# 25 Algorithms library [algorithms]

## 25.9 Generalized numeric operations [numeric.ops]

### 25.9.10 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 26) 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
:
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 may be nondeterministic.
transform_­inclusive_­scan does not apply unary_­op to init.
— end note
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