std::ranges::inplace_merge(3)

NAME
std::ranges::inplace_merge - std::ranges::inplace_merge

Synopsis
   Defined in header <algorithm>
   Call signature
   template< std::bidirectional_iterator I, std::sentinel_for<I>
   S,
             class Comp = ranges::less, class Proj = std::identity (since C++20)
   > (1) (constexpr since
   requires std::sortable<I, Comp, Proj> C++26)
       I inplace_merge( I first, I middle, S last,
                        Comp comp = {}, Proj proj = {} );
   template< ranges::bidirectional_range R, class Comp =
   ranges::less,
             class Proj = std::identity > (since C++20)
   requires std::sortable<ranges::iterator_t<R>, Comp, Proj> (2) (constexpr since
   ranges::borrowed_iterator_t<R> C++26)
       inplace_merge( R&& r, ranges::iterator_t<R> middle,
                      Comp comp = {}, Proj proj = {} );
   Merges two consecutive sorted ranges [first, middle) and [middle, last) into one
   sorted range [first, last).
   A sequence is said to be sorted with respect to the comparator comp and projection
   proj if for any iterator it pointing to the sequence and any non-negative integer n
   such that it + n is a valid iterator pointing to an element of the sequence,
   std::invoke(comp, std::invoke(proj, *(it + n)), std::invoke(proj, *it))) evaluates
   to false.
   This merge function is stable, which means that for equivalent elements in the
   original two ranges, the elements from the first range (preserving their original
   order) precede the elements from the second range (preserving their original order).
   1) Elements are compared using the given binary comparison function comp and
   projection object proj, and the ranges must be sorted with respect to the same.
   2) Same as (1), but uses r as the range, as if using ranges::begin(r) as first, and
   ranges::end(r) as last.
   The function-like entities described on this page are niebloids, that is:
     * Explicit template argument lists cannot be specified when calling any of them.
     * None of them are visible to argument-dependent lookup.
     * When any of them are found by normal unqualified lookup as the name to the left
       of the function-call operator, argument-dependent lookup is inhibited.
   In practice, they may be implemented as function objects, or with special compiler
   extensions.

Parameters
   first - the beginning of the first sorted range
   middle - the end of the first range and the beginning of the second range
   last - the end of the second sorted range
   r - the range of elements to merge inplace
   comp - comparison to apply to the projected elements
   proj - projection to apply to the elements in the range

Return value
   An iterator equal to last.

Complexity
   Exactly N − 1 comparisons, if additional memory buffer is available, where N =
   ranges::distance(first, last). Otherwise, \(\scriptsize
   \mathcal{O}(N\cdot\log{(N)})\)𝓞(N*log(N)) comparisons. Additionally, twice as many
   projections as comparisons in both cases.

Notes
   This function attempts to allocate a temporary buffer. If the allocation fails, the
   less efficient algorithm is chosen.
         Feature-test macro Value Std Feature
   __cpp_lib_constexpr_algorithms 202306L constexpr stable sorting

