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Difference between revisions of "cpp/algorithm/partial sort"

From cppreference.com
< cpp‎ | algorithm
(Rearrange impls, think it makes a lot more sense to put the simple one first. Weaken bold claim about complicated impl always being better. Fix function signature in the complicated impl. Still think we should remove all these impl details altogether...)
(Wording update (P0896R4 is treated as a DR here).)
 
(6 intermediate revisions by 3 users not shown)
Line 2: Line 2:
 
{{cpp/algorithm/navbar}}
 
{{cpp/algorithm/navbar}}
 
{{dcl begin}}
 
{{dcl begin}}
−
{{dcl header | algorithm}}
+
{{dcl header|algorithm}}
−
{{dcl rev multi | num=1 | since1= | until1=c++20 |dcl1=
+
{{dcla|num=1|notes={{mark constexpr since c++20}}|
 
template< class RandomIt >
 
template< class RandomIt >
 
void partial_sort( RandomIt first, RandomIt middle, RandomIt last );
 
void partial_sort( RandomIt first, RandomIt middle, RandomIt last );
−
|dcl2=
 
−
template< class RandomIt >
 
−
constexpr void partial_sort( RandomIt first, RandomIt middle, RandomIt last );
 
 
}}
 
}}
−
{{dcl| since=c++17 | num= 2 |1=
+
{{dcl|num=2|since=c++17|
 
template< class ExecutionPolicy, class RandomIt >
 
template< class ExecutionPolicy, class RandomIt >
−
void partial_sort( ExecutionPolicy&& policy,  
+
void partial_sort( ExecutionPolicy&& policy,
 
                   RandomIt first, RandomIt middle, RandomIt last );
 
                   RandomIt first, RandomIt middle, RandomIt last );
 
}}
 
}}
−
{{dcl rev multi | num=3 | since1= | until1=c++20 |dcl1=
+
{{dcla|num=3|notes={{mark constexpr since c++20}}|
 
template< class RandomIt, class Compare >
 
template< class RandomIt, class Compare >
 
void partial_sort( RandomIt first, RandomIt middle, RandomIt last,
 
void partial_sort( RandomIt first, RandomIt middle, RandomIt last,
 
                   Compare comp );
 
                   Compare comp );
−
|dcl2=
 
−
template< class RandomIt, class Compare >
 
−
constexpr void partial_sort( RandomIt first, RandomIt middle, RandomIt last,
 
−
                            Compare comp );
 
 
}}
 
}}
−
{{dcl | since=c++17 | until= | num=4 |1=
+
{{dcl|num=4|since=c++17|
 
template< class ExecutionPolicy, class RandomIt, class Compare >
 
template< class ExecutionPolicy, class RandomIt, class Compare >
 
void partial_sort( ExecutionPolicy&& policy,
 
void partial_sort( ExecutionPolicy&& policy,
Line 32: Line 25:
 
{{dcl end}}
 
{{dcl end}}
  
−
Rearranges elements such that the range {{tt|[first, middle)}} contains the sorted {{tt|middle − first}} smallest elements in the range {{tt|[first, last)}}.
+
Rearranges elements such that the range {{range|first|middle}} contains the sorted {{c|middle − first}} smallest elements in the range {{range|first|last}}.
  
−
The order of equal elements is not guaranteed to be preserved. The order of the remaining elements in the range {{tt|[middle, last)}} is unspecified.
+
The order of equal elements is not guaranteed to be preserved. The order of the remaining elements in the range {{range|middle|last}} is unspecified.
  
−
@1@ Elements are compared using {{tt|operator<}}.
+
@1@ Elements are {{rlp|/#Requirements|sorted}} with respect to {{rev inl|until=c++20|{{c/core|operator<}}}}{{rev inl|since=c++20|{{c|std::less{}<!---->}}}}.
−
@3@ Elements are compared using the given binary comparison function {{tt|comp}}.
+
 
−
@2,4@ Same as {{v|1,3}}, but executed according to {{tt|policy}}. {{cpp/algorithm/parallel overload precondition|plural=true}}
+
@3@ Elements are sorted with respect to {{c|comp}}.
 +
 
 +
@2,4@ Same as {{v|1,3}}, but executed according to {{c|policy}}.
 +
@@ {{cpp/algorithm/parallel overload precondition|plural=yes}}
 +
 
