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)
template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2 > ForwardtIt2 inclusive_scan( ExecutionPolicy&& policy, ForwardIt1 first, ForwardIt1 last, ForwardIt2 d_first );	(2)	(since C++17)
template< class InputIt, class OutputIt, class BinaryOperation > OutputIt inclusive_scan( InputIt first, InputIt last, OutputIt d_first, BinaryOperation binary_op );	(3)	(since C++17)
template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class BinaryOperation > ForwardIt2 inclusive_scan( ExecutionPolicy&& policy, ForwardIt1 first, ForwardIt1 last, ForwardIt2 d_first, BinaryOperation binary_op );	(4)	(since C++17)
template< class InputIt, class OutputIt, class BinaryOperation, class T > OutputIt inclusive_scan( InputIt first, InputIt last, OutputIt d_first, BinaryOperation binary_op, T init );	(5)	(since C++17)
template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class BinaryOperation, class T > ForwardIt2 inclusive_scan( ExecutionPolicy&& policy, ForwardIt1 first, ForwardIt1 last, ForwardIt2 d_first, BinaryOperation binary_op, T init );	(6)	(since C++17)

Computes an inclusive prefix sum operation using binary_op (or std::plus<>() for overloads (1-2)) for the range [first, last), using init as the initial value (if provided), 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 (1-4), the generalized noncommutative sum of *j... for every j in $[first, first + (i - d_first + 1))$ over binary_op
for overloads (5-6), the generalized noncommutative sum of init, *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 (2,4,6) are executed according to policy. This overload only participates in overload resolution if std::is_execution_policy_v<std::decay_t<ExecutionPolicy>> is true.

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 (optional)
binary_op	-	binary FunctionObject that will be applied in to the result of dereferencing the input iterators, 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(first, 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, first)`, `binary_op(init, init)`, and `binary_op(first, *first)` must be convertible to T

Return value

Iterator to the element past the last element written.

Complexity

$O(last - first)$ applications of the binary operation

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

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};
 
  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

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