Difference between revisions of "cpp/algorithm/ranges/is permutation"

Revision as of 09:13, 10 July 2021

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>> Pred = ranges::equal_to > constexpr bool is_permutation( I1 first1, S1 last1, I2 first2, S2 last2, Pred pred = {}, Proj1 proj1 = {}, Proj2 proj2 = {} );	(1)	(since C++20)
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 = {} );	(2)	(since C++20)

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.

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, 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 std::is_permutation(x, y) == true means that y consist of "the same" elements, maybe staying at other positions.

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 (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';
}

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

@@ Line 46: / Line 46: @@
 ===Complexity===
-At most {{mathjax-or|\(\scriptsize \mathcal{O}(N^2)\)|O(N<sup>2</sup>)}} applications of the predicate and each projection, or exactly {{mathjax-or|\(\scriptsize N\)|N}} if the sequences are already equal, where {{mathjax-or|\(\scriptsize N\)|N}} is {{c|last1 - first1}}.
+At most {{mathjax-or|\(\scriptsize \mathcal{O}(N^2)\)|O(N<sup>2</sup>)}} applications of the predicate and each projection, or exactly {{mathjax-or|\(\scriptsize N\)|N}} if the sequences are already equal, where {{mathjax-or|\(\scriptsize N\)|N}} is {{c|ranges::distance(first1, last1)}}.
-However if {{c|1=last1 - first1 != last2 - first2}}, no applications of the predicate and projections are made.
+However if {{c|1=ranges::distance(first1, last1) != ranges::distance(first2, last2)}}, no applications of the predicate and projections are made.
 ===Notes===

Compiler support
Freestanding and hosted
Language
Standard library
Standard library headers
Named requirements
Feature test macros (C++20)
Language support library
Concepts library (C++20)
Metaprogramming library (C++11)
Diagnostics library
General utilities library
Strings library
Containers library
Iterators library
Ranges library (C++20)
Algorithms library
Numerics library
Localizations library
Input/output library
Filesystem library (C++17)
Regular expressions library (C++11)
Concurrency support library (C++11)
Execution support library (C++26)
Technical specifications
Symbols index
External libraries

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

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Difference between revisions of "cpp/algorithm/ranges/is permutation"

Revision as of 09:13, 10 July 2021

Contents

Parameters

Return value

Complexity

Notes

Possible implementation

Example

See also

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