NAME¶

std::ranges::is_permutation - std::ranges::is_permutation

Synopsis¶

Defined in header <algorithm>
Call signature
template< std::forward_iterator I1, std::sentinel_for<I1> S1,

std::forward_iterator I2, std::sentinel_for<I2> S2,
class Proj1 = std::identity, class Proj2 = std::identity,
std::indirect_equivalence_relation<std::projected<I1, Proj1>,
std::projected<I2, Proj2>> (since
Pred = ranges::equal_to (1) C++20)
>
constexpr bool
is_permutation( I1 first1, S1 last1, I2 first2, S2 last2, Pred pred
= {},

Proj1 proj1 = {}, Proj2 proj2 = {} );
template< ranges::forward_range R1, ranges::forward_range R2,

class Proj1 = std::identity, class Proj2 = std::identity,
std::indirect_equivalence_relation<
std::projected<ranges::iterator_t<R1>, Proj1>, (since
std::projected<ranges::iterator_t<R2>, Proj2>> (2) C++20)
Pred = ranges::equal_to >
constexpr bool
is_permutation( R1&& r1, R2&& r2, Pred pred = {},

Proj1 proj1 = {}, Proj2 proj2 = {} );

1) Returns true if there exists a permutation of the elements in range
[first1, last1) that makes the range equal to [first2, last2) (after application of
corresponding projections Proj1, Proj2, and using the binary predicate Pred as a
comparator). Otherwise returns false.
2) Same as (1), but uses r1 as the first source range and r2 as the second source
range, as if using ranges::begin(r1) as first1, ranges::end(r1) as last1,
ranges::begin(r2) as first2, and ranges::end(r2) as last2.

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¶

first1, last1 - the first range of the elements
first2, last2 - the second range of the elements
r1 - the first range of the elements
r2 - the second range of the elements
pred - predicate to apply to the projected elements
proj1 - projection to apply to the elements in the first range
proj2 - projection to apply to the elements in the second range

Return value¶

true if the range [first1, last1) is a permutation of the range [first2, last2).

Complexity¶

At most \(\scriptsize \mathcal{O}(N^2)\)O(N^2) applications of the predicate and
each projection, or exactly \(\scriptsize N\)N if the sequences are already equal,
where \(\scriptsize N\)N is ranges::distance(first1, last1). However if
ranges::distance(first1, last1) != ranges::distance(first2, last2), no applications
of the predicate and projections are made.

Notes¶

The permutation relation is an equivalence relation.

The ranges::is_permutation can be used in testing, e.g. to check the correctness of
rearranging algorithms such as sorting, shuffling, partitioning. If p is an original
sequence and q is a "mutated" sequence, then ranges::is_permutation(p, q) == true
means that q consist of "the same" elements (maybe permuted) as p.

Possible implementation¶

struct is_permutation_fn {
template<std::forward_iterator I1, std::sentinel_for<I1> S1,
std::forward_iterator I2, std::sentinel_for<I2> S2,
class Proj1 = std::identity, class Proj2 = std::identity,
std::indirect_equivalence_relation<std::projected<I1, Proj1>,
std::projected<I2, Proj2>>
Pred = ranges::equal_to>
constexpr bool operator()(I1 first1, S1 last1, I2 first2, S2 last2,
Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {}) const
{
// skip common prefix
auto ret = std::ranges::mismatch(first1, last1, first2, last2,
std::ref(pred), std::ref(proj1), std::ref(proj2));
first1 = ret.in1, first2 = ret.in2;

// iterate over the rest, counting how many times each element
// from [first1, last1) appears in [first2, last2)
for (auto i {first1}; i != last1; ++i)
{
const auto i_proj {std::invoke(proj1, *i)};
auto i_cmp = [&]<typename T>(T&& t)
{
return std::invoke(pred, i_proj, std::forward<T>(t));
};

if (i != ranges::find_if(first1, i, i_cmp, proj1))
continue; // this *i has been checked

if (const auto m {ranges::count_if(first2, last2, i_cmp, proj2)};
m == 0 or m != ranges::count_if(i, last1, i_cmp, proj1))
return false;
}
return true;
}

template<ranges::forward_range R1, ranges::forward_range R2,
class Proj1 = std::identity, class Proj2 = std::identity,
std::indirect_equivalence_relation<
std::projected<ranges::iterator_t<R1>, Proj1>,
std::projected<ranges::iterator_t<R2>, Proj2>>
Pred = ranges::equal_to>
constexpr bool operator()(R1&& r1, R2&& r2, Pred pred = {},
Proj1 proj1 = {}, Proj2 proj2 = {}) const
{
return (*this)(ranges::begin(r1), ranges::end(r1),
ranges::begin(r2), ranges::end(r2),
std::move(pred), std::move(proj1), std::move(proj2));
} };

inline constexpr is_permutation_fn is_permutation {};

Example¶

// Run this code

#include <algorithm>
#include <array>
#include <cmath>
#include <iostream>
#include <ranges>

auto& operator<<(auto& os, std::ranges::forward_range auto const& v)
{
os << "{ ";
for (const auto& e : v)
os << e << ' ';
return os << "}";
}

int main()
{
static constexpr auto r1 = {1, 2, 3, 4, 5};
static constexpr auto r2 = {3, 5, 4, 1, 2};
static constexpr auto r3 = {3, 5, 4, 1, 1};

static_assert(
std::ranges::is_permutation(r1, r1) &&
std::ranges::is_permutation(r1, r2) &&
std::ranges::is_permutation(r2, r1) &&
std::ranges::is_permutation(r1.begin(), r1.end(), r2.begin(), r2.end()));

std::cout
<< std::boolalpha
<< "is_permutation(" << r1 << ", " << r2 << "): "
<< std::ranges::is_permutation(r1, r2) << '\n'
<< "is_permutation(" << r1 << ", " << r3 << "): "
<< std::ranges::is_permutation(r1, r3) << '\n'

<< "is_permutation with custom predicate and projections: "
<< std::ranges::is_permutation(
std::array {-14, -11, -13, -15, -12}, // 1st range
std::array {'F', 'E', 'C', 'B', 'D'}, // 2nd range
[](int x, int y) { return abs(x) == abs(y); }, // predicate
[](int x) { return x + 10; }, // projection for 1st range
[](char y) { return int(y - 'A'); }) // projection for 2nd range
<< '\n';
}

Output:¶

is_permutation({ 1 2 3 4 5 }, { 3 5 4 1 2 }): true
is_permutation({ 1 2 3 4 5 }, { 3 5 4 1 1 }): false
is_permutation with custom predicate and projections: true

See also¶

ranges::next_permutation generates the next greater lexicographic permutation of a
(C++20) range of elements
(niebloid)
ranges::prev_permutation generates the next smaller lexicographic permutation of a
(C++20) range of elements
(niebloid)
is_permutation determines if a sequence is a permutation of another
(C++11) sequence
(function template)
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)
equivalence_relation specifies that a relation imposes an equivalence relation
(C++20) (concept)