std::inclusive_scan

Defined in header `<numeric>`
template< class InputIt, class OutputIt > OutputIt inclusive_scan( InputIt first, InputIt last, OutputIt d_first );	(1)	(since C++17) (constexpr since C++20)
template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2 > ForwardIt2 inclusive_scan( ExecutionPolicy&& policy, ForwardIt1 first, ForwardIt1 last, ForwardIt2 d_first );	(2)	(since C++17)
template< class InputIt, class OutputIt, class BinaryOp > OutputIt inclusive_scan( InputIt first, InputIt last, OutputIt d_first, BinaryOp op );	(3)	(since C++17) (constexpr since C++20)
template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class BinaryOp > ForwardIt2 inclusive_scan( ExecutionPolicy&& policy, ForwardIt1 first, ForwardIt1 last, ForwardIt2 d_first, BinaryOp op );	(4)	(since C++17)
template< class InputIt, class OutputIt, class BinaryOp, class T > OutputIt inclusive_scan( InputIt first, InputIt last, OutputIt d_first, BinaryOp op, T init );	(5)	(since C++17) (constexpr since C++20)
template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class BinaryOp, class T > ForwardIt2 inclusive_scan( ExecutionPolicy&& policy, ForwardIt1 first, ForwardIt1 last, ForwardIt2 d_first, BinaryOp op, T init );	(6)	(since C++17)

1) Equivalent to inclusive_scan(first, last, d_first, std::plus<>().

3) Computes the inclusive 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 the elements of [first, iter] in order, where iter is the next i_th iterator of first.
Computes the generalized noncommutative sum of the sequence over op.
Assigns the result to *dest, where dest is the next i_th iterator of d_first.

5) Same as (3), but each sequence created is formed by init followed by the elements of [first, iter] in order.

2,4,6) Same as (1,3,5), but executed according to policy.

These overloads participate in overload resolution only if the value of the following expression is true:

`std::is_execution_policy_v<std::decay_t<ExecutionPolicy>>`	(until C++20)
`std::is_execution_policy_v<std::remove_cvref_t<ExecutionPolicy>>`	(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.

Given binary_op as the actual binary operation:

The result is non-deterministic if the binary_op is not associative (such as floating-point addition).
For overloads (1-4), if binary_op(*first, *first) is not convertible to the value type of decltype(first), the program is ill-formed.
For overloads (5,6), if any of the following values is not convertible to T, the program is ill-formed:

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

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

For overloads (1-4), the value type of decltype(first) is not MoveConstructible.
For overloads (5,6), T is not MoveConstructible.
binary_op modifies any element of [first, last).
binary_op invalidates any iterator or subrange of [first, last].

Parameters

first, last	-	the pair of iterators defining the source range of elements to sum
d_first	-	the beginning of the destination range; may be equal to `first`
policy	-	the execution policy to use
init	-	the initial value
op	-	binary FunctionObject that will be applied in to the result of dereferencing the input iterators, the results of other `op`, and `init` (if provided)
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) \(\scriptsize O(N)\)O(N) applications of std::plus<>().

3-6) \(\scriptsize O(N)\)O(N) applications of 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.

Example

#include <functional>
#include <iostream>
#include <iterator>
#include <numeric>
#include <vector>

int main()
{
    std::vector data{3, 1, 4, 1, 5, 9, 2, 6};
    
    std::cout << "Exclusive sum: ";
    std::exclusive_scan(data.begin(), data.end(),
                        std::ostream_iterator<int>(std::cout, " "),
                        0);
    
    std::cout << "\nInclusive sum: ";
    std::inclusive_scan(data.begin(), data.end(),
                        std::ostream_iterator<int>(std::cout, " "));
    
    std::cout << "\n\nExclusive product: ";
    std::exclusive_scan(data.begin(), data.end(),
                        std::ostream_iterator<int>(std::cout, " "),
                        1, std::multiplies<>{});
    
    std::cout << "\nInclusive product: ";
    std::inclusive_scan(data.begin(), data.end(),
                        std::ostream_iterator<int>(std::cout, " "),
                        std::multiplies<>{});
}

Output:

Exclusive sum: 0 3 4 8 9 14 23 25
Inclusive sum: 3 4 8 9 14 23 25 31

Exclusive product: 1 3 3 12 12 60 540 1080
Inclusive product: 3 3 12 12 60 540 1080 6480