std::ranges::is_permutation() algorithm

od C++20

Simplified

// (1)
constexpr bool
    is_partitioned( I first, S last, Pred pred, Proj proj = {} );

// (2)
constexpr bool
    is_partitioned( R&& r, Pred pred, Proj proj = {} );

The type of arguments are generic and have the following constraints:

• I - std::input_iterator
• S - std::sentinel_for<I>
• R - std::ranges::input_range
• Pred:
  • (1) - std::indirect_unary_predicate<std::projected<I, Proj>>
  • (2) - std::indirect_unary_predicate<std::projected<ranges::iterator_t<R>, Proj>>
• Proj - (none)

The Proj template argument has a default type std::identity for all overloads.

Detailed

// (1)
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 is_permutation( I1 first1, S1 last1, I2 first2, S2 last2,
                               Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {} );

// (2)
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 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.

Parameters

first1 last1	The first range of elements to process.
r	The first range of elements to process.
first2 last2	The second range of elements to process.
r	The second range of elements to process.
pred	The predicate to apply to the projected elemenets.
proj	The projection to apply to the elements.

Return value

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

Complexity

Given N is ranges::distance(first1, last1).

At most O(N2) applications of the predicate and each projection, or exactly N if the sequences are already equal,

However if ranges::distance(first1, last1) != ranges::distance(first2, last2), no applications of the predicate and projections are made.

Exceptions

(none)

Possible implementation

is_permutation(1) and is_permutation(2)

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 {};

Notes

The permutation relation is an equivalence relation.

The ranges::is_permutation can be used in testing, namely to check the correctness of rearranging algorithms (e.g. sorting, shuffling, partitioning).

If x is an original range and y is a permuted range then ranges::is_permutation(x, y) == true means that y consist of "the same" elements, maybe staying at other positions.

Examples

Main.cpp

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

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

Possible 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