Permutations of a given string using STL

Given a string s, the task is to return all unique permutations of a given string in lexicographically sorted order.

Note: A permutation is the rearrangement of all the elements of a string.

Examples:

Input: s = "ABC"
Output: "ABC", "ACB", "BAC", "BCA", "CBA", "CAB"

Input: s = "XY"
Output: "XY", "YX"

Input: s = "AAA"
Output: "AAA"

Note: An approach using backtracking has already been discussed in Distinct Permutation of String. In this article two approaches using STL has been discussed.

Using Rotate() - O(n * n!) Time and O(n) Space

The idea is to generate all possible permutation of given string s using the rotate() function which rotates elements of string such that the passed middle element becomes first. To do so create an auxiliary string x and a HashSetres to store unique permutation in sorted order.
Start iterating from the first element and for each recursive call check if string s is empty, if so store the string x in res else recur again by removing the first element of string s and adding to last of string x. At last rotate the string s byremoving the first character from string s and appending it to the lastto generate the next permutation.

Note: For C++, rotate() stl is used, while for other languages, same operation has been done by removing the first character from string s and appending it to the last.

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Below is given the implementation. 

ABC ACB BAC BCA CAB CBA 

Time Complexity: O(n*n!) 
Auxiliary Space: O(n) 

Using next_permutation() Function - O(n * n!) Time and O(1) Space

C++ provides an in-built function called next_permutation(), that return directly lexicographically in the next greater permutation of the input. The idea is to firstly sort the string s and then call this function until all the permutations are not generated.

Note: Python also have a function permutations() similar to c++.For other programming languages similar function is available in different libraries which can be used to implement same.

Below is given the implementation:

ABC ACB BAC BCA CAB CBA 

Time Complexity: O(n*n!) 
Auxiliary Space: O(1)