[transform.inclusive.scan]

# 26 Algorithms library [[algorithms]](./#algorithms)

## 26.10 Generalized numeric operations [[numeric.ops]](numeric.ops#transform.inclusive.scan)

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

[ð](#lib: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);
`

[1](#1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L13046)

Let U be the value type of decltype(first)[.](#1.sentence-1)

[2](#2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L13049)

*Mandates*: If init is provided, all of

- [(2.1)](#2.1)

binary_op(init, init),

- [(2.2)](#2.2)

binary_op(init, unary_op(*first)), and

- [(2.3)](#2.3)

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[.](#2.sentence-1)

[3](#3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L13061)

*Preconditions*: 

- [(3.1)](#3.1)

  If init is provided, T meets the [*Cpp17MoveConstructible*](utility.arg.requirements#:Cpp17MoveConstructible "16.4.4.2 Template argument requirements [utility.arg.requirements]") (Table [31](utility.arg.requirements#tab:cpp17.moveconstructible "Table 31: Cpp17MoveConstructible requirements")) requirements;
 otherwise, U meets the [*Cpp17MoveConstructible*](utility.arg.requirements#:Cpp17MoveConstructible "16.4.4.2 Template argument requirements [utility.arg.requirements]") requirements[.](#3.1.sentence-1)

- [(3.2)](#3.2)

  Neither unary_op nor binary_op invalidates
 iterators or subranges, nor modifies elements in
 the ranges [first, last] or [result, result + (last - first)][.](#3.2.sentence-1)

[4](#4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L13075)

*Effects*: For each integer K in [0, last - first)
assigns through result + K the value of

- [(4.1)](#4.1)

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

- [(4.2)](#4.2)

  *GENERALIZED_NONCOMMUTATIVE_SUM*(  
 binary_op,  
 unary_op(*(first + 0)), unary_op(*(first + 1)), …, unary_op(*(first + K)))  
   otherwise[.](#4.2.sentence-2)

[5](#5)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L13088)

*Returns*: The end of the resulting range beginning at result[.](#5.sentence-1)

[6](#6)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L13092)

*Complexity*: O(last - first) applications each
of unary_op and binary_op[.](#6.sentence-1)

[7](#7)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L13097)

*Remarks*: result may be equal to first[.](#7.sentence-1)

[8](#8)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L13101)

[*Note [1](#note-1)*:

The difference between transform_exclusive_scan andtransform_inclusive_scan is that transform_inclusive_scan includes the ith input element in the ith sum[.](#8.sentence-1)

If binary_op is not mathematically associative,
the behavior of transform_inclusive_scan can be nondeterministic[.](#8.sentence-2)

transform_inclusive_scan does not
apply unary_op to init[.](#8.sentence-3)

â *end note*]
