std::ranges::prev_permutation, std::ranges::prev_permutation_result

Defined in header `<algorithm>`
Call signature
`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 prev_permutation_result<I> prev_permutation( I first, S last, Comp comp = {}, Proj proj = {} );`	(1)	(since C++20)
`template< ranges::bidirectional_range R, class Comp = ranges::less, class Proj = std::identity > requires std::sortable<ranges::iterator_t<R>, Comp, Proj> constexpr prev_permutation_result<ranges::borrowed_iterator_t<R>> prev_permutation( R&& r, Comp comp = {}, Proj proj = {} );`	(2)	(since C++20)
Helper type
`template< class I > using prev_permutation_result = ranges::in_found_result<I>;`	(3)	(since C++20)

1) Transforms the range [first, last) into the previous 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 "previous" permutation exists. Otherwise,
{last, false}, and transforms the range into the (lexicographically) last permutation, as if by

ranges::sort(first, last, comp, proj);
ranges::reverse(first, last);

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::prev_permutation_result<I>{last, true} if the new permutation is lexicographically less than the old one. ranges::prev_permutation_result<I>{last, false} if the first permutation was reached and the range was reset to the last permutation.

2) Same as (1) except that the return type is ranges::prev_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 prev_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::prev_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};
        auto i{first};
        ++i;
        if (i == last)
            return {std::move(i), false};
        auto i_last{ranges::next(first, last)};
        i = i_last;
        --i;
        // main "permutating" loop
        for (;;)
        {
            auto i1{i};
            --i;
            if (std::invoke(comp, std::invoke(proj, *i1), std::invoke(proj, *i)))
            {
                auto j{i_last};
                while (!std::invoke(comp, std::invoke(proj, *--j), std::invoke(proj, *i)))
                    ;
                ranges::iter_swap(i, j);
                ranges::reverse(i1, last);
                return {std::move(i_last), true};
            }
            // permutation "space" is exhausted
            if (i == first)
            {
                ranges::reverse(first, 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::prev_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 prev_permutation_fn prev_permutation {};

Example

#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{"cba"};
    do print(s);
    while (std::ranges::prev_permutation(s.begin(), s.end()).found);
 
    std::cout << "\nGenerate all permutations (range case):\n";
    std::array a{'c', 'b', 'a'};
    do print(a);
    while (std::ranges::prev_permutation(a).found);
 
    std::cout << "\nGenerate all permutations using comparator:\n";
    using namespace std::literals;
    std::array z{"▁"s, "▄"s, "█"s};
    do print(z);
    while (std::ranges::prev_permutation(z, std::greater()).found);
 
    std::cout << "\nGenerate all permutations using projection:\n";
    std::array<S, 3> r{S{'C',1}, S{'B',2}, S{'A',3}};
    do print(r, '\n');
    while (std::ranges::prev_permutation(r, {}, &S::c).found);
}

Output:

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

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

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