# std::partial_sort

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< cpp‎ | algorithm

Defined in header `<algorithm>` |  |
template< class RandomIt > void partial_sort( RandomIt first, RandomIt middle, RandomIt last ); | (1) | (constexpr since C++20)
template< class ExecutionPolicy, class RandomIt > void partial_sort( ExecutionPolicy&& policy, RandomIt first, RandomIt middle, RandomIt last ); | (2) | (since C++17)
template< class RandomIt, class Compare > void partial_sort( RandomIt first, RandomIt middle, RandomIt last, Compare comp ); | (3) | (constexpr since C++20)
template< class ExecutionPolicy, class RandomIt, class Compare > void partial_sort( ExecutionPolicy&& policy, RandomIt first, RandomIt middle, RandomIt last, Compare comp ); | (4) | (since C++17)

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

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 sorted with respect to operator<(until C++20) 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 all following conditions are satisfied:

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`,` 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.
- The type of *first is not MoveAssignable.

(since C++11)

### 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

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 \(\scriptsize M\)M as middle - first, \(\scriptsize N\)N as last - first:

1,2) Approximately \(\scriptsize N \cdot \log(M)\)N·log(M) comparisons using operator<(until C++20) std::less {}(since C++20).
3,4) Approximately \(\scriptsize N \cdot \log(M)\)N·log(M) applications of the comparator 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

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);
    }

### 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.

### Example

Run this code

    #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
            ^----------

### Defect reports

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

DR | Applied to | Behavior as published | Correct behavior
--- | --- | --- | ---
P0896R4 | C++98 | `[`first`,` middle`)` and `[`middle`,` last`)` were not required to be valid ranges | the behavior is undefined if any of them is invalid

### 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 (algorithm function object)

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