std::ranges::is_permutation(3)

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)