NAME¶

std::ranges::next_permutation,std::ranges::next_permutation_result - std::ranges::next_permutation,std::ranges::next_permutation_result

Synopsis¶

Defined in header <algorithm>
Call signature
template< std::bidirectional_iterator I, std::sentinel_for<I> S,

class Comp = ranges::less, class Proj = std::identity > (since
requires std::sortable<I, Comp, Proj> (1) C++20)
constexpr next_permutation_result<I>

next_permutation( I first, S last, Comp comp = {}, Proj proj = {} );
template< ranges::bidirectional_range R, class Comp = ranges::less,

class Proj = std::identity > (since
requires std::sortable<ranges::iterator_t<R>, Comp, Proj> (2) C++20)
constexpr next_permutation_result<ranges::borrowed_iterator_t<R>>

next_permutation( R&& r, Comp comp = {}, Proj proj = {} );
Helper type
template< class I > (3) (since
using next_permutation_result = ranges::in_found_result<I>; C++20)

1) Transforms the range [first, last) into the next permutation, where the set of
all permutations is ordered lexicographically with respect to binary comparison
function object comp and projection function object proj. Returns {last, true} if
such a "next permutation" exists; otherwise transforms the range into the
lexicographically first permutation as if by ranges::sort(first, last, comp, proj),
and returns {last, false}.
2) Same as (1), but uses r as the source range, as if using ranges::begin(r) as
first, and ranges::end(r) as last.

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¶

first, last - the range of elements to permute
r - the range of elements to permute
comp - comparison function object which returns true if the first argument is
less than the second
proj - projection to apply to the elements

Return value¶

1) ranges::next_permutation_result<I>{last, true} if the new permutation is
lexicographically greater than the old one. ranges::next_permutation_result<I>{last,
false} if the last permutation was reached and the range was reset to the first
permutation.
2) Same as (1) except that the return type is
ranges::next_permutation_result<ranges::borrowed_iterator_t<R>>.

Exceptions¶

Any exceptions thrown from iterator operations or the element swap.

Complexity¶

At most \(\scriptsize N/2\)N / 2 swaps, where \(\scriptsize N\)N is
ranges::distance(first, last) in case (1) or ranges::distance(r) in case (2).
Averaged over the entire sequence of permutations, typical implementations use about
3 comparisons and 1.5 swaps per call.

Notes¶

Implementations (e.g. MSVC STL) may enable vectorization when the iterator type
models contiguous_iterator and swapping its value type calls neither non-trivial
special member function nor ADL-found swap.

Possible implementation¶

struct next_permutation_fn {
template<std::bidirectional_iterator I, std::sentinel_for<I> S,
class Comp = ranges::less, class Proj = std::identity>
requires std::sortable<I, Comp, Proj>
constexpr ranges::next_permutation_result<I>
operator()(I first, S last, Comp comp = {}, Proj proj = {}) const
{
// check that the sequence has at least two elements
if (first == last)
return {std::move(first), false};
I i_last{ranges::next(first, last)};
I i{i_last};
if (first == --i)
return {std::move(i_last), false};
// main "permutating" loop
for (;;)
{
I i1{i};
if (std::invoke(comp, std::invoke(proj, *--i), std::invoke(proj, *i1)))
{
I j{i_last};
while (!std::invoke(comp, std::invoke(proj, *i), std::invoke(proj, *--j)))
{}
std::iter_swap(i, j);
std::reverse(i1, i_last);
return {std::move(i_last), true};
}
// permutation "space" is exhausted
if (i == first)
{
std::reverse(first, i_last);
return {std::move(i_last), false};
}
}
}

template<ranges::bidirectional_range R, class Comp = ranges::less,
class Proj = std::identity>
requires std::sortable<ranges::iterator_t<R>, Comp, Proj>
constexpr ranges::next_permutation_result<ranges::borrowed_iterator_t<R>>
operator()(R&& r, Comp comp = {}, Proj proj = {}) const
{
return (*this)(ranges::begin(r), ranges::end(r),
std::move(comp), std::move(proj));
} };

inline constexpr next_permutation_fn next_permutation {};

Example¶

// Run this code

#include <algorithm>
#include <array>
#include <compare>
#include <functional>
#include <iostream>
#include <string>

struct S
{
char c;
int i;
auto operator<=>(const S&) const = default;
friend std::ostream& operator<<(std::ostream& os, const S& s)
{
return os << "{'" << s.c << "', " << s.i << "}";
}
};

auto print = [](auto const& v, char term = ' ')
{
std::cout << "{ ";
for (const auto& e : v)
std::cout << e << ' ';
std::cout << '}' << term;
};

int main()
{
std::cout << "Generate all permutations (iterators case):\n";
std::string s{"abc"};
do
{
print(s);
}
while (std::ranges::next_permutation(s.begin(), s.end()).found);

std::cout << "\n" "Generate all permutations (range case):\n";
std::array a{'a', 'b', 'c'};
do
{
print(a);
}
while (std::ranges::next_permutation(a).found);

std::cout << "\n" "Generate all permutations using comparator:\n";
using namespace std::literals;
std::array z{"█"s, "▄"s, "▁"s};
do
{
print(z);
}
while (std::ranges::next_permutation(z, std::greater()).found);

std::cout << "\n" "Generate all permutations using projection:\n";
std::array<S, 3> r{S{'A',3}, S{'B',2}, S{'C',1}};
do
{
print(r, '\n');
}
while (std::ranges::next_permutation(r, {}, &S::c).found);
}

Output:¶

Generate all permutations (iterators case):
{ a b c } { a c b } { b a c } { b c a } { c a b } { c b a }
Generate all permutations (range case):
{ a b c } { a c b } { b a c } { b c a } { c a b } { c b a }
Generate all permutations using comparator:
{ █ ▄ ▁ } { █ ▁ ▄ } { ▄ █ ▁ } { ▄ ▁ █ } { ▁ █ ▄ } { ▁ ▄ █ }
Generate all permutations using projection:
{ {'A', 3} {'B', 2} {'C', 1} }
{ {'A', 3} {'C', 1} {'B', 2} }
{ {'B', 2} {'A', 3} {'C', 1} }
{ {'B', 2} {'C', 1} {'A', 3} }
{ {'C', 1} {'A', 3} {'B', 2} }
{ {'C', 1} {'B', 2} {'A', 3} }

See also¶

ranges::prev_permutation generates the next smaller lexicographic permutation of a
(C++20) range of elements
(niebloid)
ranges::is_permutation determines if a sequence is a permutation of another
(C++20) sequence
(niebloid)
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)
is_permutation determines if a sequence is a permutation of another
(C++11) sequence
(function template)