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, RandomIt (1) (constexpr since C++20)
   last );
   template< class ExecutionPolicy, class RandomIt >
   void nth_element( ExecutionPolicy&& policy, (2) (since C++17)
                     RandomIt first, RandomIt nth, RandomIt
   last );
   template< class RandomIt, class Compare >
   void nth_element( RandomIt first, RandomIt nth, RandomIt (3) (constexpr since C++20)
   last,
                     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 rearranges elements in [first, last) such that after the rearrangement:
     * The element pointed at by nth is changed to whatever element would occur in that
       position if [first, last) were sorted.
     * For every iterator i in [first, nth) and every iterator j in [nth, last), the
       following condition is met:
   1,2)
   bool(*j < *i)
   (until C++20)
   std::less{}(*j, *i)
   (since C++20) is false.
   3,4) bool(comp(*j, *i)) is false.
   1) Elements are hypothetically sorted with respect to
   operator<
   (until C++20)
   std::less{}
   (since C++20).
   3) Elements are hypothetically 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, nth) or [nth, 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 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 LegacyRandomAccessIterator.
   -
   Compare must meet the requirements of Compare.

Complexity
   Given \(\scriptsize N\)N as last - first:
   1) \(\scriptsize O(N)\)O(N) comparisons using
   operator<
   (until C++20)
   std::less{}
   (since C++20) on average.
   2) \(\scriptsize O(N)\)O(N) comparisons using
   operator<
   (until C++20)
   std::less{}
   (since C++20), and \(\scriptsize O(N \cdot \log(N))\)O(N·log(N)) swaps.
   3) \(\scriptsize O(N)\)O(N) applications of the comparator comp on average.
   4) \(\scriptsize O(N)\)O(N) applications of the comparator comp, and \(\scriptsize
   O(N \cdot \log(N))\)O(N·log(N)) swaps.

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++, libc++, and msvc stl.

Notes
   The algorithm used is typically Introselect although other Selection algorithm with
   suitable average-case complexity are allowed.

Example
// Run this code
 #include <algorithm>
 #include <cassert>
 #include <functional>
 #include <iostream>
 #include <numeric>
 #include <vector>
 void printVec(const std::vector<int>& vec)
 {
     std::cout << "v = {";
     for (char sep[]{0, ' ', 0}; const int i : vec)
         std::cout << sep << i, sep[0] = ',';
     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};
   Defect reports
   The following behavior-changing defect reports were applied retroactively to
   previously published C++ standards.
      DR Applied to Behavior as published Correct behavior
                       after the rearrangement, only one
   LWG 2150 C++98 element before nth corrected the
                       was required to be not greater than requirement
                       one element after nth
   P0896R4 C++98 [first, nth) and [nth, last) the behavior is undefined
                       were not required to be valid ranges if any of them is invalid

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)