[set.difference]

# 26 Algorithms library [[algorithms]](./#algorithms)

## 26.8 Sorting and related operations [[alg.sorting]](alg.sorting#set.difference)

### 26.8.7 Set operations on sorted structures [[alg.set.operations]](alg.set.operations#set.difference)

#### 26.8.7.5 set_difference [set.difference]

[ð](#lib:set_difference)

`template<class InputIterator1, class InputIterator2,
         class OutputIterator>
  constexpr OutputIterator
    set_difference(InputIterator1 first1, InputIterator1 last1,
                   InputIterator2 first2, InputIterator2 last2,
                   OutputIterator result);
template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2,
         class ForwardIterator>
  ForwardIterator
    set_difference(ExecutionPolicy&& exec,
                   ForwardIterator1 first1, ForwardIterator1 last1,
                   ForwardIterator2 first2, ForwardIterator2 last2,
                   ForwardIterator result);

template<class InputIterator1, class InputIterator2,
         class OutputIterator, class Compare>
  constexpr OutputIterator
    set_difference(InputIterator1 first1, InputIterator1 last1,
                   InputIterator2 first2, InputIterator2 last2,
                   OutputIterator result, Compare comp);
template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2,
         class ForwardIterator, class Compare>
  ForwardIterator
    set_difference(ExecutionPolicy&& exec,
                   ForwardIterator1 first1, ForwardIterator1 last1,
                   ForwardIterator2 first2, ForwardIterator2 last2,
                   ForwardIterator result, Compare comp);

template<[input_iterator](iterator.concept.input#concept:input_iterator "24.3.4.9 Concept input_­iterator [iterator.concept.input]") I1, [sentinel_for](iterator.concept.sentinel#concept:sentinel_for "24.3.4.7 Concept sentinel_­for [iterator.concept.sentinel]")<I1> S1, [input_iterator](iterator.concept.input#concept:input_iterator "24.3.4.9 Concept input_­iterator [iterator.concept.input]") I2, [sentinel_for](iterator.concept.sentinel#concept:sentinel_for "24.3.4.7 Concept sentinel_­for [iterator.concept.sentinel]")<I2> S2,
         [weakly_incrementable](iterator.concept.winc#concept:weakly_incrementable "24.3.4.4 Concept weakly_­incrementable [iterator.concept.winc]") O, class Comp = ranges::less,
         class Proj1 = identity, class Proj2 = identity>
  requires [mergeable](alg.req.mergeable#concept:mergeable "24.3.7.7 Concept mergeable [alg.req.mergeable]")<I1, I2, O, Comp, Proj1, Proj2>
  constexpr ranges::set_difference_result<I1, O>
    ranges::set_difference(I1 first1, S1 last1, I2 first2, S2 last2, O result,
                           Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
template<[input_range](range.refinements#concept:input_range "25.4.6 Other range refinements [range.refinements]") R1, [input_range](range.refinements#concept:input_range "25.4.6 Other range refinements [range.refinements]") R2, [weakly_incrementable](iterator.concept.winc#concept:weakly_incrementable "24.3.4.4 Concept weakly_­incrementable [iterator.concept.winc]") O,
         class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity>
  requires [mergeable](alg.req.mergeable#concept:mergeable "24.3.7.7 Concept mergeable [alg.req.mergeable]")<iterator_t<R1>, iterator_t<R2>, O, Comp, Proj1, Proj2>
  constexpr ranges::set_difference_result<borrowed_iterator_t<R1>, O>
    ranges::set_difference(R1&& r1, R2&& r2, O result,
                           Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});

