std::transform_inclusive_scan(3)

NAME
std::transform_inclusive_scan - std::transform_inclusive_scan

Synopsis
   Defined in header <numeric>
   template< class InputIt, class OutputIt,
   class BinaryOperation, class UnaryOperation >
   OutputIt transform_inclusive_scan( InputIt (since C++17)
   first, InputIt last, OutputIt d_first, (until C++20)
   BinaryOperation binary_op, UnaryOperation
   unary_op );
   template< class InputIt, class OutputIt,
   class BinaryOperation, class UnaryOperation >
   constexpr OutputIt transform_inclusive_scan(
   InputIt first, InputIt last, (since C++20)
   OutputIt d_first,
   BinaryOperation binary_op,
   UnaryOperation unary_op );
   template< class ExecutionPolicy, class
   ForwardIt1, class ForwardIt2,
   class BinaryOperation, class UnaryOperation >
   ForwardIt2 transform_inclusive_scan(
   ExecutionPolicy&& policy, (2) (since C++17)
   ForwardIt1 first, ForwardIt1 last, ForwardIt2
   d_first,
   BinaryOperation binary_op, UnaryOperation
   unary_op );
   template< class InputIt, class OutputIt,
   class BinaryOperation, class UnaryOperation, (1)
   class T >
   OutputIt transform_inclusive_scan( InputIt (since C++17)
   first, InputIt last, OutputIt d_first, (until C++20)
   BinaryOperation binary_op, UnaryOperation
   unary_op,
   T init );
   template< class InputIt, class OutputIt,
   class BinaryOperation, class UnaryOperation,
   class T >
   constexpr OutputIt transform_inclusive_scan(
   InputIt first, InputIt last, (since C++20)
   OutputIt d_first, (3)
   BinaryOperation binary_op,
   UnaryOperation unary_op,
   T init );
   template< class ExecutionPolicy, class
   ForwardIt1, class ForwardIt2,
   class BinaryOperation, class UnaryOperation,
   class T >
   ForwardIt2 transform_inclusive_scan(
   ExecutionPolicy&& policy, (4) (since C++17)
   ForwardIt1 first, ForwardIt1 last, ForwardIt2
   d_first,
   BinaryOperation binary_op, UnaryOperation
   unary_op,
   T init );
   Transforms each element in the range [first, last) with unary_op, then computes an
   inclusive prefix sum operation using binary_op over the resulting range, optionally
   with init as the initial value, 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 (1-2), the generalized noncommutative sum of unary_op(*j)... for
       every j in [first, first + (i - d_first + 1)) over binary_op,
     * for overloads (3-4), the generalized noncommutative sum of init, unary_op(*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) 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.
   unary_op and 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
                        unary FunctionObject that will be applied to each
   unary_op - element of the input range. The return type must be
                        acceptable as input to binary_op.
                        binary FunctionObject that will be applied in to the
   binary_op - result of unary_op, 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(unary_op(*first), unary_op(*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, unary_op(*first)), binary_op(init, init), and
   binary_op(unary_op(*first), unary_op(*first)) must be convertible to T

Return value
   Iterator to the element past the last element written.

Complexity
   O(last - first) applications of each of binary_op and unary_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.

Notes
   unary_op is not applied to init.
   The parameter init appears last, differing from std::transform_exclusive_scan,
   because it is optional for this function.

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};
   auto times_10 = [](int x) { return x * 10; };
   std::cout << "10 times exclusive sum: ";
   std::transform_exclusive_scan(data.begin(), data.end(),
                        std::ostream_iterator<int>(std::cout, " "),
                        0, std::plus<int>{}, times_10);
   std::cout << "\n10 times inclusive sum: ";
   std::transform_inclusive_scan(data.begin(), data.end(),
                        std::ostream_iterator<int>(std::cout, " "),
                        std::plus<int>{}, times_10);
 }

Output:
 10 times exclusive sum: 0 30 40 80 90 140 230 250
 10 times inclusive sum: 30 40 80 90 140 230 250 310

See also
   partial_sum computes the partial sum of a range of elements
                        (function template)
                        applies a function to a range of elements, storing results
   transform in a destination range
                        (function template)
   inclusive_scan similar to std::partial_sum, includes the ith input element
   (C++17) in the ith sum
                        (function template)
   transform_exclusive_scan applies an invocable, then calculates exclusive scan
   (C++17) (function template)