std::next_permutation() algorithm

since C++20

// (1)
template< class BidirIt >
constexpr bool next_permutation( BidirIt first, BidirIt last );

// (2)
template< class BidirIt, class Compare >
constexpr bool next_permutation( BidirIt first, BidirIt last, Compare comp );

until C++20

// (1)
template< class BidirIt >
bool next_permutation( BidirIt first, BidirIt last );

// (2)
template< class BidirIt, class Compare >
bool next_permutation( BidirIt first, BidirIt last, Compare comp );

Permutes the range [first; last) into the next permutation, where the set of all permutations is ordered lexicographically with respect to operator< or comp.

Returns true if such a "next permutation" exists; otherwise transforms the range into the lexicographically first permutation (as if by std::sort(first, last, comp)) and returns false.

Parameters

first last

The range of elements to permute.

comp

Comparison function object (i.e. an object that satisfies the requirements of Compare) which returns true if the first argument is less than the second. The signature of the comparison function should be equivalent to the following: bool cmp(const Type1 &a, const Type2 &b); The signature does not need to have const&, but must not modify arguments. Must accept all values of type (possibly const) Type and Type2, regardless of value category (so Type1& is not allowed, nor is Type1 unless for Type1 a move is equivalent to a copy (since C++11)) The types Type1 and Type2 must be such that an object of type BidirIt can be implicitly converted to both of them.

Type requirements

ForwardIt

ValueSwappable LegacyBidirectionalIterator

Return value

true if the new permutation is lexicographically greater than the old.
false if the last permutation was reached and the range was reset to the first permutation.

Complexity

Given N as std::distance(first, last)

At most N / 2 swaps. Averaged over the entire sequence of permutations, typical implementations use about 3 comparisons and 1.5 swaps per call.

Exceptions

Any exceptions thrown from iterator operations or the element swap.

Possible implementation

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

next_permutation (1)

template<class BidirIt>
bool next_permutation(BidirIt first, BidirIt last)
{
    auto r_first = std::make_reverse_iterator(last);
    auto r_last = std::make_reverse_iterator(first);
    auto left = std::is_sorted_until(r_first, r_last);

    if (left != r_last)
    {
        auto right = std::upper_bound(r_first, left, *left);
        std::iter_swap(left, right);
    }

    std::reverse(left.base(), last);
    return left != r_last;
}

Examples

Main.cpp

#include <algorithm>
#include <iostream>
#include <string>

int main()
{
    std::string s = "aba";

    do std::cout << s << '\n';
    while (std::next_permutation(s.begin(), s.end()));

    std::cout << s << '\n';
}

Output

aba
baa
aab