std::nth_element

 

C++

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Feature test macros (C++20)

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Ranges library (C++20)

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Technical specifications

Symbols index

External libraries

 

Algorithm library

Constrained algorithms and algorithms on ranges (C++20)
Constrained algorithms, e.g. ranges::copy, ranges::sort, ...
Execution policies (C++17)
is_execution_policy (C++17)	execution::seqexecution::parexecution::par_unseqexecution::unseq (C++17)(C++17)(C++17)(C++20)	execution::sequenced_policyexecution::parallel_policyexecution::parallel_unsequenced_policyexecution::parallel_unsequenced (C++17)(C++17)(C++17)(C++20)
Non-modifying sequence operations
all_ofany_ofnone_of (C++11)(C++11)(C++11) for_each for_each_n (C++17)	countcount_if mismatch equal adjacent_find	search search_n lexicographical_compare lexicographical_compare_three_way (C++20)	findfind_iffind_if_not (C++11) find_end find_first_of
Modifying sequence operations
copycopy_if (C++11) copy_n (C++11) copy_backward move (C++11) move_backward (C++11) shift_leftshift_right (C++20)(C++20) transform	fill fill_n generate generate_n swap iter_swap swap_ranges sample (C++17)	removeremove_if replacereplace_if reverse rotate unique random_shuffle (until C++17)	remove_copyremove_copy_if replace_copyreplace_copy_if reverse_copy rotate_copy unique_copy shuffle (C++11)
Partitioning operations
is_partitioned (C++11) partition_point (C++11)	partition partition_copy (C++11)	stable_partition
Sorting operations
is_sorted (C++11) is_sorted_until (C++11)	sort stable_sort	partial_sort partial_sort_copy	nth_element
Binary search operations
lower_bound	upper_bound	binary_search	equal_range
Set operations (on sorted ranges)
merge inplace_merge	set_difference set_intersection	set_symmetric_difference set_union	includes
Heap operations
is_heap (C++11) is_heap_until (C++11)	make_heap sort_heap	push_heap pop_heap
Minimum/maximum operations
max max_element	min min_element	minmax (C++11) minmax_element (C++11)	clamp (C++17)
Permutations
is_permutation (C++11)	next_permutation	prev_permutation
Numeric operations
iota (C++11) inner_product adjacent_difference	accumulate reduce (C++17) transform_reduce (C++17)	transform_inclusive_scan (C++17) transform_exclusive_scan (C++17)	partial_sum inclusive_scan (C++17) exclusive_scan (C++17)
Operations on uninitialized storage
uninitialized_copy uninitialized_move (C++17) uninitialized_fill	uninitialized_copy_n (C++11) uninitialized_move_n (C++17) uninitialized_fill_n	uninitialized_default_construct (C++17) uninitialized_value_construct (C++17) uninitialized_default_construct_n (C++17) uninitialized_value_construct_n (C++17)	destroy (C++17) destroy_n (C++17) destroy_at (C++17) construct_at (C++20)
C library
qsort	bsearch

 

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

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)

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.

Return value

(none)

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.

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

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 (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);
}

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};

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 (niebloid)