nth_element.h

//===----------------------------------------------------------------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//

#ifndef _LIBCPP___ALGORITHM_NTH_ELEMENT_H
#define _LIBCPP___ALGORITHM_NTH_ELEMENT_H

#include <__algorithm/comp.h>
#include <__algorithm/comp_ref_type.h>
#include <__algorithm/iterator_operations.h>
#include <__algorithm/sort.h>
#include <__config>
#include <__debug_utils/randomize_range.h>
#include <__iterator/iterator_traits.h>
#include <__utility/move.h>

#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
#  pragma GCC system_header
#endif

_LIBCPP_BEGIN_NAMESPACE_STD

template<class _Compare, class _RandomAccessIterator>
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 bool
__nth_element_find_guard(_RandomAccessIterator& __i, _RandomAccessIterator& __j,
                         _RandomAccessIterator __m, _Compare __comp)
{
    // manually guard downward moving __j against __i
    while (true) {
        if (__i == --__j) {
            return false;
        }
        if (__comp(*__j, *__m)) {
            return true;  // found guard for downward moving __j, now use unguarded partition
        }
    }
}

template <class _AlgPolicy, class _Compare, class _RandomAccessIterator>
_LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX14 void
__nth_element(_RandomAccessIterator __first, _RandomAccessIterator __nth, _RandomAccessIterator __last, _Compare __comp)
{
    using _Ops = _IterOps<_AlgPolicy>;

    // _Compare is known to be a reference type
    typedef typename iterator_traits<_RandomAccessIterator>::difference_type difference_type;
    const difference_type __limit = 7;
    while (true)
    {
        if (__nth == __last)
            return;
        difference_type __len = __last - __first;
        switch (__len)
        {
        case 0:
        case 1:
            return;
        case 2:
            if (__comp(*--__last, *__first))
                _Ops::iter_swap(__first, __last);
            return;
        case 3:
            {
            _RandomAccessIterator __m = __first;
            std::__sort3<_AlgPolicy, _Compare>(__first, ++__m, --__last, __comp);
            return;
            }
        }
        if (__len <= __limit)
        {
            std::__selection_sort<_AlgPolicy, _Compare>(__first, __last, __comp);
            return;
        }
        // __len > __limit >= 3
        _RandomAccessIterator __m = __first + __len/2;
        _RandomAccessIterator __lm1 = __last;
        unsigned __n_swaps = std::__sort3<_AlgPolicy, _Compare>(__first, __m, --__lm1, __comp);
        // *__m is median
        // partition [__first, __m) < *__m and *__m <= [__m, __last)
        // (this inhibits tossing elements equivalent to __m around unnecessarily)
        _RandomAccessIterator __i = __first;
        _RandomAccessIterator __j = __lm1;
        // j points beyond range to be tested, *__lm1 is known to be <= *__m
        // The search going up is known to be guarded but the search coming down isn't.
        // Prime the downward search with a guard.
        if (!__comp(*__i, *__m))  // if *__first == *__m
        {
            // *__first == *__m, *__first doesn't go in first part
            if (_VSTD::__nth_element_find_guard<_Compare>(__i, __j, __m, __comp)) {
                _Ops::iter_swap(__i, __j);
                ++__n_swaps;
            } else {
                // *__first == *__m, *__m <= all other elements
                // Partition instead into [__first, __i) == *__first and *__first < [__i, __last)
                ++__i;  // __first + 1
                __j = __last;
                if (!__comp(*__first, *--__j)) {  // we need a guard if *__first == *(__last-1)
                    while (true) {
                        if (__i == __j) {
                            return;  // [__first, __last) all equivalent elements
                        } else if (__comp(*__first, *__i)) {
                            _Ops::iter_swap(__i, __j);
                            ++__n_swaps;
                            ++__i;
                            break;
                        }
                        ++__i;
                    }
                }
                // [__first, __i) == *__first and *__first < [__j, __last) and __j == __last - 1
                if (__i == __j) {
                    return;
                }
                while (true) {
                    while (!__comp(*__first, *__i))
                        ++__i;
                    while (__comp(*__first, *--__j))
                        ;
                    if (__i >= __j)
                        break;
                    _Ops::iter_swap(__i, __j);
                    ++__n_swaps;
                    ++__i;
                }
                // [__first, __i) == *__first and *__first < [__i, __last)
                // The first part is sorted,
                if (__nth < __i) {
                    return;
                }
                // __nth_element the second part
                // _VSTD::__nth_element<_Compare>(__i, __nth, __last, __comp);
                __first = __i;
                continue;
            }
        }
        ++__i;
        // j points beyond range to be tested, *__lm1 is known to be <= *__m
        // if not yet partitioned...
        if (__i < __j)
        {
            // known that *(__i - 1) < *__m
            while (true)
            {
                // __m still guards upward moving __i
                while (__comp(*__i, *__m))
                    ++__i;
                // It is now known that a guard exists for downward moving __j
                while (!__comp(*--__j, *__m))
                    ;
                if (__i >= __j)
                    break;
                _Ops::iter_swap(__i, __j);
                ++__n_swaps;
                // It is known that __m != __j
                // If __m just moved, follow it
                if (__m == __i)
                    __m = __j;
                ++__i;
            }
        }
        // [__first, __i) < *__m and *__m <= [__i, __last)
        if (__i != __m && __comp(*__m, *__i))
        {
            _Ops::iter_swap(__i, __m);
            ++__n_swaps;
        }
        // [__first, __i) < *__i and *__i <= [__i+1, __last)
        if (__nth == __i)
            return;
        if (__n_swaps == 0)
        {
            // We were given a perfectly partitioned sequence.  Coincidence?
            if (__nth < __i)
            {
                // Check for [__first, __i) already sorted
                __j = __m = __first;
                while (true) {
                    if (++__j == __i) {
                        // [__first, __i) sorted
                        return;
                    }
                    if (__comp(*__j, *__m)) {
                        // not yet sorted, so sort
                        break;
                    }
                    __m = __j;
                }
            }
            else
            {
                // Check for [__i, __last) already sorted
                __j = __m = __i;
                while (true) {
                    if (++__j == __last) {
                        // [__i, __last) sorted
                        return;
                    }
                    if (__comp(*__j, *__m)) {
                        // not yet sorted, so sort
                        break;
                    }
                    __m = __j;
                }
            }
        }
        // __nth_element on range containing __nth
        if (__nth < __i)
        {
            // _VSTD::__nth_element<_Compare>(__first, __nth, __i, __comp);
            __last = __i;
        }
        else
        {
            // _VSTD::__nth_element<_Compare>(__i+1, __nth, __last, __comp);
            __first = ++__i;
        }
    }
}

