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, InputIt last, (1) (constexpr since C++20)
                        OutputIt d_first );
   template< class ExecutionPolicy,
             class ForwardIt1, class ForwardIt2 >
   ForwardIt2 inclusive_scan( ExecutionPolicy&& policy, (2) (since C++17)
                        ForwardIt1 first, ForwardIt1
   last,
                        ForwardIt2 d_first );
   template< class InputIt, class OutputIt, class BinaryOp
   >
                        (since C++17)
   OutputIt inclusive_scan( InputIt first, InputIt last, (3) (constexpr since C++20)
                        OutputIt d_first, BinaryOp op
   );
   template< class ExecutionPolicy,
             class ForwardIt1, class ForwardIt2, class
   BinaryOp >
   ForwardIt2 inclusive_scan( ExecutionPolicy&& policy, (4) (since C++17)
                        ForwardIt1 first, ForwardIt1
   last,
                        ForwardIt2 d_first, BinaryOp
   op );
   template< class InputIt, class OutputIt,
             class BinaryOp, class T > (since C++17)
   OutputIt inclusive_scan( InputIt first, InputIt last, (5) (constexpr since C++20)
                        OutputIt d_first, BinaryOp op,
   T init );
   template< class ExecutionPolicy,
             class ForwardIt1, class ForwardIt2,
             class BinaryOp, class T >
   ForwardIt2 inclusive_scan( ExecutionPolicy&& policy, (6) (since C++17)
                        ForwardIt1 first, ForwardIt1
   last,
                        ForwardIt2 d_first, BinaryOp
   op, T init );
   1) Equivalent to inclusive_scan(first, last, d_first, std::plus<>().
   3) Computes the inclusive prefix sum using op.
   For each integer i in [0, std::distance(first, last)), performs the following
   operations in order:
    1. Creates a sequence which is formed by the elements of [first, iter] in order,
       where iter is the next i
       th iterator of first.
    2. Computes the generalized noncommutative sum of the sequence over op.
    3. Assigns the result to *dest, where dest is the next i
       th iterator of d_first.
   5) Same as (3), but each sequence created is formed by init followed by the elements
   of [first, iter] in order.
   2,4,6) Same as (1,3,5), but executed according to policy.
   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)
   The generalized, noncommutative sum of a sequence of elements over a binary
   operation binary_op is defined as follows:
     * If the sequence only has one element, the sum is the value of the element.
     * Otherwise, performs the following operations in order:
    1. Selects any two adjacent elements elem1 and elem2 from the sequence.
    2. Calculates binary_op(elem1, elem2) and replaces the two elements in the sequence
       with the result.
    3. Repeats steps 1 and 2 until there is only one element in the sequence.
   Given binary_op as the actual binary operation:
     * The result is non-deterministic if the binary_op is not associative (such as
       floating-point addition).
     * For overloads (1-4), if binary_op(*first, *first) is not convertible to the
       value type of decltype(first), the program is ill-formed.
     * For overloads (5,6), if any of the following values is not convertible to T, the
       program is ill-formed:
     * binary_op(init, *first)
     * binary_op(init, init)
     * binary_op(*first, *first)
     * If any of the following conditions is satisfied, the behavior is undefined:
     * For overloads (1-4), the value type of decltype(first) is not MoveConstructible.
     * For overloads (5,6), T is not MoveConstructible.
     * binary_op modifies any element of [first, last).
     * binary_op invalidates any iterator or subrange of [first, last].

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
                 binary FunctionObject that will be applied in to the result of
   op - dereferencing the input iterators, the results of other op, and init
                 (if provided)

Type requirements
   -
   InputIt must meet the requirements of LegacyInputIterator.
   -
   OutputIt must meet the requirements of LegacyOutputIterator.
   -
   ForwardIt1, ForwardIt2 must meet the requirements of LegacyForwardIterator.

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

Complexity
   Given \(\scriptsize N\)N as std::distance(first, last):
   1,2) \(\scriptsize O(N)\)O(N) applications of std::plus<>().
   3-6) \(\scriptsize O(N)\)O(N) applications of 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.

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 or folds 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 i^th input
   (C++17) element from the i^th sum
                        (function template)