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std::next_permutation(3)       C++ Standard Libary	std::next_permutation(3)

NAME
     std::next_permutation - std::next_permutation

Synopsis
	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 );

	Permutes the range [first, last) into the next permutation. Returns true
     if such a
	anext permutationa exists; otherwise transforms the range into the lexi-
     cographically
	first permutation (as if by std::sort) and returns false.

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

	If
	the type of *first is not Swappable
	(until C++11)
	BidirIt is not ValueSwappable
	(since C++11), the behavior is undefined.

Parameters
	first, last -  the range of elements to permute
		       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 equiv-
     alent to the
		       following:

		       bool cmp(const Type1& a, const Type2& b);
	comp	    -
		       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  regard-
     less 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 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 permu-
     tation.

Complexity
	Given \(\scriptsize N\)N as std::distance(first, last):

	1,2) At most \(\scriptsize \frac{N}{2}\)

	N
	2

	swaps.

Exceptions
	Any exceptions thrown from iterator operations or the element swap.

Possible implementation
	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;
	}

Notes
	Averaged  over	the entire sequence of permutations, typical implementa-
     tions use about
	3 comparisons and 1.5 swaps per call.

	Implementations (e.g. MSVC STL) may enable vectorization when the itera-
     tor 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 three permutations of the string "aba".

     // 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

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

http://cppreference.com 	   2024.06.10		std::next_permutation(3)
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