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std::exclusive_scan(3)	       C++ Standard Libary	  std::exclusive_scan(3)

NAME
     std::exclusive_scan - std::exclusive_scan

Synopsis
	Defined in header <numeric>
	template< class InputIt, class OutputIt, class T >
								     (since
     C++17)
	OutputIt  exclusive_scan( InputIt first, InputIt last,	  (1) (constexpr
     since C++20)

				 OutputIt d_first, T init );
	template< class ExecutionPolicy,

		  class ForwardIt1, class ForwardIt2, class T >
	ForwardIt2  exclusive_scan(  ExecutionPolicy&&	policy,      (2)  (since
     C++17)
				   ForwardIt1 first, ForwardIt1
	last,

				   ForwardIt2 d_first, T init );
	template< class InputIt, class OutputIt,

		  class  T,  class  BinaryOp  > 			  (since
     C++17)
	OutputIt exclusive_scan( InputIt first, InputIt last,	 (3)  (constexpr
     since C++20)

				 OutputIt d_first, T init,
	BinaryOp op );
	template< class ExecutionPolicy,

		  class ForwardIt1, class ForwardIt2,
		  class T, class BinaryOp >
	ForwardIt2  exclusive_scan(  ExecutionPolicy&&	policy,      (4)  (since
     C++17)
				   ForwardIt1 first, ForwardIt1
	last,

				   ForwardIt2 d_first, T init,
	BinaryOp op );

	1)   Equivalent   to   exclusive_scan(first,   last,   d_first,    init,
     std::plus<>().
	3) Computes the exclusive prefix sum using op.
	For each integer i in [0, std::distance(first, last)), performs the fol-
     lowing
	operations in order:
	 1.  Creates a sequence which is formed by init followed 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.
	2,4) Same as (1,3), 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  bi-
     nary 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 se-
     quence.

	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).
	  *  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 un-
     defined:

	  * 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 de-
     tails.
	init	    - the initial value
	op	    - binary FunctionObject that will be applied in to	the  re-
     sult of
		      dereferencing  the  input  iterators, the results of other
     op, and init

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

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<>().
	3,4) \(\scriptsize O(N)\)O(N) applications of op.

Exceptions
	The overloads with a template parameter named ExecutionPolicy report er-
     rors 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-de-
     fined.
	  * 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 ele-
     ments 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_exclusive_scan applies an invocable, then calculates exclusive
     scan
	(C++17) 		 (function template)
	inclusive_scan		 similar to std::partial_sum, includes the  i^th
     input
	(C++17) 		 element in the i^th sum
				 (function template)

http://cppreference.com 	   2024.06.10		  std::exclusive_scan(3)
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