std::inclusive_scan(3)

NAME
std::inclusive_scan - std::inclusive_scan

Synopsis
   Defined in header <numeric>
   template< class InputIt, class OutputIt
   >
                        (since C++17)
   OutputIt inclusive_scan( InputIt first, (until C++20)
   InputIt last, OutputIt d_first );
   template< class InputIt, class OutputIt
   >
   constexpr OutputIt inclusive_scan( (since C++20)
   InputIt first,
   InputIt last, OutputIt d_first );
   template< class ExecutionPolicy, class
   ForwardIt1, class ForwardIt2 >
   ForwardtIt2 inclusive_scan( (2) (since C++17)
   ExecutionPolicy&& policy, ForwardIt1
   first,
   ForwardIt1 last, ForwardIt2 d_first );
   template< class InputIt, class OutputIt,
   class BinaryOperation >
   OutputIt inclusive_scan( InputIt first, (since C++17)
   InputIt last, (until C++20)
   OutputIt d_first, BinaryOperation
   binary_op );
   template< class InputIt, class OutputIt,
   class BinaryOperation >
   constexpr OutputIt inclusive_scan( (since C++20)
   InputIt first, InputIt last,
   OutputIt d_first, BinaryOperation (1)
   binary_op );
   template< class ExecutionPolicy, class
   ForwardIt1, class ForwardIt2,
   class BinaryOperation >
   ForwardIt2 inclusive_scan( (4) (since C++17)
   ExecutionPolicy&& policy,
   ForwardIt1 first, ForwardIt1 last,
   ForwardIt2 d_first, BinaryOperation
   binary_op ); (3)
   template< class InputIt, class OutputIt,
   class BinaryOperation, class T > (since
                        C++17)
   OutputIt inclusive_scan( InputIt first, (until
   InputIt last, OutputIt d_first, C++20)
   BinaryOperation binary_op, T init );
   template< class InputIt, class OutputIt,
   class BinaryOperation, class T >
   constexpr OutputIt inclusive_scan( (since
   InputIt first, InputIt last, OutputIt C++20)
   d_first, (5)
   BinaryOperation binary_op, T init );
   template< class ExecutionPolicy, class
   ForwardIt1, class ForwardIt2,
   class BinaryOperation, class T >
   ForwardIt2 inclusive_scan( (6) (since
   ExecutionPolicy&& policy, C++17)
   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. These overloads do not
   participate in overload resolution unless
   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) 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 FunctionObject that will be applied in to the result of
   binary_op - 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.
   -
   ForwardIt2 must meet the requirements of LegacyForwardIterator.
   -
   If init is not provided, decltype(first)'s value_type must be MoveConstructible and
   binary_op(*first, *first) must be convertible to decltype(first)'s value type.
   -
   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

See also
                        computes the differences between adjacent elements in a
   adjacent_difference range
                        (function template)
   accumulate sums up a range of elements
                        (function template)
   partial_sum computes the partial sum of a range of elements
                        (function template)
   transform_inclusive_scan applies an invocable, then calculates inclusive scan
   (C++17) (function template)
   exclusive_scan similar to std::partial_sum, excludes the ith input element
   (C++17) from the ith sum
                        (function template)