std::next_permutation(3)

💅 std::next_permutation(3) — C++ Standard Libary edition, bestie ✨

🌸 NAME

std::next_permutation - std::next_permutation

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✨ Synopsis

Okay so this one lives in the header <algorithm>, and the overloads are giving “two paths, same iconic energy”:

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

template< class BidirIt, class Compare >
bool next_permutation( BidirIt first, BidirIt last,      (2)
(constexpr since C++20)
Compare comp );

Here’s the vibe: it permutes the range [first, last) into the next permutation. It returns true if such a “next permutation” exists; otherwise it transforms the range into the lexicographically first permutation (as if by std::sort) and returns false. 💖

• Overload 1: the set of all permutations is ordered lexicographically with respect to operator< (until C++20), or std::less{} (since C++20). ✨
• Overload 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. Not cute. Not slay. Undefined. 💀

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🎀 Parameters

• first, last — the range of elements to permute. Literally the whole squad. 🫶
• 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. 🦋

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🦋 Type requirements

• BidirIt must meet the requirements of LegacyBidirectionalIterator. That’s the bare minimum, no cap. 💅

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💖 Return value

Returns true if the new permutation is lexicographically greater than the old. Returns false if the last permutation was reached and the range was reset to the first permutation. Iconic little boolean behavior. ✨

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🔥 Complexity

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

• 1,2) At most the fraction N over 2 — yes, N/2 — swaps. Math but make it fashion. 💅

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💀 Exceptions

Any exceptions thrown from iterator operations or the element swap. So if something throws, it throws. We don’t hide it. 🙈

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👑 Possible implementation

This is the reference implementation vibe, bestie — keep it verbatim:

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;
}

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🌈 Notes

Averaged over the entire sequence of permutations, typical implementations use about 3 comparisons and 1.5 swaps per call. Lowkey efficient. ⭐

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. 🧚

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🍓 Example

The following code prints all three permutations of the string "aba". Obsessed with the little do-while loop, honestly:

// Run this code

#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

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🧚 See also

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

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Signing off from http://cppreference.com, version/date 2024.06.10, page std::next_permutation(3) — stay swappable, bestie, mwah 💋🎀