std::partial_sort

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

3) Elements are compared using the given binary comparison function 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)

first, last	-	random access iterators defining the range
middle	-	random access iterator defining the last element 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); 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 ValueSwappable and LegacyRandomAccessIterator.
- The type of dereferenced `RandomIt` must meet the requirements of MoveAssignable and MoveConstructible.

Return value

(none)

Complexity

Approximately $(last-first)log(middle-first)$ applications of cmp.

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.

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.

Possible implementation

See also the implementations in libstdc++ and libc++.

First version

namespace impl {
template<typename RandomIt, typename Compare = std::less<typename std::iterator_traits<RandomIt>::value_type>>
void sift_down(RandomIt begin, RandomIt end, const Compare &comp = {}) { // sift down element at 'begin'
  const auto length = static_cast<size_t>(end - begin);
  size_t current = 0;
  size_t next = 2;
  while (next < length) {
    if (comp(*(begin + next), *(begin + (next - 1))))
      --next;
    if (!comp(*(begin + current), *(begin + next)))
      return;
    std::iter_swap(begin + current, begin + next);
    current = next;
    next = 2 * current + 2;
  }
  --next;
  if (next < length && comp(*(begin + current), *(begin + next)))
    std::iter_swap(begin + current, begin + next);
}
 
template<typename RandomIt, typename Compare = std::less<typename std::iterator_traits<RandomIt>::value_type>>
void heap_select(RandomIt begin, RandomIt middle, RandomIt end, const Compare &comp = {}) {
  std::make_heap(begin, middle, comp);
  for (auto i = middle; i != end; ++i)
    if (*i < *begin) {
      std::iter_swap(begin, i);
      sift_down(begin, middle, comp);
    }
}
} // namespace impl
 
template<typename RandomIt, typename Compare = std::less<typename std::iterator_traits<RandomIt>::value_type>>
void partial_sort(RandomIt begin, RandomIt middle, RandomIt end, const Compare &comp = {}) {
  impl::heap_select(begin, middle, end, comp);
  std::sort_heap(begin, middle, comp);
}

Second version

template<typename RandomIt, typename Compare>
void partial_sort(RandomIt first, RandomIt middle, RandomIt last, Compare comp) {
    if (first == middle)
        return;
    std::make_heap(first, middle, comp);
    for (auto it {middle}; it != last; ++it) {
        if (comp(*it, *first)) {
            std::pop_heap(first, middle, comp);
            std::iter_swap(middle - 1, it);
            std::push_heap(first, middle, comp);
        }
    }
    std::sort_heap(first, middle, comp);
}

Note that the second version is inefficient in practice, it is provided for illustration purpose.

Example

Run this code

#include <algorithm>
#include <array>
#include <functional>
#include <iostream>
 
auto 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);
}

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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External libraries

nth_element	partially sorts the given range making sure that it is partitioned by the given element (function template) [edit]
partial_sort_copy	copies and partially sorts a range of elements (function template) [edit]
stable_sort	sorts a range of elements while preserving order between equal elements (function template) [edit]
sort	sorts a range into ascending order (function template) [edit]
ranges::partial_sort (C++20)	sorts the first N elements of a range (niebloid)[edit]

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