std::set_difference(3)

NAME
std::set_difference - std::set_difference

Synopsis
   Defined in header <algorithm>
   template< class InputIt1, class InputIt2, class OutputIt
   >
   OutputIt set_difference( 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_difference( 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_difference( 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_difference( ExecutionPolicy&& policy,
                        ForwardIt1 first1, ForwardIt1 (4) (since C++17)
   last1,
                        ForwardIt2 first2, ForwardIt2
   last2,
                        ForwardIt3 d_first, Compare
   comp );
   Copies the elements from the sorted range [first1, last1) which are not found in the
   sorted range [first2, last2) to the range beginning at d_first. The output range is
   also sorted.
   If [first1, last1) contains m elements that are equivalent to each other and
   [first2, last2) contains n elements that are equivalent to them, the final
   std::max(m - n, 0) elements will be copied from [first1, last1) to the output range,
   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 range of elements to examine
   first2, last2 - the range of elements to search for
   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.
   -
   OutputIt must meet the requirements of LegacyOutputIterator.
   -
   ForwardIt1, ForwardIt2, ForwardIt3 must meet the requirements of
   LegacyForwardIterator.
   -
   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 \(\scriptsize 2 \cdot (N_1+N_2)-1\)2⋅(N
   1+N
   2)-1 comparisons using
   operator<
   (until C++20)
   std::less{}
   (since C++20).
   3,4) At most \(\scriptsize 2 \cdot (N_1+N_2)-1\)2⋅(N
   1+N
   2)-1 applications of the comparison function comp.

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
                        set_difference (1)
  template<class InputIt1, class InputIt2, class OutputIt>
  OutputIt set_difference(InputIt1 first1, InputIt1 last1,
                        InputIt2 first2, InputIt2 last2, OutputIt d_first)
  {
      while (first1 != last1)
      {
          if (first2 == last2)
              return std::copy(first1, last1, d_first);
          if (*first1 < *first2)
              *d_first++ = *first1++;
          else
          {
              if (! (*first2 < *first1))
                  ++first1;
              ++first2;
          }
      }
      return d_first;
  }
                        set_difference (3)
  template<class InputIt1, class InputIt2, class OutputIt, class Compare>
  OutputIt set_difference(InputIt1 first1, InputIt1 last1,
                        InputIt2 first2, InputIt2 last2, OutputIt d_first, Compare comp)
  {
      while (first1 != last1)
      {
          if (first2 == last2)
              return std::copy(first1, last1, d_first);
          if (comp(*first1, *first2))
              *d_first++ = *first1++;
          else
          {
              if (!comp(*first2, *first1))
                  ++first1;
              ++first2;
          }
      }
      return d_first;
  }

Example
// Run this code
 #include <algorithm>
 #include <iostream>
 #include <iterator>
 #include <vector>
 template<typename T>
 std::ostream& operator<<(std::ostream& os, const std::vector<T>& v)
 {
     os << '{';
     for (auto n{v.size()}; const auto& e : v)
         os << e << (--n ? ", " : "");
     return os << '}';
 }
 struct Order // a struct with very interesting data
 {
     int order_id{};
     friend std::ostream& operator<<(std::ostream& os, const Order& ord)
     {
         return os << ord.order_id;
     }
 };
 int main()
 {
     const std::vector<int> v1{1, 2, 5, 5, 5, 9};
     const std::vector<int> v2{2, 5, 7};
     std::vector<int> diff;
     std::set_difference(v1.begin(), v1.end(), v2.begin(), v2.end(),
                        std::inserter(diff, diff.begin()));
     std::cout << v1 << " ∖ " << v2 << " == " << diff << "\n\n";
     // we want to know which orders "cut" between old and new states:
     std::vector<Order> old_orders{{1}, {2}, {5}, {9}};
     std::vector<Order> new_orders{{2}, {5}, {7}};
     std::vector<Order> cut_orders;
     std::set_difference(old_orders.begin(), old_orders.end(),
                        new_orders.begin(), new_orders.end(),
                        std::back_inserter(cut_orders),
                        [](auto& a, auto& b) { return a.order_id < b.order_id; });
     std::cout << "old orders: " << old_orders << '\n'
               << "new orders: " << new_orders << '\n'
               << "cut orders: " << cut_orders << '\n';
 }

Output:
 {1, 2, 5, 5, 5, 9} ∖ {2, 5, 7} == {1, 5, 5, 9}
 old orders: {1, 2, 5, 9}
 new orders: {2, 5, 7}
 cut orders: {1, 9}
   Defect reports
   The following behavior-changing defect reports were applied retroactively to
   previously published C++ standards.
     DR Applied to Behavior as published Correct 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)
   set_symmetric_difference computes the symmetric difference between two sets
                        (function template)
   ranges::set_difference computes the difference between two sets
   (C++20) (niebloid)