[alg.permutation.generators]

# 26 Algorithms library [[algorithms]](./#algorithms)

## 26.8 Sorting and related operations [[alg.sorting]](alg.sorting#alg.permutation.generators)

### 26.8.13 Permutation generators [alg.permutation.generators]

[ð](#lib:next_permutation)

`template<class BidirectionalIterator>
  constexpr bool next_permutation(BidirectionalIterator first,
                                  BidirectionalIterator last);

template<class BidirectionalIterator, class Compare>
  constexpr bool next_permutation(BidirectionalIterator first,
                                  BidirectionalIterator last, Compare comp);

template<[bidirectional_iterator](iterator.concept.bidir#concept:bidirectional_iterator "24.3.4.12 Concept bidirectional_­iterator [iterator.concept.bidir]") I, [sentinel_for](iterator.concept.sentinel#concept:sentinel_for "24.3.4.7 Concept sentinel_­for [iterator.concept.sentinel]")<I> S, class Comp = ranges::less,
         class Proj = identity>
  requires [sortable](alg.req.sortable#concept:sortable "24.3.7.8 Concept sortable [alg.req.sortable]")<I, Comp, Proj>
  constexpr ranges::next_permutation_result<I>
    ranges::next_permutation(I first, S last, Comp comp = {}, Proj proj = {});
template<[bidirectional_range](range.refinements#concept:bidirectional_range "25.4.6 Other range refinements [range.refinements]") R, class Comp = ranges::less,
         class Proj = identity>
  requires [sortable](alg.req.sortable#concept:sortable "24.3.7.8 Concept sortable [alg.req.sortable]")<iterator_t<R>, Comp, Proj>
  constexpr ranges::next_permutation_result<borrowed_iterator_t<R>>
    ranges::next_permutation(R&& r, Comp comp = {}, Proj proj = {});
`

[1](#1)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L11918)

Let comp be less{} and proj be identity{} for overloads with no parameters by those names[.](#1.sentence-1)

[2](#2)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L11923)

*Preconditions*: For the overloads in namespace std,BidirectionalIterator meets
the [*Cpp17ValueSwappable*](swappable.requirements#:Cpp17ValueSwappable "16.4.4.3 Swappable requirements [swappable.requirements]") requirements ([[swappable.requirements]](swappable.requirements "16.4.4.3 Swappable requirements"))[.](#2.sentence-1)

[3](#3)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L11929)

*Effects*: Takes a sequence defined by the range [first, last)
and transforms it into the next permutation[.](#3.sentence-1)

The next permutation is found by assuming that the set of all permutations
is lexicographically sorted with respect to comp and proj[.](#3.sentence-2)

If no such permutation exists,
transforms the sequence into the first permutation;
that is, the ascendingly-sorted one[.](#3.sentence-3)

[4](#4)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L11939)

*Returns*: Let B be true if a next permutation was found and
otherwise false[.](#4.sentence-1)

Returns:

- [(4.1)](#4.1)

  B for the overloads in namespace std[.](#4.1.sentence-1)

- [(4.2)](#4.2)

  { last, B } for the overloads in namespace ranges[.](#4.2.sentence-1)

[5](#5)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L11949)

*Complexity*: At most (last - first) / 2 swaps[.](#5.sentence-1)

[ð](#lib:prev_permutation)

`template<class BidirectionalIterator>
  constexpr bool prev_permutation(BidirectionalIterator first,
                                  BidirectionalIterator last);

template<class BidirectionalIterator, class Compare>
  constexpr bool prev_permutation(BidirectionalIterator first,
                                  BidirectionalIterator last, Compare comp);

template<[bidirectional_iterator](iterator.concept.bidir#concept:bidirectional_iterator "24.3.4.12 Concept bidirectional_­iterator [iterator.concept.bidir]") I, [sentinel_for](iterator.concept.sentinel#concept:sentinel_for "24.3.4.7 Concept sentinel_­for [iterator.concept.sentinel]")<I> S, class Comp = ranges::less,
         class Proj = identity>
  requires [sortable](alg.req.sortable#concept:sortable "24.3.7.8 Concept sortable [alg.req.sortable]")<I, Comp, Proj>
  constexpr ranges::prev_permutation_result<I>
    ranges::prev_permutation(I first, S last, Comp comp = {}, Proj proj = {});
template<[bidirectional_range](range.refinements#concept:bidirectional_range "25.4.6 Other range refinements [range.refinements]") R, class Comp = ranges::less,
         class Proj = identity>
  requires [sortable](alg.req.sortable#concept:sortable "24.3.7.8 Concept sortable [alg.req.sortable]")<iterator_t<R>, Comp, Proj>
  constexpr ranges::prev_permutation_result<borrowed_iterator_t<R>>
    ranges::prev_permutation(R&& r, Comp comp = {}, Proj proj = {});
`

[6](#6)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L11977)

Let comp be less{} and proj be identity{} for overloads with no parameters by those names[.](#6.sentence-1)

[7](#7)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L11982)

*Preconditions*: For the overloads in namespace std,BidirectionalIterator meets
the [*Cpp17ValueSwappable*](swappable.requirements#:Cpp17ValueSwappable "16.4.4.3 Swappable requirements [swappable.requirements]") requirements ([[swappable.requirements]](swappable.requirements "16.4.4.3 Swappable requirements"))[.](#7.sentence-1)

[8](#8)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L11988)

*Effects*: Takes a sequence defined by the range [first, last)
and transforms it into the previous permutation[.](#8.sentence-1)

The previous permutation is found by assuming that the set of all permutations
is lexicographically sorted with respect to comp and proj[.](#8.sentence-2)

If no such permutation exists,
transforms the sequence into the last permutation;
that is, the descendingly-sorted one[.](#8.sentence-3)

[9](#9)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L11998)

*Returns*: Let B be true if a previous permutation was found and
otherwise false[.](#9.sentence-1)

Returns:

- [(9.1)](#9.1)

  B for the overloads in namespace std[.](#9.1.sentence-1)

- [(9.2)](#9.2)

  { last, B } for the overloads in namespace ranges[.](#9.2.sentence-1)

[10](#10)

[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L12008)

*Complexity*: At most (last - first) / 2 swaps[.](#10.sentence-1)
