std::nth_element(3)

NAME
std::nth_element - std::nth_element

Synopsis
   Defined in header <algorithm>
   template< class RandomIt >
   void nth_element( RandomIt first, RandomIt nth, (until C++20)
   RandomIt last );
   template< class RandomIt >
   constexpr void nth_element( RandomIt first, (since C++20)
   RandomIt nth, RandomIt last );
   template< class ExecutionPolicy, class RandomIt
   >
                        (2) (since C++17)
   void nth_element( ExecutionPolicy&& policy,
   RandomIt first, RandomIt nth, RandomIt last );
   template< class RandomIt, class Compare >
   void nth_element( RandomIt first, RandomIt nth, (until C++20)
   RandomIt last, (1)
   Compare comp );
   template< class RandomIt, class Compare >
   constexpr void nth_element( RandomIt first, (since C++20)
   RandomIt nth, RandomIt last, (3)
   Compare comp );
   template< class ExecutionPolicy, class RandomIt,
   class Compare >
   void nth_element( ExecutionPolicy&& policy, (4) (since C++17)
   RandomIt first, RandomIt nth, RandomIt last,
   Compare comp );
   nth_element is a partial sorting algorithm that rearranges elements in [first, last)
   such that:
     * The element pointed at by nth is changed to whatever element would occur in that
       position if [first, last) were sorted.
     * All of the elements before this new nth element are less than or equal to the
       elements after the new nth element.
   More formally, nth_element partially sorts the range [first, last) in ascending
   order so that the condition !(*j < *i) (for (1-2), or comp(*j, *i) == false for
   (3-4)) is met for any i in the range [first, nth) and for any j in the range [nth,
   last). The element placed in the nth position is exactly the element that would
   occur in this position if the range was fully sorted.
   nth may be the end iterator, in this case the function has no effect.
   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 sort
   nth - random access iterator defining the sort partition point
   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
   1,3) Linear in std::distance(first, last) on average.
   2,4) O(N) applications of the predicate, and O(N log N) swaps, where N = last -
   first.

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
   The algorithm used is typically introselect although other selection algorithms with
   suitable average-case complexity are allowed.

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

Example
// Run this code
 #include <vector>
 #include <cassert>
 #include <numeric>
 #include <iostream>
 #include <algorithm>
 #include <functional>
 void printVec(const std::vector<int> &vec)
 {
     std::cout << "v= {";
     for (int i : vec)
         std::cout << i << ", ";
     std::cout << "}\n";
 }
 int main()
 {
     std::vector<int> v{5, 10, 6, 4, 3, 2, 6, 7, 9, 3};
     printVec(v);
     auto m = v.begin() + v.size()/2;
     std::nth_element(v.begin(), m, v.end());
     std::cout << "\nThe median is " << v[v.size()/2] << '\n';
     // The consequence of the inequality of elements before/after the Nth one:
     assert(std::accumulate(v.begin(), m, 0) < std::accumulate(m, v.end(), 0));
     printVec(v);
     // Note: comp function changed
     std::nth_element(v.begin(), v.begin()+1, v.end(), std::greater{});
     std::cout << "\nThe second largest element is " << v[1] << '\n';
     std::cout << "The largest element is " << v[0] << '\n';
     printVec(v);
 }

Possible output:
 v= {5, 10, 6, 4, 3, 2, 6, 7, 9, 3, }
 The median is 6
 v= {3, 2, 3, 4, 5, 6, 10, 7, 9, 6, }
 The second largest element is 9
 The largest element is 10
 v= {10, 9, 6, 7, 6, 3, 5, 4, 3, 2, }

See also
   max_element returns the largest element in a range
                       (function template)
   min_element returns the smallest element in a range
                       (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::nth_element partially sorts the given range making sure that it is
   (C++20) partitioned by the given element
                       (niebloid)