 +
If any of the following conditions is satisfied, the behavior is undefined:
 +
* {{range|first|middle}} or {{range|middle|last}} is not a [[cpp/iterator#Ranges|valid range]].
 +
{{rev begin}}
 +
{{rev|until=c++11|
 +
* The type of {{c|*first}} is not {{named req|Swappable}}.
 +
}}
 +
{{rev|since=c++11|
 +
* {{tt|RandomIt}} is not {{named req|ValueSwappable}}.
 +
* The type of {{c|*first}} is not {{named req|MoveConstructible}}.
 +
* The type of {{c|*first}} is not {{named req|MoveAssignable}}.
 +
}}
 +
{{rev end}}
  
 
===Parameters===
 
===Parameters===
 
{{par begin}}
 
{{par begin}}
−
{{par | first, last | random access iterators defining the range}}
+
{{par|first, last|random access iterators defining the range}}
−
{{par | middle | random access iterator defining the last element to be sorted}}
+
{{par|middle|random access iterator defining the one-past-the-end iterator of the range to be sorted}}
 
{{par exec pol}}
 
{{par exec pol}}
−
{{par cmp ord | comp | p1=RandomIt}}
+
{{par cmp ord|comp|p1=RandomIt}}
 
{{par hreq}}
 
{{par hreq}}
−
{{par req named | RandomIt | RandomAccessIterator | ValueSwappable}}  
+
{{par req named|RandomIt|RandomAccessIterator}}
−
{{par req named deref | RandomIt | MoveConstructible | MoveAssignable}}  
+
{{par req named|Compare|Compare}}
 
{{par end}}
 
{{par end}}
−
 
−
===Return value===
 
−
(none)
 
  
 
===Complexity===
 
===Complexity===
−
Approximately {{math|(last-first)log(middle-first)}} applications of {{tt|cmp}}.
+
Given {{mathjax-or|\(\scriptsize M\)|M}} as {{c|middle - first}}, {{mathjax-or|\(\scriptsize N\)|N}} as {{c|last - first}}:
 +
@1,2@ Approximately {{mathjax-or|\(\scriptsize N \cdot \log(M)\)|N·log(M)}} comparisons using {{rev inl|until=c++20|{{c/core|operator<}}}}{{rev inl|since=c++20|{{c|std::less{}<!---->}}}}.
 +
@3,4@ Approximately {{mathjax-or|\(\scriptsize N \cdot \log(M)\)|N·log(M)}} applications of the comparator {{c|comp}}.
  
 
===Exceptions===
 
===Exceptions===
−
{{cpp/algorithm/parallel_exceptions_reporting_behavior|singular=no}}
+
{{cpp/algorithm/parallel exceptions reporting behavior|singular=no}}
−
 
+
−
===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 [[enwiki::Heap_(data_structure)#Applications|heap]]). For example, for {{c|operator<}} as comparison function, ''max-heap'' is used to select {{tt|middle − first}} smallest elements.
+
−
 
+
−
[[enwiki::Heapsort|Heap sort]] is used after selection to sort {{tt|[first, middle)}} selected elements (see {{lc|std::sort_heap}}).
+
−
 
+
−
==== Intended use ====
+
−
{{c|std::partial_sort}} algorithms are intended to be used for ''small constant numbers'' of {{tt|[first, middle)}} selected elements.
+
  
 
===Possible implementation===
 
===Possible implementation===
−
 
 
See also the implementations in [https://github.com/gcc-mirror/gcc/blob/d9375e490072d1aae73a93949aa158fcd2a27018/libstdc%2B%2B-v3/include/bits/stl_algo.h#L1915 libstdc++] and [https://github.com/llvm-mirror/libcxx/blob/a12cb9d211019d99b5875b6d8034617cbc24c2cc/include/algorithm#L5025 libc++].
 
See also the implementations in [https://github.com/gcc-mirror/gcc/blob/d9375e490072d1aae73a93949aa158fcd2a27018/libstdc%2B%2B-v3/include/bits/stl_algo.h#L1915 libstdc++] and [https://github.com/llvm-mirror/libcxx/blob/a12cb9d211019d99b5875b6d8034617cbc24c2cc/include/algorithm#L5025 libc++].
−
{{eq fun | 1=
+
{{eq impl
−
template<typename RandomIt, typename Compare>
+
|title1=partial_sort (1)|ver1=1|1=
−
void partial_sort(RandomIt first, RandomIt middle, RandomIt last, Compare comp) {
+
template<typename RandomIt>
−
     if (first == middle)
+
constexpr //< since C++20
−
        return;
+
void partial_sort(RandomIt first, RandomIt middle, RandomIt last)
−
     std::make_heap(first, middle, comp);
+
{
−
     for (auto it {middle}; it != last; ++it) {
+
     typedef typename std::iterator_traits<RandomIt>::value_type VT;
−
         if (comp(*it, *first)) {
+
     std::partial_sort(first, middle, last, std::less<VT>());
−
             std::pop_heap(first, middle, comp);
+
}
−
             std::iter_swap(middle - 1, it);
+
|title2=partial_sort (3)|ver2=3|2=
−
             std::push_heap(first, middle, comp);
+
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);
 
