std::exclusive_scan() algorithm

since C++20

// (1)
template< class InputIt, class OutputIt >
constexpr OutputIt exclusive_scan( InputIt first, InputIt last, OutputIt d_first );

// (2)
template< class InputIt, class OutputIt, class BinaryOperation >
constexpr OutputIt exclusive_scan( InputIt first, InputIt last, OutputIt d_first, BinaryOperation binary_op );

// (3)
template< class InputIt, class OutputIt, class BinaryOperation, class T >
constexpr OutputIt exclusive_scan( InputIt first, InputIt last, OutputIt d_first, BinaryOperation binary_op, T init );

// (4)
template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2 >
ForwardtIt2 exclusive_scan( ExecutionPolicy&& policy, ForwardIt1 first, ForwardIt1 last, ForwardIt2 d_first );

// (5)
template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class BinaryOperation >
ForwardIt2 exclusive_scan( ExecutionPolicy&& policy,
                           ForwardIt1 first, ForwardIt1 last, ForwardIt2 d_first,
                           BinaryOperation binary_op );

// (6)
template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class BinaryOperation, class T >
ForwardIt2 exclusive_scan( ExecutionPolicy&& policy,
                           ForwardIt1 first, ForwardIt1 last, ForwardIt2 d_first,
                           BinaryOperation binary_op, T init );

since C++17

// (1)
template< class InputIt, class OutputIt >
OutputIt exclusive_scan( InputIt first, InputIt last, OutputIt d_first );

// (2)
template< class InputIt, class OutputIt, class BinaryOperation >
OutputIt exclusive_scan( InputIt first, InputIt last, OutputIt d_first, BinaryOperation binary_op );

// (3)
template< class InputIt, class OutputIt, class BinaryOperation, class T >
OutputIt exclusive_scan( InputIt first, InputIt last, OutputIt d_first, BinaryOperation binary_op, T init );

// (4)
template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2 >
ForwardtIt2 exclusive_scan( ExecutionPolicy&& policy, ForwardIt1 first, ForwardIt1 last, ForwardIt2 d_first );

// (5)
template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class BinaryOperation >
ForwardIt2 exclusive_scan( ExecutionPolicy&& policy,
                           ForwardIt1 first, ForwardIt1 last, ForwardIt2 d_first,
                           BinaryOperation binary_op );

// (6)
template< class ExecutionPolicy, class ForwardIt1, class ForwardIt2, class BinaryOperation, class T >
ForwardIt2 exclusive_scan( ExecutionPolicy&& policy,
                           ForwardIt1 first, ForwardIt1 last, ForwardIt2 d_first,
                           BinaryOperation binary_op, T init );

Computes an exclusive prefix sum operation using binary_op (or std::plus<>() for overloads (1, 4)) for the range [first; last), using init as the initial value (if provided), and writes the results to the range beginning at d_first.

"exclusive" means that the i-th input element is not included in the i-th sum.

The summation operations may be performed in arbitrary order, and the behavior is nondeterministic if binary_op is not associative.

Formally, assigns through each iterator i in [d_first; d_first + (last - first)) the value of:

• (1, 2, 4, 5) The generalized noncommutative sum of *j... for every j in [first; first + (i - d_first + 1) ) over binary_op
• (3, 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, a1, ..., aN) is defined as follows:

• If N = 1, a1

• If N > 1, op(GNSUM(op, a1, ..., aK), GNSUM(op, aM, ..., aN)) for any K where 1 < K + 1 = M ≤ N

• (4 - 6) Same as (1 - 3), but executed according to policy.

  Overload Resolution

  These overloads participate 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)

Undefined Behaviour

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.
init	The initial value of the generalized sum.
policy	The execution policy to use. See execution policy for details.
binary_op	Binary FunctionObject that will be applied in unspecified order to the result of dereferencing the input iterators, the results of other binary_op and init.

Type requirements

InputIt	LegacyInputIterator
OutputIt	LegacyOutputIterator
ForwardIt1 ForwardIt2	LegacyForwardIterator

• T (if init is provided) must meet the requirements of MoveConstructible. The following expressions must be convertible to T:
  • binary_op(init, *first)
  • binary_op(init, init)
  • binary_op(*first, *first)

Return value

Iterator to the element past the last element written.

Complexity

O(last - first) applications of binary_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.

Examples

Main.cpp

#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<>{});
}

Possible 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