# 25 Algorithms library [algorithms]

## 25.4 Sorting and related operations [alg.sorting]

### 25.4.5 Set operations on sorted structures [alg.set.operations]

This section defines all the basic set operations on sorted structures. They also work with multisets ([multiset]) containing multiple copies of equivalent elements. The semantics of the set operations are generalized to multisets in a standard way by defining set_union() to contain the maximum number of occurrences of every element, set_intersection() to contain the minimum, and so on.

#### 25.4.5.1includes[includes]

``` template<class InputIterator1, class InputIterator2> bool includes(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2); template<class InputIterator1, class InputIterator2, class Compare> bool includes(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2, Compare comp); ```

Returns: true if [first2,last2) is empty or if every element in the range [first2,last2) is contained in the range [first1,last1). Returns false otherwise.

Complexity: At most 2 * ((last1 - first1) + (last2 - first2)) - 1 comparisons.

#### 25.4.5.2set_union[set.union]

``` template<class InputIterator1, class InputIterator2, class OutputIterator> OutputIterator set_union(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2, OutputIterator result); template<class InputIterator1, class InputIterator2, class OutputIterator, class Compare> OutputIterator set_union(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2, OutputIterator result, Compare comp); ```

Effects: Constructs a sorted union of the elements from the two ranges; that is, the set of elements that are present in one or both of the ranges.

Requires: The resulting range shall not overlap with either of the original ranges.

Returns: The end of the constructed range.

Complexity: At most 2 * ((last1 - first1) + (last2 - first2)) - 1 comparisons.

Remarks: 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 from the first range shall be copied to the output range, in order, and then max(n - m, 0) elements from the second range shall be copied to the output range, in order.

#### 25.4.5.3set_intersection[set.intersection]

``` template<class InputIterator1, class InputIterator2, class OutputIterator> OutputIterator set_intersection(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2, OutputIterator result); template<class InputIterator1, class InputIterator2, class OutputIterator, class Compare> OutputIterator set_intersection(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2, OutputIterator result, Compare comp); ```

Effects: Constructs a sorted intersection of the elements from the two ranges; that is, the set of elements that are present in both of the ranges.

Requires: The resulting range shall not overlap with either of the original ranges.

Returns: The end of the constructed range.

Complexity: At most 2 * ((last1 - first1) + (last2 - first2)) - 1 comparisons.

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 first min(m, n) elements shall be copied from the first range to the output range, in order.

#### 25.4.5.4set_difference[set.difference]

``` template<class InputIterator1, class InputIterator2, class OutputIterator> OutputIterator set_difference(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2, OutputIterator result); template<class InputIterator1, class InputIterator2, class OutputIterator, class Compare> OutputIterator set_difference(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2, OutputIterator result, Compare comp); ```

Effects: Copies the elements of the range [first1,last1) which are not present in the range [first2,last2) to the range beginning at result. The elements in the constructed range are sorted.

Requires: The resulting range shall not overlap with either of the original ranges.

Returns: The end of the constructed range.

Complexity: At most 2 * ((last1 - first1) + (last2 - first2)) - 1 comparisons.

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(m - n, 0) elements from [first1,last1) shall be copied to the output range.

#### 25.4.5.5set_symmetric_difference[set.symmetric.difference]

``` template<class InputIterator1, class InputIterator2, class OutputIterator> OutputIterator set_symmetric_difference(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2, OutputIterator result); template<class InputIterator1, class InputIterator2, class OutputIterator, class Compare> OutputIterator set_symmetric_difference(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2, OutputIterator result, Compare comp); ```

Effects: Copies the elements of the range [first1,last1) that are not present in the range [first2,last2), and the elements of the range [first2,last2) that are not present in the range [first1,last1) to the range beginning at result. The elements in the constructed range are sorted.

Requires: The resulting range shall not overlap with either of the original ranges.

Returns: The end of the constructed range.

Complexity: At most 2 * ((last1 - first1) + (last2 - first2)) - 1 comparisons.

Remarks: If [first1,last1) contains m elements that are equivalent to each other and [first2,last2) contains n elements that are equivalent to them, then |m - n| of those elements shall be copied to the output range: the last m - n of these elements from [first1,last1) if m > n, and the last n - m of these elements from [first2,last2) if m < n.