std::nth_element(3)

🌸 NAME 🌸

std::nth_element — the name is literally std::nth_element, no cap. This page is from the C++ Standard Libary manual (manual name folded in near the top, bestie 💖). It’s the algorithm that puts the element at nth exactly where it would land if [first, last) were sorted, and makes the before/after sides respect that split. Iconic behavior, honestly. ✨

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✨ Synopsis ✨

Defined in header <algorithm> 🌸

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

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

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

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

• (1) (constexpr since C++20)
• (2) (since C++17)
• (3) (constexpr since C++20)
• (4) (since C++17)

Okay so here’s the whole vibe: 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.

Then the overload tea ☕:

• 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)

🚨 Behavior is undefined if any of the following conditions is satisfied, and this is not the cute kind of undefined, bestie: - [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.

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🦋 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. 🫶

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💅 Type requirements 💅

• RandomIt must meet the requirements of LegacyRandomAccessIterator.
• Compare must meet the requirements of Compare.

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

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😭 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.

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🧚 Possible implementation 🧚

See also the implementations in libstdc++, libc++, and msvc stl. 👑

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🌈 Notes 🌈

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

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🍓 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);
}

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🎀 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};

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💜 Defect reports 💜

The following behavior-changing defect reports were applied retroactively to previously published C++ standards.

• LWG 2150, applied to C++98 — behavior as published: after the rearrangement, only one element before nth was required to be not greater than one element after nth; correct behavior: corrected the requirement.
• P0896R4, applied to C++98 — behavior as published: [first, nth) and [nth, last) were not required to be valid ranges; correct behavior: the behavior is undefined if any of them is invalid.

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👑 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)

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Source/version/date footer vibes, folded in all cute-like: http://cppreference.com, 2024.06.10, and the manual page is std::nth_element(3) — that’s the whole page, preserved and slayed 💅✨🫶