     }
 
     }
−
    std::sort_heap(first, middle, comp);
 
−
}
 
−
| 2=
 
−
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>>
+
    template<typename RandomIt, typename Compare>
−
void heap_select(RandomIt begin, RandomIt middle, RandomIt end, const Compare &comp = {}) {
+
    constexpr //< since C++20
−
  std::make_heap(begin, middle, comp);
+
    void heap_select(RandomIt first, RandomIt middle, RandomIt last, const Compare& comp)
−
  for (auto i = middle; i != end; ++i)
+
    {
−
    if (comp(*i, *begin)) {
+
        std::make_heap(first, middle, comp);
−
      std::iter_swap(begin, i);
+
        for (auto i = middle; i != last; ++i)
−
      sift_down(begin, middle, comp);
+
        {
 +
            if (comp(*i, *first))
 +
            {
 +
                std::iter_swap(first, i);
 +
                sift_down(first, middle, comp);
 +
            }
 +
        }
 
     }
 
     }
−
}
 
 
} // namespace impl
 
} // namespace impl
  
−
template<typename RandomIt, typename Compare = std::less<typename std::iterator_traits<RandomIt>::value_type>>
+
template<typename RandomIt, typename Compare>
−
void partial_sort(RandomIt begin, RandomIt middle, RandomIt end, Compare comp = {}) {
+
constexpr //< since C++20
−
  impl::heap_select(begin, middle, end, comp);
+
void partial_sort(RandomIt first, RandomIt middle, RandomIt last, Compare comp)
−
  std::sort_heap(begin, middle, comp);
+
{
 +
    impl::heap_select(first, middle, last, comp);
 +
    std::sort_heap(first, middle, comp);
 
}
 
}
 
}}
 
}}
  
−
Note that the first version may be less efficient in practice.
+
===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 {{enwiki|Heap (data structure)#Applications|heap}}). For example, for {{c|operator<}} as comparison function, ''max-heap'' is used to select {{c|middle − first}} smallest elements.
 +
 
 +
{{enwiki|Heapsort|Heap sort}} is used after selection to sort {{range|first|middle}} selected elements (see {{lc|std::sort_heap}}).
 +
 
 +
====Intended use====
 +
{{tt|std::partial_sort}} algorithms are intended to be used for ''small constant numbers'' of {{range|first|middle}} selected elements.
  
 
===Example===
 
===Example===
 
{{example
 
{{example
−
|
+
|code=
−
| code=
+
 
#include <algorithm>
 
#include <algorithm>
 
#include <array>
 
#include <array>
Line 139: Line 149:
 
#include <iostream>
 
#include <iostream>
  
−
auto print = [](auto const& s, int middle) {
+
void print(const auto& s, int middle)
−
     for (int a : s) { std::cout << a << ' '; }
+
{
 +
     for (int a : s)
 +
        std::cout << a << ' ';
 
     std::cout << '\n';
 
     std::cout << '\n';
−
     if (middle > 0) {
+
     if (middle > 0)
−
         while (middle-->0) { std::cout << "──"; }
+
    {
 +
         while (middle-- > 0)
 +
            std::cout << "--";
 
         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';
+
    else if (middle < 0)
 +
    {
 +
        for (auto i = s.size() + middle; --i; std::cout << "  ")
 +
        {}
 +
       
 +
        for (std::cout << '^'; middle++ < 0; std::cout << "--")
 +
        {}
 +
    }
 +
     std::cout << '\n';
 
};
 
};
  
Line 155: Line 174:
 
{
 
{
 
     std::array<int, 10> s{5, 7, 4, 2, 8, 6, 1, 9, 0, 3};
 
     std::array<int, 10> s{5, 7, 4, 2, 8, 6, 1, 9, 0, 3};
−
 
 
     print(s, 0);
 
     print(s, 0);
 
     std::partial_sort(s.begin(), s.begin() + 3, s.end());
 
     std::partial_sort(s.begin(), s.begin() + 3, s.end());
Line 164: Line 182:
 
     print(s, -5);
 
     print(s, -5);
 
}
 
}
−
| p=true | output=
+
|p=true
−
5 7 4 2 8 6 1 9 0 3  
+
|output=
 +
5 7 4 2 8 6 1 9 0 3
  
