# 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. | (until C++20)
std::is_execution_policy_v<std::remove_cvref_t<ExecutionPolicy>> is true. | (since C++20)

### 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 algorithm with suitable average-case complexity are allowed.

### Possible implementation

See also the implementations in libstdc++, libc++, and msvc stl.

### Example

Run this code

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

    void printVec(const std::vector<int>& vec)
    {
        std::cout << "v = {";
        for (auto n {vec.size()}; const int i : vec)
            std::cout << i << (--n ? ", " : "");
        std::cout << "};\n";
    }

    int main()
    {
        std::vector<int> v {5, 10, 6, 4, 3, 2, 6, 7, 9, 3};
        printVec(v);

        auto m = v.begin() + v.size() / 2;
        std::nth_element(v.begin(), m, v.end());
        std::cout << "\nThe median is " << v[v.size() / 2] << '\n';
        // The consequence of the inequality of elements before/after the Nth one:
        assert(std::accumulate(v.begin(), m, 0) < std::accumulate(m, v.end(), 0));
        printVec(v);

        // Note: comp function changed
        std::nth_element(v.begin(), v.begin() + 1, v.end(), std::greater{});
        std::cout << "\nThe second largest element is " << v[1] << '\n';
        std::cout << "The largest element is " << v[0] << '\n';
        printVec(v);
    }

Possible output:

    v = {5, 10, 6, 4, 3, 2, 6, 7, 9, 3};

    The median is 6
    v = {3, 2, 3, 4, 5, 6, 10, 7, 9, 6};

    The second largest element is 9
    The largest element is 10
    v = {10, 9, 6, 7, 6, 3, 5, 4, 3, 2};

### See also

max_element | returns the largest element in a range (function template)
min_element | returns the smallest element in a range (function template)
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)
ranges::nth_element (C++20) | partially sorts the given range making sure that it is partitioned by the given element (niebloid)

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