_op, T init); ```
Let U be the value type of decltype(first).
Mandates: If init is provided, all of
• binary_op(init, init),
• binary_op(init, unary_op(*first)), and
• binary_op(unary_op(*first), unary_op(*first))
are convertible to T; otherwise, binary_op(unary_op(*first), unary_op(*first)) is convertible to U.
Preconditions:
• If init is provided, T meets the Cpp17MoveConstructible (Table 31) requirements; otherwise, U meets the Cpp17MoveConstructible requirements.
• Neither unary_op nor binary_op invalidates iterators or subranges, nor modifies elements in the ranges [first, last] or [result, result + (last - first)].
Effects: For each integer K in [0, last - first) assigns through result + K the value of
• GENERALIZED_NONCOMMUTATIVE_SUM(
binary_op, init,
unary_op(*(first + 0)), unary_op(*(first + 1)), ..., unary_op(*(first + K)))

if init is provided, or
• GENERALIZED_NONCOMMUTATIVE_SUM(
binary_op,
unary_op(*(first + 0)), unary_op(*(first + 1)), ..., unary_op(*(first + K)))

otherwise.
Returns: The end of the resulting range beginning at result.
Complexity: applications each of unary_op and binary_op.
Remarks: result may be equal to first.
[Note 1:
The difference between transform_exclusive_scan and transform_inclusive_scan is that transform_inclusive_scan includes the input element in the sum.
If binary_op is not mathematically associative, the behavior of transform_inclusive_scan can be nondeterministic.
transform_inclusive_scan does not apply unary_op to init.
â€” end note]