std::partial_sort(3)

NAME
std::partial_sort - std::partial_sort

Synopsis
   Defined in header <algorithm>
   template< class RandomIt >
   void partial_sort( RandomIt first, RandomIt (until C++20)
   middle, RandomIt last );
   template< class RandomIt >
   constexpr void partial_sort( RandomIt first, (since C++20)
   RandomIt middle, RandomIt last );
   template< class ExecutionPolicy, class RandomIt
   >
   void partial_sort( ExecutionPolicy&& policy, (2) (since C++17)
   RandomIt first, RandomIt middle, RandomIt last
   );
   template< class RandomIt, class Compare >
   void partial_sort( RandomIt first, RandomIt (1) (until C++20)
   middle, RandomIt last,
   Compare comp );
   template< class RandomIt, class Compare >
   constexpr void partial_sort( RandomIt first, (since C++20)
   RandomIt middle, RandomIt last, (3)
   Compare comp );
   template< class ExecutionPolicy, class RandomIt,
   class Compare >
   void partial_sort( ExecutionPolicy&& policy, (4) (since C++17)
   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).
   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 do not
   participate in overload resolution unless
   std::is_execution_policy_v<std::decay_t<ExecutionPolicy>>
   (until C++20)
   std::is_execution_policy_v<std::remove_cvref_t<ExecutionPolicy>>
   (since C++20) is true.

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.
                 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);
   comp -
                 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
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); }

Second 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 (comp(*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, Compare comp = {}) {
  impl::heap_select(begin, middle, end, comp);
  std::sort_heap(begin, middle, comp); }
   Note that the first version may be less efficient in practice.

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
         ^──────────

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