std::nth_element

template< class RandomIt >
void nth_element( RandomIt first, RandomIt nth, RandomIt last );

template< class RandomIt >
constexpr void nth_element( RandomIt first, RandomIt nth, RandomIt last );

template< class ExecutionPolicy, class RandomIt >
void nth_element( ExecutionPolicy&& policy,
                  RandomIt first, RandomIt nth, RandomIt last );

template< class RandomIt, class Compare >
void nth_element( RandomIt first, RandomIt nth, RandomIt last,
                  Compare comp );

template< class RandomIt, class Compare >
constexpr void nth_element( RandomIt first, RandomIt nth, RandomIt last,
                            Compare comp );

template< class ExecutionPolicy, class RandomIt, class Compare >
void nth_element( ExecutionPolicy&& policy,
                  RandomIt first, RandomIt nth, RandomIt last,
                  Compare comp );

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.

Parameters

Return value

(none).

Complexity

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

#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);
}

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