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

NAME
     std::set_union - std::set_union

Synopsis
	Defined in header <algorithm>
	template< class InputIt1, class InputIt2, class OutputIt
	>

	OutputIt  set_union( InputIt1 first1, InputIt1 last1,	  (1) (constexpr
     since C++20)
			    InputIt2 first2, InputIt2 last2,

			    OutputIt d_first );
	template< class ExecutionPolicy,

		  class ForwardIt1, class ForwardIt2, class
	ForwardIt3 >
	ForwardIt3 set_union( ExecutionPolicy&& policy,
			      ForwardIt1  first1,  ForwardIt1	    (2)   (since
     C++17)
	last1,
			      ForwardIt2 first2, ForwardIt2
	last2,

			      ForwardIt3 d_first );
	template< class InputIt1, class InputIt2,

		  class OutputIt, class Compare >
	OutputIt  set_union( InputIt1 first1, InputIt1 last1,	  (3) (constexpr
     since C++20)
			    InputIt2 first2, InputIt2 last2,

			    OutputIt d_first, Compare comp );
	template< class ExecutionPolicy,

		  class ForwardIt1, class ForwardIt2,
		  class ForwardIt3, class Compare >
	ForwardIt3 set_union( ExecutionPolicy&& policy,
			      ForwardIt1  first1,  ForwardIt1	    (4)   (since
     C++17)
	last1,
			      ForwardIt2 first2, ForwardIt2
	last2,

			      ForwardIt3 d_first, Compare comp
	);

	Constructs  a sorted union beginning at d_first consisting of the set of
     elements
	present in one or  both  sorted  ranges  [first1,  last1)  and	[first2,
     last2).

	If [first1, last1) contains m elements that are equivalent to each other
     and
	[first2,  last2)  contains  n elements that are equivalent to them, then
     all m elements
	will be copied from [first1, last1) to the output range, preserving  or-
     der, and then
	the  final  std::max(n	-  m,  0)  elements will be copied from [first2,
     last2) to the
	output range, also preserving order.

	1) If [first1, last1) or [first2, last2) is not sorted with respect to
	operator<
	(until C++20)
	std::less{}
	(since C++20), the behavior is undefined.
	3) If [first1, last1) or [first2, last2) is not sorted with  respect  to
     comp, the
	behavior is undefined.
	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)

	If  the  output  range overlaps with [first1, last1) or [first2, last2),
     the behavior
	is undefined.

Parameters
	first1, last1 - the first input sorted range
	first2, last2 - the second input sorted range
	d_first       - the beginning of the output range
	policy	      - the execution policy to use. See  execution  policy  for
     details.
			comparison  function  object (i.e. an object that satis-
     fies the
			requirements of Compare) which returns true if the first
     argument is
			less than (i.e. is ordered before) the second.

			The signature  of  the	comparison  function  should  be
     equivalent to the
			following:

			bool cmp(const Type1& a, const Type2& b);
	comp	      -
			While  the  signature  does not need to have const&, the
     function must
			not modify the objects passed to it and must be able  to
     accept all
			values	of type (possibly const) Type1 and Type2 regard-
     less of value
			category (thus, Type1& is not allowed
			, nor is Type1 unless for Type1 a move is equivalent  to
     a copy
			(since C++11)).
			The  types  Type1 and Type2 must be such that objects of
     types
			InputIt1 and InputIt2 can be dereferenced and  then  im-
     plicitly
			converted to both Type1 and Type2.

Type requirements
	-
	InputIt1, InputIt2 must meet the requirements of LegacyInputIterator.
	-
	ForwardIt1, ForwardIt2, ForwardIt3 must meet the requirements of
	LegacyForwardIterator.
	-
	OutputIt must meet the requirements of LegacyOutputIterator.
	-
	Compare must meet the requirements of Compare.

Return value
	Iterator past the end of the constructed range.

Complexity
	Given \(\scriptsize N_1\)N
	1 as std::distance(first1, last1) and \(\scriptsize N_2\)N
	2 as std::distance(first2, last2):

	1,2) At most \(\scriptsize 2 \cdot (N_1+N_2)-1\)2a(N
	1+N
	2)-1 comparisons using
	operator<
	(until C++20)
	std::less{}
	(since C++20).
	3,4) At most \(\scriptsize 2 \cdot (N_1+N_2)-1\)2a(N
	1+N
	2)-1 applications of the comparison function comp.

