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 (until C++20)
   last1,
   InputIt2 first2, InputIt2 last2,
   OutputIt d_first );
   template< class InputIt1, class InputIt2, class
   OutputIt >
   constexpr OutputIt set_union( InputIt1 first1, (since C++20)
   InputIt1 last1,
   InputIt2 first2, InputIt2 last2,
   OutputIt d_first );
   template< class ExecutionPolicy, class
   ForwardIt1, class ForwardIt2, class ForwardIt3 >
   ForwardIt3 set_union( ExecutionPolicy&& policy, (2) (since C++17)
   ForwardIt1 first1, ForwardIt1 last1,
   ForwardIt2 first2, ForwardIt2 last2,
   ForwardIt3 d_first );
   template< class InputIt1, class InputIt2, (1)
   class OutputIt, class Compare >
   OutputIt set_union( InputIt1 first1, InputIt1 (until C++20)
   last1,
   InputIt2 first2, InputIt2 last2,
   OutputIt d_first, Compare comp );
   template< class InputIt1, class InputIt2,
   class OutputIt, class Compare >
   constexpr OutputIt set_union( InputIt1 first1, (since C++20)
   InputIt1 last1, (3)
   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, (4) (since C++17)
   ForwardIt1 first1, ForwardIt1 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 some element is found m times in [first1, last1) and n times in [first2, last2),
   then all m elements will be copied from [first1, last1) to d_first, preserving
   order, and then exactly std::max(n-m, 0) elements will be copied from [first2,
   last2) to d_first, also preserving order.
   The resulting range cannot overlap with either of the input ranges.
   1) Elements are compared using operator< and the ranges must be sorted with respect
   to the same.
   3) Elements are compared using the given binary comparison function comp and the
   ranges must be sorted with respect to the same.
   2,4) Same as (1,3), but 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.

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 satisfies 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 regardless 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 implicitly
                   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.

Return value
   Iterator past the end of the constructed range.

Complexity
   At most \(\scriptsize 2\cdot(N_1+N_2)-1\)2·(N
   1+N
   2)-1 comparisons, where \(\scriptsize N_1\)N
   1 and \(\scriptsize N_2\)N
   2 are std::distance(first1, last1) and std::distance(first2, last2), respectively.

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
   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.

Possible implementation

First version
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); }

Second version
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); }

Example
   Example with vectors : // Run this code
 #include <vector>
 #include <iostream>
 #include <algorithm>
 #include <iterator>
 int main()
 {
     {
         std::vector<int> v1 = {1, 2, 3, 4, 5};
         std::vector<int> v2 = { 3, 4, 5, 6, 7};
         std::vector<int> dest1;
         std::set_union(v1.begin(), v1.end(),
                        v2.begin(), v2.end(),
                        std::back_inserter(dest1));
         for (const auto &i : dest1) {
             std::cout << i << ' ';
         }
         std::cout << '\n';
     }
     {
         std::vector<int> v1 = {1, 2, 3, 4, 5, 5, 5};
         std::vector<int> v2 = { 3, 4, 5, 6, 7};
         std::vector<int> dest1;
         std::set_union(v1.begin(), v1.end(),
                        v2.begin(), v2.end(),
                        std::back_inserter(dest1));
         for (const auto &i : dest1) {
             std::cout << i << ' ';
         }
         std::cout << '\n';
     }
 }

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

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)