< cpp‎ | algorithm
Algorithm library
Constrained algorithms and algorithms on ranges (C++20)
Constrained algorithms, e.g. ranges::copy, ranges::sort, ...
Execution policies (C++17)
Non-modifying sequence operations
Batch operations
Search operations
(C++11)                (C++11)(C++11)

Modifying sequence operations
Copy operations
Swap operations
Transformation operations
Generation operations
Removing operations
Order-changing operations
(until C++17)(C++11)
Sampling operations

Sorting and related operations
Partitioning operations
Sorting operations

Binary search operations
(on partitioned ranges)
Set operations (on sorted ranges)
Merge operations (on sorted ranges)
Heap operations
Minimum/maximum operations
Lexicographical comparison operations
Permutation operations
C library
Numeric operations
Operations on uninitialized memory
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 is a partial sorting algorithm that rearranges elements in [firstlast) such that:

  • The element pointed at by nth is changed to whatever element would occur in that position if [firstlast) 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 [firstlast) in ascending order so that for any i in the range
[firstnth) and for any j in the range [nthlast) the following condition is met:

1,2) !(*j < *i),
3,4) comp(*j, *i) == false.

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)


[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);

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.

[edit] Return value


[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 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 algorithm with suitable average-case complexity are allowed.

[edit] Possible implementation

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

[edit] Example

#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};
    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));
    // 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';

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};

[edit] See also

returns the largest element in a range
(function template) [edit]
returns the smallest element in a range
(function template) [edit]
copies and partially sorts a range of elements
(function template) [edit]
sorts a range of elements while preserving order between equal elements
(function template) [edit]
sorts a range into ascending order
(function template) [edit]
partially sorts the given range making sure that it is partitioned by the given element