−
0 1 2 7 8 6 5 9 4 3  
+
0 1 2 7 8 6 5 9 4 3
−
──────^
+
------^
−
4 5 6 7 8 9 3 2 1 0  
+
4 5 6 7 8 9 3 2 1 0
−
           ^────────
+
           ^--------
−
4 3 2 1 0 5 6 7 8 9  
+
4 3 2 1 0 5 6 7 8 9
−
         ^──────────
+
         ^----------
 
}}
 
}}
 +
 +
===Defect reports===
 +
{{dr list begin}}
 +
{{dr list item|paper=P0896R4|std=C++98|before={{range|first|middle}} and {{range|middle|last}}<br>were not required to be valid ranges|after=the behavior is undefined<br>if any of them is invalid}}
 +
{{dr list end}}
  
 
===See also===
 
===See also===
 
{{dsc begin}}
 
{{dsc begin}}
−
{{dsc inc | cpp/algorithm/dsc nth_element}}
+
{{dsc inc|cpp/algorithm/dsc nth_element}}
−
{{dsc inc | cpp/algorithm/dsc partial_sort_copy}}
+
{{dsc inc|cpp/algorithm/dsc partial_sort_copy}}
−
{{dsc inc | cpp/algorithm/dsc stable_sort}}
+
{{dsc inc|cpp/algorithm/dsc stable_sort}}
−
{{dsc inc | cpp/algorithm/dsc sort}}
+
{{dsc inc|cpp/algorithm/dsc sort}}
−
{{dsc inc | cpp/algorithm/ranges/dsc partial_sort}}
+
{{dsc inc|cpp/algorithm/ranges/dsc partial_sort}}
 
{{dsc end}}
 
{{dsc end}}
  
 
{{langlinks|de|es|fr|it|ja|pt|ru|zh}}
 
{{langlinks|de|es|fr|it|ja|pt|ru|zh}}

Latest revision as of 23:27, 1 April 2024

 
C++
 
Algorithm library
Constrained algorithms and algorithms on ranges (C++20)
Constrained algorithms, e.g. ranges::copy, ranges::sort, ...
Execution policies (C++17)
Non-modifying sequence operations
Batch operations
(C++17)
Search operations
(C++11)                (C++11)(C++11)

Modifying sequence operations
Copy operations
(C++11)
(C++11)
(C++11)
Swap operations
Transformation operations
Generation operations
Removing operations
Order-changing operations
(until C++17)(C++11)
(C++20)(C++20)
Sampling operations
(C++17)

Sorting and related operations
Partitioning operations
Sorting operations
Binary search operations
(on partitioned ranges)
Set operations (on sorted ranges)
Merge operations (on sorted ranges)
Heap operations
Minimum/maximum operations
(C++11)
(C++17)
Lexicographical comparison operations
(C++20)
Permutation operations
C library
Numeric operations
Operations on uninitialized memory
 
Defined in header <algorithm>
template< class RandomIt >
void partial_sort( RandomIt first, RandomIt middle, RandomIt last );
 (1) (constexpr since C++20)
template< class ExecutionPolicy, class RandomIt >

void partial_sort( ExecutionPolicy&& policy,

                   RandomIt first, RandomIt middle, RandomIt last );
 (2) (since C++17)
template< class RandomIt, class Compare >

void partial_sort( RandomIt first, RandomIt middle, RandomIt last,

                   Compare comp );
 (3) (constexpr since C++20)
template< class ExecutionPolicy, class RandomIt, class Compare >

void partial_sort( ExecutionPolicy&& policy,
                   RandomIt first, RandomIt middle, RandomIt last,

                   Compare comp );
 (4) (since C++17)

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.
(until C++11)
(since C++11)

Contents

[edit] 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.
comp - 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);

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.

[edit] Complexity

Given M as middle - first, N as last - first:

1,2) Approximately N·log(M) comparisons using operator<(until C++20)std::less{}(since C++20).
3,4) Approximately N·log(M) applications of the comparator comp.

[edit] 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.

[edit] 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);
}

[edit] Notes

[edit] 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).

[edit] Intended use

std::partial_sort algorithms are intended to be used for small constant numbers of [first, middle) selected elements.

[edit] 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
        ^----------

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

[edit] See also

 partially sorts the given range making sure that it is partitioned by the given element
(function template) [edit]
copies and partially sorts a range of elements
(function template) [edit]
sorts a range of elements while preserving order between equal elements
(function template) [edit]
sorts a range into ascending order
(function template) [edit]
(C++20)
 sorts the first N elements of a range
(niebloid)[edit]
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