template<[execution-policy](algorithms.parallel.defns#concept:execution-policy "26.3.1 Preamble [algorithms.parallel.defns]") Ep, [random_access_iterator](iterator.concept.random.access#concept:random_access_iterator "24.3.4.13 Concept random_­access_­iterator [iterator.concept.random.access]") I1, [sized_sentinel_for](iterator.concept.sizedsentinel#concept:sized_sentinel_for "24.3.4.8 Concept sized_­sentinel_­for [iterator.concept.sizedsentinel]")<I1> S1,
         [random_access_iterator](iterator.concept.random.access#concept:random_access_iterator "24.3.4.13 Concept random_­access_­iterator [iterator.concept.random.access]") I2, [sized_sentinel_for](iterator.concept.sizedsentinel#concept:sized_sentinel_for "24.3.4.8 Concept sized_­sentinel_­for [iterator.concept.sizedsentinel]")<I2> S2,
         [random_access_iterator](iterator.concept.random.access#concept:random_access_iterator "24.3.4.13 Concept random_­access_­iterator [iterator.concept.random.access]") O, [sized_sentinel_for](iterator.concept.sizedsentinel#concept:sized_sentinel_for "24.3.4.8 Concept sized_­sentinel_­for [iterator.concept.sizedsentinel]")<O> OutS, class Comp = ranges::less,
         class Proj1 = identity, class Proj2 = identity>
  requires [mergeable](alg.req.mergeable#concept:mergeable "24.3.7.7 Concept mergeable [alg.req.mergeable]")<I1, I2, O, Comp, Proj1, Proj2>
  ranges::set_difference_result<I1, O>
    ranges::set_difference(Ep&& exec, I1 first1, S1 last1,
                           I2 first2, S2 last2, O result, OutS result_last,
                           Comp comp = {}, Proj1 proj1 = {}, Proj2 proj2 = {});
template<[execution-policy](algorithms.parallel.defns#concept:execution-policy "26.3.1 Preamble [algorithms.parallel.defns]") Ep, [sized-random-access-range](range.refinements#concept:sized-random-access-range "25.4.6 Other range refinements [range.refinements]") R1, [sized-random-access-range](range.refinements#concept:sized-random-access-range "25.4.6 Other range refinements [range.refinements]") R2,
         [sized-random-access-range](range.refinements#concept:sized-random-access-range "25.4.6 Other range refinements [range.refinements]") OutR, class Comp = ranges::less,
         class Proj1 = identity, class Proj2 = identity>
  requires [mergeable](alg.req.mergeable#concept:mergeable "24.3.7.7 Concept mergeable [alg.req.mergeable]")<iterator_t<R1>, iterator_t<R2>, iterator_t<OutR>, Comp, Proj1, Proj2>
  ranges::set_difference_result<borrowed_iterator_t<R1>, borrowed_iterator_t<OutR>>
    ranges::set_difference(Ep&& exec, R1&& r1, R2&& r2, OutR&& result_r, Comp comp = {},
                           Proj1 proj1 = {}, Proj2 proj2 = {});
`

[1](#1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L10673)

Let:

- [(1.1)](#1.1)

comp be less{},
 and proj1 and proj2 be identity{} for the overloads with no parameters by those names;

- [(1.2)](#1.2)

M be the number of elements in [first1, last1)
 that are not present in [first2, last2);

- [(1.3)](#1.3)

result_last be result + M for the overloads with no parameter result_last or result_r;

- [(1.4)](#1.4)

N be min(M, result_last - result)[.](#1.sentence-1)

[2](#2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L10690)

*Preconditions*: The ranges [first1, last1) and [first2, last2) are sorted
with respect to comp and proj1 or proj2, respectively[.](#2.sentence-1)

The resulting range does not overlap with either of the original ranges[.](#2.sentence-2)

[3](#3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L10696)

*Effects*: Copies N elements of the range [first1, last1)
which are not present in the range [first2, last2)
to the range [result, result + N)[.](#3.sentence-1)

The elements in the constructed range are sorted[.](#3.sentence-2)

[4](#4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L10703)

*Returns*: 

- [(4.1)](#4.1)

  result_last for the overloads in namespace std[.](#4.1.sentence-1)

- [(4.2)](#4.2)

  {last1, result + N} for the overloads in namespace ranges,
 if N is equal to M[.](#4.2.sentence-1)

- [(4.3)](#4.3)

  Otherwise, {j1, result_last} for the overloads in namespace ranges,
 where the iterator j1 points to positions past the last copied or skipped elements
 in [first1, last1) and [first2, last2), respectively[.](#4.3.sentence-1)

[5](#5)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L10721)

*Complexity*: At most 2 * ((last1 - first1) + (last2 - first2)) - 1 comparisons and applications of each projection[.](#5.sentence-1)

[6](#6)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L10726)

*Remarks*: If [first1, last1) contains m elements
that are equivalent to each other and
[first2, last2) contains n elements
that are equivalent to them,
the last max(mân,0) elements from [first1, last1)
are copied to the output range, in order[.](#6.sentence-1)