template <class _AlgPolicy, class _RandomAccessIterator, class _Compare>
inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20
void __nth_element_impl(_RandomAccessIterator __first, _RandomAccessIterator __nth, _RandomAccessIterator __last,
                        _Compare& __comp) {
  if (__nth == __last)
    return;

  std::__debug_randomize_range<_AlgPolicy>(__first, __last);

  std::__nth_element<_AlgPolicy, __comp_ref_type<_Compare> >(__first, __nth, __last, __comp);

  std::__debug_randomize_range<_AlgPolicy>(__first, __nth);
  if (__nth != __last) {
    std::__debug_randomize_range<_AlgPolicy>(++__nth, __last);
  }
}

template <class _RandomAccessIterator, class _Compare>
inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20
void nth_element(_RandomAccessIterator __first, _RandomAccessIterator __nth, _RandomAccessIterator __last,
                 _Compare __comp) {
  std::__nth_element_impl<_ClassicAlgPolicy>(std::move(__first), std::move(__nth), std::move(__last), __comp);
}

template <class _RandomAccessIterator>
inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_SINCE_CXX20
void nth_element(_RandomAccessIterator __first, _RandomAccessIterator __nth, _RandomAccessIterator __last) {
  std::nth_element(std::move(__first), std::move(__nth), std::move(__last), __less<>());
}

_LIBCPP_END_NAMESPACE_STD

#endif // _LIBCPP___ALGORITHM_NTH_ELEMENT_H