# std::nth_element

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< cpp‎ | algorithm

Defined in header `<algorithm>` |  |
| (1) |
template< class RandomIt > void nth_element( RandomIt first, RandomIt nth, RandomIt last ); |  | (until C++20)
template< class RandomIt > constexpr void nth_element( RandomIt first, RandomIt nth, RandomIt last ); |  | (since C++20)
template< class ExecutionPolicy, class RandomIt > void nth_element( ExecutionPolicy&& policy, RandomIt first, RandomIt nth, RandomIt last ); | (2) | (since C++17)
| (3) |
template< class RandomIt, class Compare > void nth_element( RandomIt first, RandomIt nth, RandomIt last, Compare comp ); |  | (until C++20)
template< class RandomIt, class Compare > constexpr void nth_element( RandomIt first, RandomIt nth, RandomIt last, Compare comp ); |  | (since C++20)
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)` were 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

### 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);

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 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 LegacyRandomAccessIterator.
- The type of dereferenced `RandomIt` must meet the requirements of MoveAssignable and MoveConstructible.

### Return value

(none)

### 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.

### 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.

### Notes

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

### 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

### See also

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

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