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[alg.is.permutation]
# 26 Algorithms library [[algorithms]](./#algorithms)
## 26.6 Non-modifying sequence operations [[alg.nonmodifying]](alg.nonmodifying#alg.is.permutation)
### 26.6.14 Is permutation [alg.is.permutation]
[🔗](#lib:is_permutation)
`template<class ForwardIterator1, class ForwardIterator2>
constexpr bool is_permutation(ForwardIterator1 first1, ForwardIterator1 last1,
ForwardIterator2 first2);
template<class ForwardIterator1, class ForwardIterator2,
class BinaryPredicate>
constexpr bool is_permutation(ForwardIterator1 first1, ForwardIterator1 last1,
ForwardIterator2 first2, BinaryPredicate pred);
template<class ForwardIterator1, class ForwardIterator2>
constexpr bool is_permutation(ForwardIterator1 first1, ForwardIterator1 last1,
ForwardIterator2 first2, ForwardIterator2 last2);
template<class ForwardIterator1, class ForwardIterator2,
class BinaryPredicate>
constexpr bool is_permutation(ForwardIterator1 first1, ForwardIterator1 last1,
ForwardIterator2 first2, ForwardIterator2 last2,
BinaryPredicate pred);
`
[1](#1)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L5722)
Let last2 be first2 + (last1 - first1) for the overloads with no parameter named last2,
and let pred be equal_to{} for the overloads with no parameter pred[.](#1.sentence-1)
[2](#2)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L5728)
*Mandates*: ForwardIterator1 and ForwardIterator2 have the same value type[.](#2.sentence-1)
[3](#3)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L5732)
*Preconditions*: The comparison function is an equivalence relation[.](#3.sentence-1)
[4](#4)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L5736)
*Returns*: If last1 - first1 != last2 - first2, return false[.](#4.sentence-1)
Otherwise return true if there exists a permutation of the elements
in the range [first2, last2),
beginning with ForwardIterator2 begin,
such that equal(first1, last1, begin, pred) returns true;
otherwise, returns false[.](#4.sentence-2)
[5](#5)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L5746)
*Complexity*: No applications of the corresponding predicate
if ForwardIterator1 and ForwardIterator2 meet the requirements of random access iterators andlast1 - first1 != last2 - first2[.](#5.sentence-1)
Otherwise, exactly last1 - first1 applications
of the corresponding predicate
if equal(first1, last1, first2, last2, pred) would return true;
otherwise, at worst O(N2), where N has the value last1 - first1[.](#5.sentence-2)
[🔗](#lib:is_permutation_)
`template<[forward_iterator](iterator.concept.forward#concept:forward_iterator "24.3.4.11 Concept forward_­iterator [iterator.concept.forward]") I1, [sentinel_for](iterator.concept.sentinel#concept:sentinel_for "24.3.4.7 Concept sentinel_­for [iterator.concept.sentinel]")<I1> S1, [forward_iterator](iterator.concept.forward#concept:forward_iterator "24.3.4.11 Concept forward_­iterator [iterator.concept.forward]") I2,
[sentinel_for](iterator.concept.sentinel#concept:sentinel_for "24.3.4.7 Concept sentinel_­for [iterator.concept.sentinel]")<I2> S2, class Proj1 = identity, class Proj2 = identity,
[indirect_equivalence_relation](indirectcallable.indirectinvocable#concept:indirect_equivalence_relation "24.3.6.3 Indirect callables [indirectcallable.indirectinvocable]")<projected<I1, Proj1>,
projected<I2, Proj2>> Pred = ranges::equal_to>
constexpr bool ranges::is_permutation(I1 first1, S1 last1, I2 first2, S2 last2,
Pred pred = {},
Proj1 proj1 = {}, Proj2 proj2 = {});
template<[forward_range](range.refinements#concept:forward_range "25.4.6 Other range refinements [range.refinements]") R1, [forward_range](range.refinements#concept:forward_range "25.4.6 Other range refinements [range.refinements]") R2,
class Proj1 = identity, class Proj2 = identity,
[indirect_equivalence_relation](indirectcallable.indirectinvocable#concept:indirect_equivalence_relation "24.3.6.3 Indirect callables [indirectcallable.indirectinvocable]")<projected<iterator_t<R1>, Proj1>,
projected<iterator_t<R2>, Proj2>> Pred = ranges::equal_to>
constexpr bool ranges::is_permutation(R1&& r1, R2&& r2, Pred pred = {},
Proj1 proj1 = {}, Proj2 proj2 = {});
`
[6](#6)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L5776)
*Returns*: If last1 - first1 != last2 - first2, return false[.](#6.sentence-1)
Otherwise return true if there exists a permutation of the elements
in the range [first2, last2), bounded by [pfirst, plast),
such thatranges​::​equal(first1, last1, pfirst, plast, pred, proj1, proj2) returns true;
otherwise, returns false[.](#6.sentence-2)
[7](#7)
[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/algorithms.tex#L5786)
*Complexity*: No applications of the corresponding predicate and projections if
- [(7.1)](#7.1)
for the first overload,
* [(7.1.1)](#7.1.1)
S1 and I1 model [sized_sentinel_for](iterator.concept.sizedsentinel#concept:sized_sentinel_for "24.3.4.8 Concept sized_­sentinel_­for [iterator.concept.sizedsentinel]")<S1, I1>,
* [(7.1.2)](#7.1.2)
S2 and I2 model [sized_sentinel_for](iterator.concept.sizedsentinel#concept:sized_sentinel_for "24.3.4.8 Concept sized_­sentinel_­for [iterator.concept.sizedsentinel]")<S2, I2>, and
* [(7.1.3)](#7.1.3)
last1 - first1 != last2 - first2;
- [(7.2)](#7.2)
for the second overload,R1 and R2 each model [sized_range](range.sized#concept:sized_range "25.4.4 Sized ranges [range.sized]"), andranges​::​distance(r1) != ranges​::​distance(r2)[.](#7.sentence-1)
Otherwise, exactly last1 - first1 applications
of the corresponding predicate and projections
if ranges​::​equal(​first1, last1, first2, last2, pred, proj1, proj2) would return true;
otherwise, at worst O(N2), where N has the value last1 - first1[.](#7.sentence-2)