# 28 Algorithms library [algorithms]

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

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

This section defines all the basic set operations on sorted structures. They also work with multisets 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.

#### 28.7.6.1includes[includes]

```template<class InputIterator1, class InputIterator2> bool includes(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2> bool includes(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2); template<class InputIterator1, class InputIterator2, class Compare> bool includes(InputIterator1 first1, InputIterator1 last1, InputIterator2 first2, InputIterator2 last2, Compare comp); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class Compare> bool includes(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 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.

#### 28.7.6.2set_­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 ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class ForwardIterator> ForwardIterator set_union(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2, ForwardIterator 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); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class ForwardIterator, class Compare> ForwardIterator set_union(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2, ForwardIterator result, Compare comp); ```

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

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.

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(nm,0) elements from the second range shall be copied to the output range, in order.

#### 28.7.6.3set_­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 ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class ForwardIterator> ForwardIterator set_intersection(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2, ForwardIterator 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); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class ForwardIterator, class Compare> ForwardIterator set_intersection(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2, ForwardIterator result, Compare comp); ```

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

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.

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.

#### 28.7.6.4set_­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 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> 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); ```

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

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.

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

#### 28.7.6.5set_­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 ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class ForwardIterator> ForwardIterator set_symmetric_difference(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2, ForwardIterator 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); template<class ExecutionPolicy, class ForwardIterator1, class ForwardIterator2, class ForwardIterator, class Compare> ForwardIterator set_symmetric_difference(ExecutionPolicy&& exec, ForwardIterator1 first1, ForwardIterator1 last1, ForwardIterator2 first2, ForwardIterator2 last2, ForwardIterator result, Compare comp); ```

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

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.

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 |mn| of those elements shall be copied to the output range: the last mn of these elements from [first1, last1) if m>n, and the last nm of these elements from [first2, last2) if m<n.