std::transform_exclusive_scan

Defined in header `<numeric>`
template< class InputIt, class OutputIt, class T, class BinaryOp, class UnaryOp > OutputIt transform_exclusive_scan ( InputIt first, InputIt last, OutputIt d_first, T init, BinaryOp binary_op, UnaryOp unary_op );	(1)	(since C++17) (constexpr since C++20)
template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class T, class BinaryOp, class UnaryOp > ForwardIt2 transform_exclusive_scan ( ExecutionPolicy&& policy, ForwardIt1 first, ForwardIt1 last, ForwardIt2 d_first, T init, BinaryOp binary_op, UnaryOp unary_op );	(2)	(since C++17)

1) Computes the exclusive prefix sum using op.

For each integer i in [0, std::distance(first, last)), performs the following operations in order:

Creates a sequence which is formed by init followed by the values transformed from the elements of [first, iter) in order by unary_op, where iter is the next i
th iterator of first.
Computes the generalized noncommutative sum of the sequence over binary_op.
Assigns the result to *dest, where dest is the next i
th iterator of d_first.

2) Same as (1), but executed according to policy.

This overload participates in overload resolution only if

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)

The generalized noncommutative sum of a sequence of elements over a binary operation binary_op is defined as follows:

If the sequence only has one element, the sum is the value of the element.
Otherwise, performs the following operations in order:

Selects any two adjacent elements elem1 and elem2 from the sequence.
Calculates binary_op(elem1, elem2) and replaces the two elements in the sequence with the result.
Repeats steps 1 and 2 until there is only one element in the sequence.

The result is non-deterministic if the binary_op is not associative (such as floating-point addition).

If any of the following values is not convertible to T, the program is ill-formed:

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

If any of the following conditions is satisfied, the behavior is undefined:

T is not MoveConstructible.
unary_op or binary_op modifies any element of [first, last).
unary_op or binary_op invalidates any iterator or subrange of [first, last].

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.
Type requirements
- `InputIt` must meet the requirements of LegacyInputIterator.
- `OutputIt` must meet the requirements of LegacyOutputIterator.
- `ForwardIt1, ForwardIt2` must meet the requirements of LegacyForwardIterator.

Return value

Iterator to the element past the last element written.

Complexity

Given $\scriptsize N$ $N$ as std::distance(first, last):

1,2)

O(N)

applications of unary_op and binary_op respectively.

Exceptions

The overload with a template parameter named ExecutionPolicy reports 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 never applied to init.

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);
    std::cout << '\n';
}

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

Compiler support
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Language
Standard library
Standard library headers
Named requirements
Feature test macros (C++20)
Language support library
Concepts library (C++20)
Metaprogramming library (C++11)
Diagnostics library
General utilities library
Strings library
Containers library
Iterators library
Ranges library (C++20)
Algorithms library
Numerics library
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Filesystem library (C++17)
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Concurrency support library (C++11)
Execution support library (C++26)
Technical specifications
Symbols index
External libraries

partial_sum	computes the partial sum of a range of elements (function template)
exclusive_scan (C++17)	similar to std::partial_sum, excludes the $i$ ^th input element from the $i$ ^th sum (function template)
transform_inclusive_scan (C++17)	applies an invocable, then calculates inclusive scan (function template)