std::partial_sort() algorithm

since C++20

// (1)
template< class RandomIt >
constexpr void partial_sort( RandomIt first, RandomIt middle, RandomIt last );

// (2)
template< class RandomIt, class Compare >
constexpr void partial_sort( RandomIt first, RandomIt middle, RandomIt last, Compare comp );

// (3)
template< class ExecutionPolicy, class RandomIt >
void partial_sort( ExecutionPolicy&& policy, RandomIt first, RandomIt middle, RandomIt last );

// (4)
template< class ExecutionPolicy, class RandomIt, class Compare >
void partial_sort( ExecutionPolicy&& policy, RandomIt first, RandomIt middle, RandomIt last, Compare comp );

since C++17

// (1)
template< class RandomIt >
void partial_sort( RandomIt first, RandomIt middle, RandomIt last );

// (2)
template< class RandomIt, class Compare >
void partial_sort( RandomIt first, RandomIt middle, RandomIt last, Compare comp );

// (3)
template< class ExecutionPolicy, class RandomIt >
void partial_sort( ExecutionPolicy&& policy, RandomIt first, RandomIt middle, RandomIt last );

// (4)
template< class ExecutionPolicy, class RandomIt, class Compare >
void partial_sort( ExecutionPolicy&& policy, RandomIt first, RandomIt middle, RandomIt last, Compare comp );

until C++17

// (1)
template< class RandomIt >
void partial_sort( RandomIt first, RandomIt middle, RandomIt last );

// (2)
template< class RandomIt, class Compare >
void partial_sort( RandomIt first, RandomIt middle, RandomIt last,
                   Compare comp );

Rearranges elements such that the range [first; middle) contains the sorted middle − first smallest elements in the range [first; last).

caution

The order of equal elements is not guaranteed to be preserved. The order of the remaining elements in the range [middle; last) is unspecified.

• (1) Elements are compared using operator<.

• (2) Elements are compared using the given binary comparison function comp.

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

  Overload Resolution

  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)

Parameters

first last	The range of elements to sort partially.
middle	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.
cmp	Comparison function object (i.e. an object that satisfies the requirements of Compare). The signature of the comparison function should be equivalent to the following: bool cmp(const Type1 &a, const Type2 &b); The signature does not need to have const&, but must not modify arguments. Must accept all values of type (possibly const) Type and Type2, regardless of value category (so 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 implicitly converted to both of them.

Type requirements

RandomIt	ValueSwappable LegacyRandomAccessIterator
Type of dereferenced RandomIt	MoveAssignable MoveConstructible
Compare	Compare

Return value

(none)

Complexity

Approximately (last - first) * log(middle - first) applications of comp.

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

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(2)

namespace impl {

template<typename RandomIt, typename Compare>
// constexpr
void sift_down(RandomIt first, RandomIt last, const Compare& comp)
{
    // sift down element at 'first'
    const auto length = static_cast<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
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);
}

Notes

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. 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).

std::partial_sort algorithms are intended to be used for small constant numbers of [first; middle) selected elements.

Examples

Main.cpp

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

void print(auto const& 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);
}

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
        ^----------