NAME¶

std::nth_element - std::nth_element

Synopsis¶

Defined in header <algorithm>
template< class RandomIt >
void nth_element( RandomIt first, RandomIt nth, RandomIt (1) (constexpr since C++20)
last );
template< class ExecutionPolicy, class RandomIt >

void nth_element( ExecutionPolicy&& policy, (2) (since C++17)

RandomIt first, RandomIt nth, RandomIt
last );
template< class RandomIt, class Compare >

void nth_element( RandomIt first, RandomIt nth, RandomIt (3) (constexpr since C++20)
last,

Compare comp );
template< class ExecutionPolicy, class RandomIt, class
Compare >

void nth_element( ExecutionPolicy&& policy, (4) (since C++17)
RandomIt first, RandomIt nth, RandomIt
last,

Compare comp );

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. (since C++11)
* The type of *first is not MoveAssignable.

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.
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);
comp -
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
after the rearrangement, only one
LWG 2150 C++98 element before nth corrected the
was required to be not greater than requirement
one element after nth
P0896R4 C++98 [first, nth) and [nth, last) the behavior is undefined
were not required to be valid ranges 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)
sorts a range of elements while preserving order between equal
stable_sort elements
(function template)
sort sorts a range into ascending order
(function template)
ranges::nth_element partially sorts the given range making sure that it is
(C++20) partitioned by the given element
(niebloid)