std::ranges::inplace_merge

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 algorithm function objects (informally known as 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.

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 {};

[edit] 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