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 middle, (1) (constexpr since C++20)
   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 middle, (3) (constexpr since C++20)
   RandomIt last,
                      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 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
   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. (since C++11)
     * The type of *first is not MoveAssignable.

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 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) the behavior is undefined
                      were not required to be valid ranges if any of them is invalid

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)