std::set_intersection(3)

NAME
std::set_intersection - std::set_intersection

Synopsis
   Defined in header <algorithm>
   template< class InputIt1, class InputIt2, class
   OutputIt >
   OutputIt set_intersection( InputIt1 first1, (until C++20)
   InputIt1 last1,
   InputIt2 first2, InputIt2 last2,
   OutputIt d_first );
   template< class InputIt1, class InputIt2, class
   OutputIt >
   constexpr OutputIt set_intersection( InputIt1 (since C++20)
   first1, InputIt1 last1,
   InputIt2 first2, InputIt2 last2,
   OutputIt d_first );
   template< class ExecutionPolicy, class
   ForwardIt1, class ForwardIt2, class ForwardIt3 >
   ForwardIt3 set_intersection( ExecutionPolicy&& (2) (since C++17)
   policy, ForwardIt1 first1, ForwardIt1 last1,
   ForwardIt2 first2, ForwardIt2 last2,
   ForwardIt3 d_first );
   template< class InputIt1, class InputIt2, class (1)
   OutputIt, class Compare >
   OutputIt set_intersection( InputIt1 first1, (until C++20)
   InputIt1 last1,
   InputIt2 first2, InputIt2 last2,
   OutputIt d_first, Compare comp );
   template< class InputIt1, class InputIt2, class
   OutputIt, class Compare >
   constexpr OutputIt set_intersection( InputIt1 (since C++20)
   first1, 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_intersection( ExecutionPolicy&& (4) (since C++17)
   policy, ForwardIt1 first1, ForwardIt1 last1,
   ForwardIt2 first2, ForwardIt2 last2,
   ForwardIt3 d_first, Compare comp );
   Constructs a sorted range beginning at d_first consisting of elements that are found
   in both sorted ranges [first1, last1) and [first2, last2). If some element is found
   m times in [first1, last1) and n times in [first2, last2), the first std::min(m, n)
   elements will be copied from the first range to the destination range. The order of
   equivalent elements is preserved. 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 range of elements to examine
   first2, last2 - the second range of elements to examine
   d_first - the beginning of the destination 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.
   -
   OutputIt must meet the requirements of LegacyOutputIterator.
   -
   ForwardIt1, ForwardIt2, ForwardIt3 must meet the requirements of
   LegacyForwardIterator.

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.

Possible implementation

First version
   template<class InputIt1, class InputIt2, class OutputIt>
   OutputIt set_intersection(InputIt1 first1, InputIt1 last1,
                        InputIt2 first2, InputIt2 last2,
                        OutputIt d_first)
   {
       while (first1 != last1 && first2 != last2) {
           if (*first1 < *first2) {
               ++first1;
           } else {
               if (!(*first2 < *first1)) {
                   *d_first++ = *first1++; // *first1 and *first2 are equivalent.
               }
               ++first2;
           }
       }
       return d_first;
   }

Second version
   template<class InputIt1, class InputIt2,
            class OutputIt, class Compare>
   OutputIt set_intersection(InputIt1 first1, InputIt1 last1,
                        InputIt2 first2, InputIt2 last2,
                        OutputIt d_first, Compare comp)
   {
       while (first1 != last1 && first2 != last2) {
           if (comp(*first1, *first2)) {
               ++first1;
           } else {
               if (!comp(*first2, *first1)) {
                   *d_first++ = *first1++; // *first1 and *first2 are equivalent.
               }
               ++first2;
           }
       }
       return d_first;
   }

Example
// Run this code
 #include <iostream>
 #include <vector>
 #include <algorithm>
 #include <iterator>
 int main()
 {
     std::vector<int> v1{1,2,3,4,5,6,7,8};
     std::vector<int> v2{ 5, 7, 9,10};
     std::sort(v1.begin(), v1.end());
     std::sort(v2.begin(), v2.end());
     std::vector<int> v_intersection;
     std::set_intersection(v1.begin(), v1.end(),
                        v2.begin(), v2.end(),
                        std::back_inserter(v_intersection));
     for(int n : v_intersection)
         std::cout << n << ' ';
 }

Output:
 5 7

See also
   set_union computes the union of two sets
                        (function template)
   ranges::set_intersection computes the intersection of two sets
   (C++20) (niebloid)