std::nth_element

 

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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 Batch operations for_each for_each_n (C++17) Search operations all_ofany_ofnone_of (C++11)                (C++11)(C++11) countcount_if mismatch equal findfind_iffind_if_not (C++11) find_end find_first_of adjacent_find search search_n Modifying sequence operations Copy operations copycopy_if (C++11) copy_backward copy_n (C++11) move (C++11) move_backward (C++11) Swap operations swap iter_swap swap_ranges Transformation operations replacereplace_if transform replace_copyreplace_copy_if Generation operations fill fill_n generate generate_n Removing operations removeremove_if unique remove_copyremove_copy_if unique_copy Order-changing operations reverse reverse_copy rotate rotate_copy random_shuffleshuffle (until C++17)(C++11) shift_leftshift_right (C++20)(C++20) Sampling operations sample (C++17)	Sorting and related operations Partitioning operations partition partition_copy (C++11)   stable_partition is_partitioned (C++11) partition_point (C++11) Sorting operations sort stable_sort partial_sort partial_sort_copy is_sorted (C++11) is_sorted_until (C++11) nth_element Binary search operations (on partitioned ranges) lower_bound upper_bound equal_range binary_search Set operations (on sorted ranges) includes set_union set_intersection set_difference set_symmetric_difference Merge operations (on sorted ranges) merge inplace_merge Heap operations push_heap pop_heap make_heap sort_heap is_heap (C++11) is_heap_until (C++11) Minimum/maximum operations max min minmax (C++11) clamp (C++17) max_element min_element minmax_element (C++11) Lexicographical comparison operations lexicographical_compare lexicographical_compare_three_way (C++20) Permutation operations next_permutation prev_permutation is_permutation (C++11) C library qsort bsearch
Numeric operations
iota (C++11) inner_product adjacent_difference    accumulate reduce (C++17) transform_reduce (C++17)	partial_sum inclusive_scan (C++17)    exclusive_scan (C++17) transform_inclusive_scan (C++17) transform_exclusive_scan (C++17)
Operations on uninitialized memory
uninitialized_copy uninitialized_move (C++17)    uninitialized_fill uninitialized_copy_n (C++11) uninitialized_move_n (C++17) uninitialized_fill_n	destroy (C++17) destroy_n (C++17) destroy_at (C++17) construct_at (C++20)       uninitialized_default_construct (C++17) uninitialized_value_construct (C++17) uninitialized_default_construct_n (C++17) uninitialized_value_construct_n (C++17)

 

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 rearranges elements in [first, last) such that after the rearrangement:

• The element pointed at by nth is changed to whatever element would occur in that position if [first, last) were sorted.
• For every iterator i in [first, nth) and every iterator j in [nth, last), the following condition is met:

1,2) bool(*j < *i)(until C++20)std::less{}(*j, *i)(since C++20) is false.

3,4) bool(comp(*j, *i)) is false.

1) Elements are hypothetically sorted with respect to operator<(until C++20)std::less{}(since C++20).

3) Elements are hypothetically sorted with respect to comp.

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

These overloads participate in overload resolution only if

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)

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

• [first, nth) or [nth, last) is not a valid range.

The type of *first is not Swappable.	(until C++11)
RandomIt is not ValueSwappable. The type of *first is not MoveConstructible. The type of *first is not MoveAssignable.	(since C++11)

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 LegacyRandomAccessIterator.
- Compare must meet the requirements of Compare.

Complexity

Given \(\scriptsize N\)N as last - first:

1) \(\scriptsize O(N)\)O(N) comparisons using operator<(until C++20)std::less{}(since C++20) on average.

2) \(\scriptsize O(N)\)O(N) comparisons using operator<(until C++20)std::less{}(since C++20), and \(\scriptsize O(N \cdot \log(N))\)O(N·log(N)) swaps.

3) \(\scriptsize O(N)\)O(N) applications of the comparator comp on average.

4) \(\scriptsize O(N)\)O(N) applications of the comparator comp, and \(\scriptsize O(N \cdot \log(N))\)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.

Possible implementation

See also the implementations in libstdc++, libc++, and MSVC STL.

Notes

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

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 (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};
    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};

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

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)