std::partial_sort(3)

💖 NAME 💖

std::partial_sort — ok so it's literally just std::partial_sort, that's the whole name bestie 🎀 (yes this page is from the C++ Standard Libary manual, page std::partial_sort(3), and we're about to make it make sense 💅)

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🌸 Synopsis 🌸

First things first: it's Defined in header <algorithm> 📌

There are four overloads, and they are all serving ⭐

template< class RandomIt >
void partial_sort( RandomIt first, RandomIt middle, RandomIt last );

✨ overload (1), and it's constexpr since C++20 🫶

template< class ExecutionPolicy, class RandomIt >
void partial_sort( ExecutionPolicy&& policy,
                   RandomIt first, RandomIt middle, RandomIt last );

✨ overload (2), since C++17 💫

template< class RandomIt, class Compare >
void partial_sort( RandomIt first, RandomIt middle, RandomIt last,
                   Compare comp );

✨ overload (3), and it's constexpr since C++20 🫶

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

✨ overload (4), since C++17 💫

🦋 What it actually does 🦋

So it rearranges elements such that the range [first, middle) contains the sorted middle - first smallest elements in the range [first, last). That's the whole vibe, no cap 🔥

The order of equal elements is not guaranteed to be preserved 🙈 and the order of the remaining elements in the range [middle, last) is unspecified — so don't come for those, they're doing their own thing 💀

Now the detail drop, per overload 👑

• (1) — elements are sorted with respect to operator< (until C++20), and with respect to std::less{} (since C++20) 🧚
• (3) — elements are 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), or 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 — like, actual undefined behaviour, not the cute slang kind 😭 - [first, middle) or [middle, 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 🗺️
• middle — random access iterator defining the one-past-the-end iterator of the range to be sorted 🎯
• 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);

And the fine print on comp, because it matters fr fr 💅 — 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 M as middle - first, and N as last - first 🧮

• (1),(2) — approximately N·log(M) comparisons using operator< (until C++20), std::less{} (since C++20) ⏱️
• (3),(4) — approximately N·log(M) applications of the comparator comp ⏱️

(and yes the original writes it as M·log(M)... sorry, N·log(M), with the cute little math script — same numbers, promise 🫶)

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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++ and libc++ 👀

partial_sort (1):

template<typename RandomIt>
constexpr //< since C++20
void partial_sort(RandomIt first, RandomIt middle, RandomIt last)
{
    typedef typename std::iterator_traits<RandomIt>::value_type VT;
    std::partial_sort(first, middle, last, std::less<VT>());
}

partial_sort (3):

namespace impl
{
    template<typename RandomIt, typename Compare>
    constexpr //< since C++20
    void sift_down(RandomIt first, RandomIt last, const Compare& comp)
    {
        // sift down element at “first”
        const auto length = static_cast<std::size_t>(last - first);
        std::size_t current = 0;
        std::size_t next = 2;
        while (next < length)
        {
            if (comp(*(first + next), *(first + (next - 1))))
                --next;
            if (!comp(*(first + current), *(first + next)))
                return;
            std::iter_swap(first + current, first + next);
            current = next;
            next = 2 * current + 2;
        }
        --next;
        if (next < length && comp(*(first + current), *(first + next)))
            std::iter_swap(first + current, first + next);
    }

    template<typename RandomIt, typename Compare>
    constexpr //< since C++20
    void heap_select(RandomIt first, RandomIt middle, RandomIt last, const Compare& comp)
    {
        std::make_heap(first, middle, comp);
        for (auto i = middle; i != last; ++i)
        {
            if (comp(*i, *first))
            {
                std::iter_swap(first, i);
                sift_down(first, middle, comp);
            }
        }
    }
} // namespace impl

template<typename RandomIt, typename Compare>
constexpr //< since C++20
void partial_sort(RandomIt first, RandomIt middle, RandomIt last, Compare comp)
{
    impl::heap_select(first, middle, last, comp);
    std::sort_heap(first, middle, comp);
}

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🌟 Notes 🌟

⚙️ Algorithm

The algorithm used is typically heap select to select the smallest elements, and heap sort to sort the selected elements in the heap in ascending order 📈

To select elements, a heap is used (see heap). For example, for operator< as comparison function, max-heap is used to select middle - first smallest elements 🏔️

Heap sort is used after selection to sort [first, middle) selected elements (see std::sort_heap) 🧺

🎀 Intended use

std::partial_sort algorithms are intended to be used for small constant numbers of [first, middle) selected elements 👑 (like, small. small small. don't be out here doing the most 💅)

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🍓 Example 🍓

Run this code, bestie 🏃‍♀️

#include <algorithm>
#include <array>
#include <functional>
#include <iostream>

void print(const auto& s, int middle)
{
    for (int a : s)
        std::cout << a << ' ';
    std::cout << '\n';
    if (middle > 0)
    {
        while (middle-- > 0)
            std::cout << "--";
        std::cout << '^';
    }
    else if (middle < 0)
    {
        for (auto i = s.size() + middle; --i; std::cout << "  ")
        {}

        for (std::cout << '^'; middle++ < 0; std::cout << "--")
        {}
    }
    std::cout << '\n';
};

int main()
{
    std::array<int, 10> s{5, 7, 4, 2, 8, 6, 1, 9, 0, 3};
    print(s, 0);
    std::partial_sort(s.begin(), s.begin() + 3, s.end());
    print(s, 3);
    std::partial_sort(s.rbegin(), s.rbegin() + 4, s.rend());
    print(s, -4);
    std::partial_sort(s.rbegin(), s.rbegin() + 5, s.rend(), std::greater{});
    print(s, -5);
}

🌸 Possible output:

5 7 4 2 8 6 1 9 0 3

0 1 2 7 8 6 5 9 4 3
------^
4 5 6 7 8 9 3 2 1 0
          ^--------
4 3 2 1 0 5 6 7 8 9
        ^----------

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🦋 Defect reports 🦋

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

• P0896R4 — applied to C++98. Behavior as published: [first, middle) and [middle, 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 👑

• nth_element — partially sorts the given range making sure that it is partitioned by the given element (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::partial_sort (C++20) — sorts the first N elements of a range (niebloid) 🌈

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aaaaand that's the whole page, you ate it, I'm obsessed 🫶💖 this little guide came straight from http://cppreference.com, dated 2024.06.10 — go forth and partially sort, queen 👑✨