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    std::nth_element

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    C++
     
    Algorithm library
    Constrained algorithms and algorithms on ranges (C++20)
    Constrained algorithms, e.g. ranges::copy, ranges::sort, ...
    Non-modifying sequence operations    
    Batch operations
    (C++17)
    Search operations
    Modifying sequence operations
    Copy operations
    (C++11)
    (C++11)
    (C++11)
    Swap operations
    Transformation operations
    Generation operations
    Removing operations
    Order-changing operations
    (until C++17)(C++11)
    (C++20)(C++20)
    Sampling operations
    (C++17)

    Sorting and related operations
    Partitioning operations
    (C++11)    
    (C++11)

    Sorting operations
    Binary search operations
    (on partitioned ranges)
    Set operations (on sorted ranges)
    Merge operations (on sorted ranges)
    Heap operations
    Minimum/maximum operations
    (C++11)
    (C++17)
    Lexicographical comparison operations
    (C++20)
    Permutation operations


     
    Defined in header <algorithm> 
    template< class RandomIt >
void nth_element( RandomIt first, RandomIt nth, RandomIt last );
    		(1) (constexpr since C++20) 
    template< class RandomIt, class Compare >
void nth_element( RandomIt first, RandomIt nth, RandomIt last,
                  Compare comp );
    		(2) (constexpr since C++20) 
    template< class ExecutionPolicy, class RandomIt >
void nth_element( ExecutionPolicy&& policy,
                  RandomIt first, RandomIt nth, RandomIt last );
    		(3) (since C++17) 
    template< class ExecutionPolicy, class RandomIt, class Compare >
void nth_element( ExecutionPolicy&& policy,
                  RandomIt first, RandomIt nth, RandomIt last,
                  Compare comp );
    		(4) (since C++17)

    Let [sorted_first, sorted_last) be a sorted hypothetical (random-access) range containing all elements of the target range [first, last). Rearranges elements in the target range such that after the rearrangement:

    • [first, nth) is a permutation of [sorted_first, sorted_first + (nth - first)).
    • If nth == last is false:
      • nth points to the element corresponding to the element at sorted_first + (nth - first).
      • [nth + 1, last) is a permutation of [sorted_first + (nth - first) + 1, sorted_last).


    1) [sorted_first, sorted_last) is sorted with respect to operator<(until C++20)std::less{}(since C++20).
    2) [sorted_first, sorted_last) is hypothetically sorted with respect to comp.
    3,4) Same as (1,2), but executed according to policy.
    These overloads participate in overload resolution only if the value of the following expression is true:

    std::is_execution_policy_v<std::decay_t<ExecutionPolicy>>

    		(until C++20)

    std::is_execution_policy_v<std::remove_cvref_t<ExecutionPolicy>>

    		(since C++20)

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

    (until C++11)
    (since C++11)

    Parameters

    first, last - the pair of iterators defining the target range
    nth - the iterator indicating the “partition” point
    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. ​

    policy - the execution policy to use
    Type requirements
    -
    RandomIt must meet the requirements of LegacyRandomAccessIterator.
    -
    Compare must meet the requirements of Compare.

    Complexity

    Given N as last - first:

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

    Exceptions

    3,4) During the execution process:
    • If the temporary memory resources required for parallelization are not available, std::bad_alloc is thrown.
    • If an uncaught exception is thrown while accessing objects via an algorithm argument, the behavior is determined by the execution policy (for standard policies, std::terminate is invoked).

    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 print_vec(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};
    print_vec(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));
    print_vec(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';
    print_vec(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