std::inclusive_scan

template< class InputIt, class OutputIt >
OutputIt inclusive_scan( InputIt first, 
                         InputIt last, OutputIt d_first );

template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2 >
ForwardtIt2 inclusive_scan( ExecutionPolicy&& policy, ForwardIt1 first, 
                            ForwardIt1 last, ForwardIt2 d_first );

template< class InputIt, class OutputIt, class BinaryOperation >
OutputIt inclusive_scan( InputIt first, InputIt last,
                         OutputIt d_first, BinaryOperation binary_op );

template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2,
          class BinaryOperation >
ForwardIt2 inclusive_scan( ExecutionPolicy&& policy, 
                           ForwardIt1 first, ForwardIt1 last,
                           ForwardIt2 d_first, BinaryOperation binary_op );

template< class InputIt, class OutputIt, class BinaryOperation, class T >
OutputIt inclusive_scan( InputIt first, InputIt last, OutputIt d_first,
                         BinaryOperation binary_op, T init );

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 );

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 ≤ 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

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

#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<>{});                      
}

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

See also