std::transform_inclusive_scan

Defined in header `<numeric>`
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 );	(1)	(since C++17)
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)
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 );	(3)	(since C++17)
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 i-th input element is included in the i-th 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 $1 < K+1 = M \leq N$

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, and do not participate in overload resolution unless std::is_execution_policy_v<std::decay_t<ExecutionPolicy>> is true.

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. and, if `init` is not provided, ForwardIt1's value_type must be MoveConstructible and `binary_op(unary_op(first), unary_op(first))` must be convertible to ForwardIt1's value type
- `ForwardIt2` must meet the requirements of LegacyForwardIterator.
- `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 times_10(int x)
{
  return x * 10;
}
 
int main()
{
  std::vector data {3, 1, 4, 1, 5, 9, 2, 6};
 
  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

Language
Standard Library Headers
Freestanding and hosted implementations
Named requirements
Language support library
Concepts library (C++20)
Diagnostics library
Utilities library
Strings library
Containers library
Iterators library
Ranges library (C++20)
Algorithms library
Numerics library
Input/output library
Localizations library
Regular expressions library (C++11)
Atomic operations library (C++11)
Thread support library (C++11)
Filesystem library (C++17)
Technical Specifications

partial_sum	computes the partial sum of a range of elements (function template)
transform	applies a function to a range of elements (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 a functor, then calculates exclusive scan (function template)