# std::nth_element

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< cpp‎ | algorithm

Defined in header `<algorithm>` |  |
template< class RandomIt > void nth_element( RandomIt first, RandomIt nth, RandomIt last ); | (1) | (constexpr since C++20)
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) | (constexpr 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` rearranges elements in `[`first`,` last`)` such that after the rearrangement:

- The element pointed at by nth is changed to whatever element would occur in that position if `[`first`,` last`)` were sorted.
- For every iterator i in `[`first`,` nth`)` and every iterator j in `[`nth`,` last`)`, the following condition is met:

1,2) bool(*j < *i)(until C++20) std::less {}(*j, *i)(since C++20) is false.
3,4) bool(comp(*j, *i)) is false.

1) Elements are hypothetically sorted with respect to operator<(until C++20) std::less {}(since C++20).
3) Elements are hypothetically sorted with respect to comp.
2,4) Same as (1,3), but executed according to policy.
These overloads participate in overload resolution only if all following conditions are satisfied:

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)

If any of the following conditions is satisfied, the behavior is undefined:

- `[`first`,` nth`)` or `[`nth`,` last`)` is not a valid range.

- The type of *first is not Swappable.

(until C++11)

- `RandomIt` is not ValueSwappable.
- The type of *first is not MoveConstructible.
- The type of *first is not MoveAssignable.

(since C++11)

### 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

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 LegacyRandomAccessIterator.
- `Compare` must meet the requirements of Compare.

### Complexity

Given \(\scriptsize N\)N as last - first:

1) \(\scriptsize O(N)\)O(N) comparisons using operator<(until C++20) std::less {}(since C++20) on average.
2) \(\scriptsize O(N)\)O(N) comparisons using operator<(until C++20) std::less {}(since C++20), and \(\scriptsize O(N \cdot \log(N))\)O(N·log(N)) swaps.
3) \(\scriptsize O(N)\)O(N) applications of the comparator comp on average.
4) \(\scriptsize O(N)\)O(N) applications of the comparator comp, and \(\scriptsize O(N \cdot \log(N))\)O(N·log(N)) swaps.

### 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.

### Possible implementation

See also the implementations in libstdc++, libc++, and MSVC STL.

### Notes

The algorithm used is typically Introselect although other Selection algorithm with suitable average-case complexity are allowed.

### 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 (char sep[]{0, ' ', 0}; const int i : vec)
            std::cout << sep << i, sep[0] = ',';
        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};

### Defect reports

The following behavior-changing defect reports were applied retroactively to previously published C++ standards.

DR | Applied to | Behavior as published | Correct behavior
--- | --- | --- | ---
LWG 2150 | C++98 | after the rearrangement, only one element before nth was required to be not greater than one element after nth | corrected the requirement
LWG 2163 | C++98 | overload (1) used operator> to compare the elements | changed to operator<
P0896R4 | C++98 | `[`first`,` nth`)` and `[`nth`,` last`)` were not required to be valid ranges | the behavior is undefined if any of them is invalid

### 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 (algorithm function object)

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