Possible implementation
   This implementation only shows the slower algorithm used when no additional memory
   is available. See also the implementation in MSVC STL and libstdc++. struct inplace_merge_fn {
    template<std::bidirectional_iterator I, std::sentinel_for<I> S,
             class Comp = ranges::less, class Proj = std::identity>
    requires std::sortable<I, Comp, Proj>
    constexpr I operator()(I first, I middle, S last, Comp comp = {}, Proj proj = {}) const
    {
        I last_it = ranges::next(middle, last);
        inplace_merge_slow(first, middle, last_it,
                        ranges::distance(first, middle),
                        ranges::distance(middle, last_it),
                        std::ref(comp), std::ref(proj));
        return last_it;
    }
    template<ranges::bidirectional_range R, class Comp = ranges::less,
             class Proj = std::identity>
    requires std::sortable<ranges::iterator_t<R>, Comp, Proj>
    constexpr ranges::borrowed_iterator_t<R>
        operator()(R&& r, ranges::iterator_t<R> middle,
                   Comp comp = {}, Proj proj = {}) const
    {
        return (*this)(ranges::begin(r), std::move(middle), ranges::end(r),
                       std::move(comp), std::move(proj));
    } private:
    template<class I, class Comp, class Proj>
    static constexpr void inplace_merge_slow(I first, I middle, I last,
                        std::iter_difference_t<I> n1,
                        std::iter_difference_t<I> n2,
                        Comp comp, Proj proj)
    {
        if (n1 == 0 || n2 == 0)
            return;
        if (n1 + n2 == 2 && comp(proj(*middle), proj(*first)))
        {
            ranges::iter_swap(first, middle);
            return;
        }
        I cut1 = first, cut2 = middle;
        std::iter_difference_t<I> d1{}, d2{};
        if (n1 > n2)
        {
            d1 = n1 / 2;
            ranges::advance(cut1, d1);
            cut2 = ranges::lower_bound(middle, last, *cut1,
                        std::ref(comp), std::ref(proj));
            d2 = ranges::distance(middle, cut2);
        }
        else
        {
            d2 = n2 / 2;
            ranges::advance(cut2, d2);
            cut1 = ranges::upper_bound(first, middle, *cut2,
                        std::ref(comp), std::ref(proj));
            d1 = ranges::distance(first, cut1);
        }
        I new_middle = ranges::rotate(cut1, middle, cut2);
        inplace_merge_slow(first, cut1, new_middle, d1, d2,
                        std::ref(comp), std::ref(proj));
        inplace_merge_slow(new_middle, cut2, last, n1 - d1, n2 - d2,
                        std::ref(comp), std::ref(proj));
    } }; inline constexpr inplace_merge_fn inplace_merge {};

Example
// Run this code
 #include <algorithm>
 #include <complex>
 #include <functional>
 #include <iostream>
 #include <iterator>
 #include <vector>
 void print(auto const& v, auto const& rem, int middle = -1)
 {
     for (int i{}; auto n : v)
         std::cout << (i++ == middle ? "│ " : "") << n << ' ';
     std::cout << rem << '\n';
 }
 template<std::random_access_iterator I, std::sentinel_for<I> S>
 requires std::sortable<I>
 void merge_sort(I first, S last)
 {
     if (last - first > 1)
     {
         I middle{first + (last - first) / 2};
         merge_sort(first, middle);
         merge_sort(middle, last);
         std::ranges::inplace_merge(first, middle, last);
     }
 }
 int main()
 {
     // custom merge-sort demo
     std::vector v{8, 2, 0, 4, 9, 8, 1, 7, 3};
     print(v, ": before sort");
     merge_sort(v.begin(), v.end());
     print(v, ": after sort\n");
     // merging with comparison function object and projection
     using CI = std::complex<int>;
     std::vector<CI> r{{0,1}, {0,2}, {0,3}, {1,1}, {1,2}};
     const auto middle{std::ranges::next(r.begin(), 3)};
     auto comp{std::ranges::less{}};
     auto proj{[](CI z) { return z.imag(); }};
     print(r, ": before merge", middle - r.begin());
     std::ranges::inplace_merge(r, middle, comp, proj);
     print(r, ": after merge");
 }

Output:
 8 2 0 4 9 8 1 7 3 : before sort
 0 1 2 3 4 7 8 8 9 : after sort
 (0,1) (0,2) (0,3) │ (1,1) (1,2) : before merge
 (0,1) (1,1) (0,2) (1,2) (0,3) : after merge

See also
   ranges::merge merges two sorted ranges
   (C++20) (niebloid)
   ranges::set_union computes the union of two sets
   (C++20) (niebloid)
   ranges::is_sorted checks whether a range is sorted into ascending order
   (C++20) (niebloid)
   ranges::sort sorts a range into ascending order
   (C++20) (niebloid)
   inplace_merge merges two ordered ranges in-place
                     (function template)