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.

Possible implementation
					    set_union (1)
       template<class InputIt1, class InputIt2, class OutputIt>
       OutputIt set_union(InputIt1 first1, InputIt1 last1,
			  InputIt2 first2, InputIt2 last2, OutputIt d_first)
       {
	   for (; first1 != last1; ++d_first)
	   {
	       if (first2 == last2)
		   return std::copy(first1, last1, d_first);

	       if (*first2 < *first1)
		   *d_first = *first2++;
	       else
	       {
		   *d_first = *first1;
		   if (!(*first1 < *first2))
		       ++first2;
		   ++first1;
	       }
	   }
	   return std::copy(first2, last2, d_first);
       }
					    set_union (3)
       template<class InputIt1, class InputIt2, class OutputIt, class Compare>
       OutputIt set_union(InputIt1 first1, InputIt1 last1,
			  InputIt2 first2,  InputIt2  last2,  OutputIt	d_first,
     Compare comp)
       {
	   for (; first1 != last1; ++d_first)
	   {
	       if (first2 == last2)
		   // Finished range 2, include the rest of range 1:
		   return std::copy(first1, last1, d_first);

	       if (comp(*first2, *first1))
		   *d_first = *first2++;
	       else
	       {
		   *d_first = *first1;
		   if  (!comp(*first1,	*first2)) // Equivalent => don't need to
     include *first2.
		       ++first2;
		   ++first1;
	       }
	   }
	   // Finished range 1, include the rest of range 2:
	   return std::copy(first2, last2, d_first);
       }

Notes
	This algorithm performs a similar task as std::merge does. Both  consume
     two sorted
	input ranges and produce a sorted output with elements from both inputs.
     The
	difference  between  these  two  algorithms is with handling values from
     both input
	ranges which compare equivalent (see notes  on	LessThanComparable).  If
     any equivalent
	values	appeared  n  times in the first range and m times in the second,
     std::merge
	would output all n + m occurrences whereas std::set_union  would  output
     std::max(n,
	m) ones only. So std::merge outputs exactly std::distance(first1, last1)
     +
	std::distance(first2,  last2)  values  and  std::set_union  may  produce
     fewer.

Example
     // Run this code

      #include <algorithm>
      #include <iostream>
      #include <iterator>
      #include <vector>

      void println(const std::vector<int>& v)
      {
	  for (int i : v)
	      std::cout << i << ' ';
	  std::cout << '\n';
      }

      int main()
      {
	  std::vector<int> v1, v2, dest;

	  v1 = {1, 2, 3, 4, 5};
	  v2 = {3, 4, 5, 6, 7};

	  std::set_union(v1.cbegin(), v1.cend(),
			 v2.cbegin(), v2.cend(),
			 std::back_inserter(dest));
	  println(dest);

	  dest.clear();

	  v1 = {1, 2, 3, 4, 5, 5, 5};
	  v2 = {3, 4, 5, 6, 7};

	  std::set_union(v1.cbegin(), v1.cend(),
			 v2.cbegin(), v2.cend(),
			 std::back_inserter(dest));
	  println(dest);
      }

Output:
      1 2 3 4 5 6 7
      1 2 3 4 5 5 5 6 7

	Defect reports

	The following behavior-changing defect	reports  were  applied	retroac-
     tively to
	previously published C++ standards.

	  DR	Applied to		Behavior as published		    Cor-
     rect behavior
	LWG   291  C++98       it  was	unspecified  how  to  handle  equivalent
     specified
			   elements in the input ranges

See also
	includes		 returns true if one sequence is  a  subsequence
     of another
				 (function template)
	merge			 merges two sorted ranges
				 (function template)
	set_difference		 computes the difference between two sets
				 (function template)
	set_intersection	 computes the intersection of two sets
				 (function template)
	set_symmetric_difference  computes  the symmetric difference between two
     sets
				 (function template)
	ranges::set_union	 computes the union of two sets
	(C++20) 		 (niebloid)

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