std::nth_element() algorithm

od C++20

// (1)
template< class RandomIt >
constexpr void nth_element( RandomIt first, RandomIt nth, RandomIt last );

// (2)
template< class RandomIt, class Compare >
constexpr void nth_element( RandomIt first, RandomIt nth, RandomIt last, Compare comp );

// (3)
template< class ExecutionPolicy, class RandomIt >
void nth_element( ExecutionPolicy&& policy, RandomIt first, RandomIt nth, RandomIt last );

// (4)
template< class ExecutionPolicy, class RandomIt, class Compare >
void nth_element( ExecutionPolicy&& policy, RandomIt first, RandomIt nth, RandomIt last, Compare comp );

od C++17

// (1)
template< class RandomIt >
void nth_element( RandomIt first, RandomIt nth, RandomIt last );

// (2)
template< class RandomIt, class Compare >
void nth_element( RandomIt first, RandomIt nth, RandomIt last, Compare comp );

// (3)
template< class ExecutionPolicy, class RandomIt >
void nth_element( ExecutionPolicy&& policy, RandomIt first, RandomIt nth, RandomIt last );

// (4)
template< class ExecutionPolicy, class RandomIt, class Compare >
void nth_element( ExecutionPolicy&& policy, RandomIt first, RandomIt nth, RandomIt last, Compare comp );

do C++17

// (1)
template< class RandomIt >
void nth_element( RandomIt first, RandomIt nth, RandomIt last );

// (2)
template< class RandomIt, class Compare >
void nth_element( RandomIt first, RandomIt nth, RandomIt last, Compare comp );

std::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.
• If nth == last then the function has no effect.

More formally, nth_element partially sorts the range [first; last ) in ascending order so that the condition !(*j < *i) (for (1, 3), or !comp(*j, *i) for (2, 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.

• (1) Elements are compared using operator<.

• (2) Elements are compared using the given binary comparison function comp.

• (3, 4) Same as (1) and (2), but executed according to policy.

  Overload Resolution

  These overloads participate in overload resolution only if std::is_execution_policy_v<std::decay_t<ExecutionPolicy>> is true.  (do C++20) std::is_execution_policy_v<std::remove_cvref_t<ExecutionPolicy>> is true.  (od C++20)

Parameters

first last	The range of elements to sort.
nth	The iterator defining the sort partition point.
policy	The execution policy to use. See execution policy for details.
cmp	Comparison function object (i.e. an object that satisfies the requirements of Compare). The signature of the comparison function should be equivalent to the following: bool cmp(const Type1 &a, const Type2 &b); The signature does not need to have const&, but must not modify arguments. Must accept all values of type (possibly const) Type and Type2, regardless of value category (so Type1& is not allowed, nor is Type1 unless for Type1 a move is equivalent to a copy (od C++11)) The types Type1 and Type2 must be such that an object of type RandomIt can be implicitly converted to both of them.

Type requirements

RandomIt	ValueSwappable LegacyRandomAccessIterator
Type of dereferenced RandomIt	MoveAssignable MoveConstructible
Compare	Compare

Return value

(none)

Complexity

(1, 2) Linear in std::distance(first, last) on average.

(3, 4) Given N as last - first: O(N) applications of the predicate, and 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.

Notes

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

Examples

Main.cpp

#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);
}

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};