std::ranges::next_permutation, std::ranges::next_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 next_permutation_result<I> next_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 next_permutation_result<ranges::borrowed_iterator_t<R>> next_permutation( R&& r, Comp comp = {}, Proj proj = {} );	(2)	(since C++20)
Helper type
template<class I> using next_permutation_result = ranges::in_found_result<I>;	(3)	(since 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 may not be specified when calling any of them.
None of them is visible to argument-dependent lookup.
When one of them is found by normal unqualified lookup for the name to the left of the function-call operator, it inhibits argument-dependent lookup.

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} }

Compiler support
Freestanding and hosted
Language
Standard library headers
Named requirements
Feature test macros (C++20)
Language support library
Concepts library (C++20)
Metaprogramming library (C++11)
Diagnostics library
General utilities library
Strings library
Containers library
Iterators library
Ranges library (C++20)
Algorithms library
Numerics library
Localizations library
Input/output library
Filesystem library (C++17)
Regular expressions library (C++11)
Concurrency support library (C++11)
Technical specifications
Symbols index
External libraries

ranges::prev_permutation (C++20)	generates the next smaller 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)