std::prev_permutation(3)

💖 NAME 💖

bestie, welcome to the std::prev_permutation(3) page from the C++ Standard Libary manual — yes, that’s the header’s spelling and we’re not fixing it, it’s part of the vibe. The name is std::prev_permutation — literally std::prev_permutation. Self-titled main character energy, periodt. 💅

✨ Synopsis ✨

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

Okay so this algorithm transforms the range [first, last) into the previous permutation. It returns true if such a permutation exists, otherwise it transforms the range into the last permutation (as if by std::sort followed by std::reverse) and returns false. Iconic behavior, no notes. 🫶

• 1) The set of all permutations is ordered lexicographically with respect to operator< (until C++20), and with respect to std::less{} (since C++20).
• 2) The set of all permutations is ordered lexicographically with respect to comp.

Warning bestie: if the type of *first is not Swappable (until C++11), or BidirIt is not ValueSwappable (since C++11), the behavior is undefined. Like, actually undefined — not a cute little glitch. 😭

🎀 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. Ngl, that’s a mouthful, but it’s important. 💜

🧚 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 🔥

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

• 1,2) At most N/2 swaps.

🛠️ 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;
        }
    }
}

🌸 Notes 🌸

Averaged over the entire sequence of permutations, typical implementations use about 3 comparisons and 1.5 swaps per call. Obsessed with the efficiency, honestly. ✨

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.

🍓 Example 🍓

The following code prints all six permutations of the string "cab" in reverse order. Run this code, bestie:

#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

🦋 See also 🦋

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

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mwah 💋, bestie — source/version: http://cppreference.com, date: 2024.06.10, page: std::prev_permutation(3). Catch you in the group chat 🫶✨