std::prev_permutation

Defined in header `<algorithm>`
	(1)
`template< class BidirIt > bool prev_permutation( BidirIt first, BidirIt last );`		(until C++20)
`template< class BidirIt > constexpr bool prev_permutation( BidirIt first, BidirIt last );`		(since C++20)
	(2)
`template< class BidirIt, class Compare > bool prev_permutation( BidirIt first, BidirIt last, Compare comp );`		(until C++20)
`template< class BidirIt, class Compare > constexpr bool prev_permutation( BidirIt first, BidirIt last, Compare comp );`		(since C++20)

Transforms the range [first, last) into the previous permutation from the set of all permutations that are lexicographically ordered with respect to operator< or comp. Returns true if such permutation exists, otherwise transforms the range into the last permutation (as if by std::sort(first, last); std::reverse(first, last);) 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);` While the signature does not need to have `const&`, the function must not modify the objects passed to it and must be able to accept all values of type (possibly const) `Type1` and `Type2` regardless of value category (thus, `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 dereferenced and then implicitly converted to both of them.
Type requirements
-`BidirIt` must meet the requirements of ValueSwappable and LegacyBidirectionalIterator.

Return value

true if the new permutation precedes the old in lexicographical order. false if the first permutation was reached and the range was reset to the last permutation.

Exceptions

Any exceptions thrown from iterator operations or the element swap.

Complexity

At most (last - first) / 2 swaps. 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 satisfies LegacyContiguousIterator and swapping its value type calls neither non-trivial special member function nor ADL-found swap.

Possible implementation

template<class BidirIt>
bool prev_permutation(BidirIt first, BidirIt last)
{
    if (first == last)
        return false;
    BidirIt i = last;
    if (first == --i)
        return false;
 
    while (1)
    {
        BidirIt i1, i2;
 
        i1 = i;
        if (*i1 < *--i)
        {
            i2 = last;
            while (!(*--i2 < *i))
                ;
            std::iter_swap(i, i2);
            std::reverse(i1, last);
            return true;
        }
 
        if (i == first)
        {
            std::reverse(first, last);
            return false;
        }
    }
}

Example

The following code prints all six permutations of the string "cab" in reverse order.

#include <algorithm>
#include <iostream>
#include <string>
 
int main()
{
    std::string s = "cab";
 
    do std::cout << s << ' ';
    while (std::prev_permutation(s.begin(), s.end()));
 
    std::cout << s << '\n';
}

Output:

cab bca bac acb abc cba

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

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