std::ranges::next_permutation,std::ranges::next_permutation_result(3)

NAME
std::ranges::next_permutation,std::ranges::next_permutation_result - std::ranges::next_permutation,std::ranges::next_permutation_result

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
   requires std::sortable<I, Comp, Proj> (1) C++20)
   constexpr next_permutation_result<I>
       next_permutation( I first, S last, Comp comp = {}, Proj proj = {} );
   template< ranges::bidirectional_range R, class Comp = ranges::less,
             class Proj = std::identity > (since
   requires std::sortable<ranges::iterator_t<R>, Comp, Proj> (2) C++20)
   constexpr next_permutation_result<ranges::borrowed_iterator_t<R>>
       next_permutation( R&& r, Comp comp = {}, Proj proj = {} );
   Helper type
   template< class I > (3) (since
   using next_permutation_result = ranges::in_found_result<I>; C++20)
   1) Transforms the range [first, last) into the next permutation, where the set of
   all permutations is ordered lexicographically with respect to binary comparison
   function object comp and projection function object proj. Returns {last, true} if
   such a "next permutation" exists; otherwise transforms the range into the
   lexicographically first permutation as if by ranges::sort(first, last, comp, proj),
   and returns {last, false}.
   2) Same as (1), but uses r as the source 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, last - the range of elements to permute
   r - the range of elements to permute
   comp - comparison function object which returns true if the first argument is
                 less than the second
   proj - projection to apply to the elements

Return value
   1) ranges::next_permutation_result<I>{last, true} if the new permutation is
   lexicographically greater than the old one. ranges::next_permutation_result<I>{last,
   false} if the last permutation was reached and the range was reset to the first
   permutation.
   2) Same as (1) except that the return type is
   ranges::next_permutation_result<ranges::borrowed_iterator_t<R>>.

Exceptions
   Any exceptions thrown from iterator operations or the element swap.

Complexity
   At most \(\scriptsize N/2\)N / 2 swaps, where \(\scriptsize N\)N is
   ranges::distance(first, last) in case (1) or ranges::distance(r) in case (2).
   Averaged over the entire sequence of permutations, typical implementations use about
   3 comparisons and 1.5 swaps per call.

Notes
   Implementations (e.g. MSVC STL) may enable vectorization when the iterator type
   models contiguous_iterator and swapping its value type calls neither non-trivial
   special member function nor ADL-found swap.

Possible implementation
struct next_permutation_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 ranges::next_permutation_result<I>
        operator()(I first, S last, Comp comp = {}, Proj proj = {}) const
    {
        // check that the sequence has at least two elements
        if (first == last)
            return {std::move(first), false};
        I i_last{ranges::next(first, last)};
        I i{i_last};
        if (first == --i)
            return {std::move(i_last), false};
        // main "permutating" loop
        for (;;)
        {
            I i1{i};
            if (std::invoke(comp, std::invoke(proj, *--i), std::invoke(proj, *i1)))
            {
                I j{i_last};
                while (!std::invoke(comp, std::invoke(proj, *i), std::invoke(proj, *--j)))
                {}
                std::iter_swap(i, j);
                std::reverse(i1, i_last);
                return {std::move(i_last), true};
            }
            // permutation "space" is exhausted
            if (i == first)
            {
                std::reverse(first, i_last);
                return {std::move(i_last), false};
            }
        }
    }
    template<ranges::bidirectional_range R, class Comp = ranges::less,
             class Proj = std::identity>
    requires std::sortable<ranges::iterator_t<R>, Comp, Proj>
    constexpr ranges::next_permutation_result<ranges::borrowed_iterator_t<R>>
        operator()(R&& r, Comp comp = {}, Proj proj = {}) const
    {
        return (*this)(ranges::begin(r), ranges::end(r),
                       std::move(comp), std::move(proj));
    } }; inline constexpr next_permutation_fn next_permutation {};

Example
// Run this code
 #include <algorithm>
 #include <array>
 #include <compare>
 #include <functional>
 #include <iostream>
 #include <string>
 struct S
 {
     char c;
     int i;
     auto operator<=>(const S&) const = default;
     friend std::ostream& operator<<(std::ostream& os, const S& s)
     {
         return os << "{'" << s.c << "', " << s.i << "}";
     }
 };
 auto print = [](auto const& v, char term = ' ')
 {
     std::cout << "{ ";
     for (const auto& e : v)
         std::cout << e << ' ';
     std::cout << '}' << term;
 };
 int main()
 {
     std::cout << "Generate all permutations (iterators case):\n";
     std::string s{"abc"};
     do
     {
         print(s);
     }
     while (std::ranges::next_permutation(s.begin(), s.end()).found);
     std::cout << "\n" "Generate all permutations (range case):\n";
     std::array a{'a', 'b', 'c'};
     do
     {
         print(a);
     }
     while (std::ranges::next_permutation(a).found);
     std::cout << "\n" "Generate all permutations using comparator:\n";
     using namespace std::literals;
     std::array z{"█"s, "▄"s, "▁"s};
     do
     {
         print(z);
     }
     while (std::ranges::next_permutation(z, std::greater()).found);
     std::cout << "\n" "Generate all permutations using projection:\n";
     std::array<S, 3> r{S{'A',3}, S{'B',2}, S{'C',1}};
     do
     {
         print(r, '\n');
     }
     while (std::ranges::next_permutation(r, {}, &S::c).found);
 }

Output:
 Generate all permutations (iterators case):
 { a b c } { a c b } { b a c } { b c a } { c a b } { c b a }
 Generate all permutations (range case):
 { a b c } { a c b } { b a c } { b c a } { c a b } { c b a }
 Generate all permutations using comparator:
 { █ ▄ ▁ } { █ ▁ ▄ } { ▄ █ ▁ } { ▄ ▁ █ } { ▁ █ ▄ } { ▁ ▄ █ }
 Generate all permutations using projection:
 { {'A', 3} {'B', 2} {'C', 1} }
 { {'A', 3} {'C', 1} {'B', 2} }
 { {'B', 2} {'A', 3} {'C', 1} }
 { {'B', 2} {'C', 1} {'A', 3} }
 { {'C', 1} {'A', 3} {'B', 2} }
 { {'C', 1} {'B', 2} {'A', 3} }

See also
   ranges::prev_permutation generates the next smaller lexicographic permutation of a
   (C++20) range of elements
                        (niebloid)
   ranges::is_permutation determines if a sequence is a permutation of another
   (C++20) sequence
                        (niebloid)
                        generates the next greater lexicographic permutation of a
   next_permutation range of elements
                        (function template)
                        generates the next smaller lexicographic permutation of a
   prev_permutation range of elements
                        (function template)
   is_permutation determines if a sequence is a permutation of another
   (C++11) sequence
                        (function template)