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# std::nth_element

From cppreference.com
< cpp‎ | algorithm

Defined in header `<algorithm>` |  |
template< class RandomIt > void nth_element( RandomIt first, RandomIt nth, RandomIt last ); | (1) |
template< class ExecutionPolicy, class RandomIt > void nth_element( ExecutionPolicy&& policy, RandomIt first, RandomIt nth, RandomIt last ); | (2) | (since C++17)
template< class RandomIt, class Compare > void nth_element( RandomIt first, RandomIt nth, RandomIt last, Compare comp ); | (3) |
template< class ExecutionPolicy, class RandomIt, class Compare > void nth_element( ExecutionPolicy&& policy, RandomIt first, RandomIt nth, RandomIt last, Compare comp ); | (4) | (since C++17)

`nth_element` is a partial sorting algorithm that rearranges elements in `[first, last)` such that:

- The element pointed at by `nth` is changed to whatever element would occur in that position if `[first, last)` was sorted.
- All of the elements before this new `nth` element are less than or equal to the elements after the new `nth` element.

More formally, `nth_element` partially sorts the range `[first, last)` in ascending order so that the condition !(*j < *i) (for (1-2), or comp(*j, *i) == false for (3-4)) is met for any `i` in the range `[first, nth)` and for any `j` in the range `[nth, last)`. The element placed in the `nth` position is exactly the element that would occur in this position if the range was fully sorted.

`nth` may be the end iterator, in this case the function has no effect.

1) Elements are compared using `operator<`.
3) Elements are compared using the given binary comparison function `comp`.
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>> is true

### [edit] Parameters

first, last | - | random access iterators defining the range sort
nth | - | random access iterator defining the sort partition point
policy | - | the execution policy to use. See execution policy for details.
comp | - | 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); The signature does not need to have const &, but the function object must not modify the objects passed to it. The types Type1 and Type2 must be such that an object of type RandomIt can be dereferenced and then implicitly converted to both of them. ​
Type requirements
- `RandomIt` must meet the requirements of `ValueSwappable` and `RandomAccessIterator`.
- The type of dereferenced `RandomIt` must meet the requirements of `MoveAssignable` and `MoveConstructible`.

### [edit] Return value

(none)

### [edit] Complexity

1,3) Linear in std::distance(first, last) on average.
2.4) O(N) applications of the predicate, and O(N log N) swaps, where N = last - first.

### [edit] 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 three 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.

### [edit] Notes

The algorithm used is typically introselect although other selection algorithms with suitable average-case complexity are allowed.

### [edit] Example

Run this code

    #include <iostream>
    #include <vector>
    #include <algorithm>
    #include <functional>

    int main()
    {
        std::vector<int> v{5, 6, 4, 3, 2, 6, 7, 9, 3};

        std::nth_element(v.begin(), v.begin() + v.size()/2, v.end());
        std::cout << "The median is " << v[v.size()/2] << '\n';

        std::nth_element(v.begin(), v.begin()+1, v.end(), std::greater<int>());
        std::cout << "The second largest element is " << v[1] << '\n';
    }

Output:

    The median is 5
    The second largest element is 7

### [edit] See also

partial_sort_copy | copies and partially sorts a range of elements (function template) [edit]
stable_sort | sorts a range of elements while preserving order between equal elements (function template) [edit]
sort | sorts a range into ascending order (function template) [edit]

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